{"id":4739,"date":"2026-03-17T21:52:15","date_gmt":"2026-03-17T21:52:15","guid":{"rendered":"https:\/\/mrenglishkj.com\/?p=4739"},"modified":"2026-03-19T16:22:35","modified_gmt":"2026-03-19T16:22:35","slug":"sat-math-test-5-module-1st-prepare-learn","status":"publish","type":"post","link":"https:\/\/us.mrenglishkj.com\/sat\/sat-math-test-5-module-1st-prepare-learn\/","title":{"rendered":"SAT Math Free Test 5 (Module 1st Exam Questions Hack"},"content":{"rendered":"\n<h2 class=\"wp-block-heading\">Prepare for the SAT: Math Test Module 1st with Simple Step-by-step Solutions<\/h2>\n\n\n\n<p>Hey, not only you will take the SAT Test but also you will learn all Math problems by understanding step-by-step solutions. This is the 5th version for you to practice your SAT Math learning. Like the other exams, it has the same format and all the necessary features for you to become a master in math. You just take the SAT Test Module First to practice your skills. The best part is that you practice within the time limit, and there are explanations of the correct answers and tips and tricks to get a perfect score on the SAT. You will find Math easy after step-by-step explanations.<\/p>\n\n\n\n<div style=\"height:70px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<h3 class=\"wp-block-heading\">ABOUT THE SAT MODULES<\/h3>\n\n\n\n<p>The SAT is divided into four modules. There are two categories with each split into two modules. The first category is &#8220;Reading and Writing&#8221; with two modules. The second category is &#8220;Math&#8221; with two modules. The one, you will do below is SAT Math Practice Test Module 1st.<\/p>\n\n\n\n<p>The first module has questions ranging from easy to difficult, but the second module only contains difficult questions. If you want to take some other SATs, visit the links below.<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><a href=\"https:\/\/us.mrenglishkj.com\/sat\/category\/sat-english\/module-1st\/\" target=\"_blank\" rel=\"noopener\" title=\"\">1st Module of SAT Reading And Writing Practice Tests<\/a><\/li>\n\n\n\n<li><a href=\"https:\/\/us.mrenglishkj.com\/sat\/category\/sat-english\/module-2nd\/\" target=\"_blank\" rel=\"noopener\" title=\"\">2nd Module of SAT Reading And Writing Practice Tests<\/a><\/li>\n\n\n\n<li><a href=\"https:\/\/us.mrenglishkj.com\/sat\/category\/sat-math\/1st-module\/\" target=\"_blank\" rel=\"noopener\" title=\"\">1st Module of SAT Math Practice Tests<\/a><\/li>\n\n\n\n<li><a href=\"https:\/\/us.mrenglishkj.com\/sat\/category\/sat-math\/2nd-module\/\" target=\"_blank\" rel=\"noopener\" title=\"\">2nd Module of SAT Math Practice Tests<\/a><\/li>\n<\/ul>\n\n\n\n<div style=\"height:70px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<h3 class=\"wp-block-heading\">THE SAT MATH MODULE 1ST<\/h3>\n\n\n\n<p>The first module of Math in SAT contains four segments: Algebra, Advanced Math, Problem-Solving and Data Analysis, and Geometry and Trigonometry. The questions in Module 1st are from easy to difficult. In a real SAT exam, you must answer 22 questions within 35 minutes. We have provided you with the same in this Practice Test.<\/p>\n\n\n\n<div style=\"height:70px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<h4 class=\"wp-block-heading\">Instructions for the SAT Real-Time Exam<\/h4>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>Go Back-and-Forth:<\/strong> You will see an arrow on the right or left corner of the slide, click to move forward or backward.<\/li>\n\n\n\n<li><strong>Interaction:<\/strong> You will see a press button at the top right corner that tells you there are some interactive components in the slide. Click the press button to find out.<\/li>\n\n\n\n<li><strong>Timer: <\/strong>On the top of the slide, you will see the timer, we have divided the time based on the average of the module 1st. (The 35 minutes are equally divided into 22 questions&#8217; time.) It is best to note the time before and after finishing the practice test to measure, &#8220;Was it within 35 minutes or not?&#8221;<\/li>\n\n\n\n<li><strong>Mute:<\/strong> You can click on the speaker button to mute the audio.<\/li>\n\n\n\n<li><strong>Image:<\/strong> You can click on a graph, table, or other image to expand it and view it in full screen.<\/li>\n\n\n\n<li><strong>Mobile:<\/strong> You cannot take the real exam on mobile, but our practice exam you can give on mobile.<\/li>\n\n\n\n<li><strong>Calculator<\/strong>: Below the Test, you will see a Desmos calculator and graph for Math. The same, Desmos, will be used in real exams, so learn &#8220;How to use Desmos Calculator.&#8221;<\/li>\n\n\n\n<li><strong>Tips:<\/strong> This article will help you learn more about the SAT Exams. <a href=\"https:\/\/us.mrenglishkj.com\/sat\/everything-about-the-sat\/\" target=\"_blank\" rel=\"noopener\" title=\"SAT: EVERYTHING ABOUT THE SAT\">SAT: EVERYTHING ABOUT THE SAT<\/a><\/li>\n<\/ol>\n\n\n\n<div style=\"height:70px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<figure class=\"wp-block-embed alignfull is-type-wp-embed is-provider-genially wp-block-embed-genially\"><div class=\"wp-block-embed__wrapper\">\n<iframe class=\"wp-embedded-content\" sandbox=\"allow-scripts\" security=\"restricted\" title=\"SAT 5 Math Module 1st\" frameborder='0' width='1200' height='675' src='https:\/\/view.genially.com\/674f174ee840f1974f551280#?secret=yXJmnXrIkD' data-secret='yXJmnXrIkD' scrolling='yes'><\/iframe>\n<\/div><figcaption class=\"wp-element-caption\">Wait here for the SAT Test to appear.<\/figcaption><\/figure>\n\n\n\n<div style=\"height:40px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<p>Our team has reviewed some of the best SAT learning materials for your convenience. These materials are best for your career growth.<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Check Our Review Blog: <a href=\"https:\/\/review.mrenglishkj.com\/\" target=\"_blank\" rel=\"noopener\" title=\"\">review.mrenglishkj.com<\/a><\/li>\n<\/ul>\n\n\n\n<div style=\"height:70px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<!-- HTML for the Desmos Calculator Embed (Always Visible) -->\n<div id=\"desmos-container\">\n    <iframe loading=\"lazy\"\n        src=\"https:\/\/www.desmos.com\/calculator\/fxgemyy2gl\"\n        width=\"100%\"\n        height=\"500px\"\n        frameborder=\"0\"\n        allowfullscreen\n    ><\/iframe>\n<\/div>\n\n<!-- Button to Open Calculator in Slide-Out Panel -->\n<button id=\"desmos-toggle\" style=\"position: fixed; top: 20px; right: 20px; z-index: 1000;\">\n    Open Calculator\n<\/button>\n\n<!-- Slide-Out Desmos Calculator Panel (hidden initially) -->\n<div id=\"desmos-panel\">\n    <iframe loading=\"lazy\"\n        src=\"https:\/\/www.desmos.com\/calculator\/fxgemyy2gl\"\n        width=\"100%\"\n        height=\"95%\"\n        frameborder=\"0\"\n        allowfullscreen\n    ><\/iframe>\n<\/div>\n\n<!-- CSS Styling for the Slide-Out Panel -->\n<style>\n    \/* Main Container Styling *\/\n    #desmos-container {\n        max-width: 600px; \/* Adjust as needed *\/\n        margin: 20px auto;\n    }\n\n    \/* Slide-Out Panel Styling *\/\n    #desmos-panel {\n        position: fixed;\n        top: 0;\n        right: -400px; \/* Hidden by default *\/\n        width: 400px; \/* Adjust width as needed *\/\n        height: 100vh;\n        background-color: white;\n        border-left: 1px solid #ccc;\n        box-shadow: -2px 0 5px rgba(0, 0, 0, 0.2);\n        transition: right 0.3s ease;\n        z-index: 999; \/* Ensure it overlays content *\/\n    }\n\n    #desmos-panel.open {\n        right: 0;\n    }\n<\/style>\n\n<!-- JavaScript to Toggle the Slide-Out Panel -->\n<script>\n    document.getElementById(\"desmos-toggle\").onclick = function() {\n        var panel = document.getElementById(\"desmos-panel\");\n        if (panel.classList.contains(\"open\")) {\n            panel.classList.remove(\"open\");\n        } else {\n            panel.classList.add(\"open\");\n        }\n    };\n<\/script>\n\n\n\n<p class=\"has-text-align-center has-small-font-size\">Wait for the Desmos Calculator to appear.<\/p>\n\n\n\n<div style=\"height:70px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<h3 class=\"wp-block-heading\">SAT MATH TEST SOLUTIONS WITH STEP-BY-STEP EXPLANATION<\/h3>\n\n\n\n<p>Do not open the tabs before finishing the practice test above! For your convenience, we have compiled all the solutions and their explanations here. We will also give you some tips or advice to help you understand them better. You&#8217;ll see <strong>&#8216;why this answer is correct&#8217;<\/strong> and <strong>&#8216;why this is incorrect.&#8217;<\/strong><\/p>\n\n\n\n<div style=\"height:70px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<h4 class=\"wp-block-heading\">Math Solutions and Explanations:<\/h4>\n\n\n\n<p>The light red color shows the Question, green shows the Correct answer, red shows the Incorrect one, and blue shows Tips or Tricks with step-by-step explanations.<\/p>\n\n\n\n<div class=\"wp-block-coblocks-accordion alignfull\">\n<div class=\"wp-block-coblocks-accordion-item\"><details><summary class=\"wp-block-coblocks-accordion-item__title\"><strong>1st Question<\/strong><\/summary><div class=\"wp-block-coblocks-accordion-item__content\">\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"313\" height=\"247\" src=\"https:\/\/us.mrenglishkj.com\/sat\/sat\/wp-content\/uploads\/2024\/12\/image-6.png\" alt=\"SAT Math topic Problem Solving Questions and step-by-step solution\" class=\"wp-image-4746\" srcset=\"https:\/\/us.mrenglishkj.com\/sat\/wp-content\/uploads\/sites\/2\/2024\/12\/image-6.png 313w, https:\/\/us.mrenglishkj.com\/sat\/wp-content\/uploads\/sites\/2\/2024\/12\/image-6-300x237.png 300w\" sizes=\"auto, (max-width: 313px) 100vw, 313px\" \/><\/figure>\n\n\n\n<p class=\"is-style-warning\" style=\"font-size:0.9em\"><strong>Question:<\/strong> For what model year is the percent of cars for sale the smallest?<br>A) 2012<br>B) 2013<br>C) 2014<br>D) 2015<\/p>\n\n\n\n<p class=\"is-style-success\" style=\"font-size:0.9em\"><strong>Choice C<\/strong> is correct. For the given line graph, the percent of cars for sale at a used car lot on a given day is represented on the vertical axis. The percent of cars for sale is the smallest when the height of the line graph is the lowest. The lowest height of the line graph occurs for cars with a model year of 2014.<\/p>\n\n\n\n<p class=\"is-style-error\" style=\"font-size:0.9em\">Choice A is incorrect and may result from conceptual or calculation errors.<\/p>\n\n\n\n<p class=\"is-style-error\" style=\"font-size:0.9em\">Choice B is incorrect and may result from conceptual or calculation errors.<\/p>\n\n\n\n<p class=\"is-style-error\" style=\"font-size:0.9em\">Choice D is incorrect and may result from conceptual or calculation errors.<\/p>\n\n\n\n<p class=\"is-style-info\" style=\"font-size:0.9em\"><strong>Problem Analysis:<\/strong><br>The line graph shows the percentage of cars for sale at a used car lot for various model years (2010 to 2019). The question asks us to determine <strong>the model year corresponding to the smallest percentage of cars for sale<\/strong>.<br><br><strong>Step-by-Step Solution:<\/strong><br><strong>Step 1: Understand the graph<\/strong><br>~ The <strong>x-axis<\/strong> represents the model year (2010 to 2019).<br>~ The <strong>y-axis<\/strong> represents the percentage of cars for sale (from 0% to 15%).<br>Each point on the graph represents the percentage of cars for sale for the corresponding model year.<br><br><strong>Step 2: Identify the smallest percentage<\/strong><br>~ From the graph, visually inspect the lowest point of the line.<br>~ The lowest percentage occurs around <strong>5%<\/strong>.<br>~ This lowest point corresponds to the model year <strong>2014<\/strong>.<br><br><strong>Step 3: Verify the solution<\/strong><br>To ensure the correct interpretation:<br>~ The percentages are highest around 10-15% for other model years.<br>~ The line dips significantly for <strong>2014<\/strong>, indicating the smallest percentage of cars for sale.<br><br><strong>Final Answer:<\/strong><br>The model year with the smallest percentage of cars for sale is: <strong>2014\u200b<\/strong><\/p>\n<\/div><\/details><\/div>\n\n\n\n<div class=\"wp-block-coblocks-accordion-item\"><details><summary class=\"wp-block-coblocks-accordion-item__title\"><strong>2nd Question<\/strong><\/summary><div class=\"wp-block-coblocks-accordion-item__content\">\n<p class=\"is-style-warning\" style=\"font-size:0.9em\"><strong>Question:<\/strong> For a particular machine that produces beads, 29 out of every 100 beads it produces have a defect. A bead produced by the machine will be selected at random. What is the probability of selecting a bead that has a defect?<br>A) 1\/2,900<br>B) 1\/29<br>C) 29\/100<br>D) 29\/10<\/p>\n\n\n\n<p class=\"is-style-success\" style=\"font-size:0.9em\"><strong>Choice C <\/strong>is correct.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"491\" height=\"162\" src=\"https:\/\/us.mrenglishkj.com\/sat\/sat\/wp-content\/uploads\/2024\/12\/image-7.png\" alt=\"Solutions of the SAT Math problems\" class=\"wp-image-4748\" srcset=\"https:\/\/us.mrenglishkj.com\/sat\/wp-content\/uploads\/sites\/2\/2024\/12\/image-7.png 491w, https:\/\/us.mrenglishkj.com\/sat\/wp-content\/uploads\/sites\/2\/2024\/12\/image-7-300x99.png 300w\" sizes=\"auto, (max-width: 491px) 100vw, 491px\" \/><\/figure>\n\n\n\n<p class=\"is-style-error\" style=\"font-size:0.9em\">Choice A is incorrect and may result from conceptual or calculation errors.<\/p>\n\n\n\n<p class=\"is-style-error\" style=\"font-size:0.9em\">Choice B is incorrect and may result from conceptual or calculation errors.<\/p>\n\n\n\n<p class=\"is-style-error\" style=\"font-size:0.9em\">Choice D is incorrect and may result from conceptual or calculation errors.<\/p>\n\n\n\n<p class=\"is-style-info\" style=\"font-size:0.9em\"><strong>Question Breakdown:<\/strong><br>The question asks us to find the probability of selecting a defective bead produced by a machine. For every 100 beads produced, <strong>29 are defective<\/strong>.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"778\" height=\"589\" src=\"https:\/\/us.mrenglishkj.com\/sat\/sat\/wp-content\/uploads\/2024\/12\/image-9.png\" alt=\"Step-by-step solutions of the SAT Math tests\" class=\"wp-image-4758\" srcset=\"https:\/\/us.mrenglishkj.com\/sat\/wp-content\/uploads\/sites\/2\/2024\/12\/image-9.png 778w, https:\/\/us.mrenglishkj.com\/sat\/wp-content\/uploads\/sites\/2\/2024\/12\/image-9-300x227.png 300w, https:\/\/us.mrenglishkj.com\/sat\/wp-content\/uploads\/sites\/2\/2024\/12\/image-9-768x581.png 768w\" sizes=\"auto, (max-width: 778px) 100vw, 778px\" \/><\/figure>\n\n\n\n<p class=\"is-style-info\" style=\"font-size:0.9em\"><strong>Final Answer:<\/strong> <strong>C) 29\/100.<\/strong><\/p>\n<\/div><\/details><\/div>\n\n\n\n<div class=\"wp-block-coblocks-accordion-item\"><details><summary class=\"wp-block-coblocks-accordion-item__title\"><strong>3rd Question<\/strong><\/summary><div class=\"wp-block-coblocks-accordion-item__content\">\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"228\" height=\"258\" src=\"https:\/\/us.mrenglishkj.com\/sat\/sat\/wp-content\/uploads\/2024\/12\/image-8.png\" alt=\"Solve SAT Geometry and Trigonometry question solution in detail \" class=\"wp-image-4753\"\/><\/figure>\n\n\n\n<p class=\"is-style-warning\" style=\"font-size:0.9em\"><strong>Question:<\/strong> In the figure, line <em>m<\/em> is parallel to line <em>n<\/em>, and line <em>t<\/em> intersects both lines. What is the value of <em>x<\/em>?<br>A) 33<br>B) 57<br>C) 123<br>D) 147<\/p>\n\n\n\n<p class=\"is-style-success\" style=\"font-size:0.9em\"><strong>Choice D<\/strong> is correct. It\u2019s given that line <em>m<\/em> is parallel to line <em>n<\/em>, and line <em>t<\/em> intersects both lines. It follows that line <em>t<\/em> is a transversal. When two lines are parallel and intersected by a transversal, exterior angles on the same side of the transversal are supplementary. Thus, <em>x<\/em> + 33 = 180. Subtracting 33 from both sides of this equation yields <em>x<\/em> = 147. Therefore, the value of <em>x<\/em> is 147.<\/p>\n\n\n\n<p class=\"is-style-error\" style=\"font-size:0.9em\">Choice A is incorrect and may result from conceptual or calculation errors.<\/p>\n\n\n\n<p class=\"is-style-error\" style=\"font-size:0.9em\">Choice B is incorrect and may result from conceptual or calculation errors.<\/p>\n\n\n\n<p class=\"is-style-error\" style=\"font-size:0.9em\">Choice C is incorrect and may result from conceptual or calculation errors.<\/p>\n\n\n\n<p class=\"is-style-info\" style=\"font-size:0.9em\"><strong>Step-by-Step Evaluation:<\/strong><br><strong>Step 1: Analyze the given information<\/strong><br>~ Lines <em>m<\/em> and <em>n<\/em> are parallel.<br>~ Line <em>t<\/em> is a transversal that intersects both <em>m<\/em> and <em>n<\/em>.<br>~ An angle of 33<sup>\u2218<\/sup> is formed at the intersection of line <em>t<\/em> with line <em>n<\/em>.<br>~ The angle <em>x<\/em><sup>\u2218<\/sup> is formed at the intersection of line <em>t<\/em> with line <em>m<\/em>.<br>We aim to find the value of <em>x<\/em>, considering the relationship between the angles formed by transversal and parallel lines.<br><br><strong>Step 2: Understand angle relationships<\/strong><br>1. <strong>Interior and exterior angles<\/strong>: When a transversal intersects parallel lines:<br>~ <strong>Same-side interior angles are supplementary<\/strong> (they add up to 180<sup>\u2218<\/sup>).<br>~ <strong>Corresponding angles are congruent<\/strong>.<br>2. The 33<sup>\u2218<\/sup> angle is an <strong>interior angle<\/strong> on the lower side of <em>t<\/em>, relative to line <em>n<\/em>.<br>~ The angle <em>x<\/em><sup>\u2218<\/sup>, on the upper side of <em>t<\/em> relative to line <em>m<\/em>, is its <strong>same-side interior angle<\/strong>.<br><br><strong>Step 3: Use the same-side interior angle property<\/strong><br>For same-side interior angles formed by a transversal with parallel lines:<br><em>x<\/em> + 33 = 180<br><br><strong>Step 4: Solve for <em>x<\/em><\/strong><br><em>x<\/em> = 180 \u2212 33<br><em>x<\/em> = 147<br><br><strong>Final Answer:<\/strong> <strong>147<sup>\u2218<\/sup><\/strong>\u200b<\/p>\n<\/div><\/details><\/div>\n\n\n\n<div class=\"wp-block-coblocks-accordion-item\"><details><summary class=\"wp-block-coblocks-accordion-item__title\"><strong>4th Question<\/strong><\/summary><div class=\"wp-block-coblocks-accordion-item__content\">\n<p class=\"is-style-warning\" style=\"font-size:0.9em\"><strong>Question:<\/strong> Amar deposited a fixed amount into his savings account each month. The function <em>f<\/em>(<em>t<\/em>) = 200 + 50<em>t<\/em> gives the amount, in dollars, in Amar\u2019s savings account after <em>t<\/em> monthly deposits. What is the best interpretation of 50 in this context?<br>A) With each monthly deposit, the amount in Amar\u2019s savings account increased by $50.<br>B) Before Amar made any monthly deposits, the amount in his savings account was $50.<br>C) After 1 monthly deposit, the amount in Amar\u2019s savings account was $50.<br>D) Amar made a total of 50 monthly deposits.<\/p>\n\n\n\n<p class=\"is-style-success\" style=\"font-size:0.9em\"><strong>Option A <\/strong>is<strong> <\/strong>the correct answer.<\/p>\n\n\n\n<p class=\"is-style-error\" style=\"font-size:0.9em\">Choice B is incorrect and may result from conceptual or calculation errors.<\/p>\n\n\n\n<p class=\"is-style-error\" style=\"font-size:0.9em\">Choice C is incorrect and may result from conceptual or calculation errors.<\/p>\n\n\n\n<p class=\"is-style-error\" style=\"font-size:0.9em\">Choice D is incorrect and may result from conceptual or calculation errors.<\/p>\n\n\n\n<p class=\"is-style-info\" style=\"font-size:0.9em\"><strong>Step-by-Step Solution:<\/strong><br><strong>Step 1: Analyze the function <em>f<\/em>(<em>t<\/em>) = 200 + 50<em>t<\/em><\/strong><br>The function <em>f<\/em>(<em>t<\/em>) describes the total amount in Amar&#8217;s savings account after <em>t<\/em> months. Let&#8217;s break it down:<br>~ <strong>Initial amount (200)<\/strong>: The constant term (200) represents the amount already in Amar\u2019s account before he starts depositing money.<br>~ <strong>Rate of change (50)<\/strong>: The coefficient of <em>t<\/em> (50) represents the increase in the account balance for each monthly deposit. This is the amount Amar deposits each month.<br><br><strong>Step 2: Interpret the meaning of 50<\/strong><br>From the structure of the function, 50<em>t<\/em> means that for every additional month (<em>t<\/em>), the account balance increases by $50. Thus, <strong>50 represents the amount Amar deposits into his savings account each month.<\/strong><br><br><strong>Step 3: Determine the best answer<\/strong><br>The correct answer is: A) With each monthly deposit, the amount in Amar\u2019s savings account increased by $50.<br><br><strong>Verification:<\/strong><br>Let\u2019s test the function for a couple of values of <em>t<\/em>:<br>1. <strong>When <em>t<\/em> = 0<\/strong>: <em>f<\/em>(0) = 200 + 50(0) = 200<br>This confirms that the initial amount in the account is $200, before any deposits.<br>2. <strong>When <em>t<\/em> = 1<\/strong>: <em>f<\/em>(1) = 200 + 50(1) = 250<br>After one monthly deposit, the balance increases by $50 to $250.<br>3. <strong>When <em>t<\/em> = 2<\/strong>: <em>f<\/em>(2) = 200 + 50(2) = 300<br>After two monthly deposits, the balance increases by another $50 to $300.<br>This confirms that 50 is the amount Amar deposits into his savings account each month.<\/p>\n<\/div><\/details><\/div>\n\n\n\n<div class=\"wp-block-coblocks-accordion-item\"><details><summary class=\"wp-block-coblocks-accordion-item__title\"><strong>5th Question<\/strong><\/summary><div class=\"wp-block-coblocks-accordion-item__content\">\n<p class=\"is-style-warning\" style=\"font-size:0.9em\"><strong>Question:<\/strong> A machine produces boxes at a constant rate of 36 boxes per minute. At what rate, in boxes per hour, does the machine produce the boxes?<br>A) 60<br>B) 2,160<br>C) 36<br>D) 96<br>[Type-Based Answer: In the final exam, you will type the answer rather than choose from options.]<\/p>\n\n\n\n<p class=\"is-style-success\" style=\"font-size:0.9em\"><strong>Choice B<\/strong> is correct.<\/p>\n\n\n\n<p class=\"is-style-error\" style=\"font-size:0.9em\">Choice A is incorrect and may result from conceptual or calculation errors.<\/p>\n\n\n\n<p class=\"is-style-error\" style=\"font-size:0.9em\">Choice C is incorrect and may result from conceptual or calculation errors.<\/p>\n\n\n\n<p class=\"is-style-error\" style=\"font-size:0.9em\">Choice D is incorrect and may result from conceptual or calculation errors.<\/p>\n\n\n\n<p class=\"is-style-info\" style=\"font-size:0.9em\"><strong>Step-by-Step Solution:<\/strong><br><strong>Step 1: Understand the problem<\/strong><br>The machine produces 36 boxes per minute. To calculate the rate in <strong>boxes per hour<\/strong>, we need to determine how many minutes are in one hour and then multiply the given rate by that time.<br><br><strong>Step 2: Convert minutes to hours<\/strong><br>There are 60 minutes in one hour. If the machine produces 36 boxes in 1 minute, in 60 minutes it will produce:<br>Rate&nbsp;in&nbsp;boxes&nbsp;per&nbsp;hour = 36 \u00d7 60<br><br><strong>Step 3: Perform the calculation<\/strong><br>36 \u00d7 60 = 2,160<br>Thus, the machine produces <strong>2,160 boxes per hour<\/strong>.<br><br><strong>Final Answer: The machine produces 2,160 boxes per hour.<\/strong><\/p>\n<\/div><\/details><\/div>\n\n\n\n<div class=\"wp-block-coblocks-accordion-item\"><details><summary class=\"wp-block-coblocks-accordion-item__title\"><strong>6th Question<\/strong><\/summary><div class=\"wp-block-coblocks-accordion-item__content\">\n<p class=\"is-style-warning\" style=\"font-size:0.9em\"><strong>Data set <em>X<\/em>: 5, 9, 9, 13<br>Data set <em>Y<\/em>: 5, 9, 9, 13, 27<\/strong><br><strong>Question:<\/strong> The lists give the values in data sets X and Y. Which statement correctly compares the mean of data set X and the mean of data set Y?<br>A) The mean of data set X is greater than the mean of data set Y.<br>B) The mean of data set X is less than the mean of data set Y.<br>C) The means of data set X and data set Y are equal.<br>D) There is not enough information to compare the means.<\/p>\n\n\n\n<p class=\"is-style-success\" style=\"font-size:0.9em\"><strong>Choice B<\/strong> is correct.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"497\" height=\"154\" src=\"https:\/\/us.mrenglishkj.com\/sat\/wp-content\/uploads\/sites\/2\/2024\/12\/image-11.png\" alt=\"SAT Math question answer solution and explanations\" class=\"wp-image-4774\" srcset=\"https:\/\/us.mrenglishkj.com\/sat\/wp-content\/uploads\/sites\/2\/2024\/12\/image-11.png 497w, https:\/\/us.mrenglishkj.com\/sat\/wp-content\/uploads\/sites\/2\/2024\/12\/image-11-300x93.png 300w\" sizes=\"auto, (max-width: 497px) 100vw, 497px\" \/><\/figure>\n\n\n\n<p class=\"is-style-error\" style=\"font-size:0.9em\">Choice A is incorrect and may result from conceptual or calculation errors.<\/p>\n\n\n\n<p class=\"is-style-error\" style=\"font-size:0.9em\">Choice C is incorrect and may result from conceptual or calculation errors.<\/p>\n\n\n\n<p class=\"is-style-error\" style=\"font-size:0.9em\">Choice D is incorrect and may result from conceptual or calculation errors.<\/p>\n\n\n\n<p class=\"is-style-info\" style=\"font-size:0.9em\"><strong>Step-by-Step Solution:<\/strong><br><strong>Step 1: Understand the problem<\/strong><br>The problem involves two data sets, <strong>X<\/strong> and <strong>Y<\/strong>:<br>~ Data set X = {5, 9, 9, 13}<br>~ Data set Y = {5, 9, 9, 13, 27}<br>We need to determine which statement correctly compares the means (average values) of the two data sets.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"580\" height=\"620\" src=\"https:\/\/us.mrenglishkj.com\/sat\/wp-content\/uploads\/sites\/2\/2024\/12\/image-12.png\" alt=\"SAT Math problems step-by-step solutions and answers\" class=\"wp-image-4779\" srcset=\"https:\/\/us.mrenglishkj.com\/sat\/wp-content\/uploads\/sites\/2\/2024\/12\/image-12.png 580w, https:\/\/us.mrenglishkj.com\/sat\/wp-content\/uploads\/sites\/2\/2024\/12\/image-12-281x300.png 281w\" sizes=\"auto, (max-width: 580px) 100vw, 580px\" \/><\/figure>\n\n\n\n<p class=\"is-style-info\" style=\"font-size:0.9em\"><strong>Step 4: Compare the means<\/strong><br>~ The mean of data set X is <strong>9<\/strong>.<br>~ The mean of data set Y is <strong>12.6<\/strong>.<br>Since 9 &lt; 12.69, the mean of data set <em>X<\/em> is <strong>less than<\/strong> the mean of data set <em>Y<\/em>.<br><br><strong>Final Answer:<\/strong> <strong>B) The mean of data set X is less than the mean of data set Y.<\/strong><\/p>\n<\/div><\/details><\/div>\n\n\n\n<div class=\"wp-block-coblocks-accordion-item\"><details><summary class=\"wp-block-coblocks-accordion-item__title\"><strong>7th Question<\/strong><\/summary><div class=\"wp-block-coblocks-accordion-item__content\">\n<p class=\"is-style-warning\" style=\"font-size:0.9em\"><strong>Question:<\/strong> A rocket contained 467,000 kilograms (kg) of propellant before launch. Exactly 21 seconds after launch, 362,105 kg of this propellant remained. On average, approximately how much propellant, in kg, did the rocket burn each second after launch?<br>A) 4,995<br>B) 17,243<br>C) 39,481<br>D) 104,895<\/p>\n\n\n\n<p class=\"is-style-success\" style=\"font-size:0.9em\"><strong>Choice A<\/strong> is correct. It\u2019s given that the rocket contained 467,000 kilograms (kg) of propellant before launch and had 362,105 kg remaining exactly 21 seconds after launch. Finding the difference between the amount, in kg, of propellant before launch and the remaining amount, in kg, of propellant after launch gives the amount, in kg, of propellant burned during the 21 seconds: 467,000 &#8211; 362,105 = 104,895. Dividing the amount of propellant burned by the number of seconds yields 104,895\/21= 4,995. Thus, an average of 4,995 kg of propellant burned each second after launch.<\/p>\n\n\n\n<p class=\"is-style-error\" style=\"font-size:0.9em\">Choice B is incorrect and may result from conceptual or calculation errors.<\/p>\n\n\n\n<p class=\"is-style-error\" style=\"font-size:0.9em\">Choice C is incorrect and may result from conceptual or calculation errors.<\/p>\n\n\n\n<p class=\"is-style-error\" style=\"font-size:0.9em\">Choice D is incorrect and may result from finding the amount of propellant burned, rather than the amount of propellant burned each second.<\/p>\n\n\n\n<p class=\"is-style-info\" style=\"font-size:0.9em\"><strong>Step-by-Step Solution:<\/strong><br><strong>Step 1: Understand the problem<\/strong><br>We are tasked with calculating the <strong>average amount of propellant burned per second<\/strong> by the rocket after launch.<br>~ <strong>Initial amount of propellant<\/strong>: 467,000 kg<br>~ <strong>Remaining amount after 21 seconds<\/strong>: 362,105 kg<br>~ <strong>Time elapsed<\/strong>: 21 seconds<br>The average rate of propellant burned per second can be calculated using the formula:<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"864\" height=\"617\" src=\"https:\/\/us.mrenglishkj.com\/sat\/wp-content\/uploads\/sites\/2\/2024\/12\/image-13.png\" alt=\"Learn SATs for free by taking tests and learning from solutions\" class=\"wp-image-4783\" srcset=\"https:\/\/us.mrenglishkj.com\/sat\/wp-content\/uploads\/sites\/2\/2024\/12\/image-13.png 864w, https:\/\/us.mrenglishkj.com\/sat\/wp-content\/uploads\/sites\/2\/2024\/12\/image-13-300x214.png 300w, https:\/\/us.mrenglishkj.com\/sat\/wp-content\/uploads\/sites\/2\/2024\/12\/image-13-768x548.png 768w\" sizes=\"auto, (max-width: 864px) 100vw, 864px\" \/><\/figure>\n\n\n\n<p class=\"is-style-info\" style=\"font-size:0.9em\">Perform the division:<br>Rate = 4,995\u2009kg\/second.<br><br><strong>Step 4: Identify the correct answer<\/strong><br>The average amount of propellant burned each second is <strong>4,995 kg\/second<\/strong>, which corresponds to <strong>Option A<\/strong>.<br><br><strong>Final Answer:<\/strong> <strong>A) 4,995<\/strong><\/p>\n<\/div><\/details><\/div>\n\n\n\n<div class=\"wp-block-coblocks-accordion-item\"><details><summary class=\"wp-block-coblocks-accordion-item__title\"><strong>8th Question<\/strong><\/summary><div class=\"wp-block-coblocks-accordion-item__content\">\n<p class=\"is-style-warning\" style=\"font-size:0.9em\"><strong>Question:<\/strong> If 4<em>x<\/em> + 2 = 12, what is the value of 16<em>x<\/em> + 8?<br>A) 40<br>B) 48<br>C) 56<br>D) 60<\/p>\n\n\n\n<p class=\"is-style-success\" style=\"font-size:0.9em\"><strong>Choice B<\/strong> is correct. Multiplying both sides of the given equation by 4 yields (4)(4<em>x<\/em> + 2) = (4)(12), or 16<em>x<\/em> + 8 = 48. Therefore, the value of 16<em>x<\/em> + 8 is 48.<\/p>\n\n\n\n<p class=\"is-style-error\" style=\"font-size:0.9em\">Choice A is incorrect and may result from conceptual or calculation errors.<\/p>\n\n\n\n<p class=\"is-style-error\" style=\"font-size:0.9em\">Choice C is incorrect and may result from conceptual or calculation errors.<\/p>\n\n\n\n<p class=\"is-style-error\" style=\"font-size:0.9em\">Choice D is incorrect and may result from conceptual or calculation errors.<\/p>\n\n\n\n<p class=\"is-style-info\" style=\"font-size:0.9em\"><strong>Step-by-Step Solution:<\/strong><br>We are solving the equation 4 + x<sup>2<\/sup> = 12 and determining the value of 16<em>x<\/em> + 8.<br><br><strong>Step 1: Solve for <em>x<\/em><sup>2<\/sup><\/strong><br>Start with: 4 + <em>x<\/em><sup>2<\/sup> = 12<br>Subtract 4 from both sides: <em>x<\/em><sup>2<\/sup> = 8<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"663\" height=\"551\" src=\"https:\/\/us.mrenglishkj.com\/sat\/wp-content\/uploads\/sites\/2\/2024\/12\/image-14.png\" alt=\"Step-by-step sat math solutions and solve tests\" class=\"wp-image-4786\" srcset=\"https:\/\/us.mrenglishkj.com\/sat\/wp-content\/uploads\/sites\/2\/2024\/12\/image-14.png 663w, https:\/\/us.mrenglishkj.com\/sat\/wp-content\/uploads\/sites\/2\/2024\/12\/image-14-300x249.png 300w\" sizes=\"auto, (max-width: 663px) 100vw, 663px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"764\" height=\"532\" src=\"https:\/\/us.mrenglishkj.com\/sat\/wp-content\/uploads\/sites\/2\/2024\/12\/image-15.png\" alt=\"SAT math problems step-by-step solutions\" class=\"wp-image-4787\" srcset=\"https:\/\/us.mrenglishkj.com\/sat\/wp-content\/uploads\/sites\/2\/2024\/12\/image-15.png 764w, https:\/\/us.mrenglishkj.com\/sat\/wp-content\/uploads\/sites\/2\/2024\/12\/image-15-300x209.png 300w\" sizes=\"auto, (max-width: 764px) 100vw, 764px\" \/><\/figure>\n\n\n\n<p class=\"is-style-info\" style=\"font-size:0.9em\"><strong>Step 5: Verify the Answer<\/strong><br>The question specifically asks for 16<em>x<\/em> + 8, and the correct numerical value that matches the options is: <strong>48<\/strong><\/p>\n<\/div><\/details><\/div>\n\n\n\n<div class=\"wp-block-coblocks-accordion-item\"><details><summary class=\"wp-block-coblocks-accordion-item__title\"><strong>9th Question<\/strong><\/summary><div class=\"wp-block-coblocks-accordion-item__content\">\n<p class=\"is-style-warning\" style=\"font-size:0.9em\"><strong>Question:<\/strong> A small business owner budgets $2,200 to purchase candles. The owner must purchase a minimum of 200 candles to maintain the discounted pricing. If the owner pays $4.90 per candle to purchase small candles and $11.60 per candle to purchase large candles, what is the maximum number of large candles the owner can purchase to stay within the budget and maintain the discounted pricing?<br>A) 182<br>B)183<br>C) 184<br>D) 185<br>[Type-Based Answer: In the final exam, you will type the answer rather than choose from options.]<\/p>\n\n\n\n<p class=\"is-style-success\" style=\"font-size:0.9em\"><strong>Option A:<\/strong> The correct answer is 182. Let&#8217;s represent the number of small candles the owner can purchase, and let <em>l<\/em> represent the number of large candles the owner can purchase. It\u2019s given that the owner pays $4.90 per candle to purchase small candles and $11.60 per candle to purchase large candles. Therefore, the owner pays 4.90s dollars for <em>s<\/em> small candles and 11.60<em>l<\/em> dollars for <em>l<\/em> large candles, which means the owner pays a total of 4.90s + 11.60<em>l<\/em> dollars to purchase candles. It\u2019s given that the owner budgets $2,200 to purchase candles. Therefore, 4.90s + 11.60<em>l <\/em><span style=\"text-decoration: underline\">&lt;<\/span> 2,200. It\u2019s also given that the owner must purchase a minimum of 200 candles. Therefore, <em>s<\/em> + <em>l<\/em> <span style=\"text-decoration: underline\">&gt;<\/span> 200. The inequalities 4.90<em>s<\/em> + 11.60<em>l<\/em> <span style=\"text-decoration: underline\">&lt;<\/span> 2,200 and <em>s<\/em> + <em>l<\/em> <span style=\"text-decoration: underline\">&gt;<\/span> 200 can be combined into one compound inequality by rewriting the second inequality so that its left-hand side is equivalent to the left-hand side of the first inequality. Subtracting <em>l<\/em> from both sides of the inequality <em>s<\/em> + <em>l<\/em> <span style=\"text-decoration: underline\">&gt;<\/span> 200 yields <em>s<\/em> <span style=\"text-decoration: underline\">&gt;<\/span> 200 &#8211; <em>l<\/em>. Multiplying both sides of this inequality by 4.90 yields 4.90<em>s<\/em> <span style=\"text-decoration: underline\">&gt;<\/span> 4.90(200 &#8211; <em>l<\/em>), or 4.90<em>s<\/em> <span style=\"text-decoration: underline\">&gt;<\/span> 980 &#8211; 4.90<em>l<\/em>. Adding 11.60<em>l<\/em> to both sides of this inequality yields 4.90<em>s<\/em> + 11.60<em>l<\/em> <span style=\"text-decoration: underline\">&gt;<\/span> 980 &#8211; 4.90<em>l<\/em> + 11.60<em>l<\/em>, or 4.90<em>s<\/em> + 11.60<em>l<\/em> <span style=\"text-decoration: underline\">&gt;<\/span> 980 + 6.70<em>l<\/em>. This inequality can be combined with the inequality 4.90<em>s<\/em> + 11.60<em>l<\/em> <span style=\"text-decoration: underline\">&lt;<\/span> 2,200, which yields the compound inequality 980 + 6.70<em>l<\/em> <span style=\"text-decoration: underline\">&lt;<\/span> 4.90<em>s<\/em> + 11.60<em>l<\/em> <span style=\"text-decoration: underline\">&lt;<\/span> 2,200. It follows that 980 + 6.70<em>l<\/em> <span style=\"text-decoration: underline\">&lt;<\/span> 2,200. Subtracting 980 from both sides of this inequality yields 6.70<em>l<\/em> <span style=\"text-decoration: underline\">&lt;<\/span> 2,200. Dividing both sides of this inequality by 6.70 yields approximately <em>l<\/em> <span style=\"text-decoration: underline\">&lt;<\/span> 182.09. Since the number of large candles the owner purchases must be a whole number, the maximum number of large candles the owner can purchase is the largest whole number less than 182.09, which is 182.<\/p>\n\n\n\n<p class=\"is-style-error\" style=\"font-size:0.9em\">Choice B is incorrect and may result from conceptual or calculation errors.<\/p>\n\n\n\n<p class=\"is-style-error\" style=\"font-size:0.9em\">Choice C is incorrect and may result from conceptual or calculation errors.<\/p>\n\n\n\n<p class=\"is-style-error\" style=\"font-size:0.9em\">Choice D is incorrect and may result from conceptual or calculation errors.<\/p>\n\n\n\n<p class=\"is-style-info\" style=\"font-size:0.9em\">We are tasked with finding the maximum number of <strong>large candles<\/strong> the business owner can purchase while staying within a budget of $2,200 and ensuring at least 200 candles are purchased.<br><strong>Step-by-Step Solution:<\/strong><br><strong>Step 1: Define variables<\/strong><br>Let:<br>~ <em>x<\/em> = the number of <strong>small candles<\/strong> purchased<br>~ <em>y<\/em> = the number of <strong>large candles<\/strong> purchased<br>We need to maximize <em>y<\/em> under the constraints of the budget and minimum candle requirements.<br><br><strong>Step 2: Write the constraints<\/strong><br>1. <strong>Total candles constraint:<\/strong> <em>x<\/em> + <em>y<\/em> \u2265 200<br>This ensures that at least 200 candles are purchased.<br>2. <strong>Budget constraint<\/strong>:<br>The cost of small candles is 4.90<em>x<\/em>, and the cost of large candles is 11.60<em>y<\/em>. Together, the total cost must not exceed $2,200:<br>4.90<em>x<\/em> + 11.60<em>y<\/em> \u2264 2,200<br><br><strong>Step 3: Solve for <em>x<\/em> in terms of <em>y<\/em><\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"528\" height=\"675\" src=\"https:\/\/us.mrenglishkj.com\/sat\/wp-content\/uploads\/sites\/2\/2024\/12\/image-16.png\" alt=\"Data analysis question and answer free explanations and free SAT learning\" class=\"wp-image-4798\" srcset=\"https:\/\/us.mrenglishkj.com\/sat\/wp-content\/uploads\/sites\/2\/2024\/12\/image-16.png 528w, https:\/\/us.mrenglishkj.com\/sat\/wp-content\/uploads\/sites\/2\/2024\/12\/image-16-235x300.png 235w\" sizes=\"auto, (max-width: 528px) 100vw, 528px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"661\" height=\"514\" src=\"https:\/\/us.mrenglishkj.com\/sat\/wp-content\/uploads\/sites\/2\/2024\/12\/image-17.png\" alt=\"Free SAT preparation, step-by-step math solution\" class=\"wp-image-4799\" srcset=\"https:\/\/us.mrenglishkj.com\/sat\/wp-content\/uploads\/sites\/2\/2024\/12\/image-17.png 661w, https:\/\/us.mrenglishkj.com\/sat\/wp-content\/uploads\/sites\/2\/2024\/12\/image-17-300x233.png 300w\" sizes=\"auto, (max-width: 661px) 100vw, 661px\" \/><\/figure>\n\n\n\n<p class=\"is-style-info\" style=\"font-size:0.9em\">Thus, the maximum number of <strong>large candles<\/strong> the owner can purchase is: <strong>182<\/strong> (Well, it is 182.09. You can write 182 in the Type-Based question in the final exam and it will be correct.)<br><br><strong>Step 7: Verify the solution<\/strong><br>~ If <em>y<\/em> = 182, then <em>x<\/em> = 200 \u2212 182 = 18.<br>~ Total cost: 4.90(18) + 11.60(182)<br>88.20 + 2,111.20 = 2,199.40<br>This is within the budget of $2,200.<br>The solution satisfies all constraints.<\/p>\n<\/div><\/details><\/div>\n\n\n\n<div class=\"wp-block-coblocks-accordion-item\"><details><summary class=\"wp-block-coblocks-accordion-item__title\"><strong>10th Question<\/strong><\/summary><div class=\"wp-block-coblocks-accordion-item__content\">\n<p class=\"is-style-warning\" style=\"font-size:0.9em\"><strong>Question:<\/strong> In the linear function <em>f<\/em>, <em>f<\/em>(0) = 8 and <em>f<\/em>(1) = 12. Which equation defines <em>f<\/em>?<br>A) <em>f<\/em>(<em>x<\/em>) = 12<em>x<\/em> + 8<br>B) <em>f<\/em>(<em>x<\/em>) = 4<em>x<\/em><br>C) <em>f<\/em>(<em>x<\/em>) = 4<em>x<\/em> + 12<br>D) <em>f<\/em>(<em>x<\/em>) = 4<em>x<\/em> + 8<\/p>\n\n\n\n<p class=\"is-style-success\" style=\"font-size:0.9em\"><strong>Choice D<\/strong> is correct. Since <em>f<\/em> is a linear function, it can be defined by an equation of the form <em>f<\/em>(<em>x<\/em>) = <em>ax<\/em> + <em>b<\/em>, where <em>a<\/em> and <em>b<\/em> are constants. It\u2019s given that <em>f<\/em>(0) = 8. Substituting 0 for <em>x<\/em> and 8 for <em>f<\/em>(<em>x<\/em>) in the equation <em>f<\/em>(<em>x<\/em>) = <em>ax<\/em>+<em>b<\/em> yields 8 = <em>a<\/em>(0) + <em>b<\/em>, or 8 = <em>b<\/em>. Substituting 8 for <em>b<\/em> in the equation <em>f<\/em>(<em>x<\/em>) = <em>ax<\/em> + <em>b<\/em> yields <em>f<\/em>(<em>x<\/em>) = <em>ax<\/em> + 8. It\u2019s given that <em>f<\/em>(1) = 12. Substituting 1 for <em>x<\/em> and 12 for <em>f<\/em>(<em>x<\/em>) in the equation <em>f<\/em>(<em>x<\/em>) = <em>ax<\/em> + 8 yields 12 = <em>a<\/em>(1) + 8, or 12 = <em>a<\/em> + 8. Subtracting 8 from both sides of this equation yields <em>a<\/em> = 4. Substituting 4 for <em>a<\/em> in the equation <em>f<\/em>(<em>x<\/em>) = <em>ax<\/em> + 8 yields <em>f<\/em>(<em>x<\/em>) = 4<em>x<\/em> + 8. Therefore, an equation that defines <em>f<\/em> is <em>f<\/em>(<em>x<\/em>) = 4<em>x<\/em>+8.<\/p>\n\n\n\n<p class=\"is-style-error\" style=\"font-size:0.9em\">Choice A is incorrect and may result from conceptual or calculation errors.<\/p>\n\n\n\n<p class=\"is-style-error\" style=\"font-size:0.9em\">Choice B is incorrect and may result from conceptual or calculation errors.<\/p>\n\n\n\n<p class=\"is-style-error\" style=\"font-size:0.9em\">Choice C is incorrect and may result from conceptual or calculation errors.<\/p>\n\n\n\n<p class=\"is-style-info\" style=\"font-size:0.9em\">We are tasked with determining which equation defines the linear function <em>f<\/em>(<em>x<\/em>), given the values <em>f<\/em>(0) = 8 and <em>f<\/em>(1) = 12.<br><strong>Step-by-Step Solution:<\/strong><br><strong>Step 1: General form of a linear equation<\/strong><br>The equation of a linear function is generally written as:<br><em>f<\/em>(<em>x<\/em>) = <em>mx<\/em> + <em>b<\/em><br>where:<br>~ <em>m<\/em> is the slope of the line.<br>~ <em>b<\/em> is the <em>y<\/em>-intercept (the value of <em>f<\/em>(<em>x<\/em>) when <em>x<\/em> = 0).<br><br><strong>Step 2: Find <em>b<\/em> (the <em>y<\/em>-intercept)<\/strong><br>We are given that <em>f<\/em>(0) = 8. Substituting into the general equation:<br><em>f<\/em>(0) = <em>m<\/em>(0) + <em>b<\/em><br><em>f<\/em>(0) = 8<br>Thus: <em>b<\/em> = 8<br><br><strong>Step 3: Find <em>m<\/em> (the slope)<\/strong><br>The slope <em>m<\/em> is calculated using the formula:<br><em>m<\/em> = change&nbsp;in&nbsp;<em>f<\/em>(<em>x<\/em>)\/change&nbsp;in&nbsp;<em>x<\/em><br>(\u200bchange&nbsp;in&nbsp;<em>f<\/em>(<em>x<\/em>) is divided by change&nbsp;in&nbsp;<em>x<\/em>)<br>From the given information:<br>~ <em>f<\/em>(1) = 12<br>~ <em>f<\/em>(0) = 8<br>The change in <em>f<\/em>(<em>x<\/em>) is: 12 \u2212 8 = 4<br>The change in <em>x<\/em> is: 1 \u2212 0 = 1<br>Thus:<br><em>m<\/em> = 4\/1 = 4<br><br><strong>Step 4: Write the equation<\/strong><br>Substitute <em>m<\/em> = 4 and <em>b<\/em> = 8 into the general equation <em>f<\/em>(<em>x<\/em>) = <em>mx<\/em> + <em>b<\/em>:<br><em>f<\/em>(<em>x<\/em>) = 4<em>x<\/em> + 8<br><br><strong>Step 5: Verify the equation<\/strong><br>1. Check if <em>f<\/em>(0) = 8:<br><em>f<\/em>(0) = 4(0) + 8 = 8   \u2705 Correct.<br>2. Check if <em>f<\/em>(1) = 12:<br><em>f<\/em>(1) = 4(1) + 8 =12  \u2705 Correct.<br>Thus, the equation <em>f<\/em>(<em>x<\/em>) = 4<em>x<\/em> + 8 satisfies both conditions.<br><br><strong>Step 6: Match with the options<\/strong><br>From the given choices:<br>The correct option is <strong>D) <em>f<\/em>(<em>x<\/em>) = 4<em>x<\/em> + 8<\/strong>.<\/p>\n<\/div><\/details><\/div>\n\n\n\n<div class=\"wp-block-coblocks-accordion-item\"><details><summary class=\"wp-block-coblocks-accordion-item__title\"><strong>11th Question<\/strong><\/summary><div class=\"wp-block-coblocks-accordion-item__content\">\n<p class=\"is-style-warning\" style=\"font-size:0.9em\"><strong>14<em>j<\/em> + 5<em>k<\/em> = <em>m<\/em><br>Question:<\/strong> The given equation relates the numbers <em>j<\/em>, <em>k<\/em>, and <em>m<\/em>. Which equation correctly expresses <em>k<\/em> in terms of <em>j<\/em> and <em>m<\/em>?<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"121\" height=\"174\" src=\"https:\/\/us.mrenglishkj.com\/sat\/wp-content\/uploads\/sites\/2\/2024\/12\/image-18.png\" alt=\"Prepare for the SAT test and learn for free\" class=\"wp-image-4812\"\/><\/figure>\n\n\n\n<p class=\"is-style-success\" style=\"font-size:0.9em\"><strong>Choice A<\/strong> is correct. Subtracting 14<em>j<\/em> from each side of the given equation results in 5<em>k<\/em> = <em>m<\/em> &#8211; 14<em>j<\/em>. Dividing each side of this equation by 5 results in <em>k<\/em> = <sup><em>m<\/em> &#8211; 14<em>j<\/em><\/sup>\/<sub>5<\/sub>.<\/p>\n\n\n\n<p class=\"is-style-error\" style=\"font-size:0.9em\">Choice B is incorrect and may result from conceptual or calculation errors.<\/p>\n\n\n\n<p class=\"is-style-error\" style=\"font-size:0.9em\">Choice C is incorrect and may result from conceptual or calculation errors.<\/p>\n\n\n\n<p class=\"is-style-error\" style=\"font-size:0.9em\">Choice D is incorrect and may result from conceptual or calculation errors.<\/p>\n\n\n\n<p class=\"is-style-info\" style=\"font-size:0.9em\"><strong>Step-by-Step Solution:<\/strong><br><strong>Step 1: Isolate the term with <em>k<\/em><\/strong><br>Start with the given equation:<br>14<em>j<\/em> + 5<em>k<\/em> = <em>m<\/em><br>Subtract 14<em>j<\/em> from both sides to move the <em>j<\/em>-term to the right-hand side:<br>5<em>k <\/em>= <em>m<\/em> \u2212 14<em>j<\/em><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"442\" height=\"561\" src=\"https:\/\/us.mrenglishkj.com\/sat\/sat\/wp-content\/uploads\/2024\/12\/image-19.png\" alt=\"SAT math linear problems solutions and tests - take free tests and free learning\" class=\"wp-image-4815\" srcset=\"https:\/\/us.mrenglishkj.com\/sat\/wp-content\/uploads\/sites\/2\/2024\/12\/image-19.png 442w, https:\/\/us.mrenglishkj.com\/sat\/wp-content\/uploads\/sites\/2\/2024\/12\/image-19-236x300.png 236w\" sizes=\"auto, (max-width: 442px) 100vw, 442px\" \/><\/figure>\n\n\n\n<p class=\"is-style-info\" style=\"font-size:0.9em\">Based on the option, we have our answer but if it is a Type-Based Question then we try to solve it further.<\/p>\n<\/div><\/details><\/div>\n\n\n\n<div class=\"wp-block-coblocks-accordion-item\"><details><summary class=\"wp-block-coblocks-accordion-item__title\"><strong>12th Question<\/strong><\/summary><div class=\"wp-block-coblocks-accordion-item__content\">\n<p class=\"is-style-warning\" style=\"font-size:0.9em\"><strong>Question:<\/strong> <\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"304\" height=\"313\" src=\"https:\/\/us.mrenglishkj.com\/sat\/sat\/wp-content\/uploads\/2024\/12\/image-20.png\" alt=\"SAT Test preparation and learning for free (SAT Lessons)\" class=\"wp-image-4818\" srcset=\"https:\/\/us.mrenglishkj.com\/sat\/wp-content\/uploads\/sites\/2\/2024\/12\/image-20.png 304w, https:\/\/us.mrenglishkj.com\/sat\/wp-content\/uploads\/sites\/2\/2024\/12\/image-20-291x300.png 291w\" sizes=\"auto, (max-width: 304px) 100vw, 304px\" \/><\/figure>\n\n\n\n<p class=\"is-style-success\" style=\"font-size:0.9em\"><strong>Choice B<\/strong> is correct. If two triangles are similar, then their corresponding angles are congruent. It\u2019s given that right triangle <em>FGH<\/em> is similar to right triangle <em>JKL<\/em> and angle <em>F<\/em> corresponds to angle <em>J<\/em>. It follows that angle <em>F<\/em> is congruent to angle <em>J<\/em> and, therefore, the measure of angle <em>F<\/em> is equal to the measure of angle <em>J<\/em>. The sine ratios of angles of equal measure are equal. Since the measure of angle <em>F<\/em> is equal to the measure of angle <em>J<\/em>, sin(<em>F<\/em>) = sin(<em>J<\/em>). It\u2019s given that sin(<em>F<\/em>) = 308\/317. Therefore, sin(<em>J<\/em>) is 308\/317.<\/p>\n\n\n\n<p class=\"is-style-error\" style=\"font-size:0.9em\">Choice A is incorrect. This is the value of cos(<em>J<\/em>), not the value of sin(<em>J<\/em>).<\/p>\n\n\n\n<p class=\"is-style-error\" style=\"font-size:0.9em\">Choice C is incorrect. This is the reciprocal of the value of sin(<em>J<\/em>), not the value of sin(<em>J<\/em>).<\/p>\n\n\n\n<p class=\"is-style-error\" style=\"font-size:0.9em\">Choice D is incorrect. This is the reciprocal of the value of cos(<em>J<\/em>), not the value of sin(<em>J<\/em>).<\/p>\n\n\n\n<p class=\"is-style-info\" style=\"font-size:0.9em\">In similar triangles, the corresponding sides are proportional.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"707\" height=\"577\" src=\"https:\/\/us.mrenglishkj.com\/sat\/sat\/wp-content\/uploads\/2024\/12\/image-21.png\" alt=\"\" class=\"wp-image-4820\" srcset=\"https:\/\/us.mrenglishkj.com\/sat\/wp-content\/uploads\/sites\/2\/2024\/12\/image-21.png 707w, https:\/\/us.mrenglishkj.com\/sat\/wp-content\/uploads\/sites\/2\/2024\/12\/image-21-300x245.png 300w\" sizes=\"auto, (max-width: 707px) 100vw, 707px\" \/><\/figure>\n\n\n\n<p class=\"is-style-info\" style=\"font-size:0.9em\"><strong>Step 3: Use Triangle Similarity<\/strong><br>1. <strong>What does &#8220;similar triangles&#8221; mean?<\/strong><br>~ ~ Similar triangles have: <br>~ ~ ~ Equal corresponding angles.<br>~ ~ ~ Corresponding sides that are proportional.<br>2. Since <em>FGH \u223c JKL<\/em>, we know that:<br>~ ~ \u2220F = \u2220J<br>~ ~ \u2220G = \u2220K = 90<sup>\u2218<\/sup><br>3. <strong>Why is this important for trigonometry?<\/strong><br>If two triangles are similar, the trigonometric ratios (like sine, cosine, and tangent) for their corresponding angles are <strong>equal<\/strong>. This is because the ratios of the corresponding sides are the same.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"696\" height=\"521\" src=\"https:\/\/us.mrenglishkj.com\/sat\/sat\/wp-content\/uploads\/2024\/12\/image-22.png\" alt=\"\" class=\"wp-image-4821\" srcset=\"https:\/\/us.mrenglishkj.com\/sat\/wp-content\/uploads\/sites\/2\/2024\/12\/image-22.png 696w, https:\/\/us.mrenglishkj.com\/sat\/wp-content\/uploads\/sites\/2\/2024\/12\/image-22-300x225.png 300w\" sizes=\"auto, (max-width: 696px) 100vw, 696px\" \/><\/figure>\n\n\n\n<p class=\"is-style-info\" style=\"font-size:0.9em\"><strong>Step 6: Verify the Answer<\/strong><br>Let\u2019s check the options:<br>Option A)\u200b: Incorrect, as it does not match sin\u2061(<em>F<\/em>).<br>Option B)\u200b: Correct, as sin\u2061(<em>F<\/em>) = sin\u2061(<em>J<\/em>) = 308\/317\u200b.<br>Option C)\u200b: Incorrect, as this is the reciprocal of sin\u2061(<em>F<\/em>), not sin\u2061(<em>F<\/em>) itself.<br>Option D)\u200b: Incorrect, as this value has no relation to sin\u2061(<em>F<\/em>).<br><br><strong>Final Answer: B) 308\/317.<\/strong><\/p>\n<\/div><\/details><\/div>\n\n\n\n<div class=\"wp-block-coblocks-accordion-item\"><details><summary class=\"wp-block-coblocks-accordion-item__title\"><strong>13th Question<\/strong><\/summary><div class=\"wp-block-coblocks-accordion-item__content\">\n<p class=\"is-style-warning\" style=\"font-size:0.9em\"><strong>Question:<\/strong> The product of two positive integers is 546. If the first integer is 11 greater than twice the second integer, what is the smaller of the two integers?<br>A) 7<br>B) 14<br>C) 39<br>D) 78<\/p>\n\n\n\n<p class=\"is-style-success\" style=\"font-size:0.9em\"><strong>Choice B<\/strong> is correct. Let <em>x<\/em> be the first integer and let <em>y<\/em> be the second integer. If the first integer is 11 greater than twice the second integer, then <em>x<\/em> = 2<em>y<\/em> + 11. If the product of the two integers is 546, then <em>xy<\/em> = 546. Substituting 2<em>y<\/em> + 11 for <em>x<\/em> in this equation results in (2<em>y<\/em> + 11)<em>y<\/em> = 546. Distributing the <em>y<\/em> to both terms in the parentheses results in 2<em>y<\/em><sup>2 + <\/sup>11<em>y<\/em> = 546. Subtracting 546 from both sides of this equation results in 2<em>y<\/em><sup>2<\/sup> + 11<em>y<\/em> &#8211; 546 = 0. The left-hand side of this equation can be factored by finding two values whose product is 2(-546), or -1,092, and whose sum is 11. The two values whose product is -1,092 and whose sum is 11 are 39 and -28. Thus, the equation 2<em>y<\/em><sup>2<\/sup> + 11y &#8211; 546 = 0 can be rewritten as 2<em>y<\/em><sup>2<\/sup> + 28<em>y<\/em> &#8211; 39<em>y<\/em> &#8211; 546 = 0, which is equivalent to 2<em>y<\/em>(<em>y<\/em> &#8211; 14) + 39(<em>y<\/em> &#8211; 14) = 0, or (2<em>y<\/em> + 39)(<em>y<\/em> &#8211; 14) = 0. By the zero product property, it follows that 2<em>y<\/em> + 39 = 0 and <em>y<\/em> &#8211; 14 = 0. Subtracting 39 from both sides of the equation 2<em>y<\/em> + 39 = 0 yields 2<em>y<\/em> = -39. Dividing both sides of this equation by 2 yields <em>y<\/em> = -39\/2. Since <em>y<\/em> is a positive integer, the value of <em>y<\/em> is not -39\/2. Adding 14 to both sides of the equation <em>y<\/em> &#8211; 14 = 0 yields <em>y<\/em> = 14. Substituting 14 for <em>y<\/em> in the equation <em>xy<\/em> = 546 yields <em>x<\/em>(14) = 546. Dividing both sides of this equation by 14 results in <em>x<\/em> = 39. Therefore, the two integers are 14 and 39, so the smaller of the two integers is 14.<\/p>\n\n\n\n<p class=\"is-style-error\" style=\"font-size:0.9em\">Choice A is incorrect and may result from conceptual or calculation errors.<\/p>\n\n\n\n<p class=\"is-style-error\" style=\"font-size:0.9em\">Choice C is incorrect. This is the larger of the two integers.<\/p>\n\n\n\n<p class=\"is-style-error\" style=\"font-size:0.9em\">Choice D is incorrect and may result from conceptual or calculation errors.<\/p>\n\n\n\n<p class=\"is-style-info\" style=\"font-size:0.9em\"><strong>Step 1: Define variables<\/strong><br>Let:<br>~ The smaller integer be <em>x<\/em>.<br>~ The larger integer be <em>y<\/em>.<br>From the problem:<br>~ <em>y<\/em> = 2<em>x<\/em> + 11 (the first integer is 11 more than twice the second integer).<br>~ <em>x \u22c5 y<\/em> = 546 (the product of the two integers is 546).<br><br><strong>Step 2: Substitute <em>y<\/em><\/strong><br>From <em>y<\/em> = 2<em>x<\/em> + 11, substitute this into <em>x \u22c5 y <\/em>= 546:<br><em>x<\/em> \u22c5 (2<em>x<\/em> + 11) = 546<br><br><strong>Step 3: Expand and simplify<\/strong><br>Expand the equation: 2<em>x<\/em><sup>2<\/sup> + 11<em>x<\/em> = 546<br>Rearrange the equation to standard quadratic form:<br>2<em>x<\/em><sup>2<\/sup> + 11<em>x<\/em> \u2212 546 = 0<br><br><strong>Step 4: Solve the quadratic equation<\/strong><br>To solve 2<em>x<\/em><sup>2<\/sup> + 11<em>x<\/em> \u2212 546 = 0, use the quadratic formula:<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"646\" height=\"582\" src=\"https:\/\/us.mrenglishkj.com\/sat\/sat\/wp-content\/uploads\/2024\/12\/image-23.png\" alt=\"prepare for the SAT Math for free by taking the SAT tests\" class=\"wp-image-4827\" srcset=\"https:\/\/us.mrenglishkj.com\/sat\/wp-content\/uploads\/sites\/2\/2024\/12\/image-23.png 646w, https:\/\/us.mrenglishkj.com\/sat\/wp-content\/uploads\/sites\/2\/2024\/12\/image-23-300x270.png 300w\" sizes=\"auto, (max-width: 646px) 100vw, 646px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"534\" height=\"369\" src=\"https:\/\/us.mrenglishkj.com\/sat\/sat\/wp-content\/uploads\/2024\/12\/image-24.png\" alt=\"Learn and take test of the SAT exam for free\" class=\"wp-image-4828\" srcset=\"https:\/\/us.mrenglishkj.com\/sat\/wp-content\/uploads\/sites\/2\/2024\/12\/image-24.png 534w, https:\/\/us.mrenglishkj.com\/sat\/wp-content\/uploads\/sites\/2\/2024\/12\/image-24-300x207.png 300w\" sizes=\"auto, (max-width: 534px) 100vw, 534px\" \/><\/figure>\n\n\n\n<p class=\"is-style-info\" style=\"font-size:0.9em\"><strong>Step 6: Verify the solution<\/strong><br>If <em>x<\/em> = 14, calculate <em>y<\/em>:<br><em>y<\/em> = 2<em>x<\/em> + 11<br><em>y<\/em> = 2(14) + 11<br><em>y<\/em> = 28 + 11<br><em>y<\/em> = 39<br>Check the product:<br><em>x<\/em> \u22c5 <em>y <\/em>=14\u22c539 = 546<br>This is correct.<br><br><strong>Final Answer: B) 14.<\/strong><\/p>\n<\/div><\/details><\/div>\n\n\n\n<div class=\"wp-block-coblocks-accordion-item\"><details><summary class=\"wp-block-coblocks-accordion-item__title\"><strong>14th Question<\/strong><\/summary><div class=\"wp-block-coblocks-accordion-item__content\">\n<p class=\"is-style-warning\" style=\"font-size:0.9em\"><strong>Question:<\/strong> The function <em>f<\/em> is defined by <em>f<\/em>(<em>x<\/em>) = (<em>x<\/em> \u2212 3)(<em>x<\/em> + 4)(<em>x<\/em> + 5). In the <em>xy<\/em>-plane, the graph of <em>y<\/em> = <em>g<\/em>(<em>x<\/em>) is the result of translating the graph of <em>y<\/em> = <em>f<\/em>(<em>x<\/em>) down 7 units. What is the value of <em>g<\/em>(0)?<br>A) -49<br>B) 49<br>C) -35<br>D) 35<\/p>\n\n\n\n<p class=\"is-style-success\" style=\"font-size:0.9em\"><strong>Choice A<\/strong> is correct.<\/p>\n\n\n\n<p class=\"is-style-error\" style=\"font-size:0.9em\">Choice B is incorrect and may result from conceptual errors.<\/p>\n\n\n\n<p class=\"is-style-error\" style=\"font-size:0.9em\">Choice C is incorrect and may result from conceptual errors.<\/p>\n\n\n\n<p class=\"is-style-error\" style=\"font-size:0.9em\">Choice D is incorrect and may result from conceptual errors.<\/p>\n\n\n\n<p class=\"is-style-info\" style=\"font-size:0.9em\"><strong>Step-by-Step Solution:<\/strong><br><strong>Step 1: Understand the problem<\/strong><br>We are given the function <em>f<\/em>(<em>x<\/em>) = (<em>x<\/em> \u2212 3)(<em>x<\/em> + 4)(<em>x<\/em> + 5), and the function <em>g<\/em>(<em>x<\/em>) is the result of translating <em>f<\/em>(<em>x<\/em>) <strong>down 7 units<\/strong>. This means:<br><em>g<\/em>(<em>x<\/em>) = <em>f<\/em>(<em>x<\/em>) \u2212 7<br>We need to find <em>g<\/em>(2), which is: <em>g<\/em>(2) = <em>f<\/em>(2) \u2212 7<br><br><strong>Step 2: Calculate <em>f<\/em>(2)<\/strong><br>Substitute <em>x<\/em> = 2 into the function <em>f<\/em>(<em>x<\/em>):<br><em>f<\/em>(2) = (2 \u2212 3)(2 + 4)(2 + 5)<br>Calculate each term: <em>f<\/em>(2) = (\u22121)(6)(7)<br><em>f<\/em>(2) = \u221242<br><br><strong>Step 3: Calculate <em>g<\/em>(2)<\/strong><br>Since <em>g<\/em>(<em>x<\/em>) = <em>f<\/em>(<em>x<\/em>) \u2212 7, substitute <em>f<\/em>(2) = \u221242 into the equation:<br><em>g<\/em>(2) = \u221242 \u22127<br><em>g<\/em>(2) = \u221249<br><br><strong>Final Answer:<\/strong> The value of <em>g<\/em>(2) is <strong>-49<\/strong>.<\/p>\n<\/div><\/details><\/div>\n\n\n\n<div class=\"wp-block-coblocks-accordion-item\"><details><summary class=\"wp-block-coblocks-accordion-item__title\"><strong>15th Question<\/strong><\/summary><div class=\"wp-block-coblocks-accordion-item__content\">\n<p class=\"is-style-warning\" style=\"font-size:0.9em\"><strong>Question:<\/strong> A container initially holds 30 liters of water. Water leaks from the container at a constant rate of 2 liters every 5 hours. If 12 liters of water remain in the container, for how many hours has the water been leaking?<br>A) 90<br>B) 45<br>C) 92<br>D) 180<\/p>\n\n\n\n<p class=\"is-style-success\" style=\"font-size:0.9em\"><strong>Choice B<\/strong> is the correct option.<\/p>\n\n\n\n<p class=\"is-style-error\" style=\"font-size:0.9em\">Choice A is incorrect and may result from conceptual errors.<\/p>\n\n\n\n<p class=\"is-style-error\" style=\"font-size:0.9em\">Choice C is incorrect and may result from conceptual errors.<\/p>\n\n\n\n<p class=\"is-style-error\" style=\"font-size:0.9em\">Choice D is incorrect and may result from conceptual errors.<\/p>\n\n\n\n<p class=\"is-style-info\" style=\"font-size:0.9em\"><strong>Step-by-Step Solution:<\/strong><br><strong>Step 1: Understand the problem<\/strong><br>The container started with 30 liters, and it is losing water at a constant rate of 2 liters every 5 hours. After some time, the amount of water remaining in the container is 12 liters. We need to determine the total time, in hours, for which the water has been leaking.<br><br><strong>Step 2: Write the equation<\/strong><br>The total water lost is the difference between the initial amount of water and the remaining amount:<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"726\" height=\"674\" src=\"https:\/\/us.mrenglishkj.com\/sat\/wp-content\/uploads\/sites\/2\/2024\/12\/image-10.png\" alt=\"Solve Advanced Math problems of the SAT Math for free\" class=\"wp-image-4770\" srcset=\"https:\/\/us.mrenglishkj.com\/sat\/wp-content\/uploads\/sites\/2\/2024\/12\/image-10.png 726w, https:\/\/us.mrenglishkj.com\/sat\/wp-content\/uploads\/sites\/2\/2024\/12\/image-10-300x279.png 300w\" sizes=\"auto, (max-width: 726px) 100vw, 726px\" \/><\/figure>\n\n\n\n<p class=\"is-style-info\" style=\"font-size:0.9em\"><strong>Step 4: Verify the solution<\/strong><br>At a rate of 2 liters every 5 hours, the total time required to lose 18 liters is:<br>Time = Water lost\/Rate per unit time (We divide using this formula.)<br>Time = 18 divided by 2\/5 (To divide an equation like this 5 will go up and multiply with 18.)<br>Time = 18 x 5 divided by 2<br>Time = 90\/2<br>Time = 45 hours.<br><br><strong>Final Answer:<\/strong> The water has been leaking for <strong>45 hours<\/strong>.<\/p>\n<\/div><\/details><\/div>\n\n\n\n<div class=\"wp-block-coblocks-accordion-item\"><details><summary class=\"wp-block-coblocks-accordion-item__title\"><strong>16th Question<\/strong> <\/summary><div class=\"wp-block-coblocks-accordion-item__content\">\n<p class=\"is-style-warning\" style=\"font-size:0.9em\"><strong>Question:<\/strong> The table shown summarizes the number of employees at each of the 17 restaurants in a town.<\/p>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"has-fixed-layout\"><thead><tr><th class=\"has-text-align-center\" data-align=\"center\">Number of Employees<\/th><th class=\"has-text-align-center\" data-align=\"center\">Number of Restaurants<\/th><\/tr><\/thead><tbody><tr><td class=\"has-text-align-center\" data-align=\"center\">2 to 7<\/td><td class=\"has-text-align-center\" data-align=\"center\">2<\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\">8 to 13<\/td><td class=\"has-text-align-center\" data-align=\"center\">4<\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\">14 to 19<\/td><td class=\"has-text-align-center\" data-align=\"center\">2<\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\">20 to 25<\/td><td class=\"has-text-align-center\" data-align=\"center\">7<\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\">26 to 31<\/td><td class=\"has-text-align-center\" data-align=\"center\">2<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p class=\"is-style-warning\" style=\"font-size:0.9em\">Which of the following could be the median number of employees for the restaurants in this town?<br>A) 2<br>B) 9<br>C) 15<br>D) 21<\/p>\n\n\n\n<p class=\"is-style-success\" style=\"font-size:0.9em\"><strong>Choice D<\/strong> is correct. If a data set contains an odd number of data values, the median is represented by the middle data value in the list when the data values are listed in ascending or descending order. Since the numbers of employees are given as ranges of values rather than specific values, it\u2019s only possible to determine the range in which the median falls, rather than the exact median. Since<br>there are 17 restaurants included in the data set and the numbers of employees are listed in ascending order, it follows that the median number of employees will be represented by the ninth restaurant in the list. Since the first 2 restaurants each have 2 to 7 employees, the number of employees in the 2 to 7 range would be represented by the first and second restaurants in the list. The next 4 restaurants<br>each have 8 to 13 employees. Therefore, the number of employees in the 8 to 13 range will be represented by the third through sixth restaurants in the list. The next 2 restaurants each have 14 to 19 employees. Therefore, the number of employees in the 14 to 19 range will be represented by the seventh and eighth restaurants in the list. Since the next 7 restaurants each have 20 to 25 employees, the number of employees in the 20 to 25 range will be represented by the ninth through fifteenth restaurants in the list. This means that the ninth restaurant in the list, which has the median number of employees for the restaurants in this town, has a number of employees in the 20 to 25 range. Of the given choices, the only number of employees in the 20 to 25 range is 21.<\/p>\n\n\n\n<p class=\"is-style-error\" style=\"font-size:0.9em\">Choice A is incorrect and may result from conceptual or calculation errors.<\/p>\n\n\n\n<p class=\"is-style-error\" style=\"font-size:0.9em\">Choice B is incorrect and may result from conceptual or calculation errors.<\/p>\n\n\n\n<p class=\"is-style-error\" style=\"font-size:0.9em\">Choice C is incorrect and may result from conceptual or calculation errors.<\/p>\n\n\n\n<p class=\"is-style-info\" style=\"font-size:0.9em\"><strong>Step-by-step Solution:<\/strong><br>We are tasked to find the <strong>median number of employees<\/strong> based on the given data.<br><strong>Step 1: Understand the Median<\/strong><br>The <strong>median<\/strong> is the middle value in a sorted data set. If there are an odd number of data points, the median is the middle data point. If there is an even number of data points, the median is the average of the two middle data points.<br><br><strong>Step 2: Compute Total Number of Restaurants<\/strong><br>From the table, the total number of restaurants is:<br>2 + 4 + 2 + 7 + 2 = 17<br>Since the total is <strong>17 restaurants<\/strong> (an odd number), the median is the value of the <strong>9th restaurant<\/strong> when the data is arranged in ascending order.<br><br><strong>Step 3: Determine the 9th Restaurant&#8217;s Group<\/strong><br>We now determine which group contains the <strong>9th restaurant<\/strong> by adding up the cumulative frequencies of restaurants:<br>~ The first 2 restaurants have <strong>2 to 7 employees<\/strong>.<br>~ The next 4 restaurants have <strong>8 to 13 employees<\/strong>.<br>Cumulative total = 2 + 4 = 6<br>~ The next 2 restaurants have <strong>14 to 19 employees<\/strong>.<br>Cumulative total = 6 + 2 = 8<br>~ The next 7 restaurants have <strong>20 to 25 employees<\/strong>.<br>Cumulative total = 8 + 7 = 15<br>Thus, the <strong>9th restaurant<\/strong> falls in the <strong>20 to 25 employees<\/strong> group.<br><br><strong>Step 4: Choose a Median Value from the Group<\/strong><br>The group <strong>20 to 25 employees<\/strong> includes all restaurants within that range. Since the exact employee count for each restaurant is not specified, any value within this range could represent the median. From the options provided, the only possible value is: <strong>21<\/strong><br><br><strong>Final Answer:<\/strong> <strong>The median number of employees is: 21<\/strong><br><br>Suppose, we do not have Options then how do we do it?\u200b<br><strong>Step 1: Understand the Problem<\/strong><br>We are tasked with finding the <strong>median number of employees<\/strong> for the 17 restaurants. The <strong>median<\/strong> is the value that separates the data set into two equal halves.<br>Since there are <strong>17 restaurants<\/strong> (an odd number), the median is the number of employees at the <strong>9th restaurant<\/strong> when all 17 restaurants are arranged in ascending order.<br><br><strong>Step 2: Organize the Data<\/strong><br>The table gives the number of restaurants in specific ranges of employee counts:<\/p>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"has-fixed-layout\"><thead><tr><th class=\"has-text-align-center\" data-align=\"center\">Number of Employees<\/th><th class=\"has-text-align-center\" data-align=\"center\">Number of Restaurants<\/th><th class=\"has-text-align-center\" data-align=\"center\">Cumulative Frequency<\/th><\/tr><\/thead><tbody><tr><td class=\"has-text-align-center\" data-align=\"center\">2 to 7<\/td><td class=\"has-text-align-center\" data-align=\"center\">2<\/td><td class=\"has-text-align-center\" data-align=\"center\"><strong>2<\/strong><\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\">8 to 13<\/td><td class=\"has-text-align-center\" data-align=\"center\">4<\/td><td class=\"has-text-align-center\" data-align=\"center\">2 + 4 = <strong>6<\/strong><\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\">14 to 19<\/td><td class=\"has-text-align-center\" data-align=\"center\">2<\/td><td class=\"has-text-align-center\" data-align=\"center\">6 + 2 = <strong>8<\/strong><\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\">20 to 25<\/td><td class=\"has-text-align-center\" data-align=\"center\">7<\/td><td class=\"has-text-align-center\" data-align=\"center\">8 + 7 = <strong>15<\/strong><\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\">26 to 31<\/td><td class=\"has-text-align-center\" data-align=\"center\">2<\/td><td class=\"has-text-align-center\" data-align=\"center\">15 + 2 = <strong>17<\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p class=\"is-style-info\" style=\"font-size:0.9em\">The <strong>cumulative frequency<\/strong> tells us the total number of restaurants accounted for up to a given range. For example, the cumulative frequency of 6 for the &#8220;8 to 13&#8221; range means the first 6 restaurants are in the &#8220;2 to 13&#8221; range.<br><br><strong>Step 3: Identify the 9th Restaurant<\/strong><br>The <strong>9th restaurant<\/strong> falls within the range where the cumulative frequency first exceeds 8. By examining the table:<br>~ Cumulative frequency for &#8220;2 to 7&#8221; = <strong>2<\/strong> \u2192 The first 2 restaurants are here.<br>~ Cumulative frequency for &#8220;8 to 13&#8221; = <strong>6<\/strong> \u2192 The next 4 restaurants are here (total = 6).<br>~ Cumulative frequency for &#8220;14 to 19&#8221; = <strong>8<\/strong> \u2192 The next 2 restaurants are here (total = 8).<br>~ Cumulative frequency for &#8220;20 to 25&#8221; = <strong>15<\/strong> \u2192 The next 7 restaurants are here (total = 15).<br>Thus, the <strong>9th restaurant<\/strong> is in the range of <strong>20 to 25 employees<\/strong>.<br><br><strong>Step 4: Locate the Median Value<\/strong><br>Since the <strong>9th restaurant<\/strong> is in the range of &#8220;20 to 25 employees,&#8221; the median number of employees must lie somewhere in this range.<br><br><strong>Step 4.1: Select a representative value<\/strong><br>If no specific values are provided for the restaurants in this range, we assume the values are evenly distributed across the range. The most natural choice for the median value in this case is the <strong>midpoint of the range<\/strong>.<br>~ The range &#8220;20 to 25&#8221; has a midpoint:<br>Midpoint = 20 + 25 divided by 2 = 22.5<br>If <strong>precise integer values<\/strong> are required, round 22.5 to either 22 or 23, based on the context.<br><br><strong>Step 5: Final Answer<\/strong><br>The <strong>median number of employees<\/strong> is: <strong>22.5&nbsp;(or&nbsp;approximately&nbsp;23&nbsp;if&nbsp;rounded).<\/strong><\/p>\n<\/div><\/details><\/div>\n\n\n\n<div class=\"wp-block-coblocks-accordion-item\"><details><summary class=\"wp-block-coblocks-accordion-item__title\"><strong>17th Question<\/strong><\/summary><div class=\"wp-block-coblocks-accordion-item__content\">\n<p class=\"is-style-warning\" style=\"font-size:0.9em\"><strong>Question:<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"294\" height=\"65\" src=\"https:\/\/us.mrenglishkj.com\/sat\/sat\/wp-content\/uploads\/2024\/12\/image-28.png\" alt=\"Practice free SAT tests with answers explanations\" class=\"wp-image-4851\"\/><\/figure>\n\n\n\n<p class=\"is-style-warning\" style=\"font-size:0.9em\">A) 38.7<br>B) 41.8<br>C) 37.8<br>D) 41.7<br>[Type-Based Answer: In the final exam, you will type the answer rather than choose from options.]<\/p>\n\n\n\n<p class=\"is-style-success\" style=\"font-size:0.9em\"><strong>Choice C<\/strong> is the correct option.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"502\" height=\"193\" src=\"https:\/\/us.mrenglishkj.com\/sat\/sat\/wp-content\/uploads\/2024\/12\/image-25.png\" alt=\"Prepare for the SAT Exam and take free SAT tests\" class=\"wp-image-4835\" srcset=\"https:\/\/us.mrenglishkj.com\/sat\/wp-content\/uploads\/sites\/2\/2024\/12\/image-25.png 502w, https:\/\/us.mrenglishkj.com\/sat\/wp-content\/uploads\/sites\/2\/2024\/12\/image-25-300x115.png 300w\" sizes=\"auto, (max-width: 502px) 100vw, 502px\" \/><\/figure>\n\n\n\n<p class=\"is-style-error\" style=\"font-size:0.9em\">Choice A is incorrect and may result from conceptual or calculation errors.<\/p>\n\n\n\n<p class=\"is-style-error\" style=\"font-size:0.9em\">Choice B is incorrect and may result from conceptual or calculation errors.<\/p>\n\n\n\n<p class=\"is-style-error\" style=\"font-size:0.9em\">Choice D is incorrect and may result from conceptual or calculation errors.<\/p>\n\n\n\n<p class=\"is-style-info\" style=\"font-size:0.9em\">he question asks for the <strong>y-coordinate of the y-intercept<\/strong> of the given equation:<br>The <strong>y-intercept<\/strong> is the point where the graph intersects the <strong>y-axis<\/strong>. At the <strong>y-intercept<\/strong>, the value of <em>x<\/em> = 0. We will solve for <em>y<\/em> by substituting <em>x<\/em> = 0 into the given equation and simplifying.<br><br><strong>Step-by-Step Solution:<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"465\" height=\"656\" src=\"https:\/\/us.mrenglishkj.com\/sat\/sat\/wp-content\/uploads\/2024\/12\/image-29.png\" alt=\"Linear Functions free learning for the SAT Test preparation\" class=\"wp-image-4854\" srcset=\"https:\/\/us.mrenglishkj.com\/sat\/wp-content\/uploads\/sites\/2\/2024\/12\/image-29.png 465w, https:\/\/us.mrenglishkj.com\/sat\/wp-content\/uploads\/sites\/2\/2024\/12\/image-29-213x300.png 213w\" sizes=\"auto, (max-width: 465px) 100vw, 465px\" \/><\/figure>\n\n\n\n<p class=\"is-style-info\" style=\"font-size:0.9em\"><strong>Step 4: Eliminate the fraction:<\/strong><br>Multiply both sides by 9 to get rid of the denominator:<br>\u22125<em>y<\/em> = \u2212189<br><br><strong>Step 5: Solve for <em>y<\/em>:<\/strong><br>Divide both sides by \u22125 to solve for <em>y<\/em>:<br><em>y<\/em> = -189\/-5<br><em>y<\/em> = 37.8<br><br><strong>Final Answer: C) 37.8<\/strong><\/p>\n<\/div><\/details><\/div>\n\n\n\n<div class=\"wp-block-coblocks-accordion-item\"><details><summary class=\"wp-block-coblocks-accordion-item__title\"><strong>18th Question<\/strong><\/summary><div class=\"wp-block-coblocks-accordion-item__content\">\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"239\" height=\"234\" src=\"https:\/\/us.mrenglishkj.com\/sat\/sat\/wp-content\/uploads\/2024\/12\/image-30.png\" alt=\"take SAT tests for free and learn by practicing solutions\" class=\"wp-image-4857\"\/><\/figure>\n\n\n\n<p class=\"is-style-warning\" style=\"font-size:0.9em\"><strong>Question:<\/strong> The graph of <em>y<\/em> = 2<em>x<\/em><sup>2<\/sup> + <em>bx<\/em> + <em>c<\/em> is shown, where <em>b<\/em> and <em>c<\/em> are constants. What is the value of <em>bc<\/em>?<br>A) 6<br>B) 24<br>C) -6<br>D) -24<br>[Type-Based Answer: In the final exam, you will type the answer rather than choose from options.]<\/p>\n\n\n\n<p class=\"is-style-success\" style=\"font-size:0.9em\"><strong>Choice D<\/strong> is the correct answer. The correct answer is -24. Since the graph passes through the point (0, -6), it follows that when the value of <em>x<\/em> is 0, the value of <em>y<\/em> is -6. Substituting 0 for <em>x<\/em> and -6 for <em>y<\/em> in the given equation yields -6 = 2(0)<sup>2<\/sup> + <em>b<\/em>(0) + <em>c<\/em>, or -6 = c. Therefore, the value of <em>c<\/em> is -6. Substituting -6 for <em>c<\/em> in the given equation yields <em>y<\/em> = 2<em>x<\/em><sup>2<\/sup> + <em>bx<\/em> &#8211; 6. Since the graph passes through the point (-1, -8), it follows that when the value of <em>x<\/em> is -1, the value of <em>y<\/em> is -8. Substituting -1 for <em>x<\/em> and -8 for <em>y<\/em> in the equation <em>y<\/em> = 2<em>x<\/em><sup>2<\/sup> + <em>bx<\/em> &#8211; 6 yields -8 = 2(-1)<sup>2<\/sup> + <em>b<\/em>(-1) &#8211; 6, or -8 = 2 &#8211; <em>b<\/em> &#8211; 6, which is equivalent to -8 = -4 &#8211; <em>b<\/em>. Adding 4 to each side of this equation yields -4 = &#8211;<em>b<\/em>. Dividing each side of this equation by -1 yields 4 = <em>b<\/em>. Since the value of <em>b<\/em> is 4 and the value of <em>c<\/em> is -6, it follows that the value of <em>bc<\/em> is (4)(-6), or -24.<br><strong>Alternate approach: <\/strong>The given equation represents a parabola in the <em>xy<\/em>-plane with a vertex at (-1, -8). Therefore, the given equation, <em>y<\/em> = 2<em>x<\/em><sup>2<\/sup> + <em>bx<\/em> + <em>c<\/em>, which is written in standard form, can be written in vertex form, <em>y<\/em> = <em>a<\/em>(<em>x<\/em> &#8211; <em>h<\/em>)<sup>2<\/sup> + <em>k<\/em>, where (<em>h<\/em>, <em>k<\/em>) is the vertex of the parabola and a is the value of the coefficient on the <em>x<\/em><sup>2<\/sup> term when the equation is written in standard form. It follows that <em>a<\/em> = 2. Substituting 2 for <em>a<\/em>, -1 for <em>h<\/em>, and -8 for <em>k<\/em> in this equation yields <em>y<\/em> = 2[<em>x<\/em> &#8211; (-1)]<sup>2<\/sup> + (-8), or <em>y<\/em> = 2(<em>x<\/em> + 1)<sup>2<\/sup> &#8211; 8. Squaring the binomial on the right-hand side of this equation yields <em>y<\/em> = 2(<em>x<\/em><sup>2<\/sup> + 2<em>x<\/em> + 1) &#8211; 8. Multiplying each term inside the parentheses on the right-hand side of this equation by 2 yields <em>y<\/em> = 2<em>x<\/em><sup>2<\/sup> + 4<em>x<\/em> + 2 &#8211; 8, which is equivalent to <em>y<\/em> = 2<em>x<\/em><sup>2<\/sup> + 4<em>x<\/em> &#8211; 6. From the given equation <em>y<\/em> = 2<em>x<\/em><sup>2<\/sup> + <em>bx<\/em> + <em>c<\/em>, it follows that the value of <em>b<\/em> is 4 and the value of <em>c<\/em> is -6. Therefore, the value of <em>bc<\/em> is (4)(-6), or -24.<\/p>\n\n\n\n<p class=\"is-style-error\" style=\"font-size:0.9em\">Choice A is incorrect and may result from conceptual or calculation errors.<\/p>\n\n\n\n<p class=\"is-style-error\" style=\"font-size:0.9em\">Choice B is incorrect and may result from conceptual or calculation errors.<\/p>\n\n\n\n<p class=\"is-style-error\" style=\"font-size:0.9em\">Choice C is incorrect and may result from conceptual or calculation errors.<\/p>\n\n\n\n<p class=\"is-style-info\" style=\"font-size:0.9em\"><strong>Step-by-Step Solution<\/strong>:<br><strong>Step 1: Understanding the question<\/strong><br>~ The equation is provided: <em>y<\/em> = 2<em>x<\/em><sup>2<\/sup> + <em>bx<\/em> + <em>c<\/em><br>~ We need to find the value of <em>b<\/em> and <em>c<\/em> which are constants.<br>~ So let&#8217;s find the values that are given in the graph <em>x<\/em>-intercept and <span style=\"margin: 0px;padding: 0px\"><em>y-<\/em>intercept<\/span> points. (You should focus on three points on the parabola that are given in the graph, they are the intercept points.)<br>~ ~ When the x-intercept is at 0 then the y-intercept is at -6.<br><em>(x<\/em> = 0, <em>y<\/em> = -6)<br>~ ~ When the x-intercept is at -1 then the y-intercept is at -8.<br>(<em>x<\/em> = -1, <em>y<\/em> = -8)<br>~ ~ When the x-intercept is at -2 then the y-intercept is at -6.<br>(<em>x<\/em> = -2, <em>y<\/em> = -6)<br>Let&#8217;s put any value out of these three intercept points.<br><br><strong>Step 2: Put the x-intercept and y-intercept<\/strong>:<br><em>y<\/em> = 2x<sup>2<\/sup> + <em>bx<\/em> + <em>c<\/em><br>Where (<em>x<\/em> = 0 and <em>y<\/em> = -6)<br>-6 = 2(0)<sup>2<\/sup> + <em>b<\/em>(0) + c<br>-6 = 2(0) + 0 + <em>c<\/em><br>-6 = <em>c<\/em><br>Hence, we find the value of <em>c<\/em> is: -6.<br><br><strong>Step 3: Find the value of <em>b<\/em><\/strong><br><em>y<\/em> = 2<em>x<\/em><sup>2<\/sup> + <em>bx<\/em> + <em>c<\/em><br>Where (x = 0, y = -6, and <em>c<\/em> = -6)<br>-6 = 2(0)<sup>2<\/sup> + <em>b<\/em>(0) + -6<br>-6 = 2(0) + 0 + -6<br>Now, here, you notice that <em>b<\/em> multiplies by 0 and becomes 0. So we cannot find the value of <em>b<\/em> if we use <em>x<\/em>-intercept 0.<br>Let&#8217;s pick the 2nd intercept point where (<em>x<\/em> = -1 and <em>y<\/em> = -8)<br><em>y<\/em> = 2<em>x<\/em><sup>2<\/sup> + <em>bx<\/em> + <em>c<\/em><br>-8 = 2(-1)<sup>2<\/sup> + <em>b<\/em>(-1) + (-6)<br>-8 = 2(1) &#8211;<em> b <\/em>&#8211; 6<br>-8 = 2 &#8211; <em>b<\/em> &#8211; 6<br>-8 = 2 &#8211; 6 &#8211; <em>b<\/em><br>-8 = -4 &#8211; <em>b<\/em><br>-8 + 4 = &#8211;<em>b<\/em><br>-4 = &#8211;<em>b<\/em> (Let&#8217;s cut minus sign of each side)<br><em>b<\/em> = 4 <br>Hence, we find the value of <em>b<\/em> is: 4.<br><br><strong>Step 4: Find the value of <em>bc<\/em><br><\/strong>Since <em>b<\/em> = 4 and <em>c<\/em> = -6<br><em>bc<\/em> = (4)(-6)<br><em>bc<\/em> = -24<br><br><strong>Final Answer:<\/strong> <strong>D) -24<\/strong><\/p>\n<\/div><\/details><\/div>\n\n\n\n<div class=\"wp-block-coblocks-accordion-item\"><details><summary class=\"wp-block-coblocks-accordion-item__title\"><strong>19th Question<\/strong><\/summary><div class=\"wp-block-coblocks-accordion-item__content\">\n<p class=\"is-style-warning\" style=\"font-size:0.9em\"><strong>Question:<\/strong> In 2008, Zinah earned 14% more than in 2007, and in 2009 Zinah earned 4% more than in 2008. If Zinah earned <em>y<\/em> times as much in 2009 as in 2007, what is the value of <em>y<\/em> ?<br>A) 0.5600<br>B) 1.0056<br>C) 1.1800<br>D) 1.1856<\/p>\n\n\n\n<p class=\"is-style-success\" style=\"font-size:0.9em\"><strong>Choice D<\/strong> is the correct answer.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"491\" height=\"178\" src=\"https:\/\/us.mrenglishkj.com\/sat\/sat\/wp-content\/uploads\/2024\/12\/image-26.png\" alt=\"Take free SAT tests and learn SAT math with solutions\" class=\"wp-image-4838\" srcset=\"https:\/\/us.mrenglishkj.com\/sat\/wp-content\/uploads\/sites\/2\/2024\/12\/image-26.png 491w, https:\/\/us.mrenglishkj.com\/sat\/wp-content\/uploads\/sites\/2\/2024\/12\/image-26-300x109.png 300w\" sizes=\"auto, (max-width: 491px) 100vw, 491px\" \/><\/figure>\n\n\n\n<p class=\"is-style-error\" style=\"font-size:0.9em\">Choice A is incorrect and may result from conceptual or calculation errors.<\/p>\n\n\n\n<p class=\"is-style-error\" style=\"font-size:0.9em\">Choice B is incorrect and may result from conceptual or calculation errors.<\/p>\n\n\n\n<p class=\"is-style-error\" style=\"font-size:0.9em\">Choice C is incorrect and may result from conceptual or calculation errors.<\/p>\n\n\n\n<p class=\"is-style-info\" style=\"font-size:0.9em\"><strong>Problem Breakdown:<\/strong><br>Zinah\u2019s earnings change over three years:<br>~ In <strong>2008<\/strong>, Zinah earned <strong>14% more than in 2007<\/strong>.<br>~ In <strong>2009<\/strong>, Zinah earned <strong>4% more than in 2008<\/strong>.<br>~ The goal is to find the ratio (<em>y<\/em>) of Zinah\u2019s 2009 earnings to her 2007 earnings.<br>We will calculate <em>y<\/em> step by step.<br><br><strong>Step-by-Step Solution<\/strong><br><strong>1. Represent earnings in terms of 2007\u2019s earnings:<\/strong><br>Let Zinah\u2019s earnings in 2007 be E (2007) = 1 (as a baseline).<br>~ <strong>Earnings in 2008:<\/strong> Zinah earned <strong>14% more<\/strong> in 2008, so:<br>E (2008) = 1 + 0.14 = 1.14.<br>~ <strong>Earnings in 2009:<\/strong> Zinah earned <strong>4% more<\/strong> in 2009 than in 2008, so:<br>E (2009) = 1.14 + (0.04 \u00d7 1.14).<br>Simplify: E (2009) = 1.14(1 + 0.04)<br>E (2009) = 1.14 \u00d7 1.04<br><br><strong>2. Calculate E (2009)\u200b:<\/strong><br>E (2009) = 1.14 \u00d7 1.04 = 1.1856.<br>This means Zinah earned <strong>1.1856 times<\/strong> her 2007 earnings in 2009.<br><br><strong>3. Interpret the result:<\/strong><br>The ratio <em>y<\/em> of Zinah\u2019s 2009 earnings to her 2007 earnings is:<br><em>y<\/em> = 1.1856.<br><br><strong>Verification:<\/strong><br>To verify:<br>~ In <strong>2008<\/strong>, Zinah earned 1.14 times her 2007 earnings.<br>~ In <strong>2009<\/strong>, she earned 1.04 times her 2008 earnings:<br>1.14 \u00d7 1.04 = 1.1856, confirming our calculation.<br><br><strong>Final Answer: D) 1.1856<\/strong><\/p>\n<\/div><\/details><\/div>\n\n\n\n<div class=\"wp-block-coblocks-accordion-item\"><details><summary class=\"wp-block-coblocks-accordion-item__title\"><strong>20th Question<\/strong><\/summary><div class=\"wp-block-coblocks-accordion-item__content\">\n<p class=\"is-style-warning\" style=\"font-size:0.9em\"><strong>Question:<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"184\" height=\"293\" src=\"https:\/\/us.mrenglishkj.com\/sat\/sat\/wp-content\/uploads\/2024\/12\/image-32.png\" alt=\"SAT Question and answer preparation, practice SAT Math for free\" class=\"wp-image-4878\"\/><\/figure>\n\n\n\n<p class=\"is-style-success\" style=\"font-size:0.9em\"><strong>Choice C<\/strong> is correct.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"479\" height=\"177\" src=\"https:\/\/us.mrenglishkj.com\/sat\/sat\/wp-content\/uploads\/2024\/12\/image-31.png\" alt=\"SAT Test and their solutions (free SAT learning)\" class=\"wp-image-4877\" srcset=\"https:\/\/us.mrenglishkj.com\/sat\/wp-content\/uploads\/sites\/2\/2024\/12\/image-31.png 479w, https:\/\/us.mrenglishkj.com\/sat\/wp-content\/uploads\/sites\/2\/2024\/12\/image-31-300x111.png 300w\" sizes=\"auto, (max-width: 479px) 100vw, 479px\" \/><\/figure>\n\n\n\n<p class=\"is-style-error\" style=\"font-size:0.9em\">Choice A is incorrect and may result from conceptual or calculation errors.<\/p>\n\n\n\n<p class=\"is-style-error\" style=\"font-size:0.9em\">Choice B is incorrect and may result from conceptual or calculation errors.<\/p>\n\n\n\n<p class=\"is-style-error\" style=\"font-size:0.9em\">Choice D is incorrect and may result from conceptual or calculation errors.<\/p>\n\n\n\n<p class=\"is-style-info\" style=\"font-size:0.9em\"><strong>Step 1: Factor and understand the denominators<\/strong><br>~ The <strong>first fraction<\/strong> has a denominator of <em>x<\/em> \u2212 8.<br>~ The <strong>second fraction<\/strong> has a denominator of <em>x<\/em><sup>2<\/sup><em>y<\/em> \u2212 8<em>xy<\/em>.<br>Notice that <em>x<\/em><sup>2<\/sup><em>y<\/em> \u2212 8<em>xy<\/em> can be factored:<br><em>x<\/em><sup>2<\/sup><em>y<\/em> \u2212 8<em>xy<\/em> = <em>xy<\/em>(<em>x<\/em> \u2212 8).<br>This shows that the second denominator is <em>xy<\/em>(<em>x<\/em> \u2212 8), which is the product of <em>x<\/em> and <em>x<\/em> \u2212 8.<br><br><strong>Step 2: Find the least common denominator (LCD)<\/strong><br>To add fractions, we need a common denominator. The denominators are:<br>~ <em>x<\/em> \u2212 8 (from the first fraction),<br>~ <em>xy<\/em>(<em>x<\/em> \u2212 8) (from the second fraction).<br>The <strong>least common denominator (LCD)<\/strong> is <em>xy<\/em>(<em>x<\/em> \u2212 8), as it includes all factors from both denominators.<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li><\/li>\n<\/ol>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"709\" height=\"656\" src=\"https:\/\/us.mrenglishkj.com\/sat\/sat\/wp-content\/uploads\/2024\/12\/image-33.png\" alt=\"SAT Math topic Equivalent Expression (Free SAT Practice)\" class=\"wp-image-4880\" srcset=\"https:\/\/us.mrenglishkj.com\/sat\/wp-content\/uploads\/sites\/2\/2024\/12\/image-33.png 709w, https:\/\/us.mrenglishkj.com\/sat\/wp-content\/uploads\/sites\/2\/2024\/12\/image-33-300x278.png 300w\" sizes=\"auto, (max-width: 709px) 100vw, 709px\" \/><\/figure>\n\n\n\n<p class=\"is-style-info\" style=\"font-size:0.9em\">Now, focus on the denominator which is <em>xy<\/em>(<em>x<\/em> &#8211; 8). If we expand it now, we will get:<br><em>xy<\/em>(<em>x<\/em> &#8211; 8)<br><strong>x<sup>2<\/sup><em>y &#8211;<\/em> 8<em>xy<\/em>.<br><\/strong>It is similar to the <strong>Option C<\/strong> denominator, hence we got our correct answer. If you are short on time, you can submit your answer after this.<br>Since we are practicing, so let&#8217;s solve it further.<br><br><strong>Step 5: Expand and simplify the numerator<\/strong><br>1. Expand <em>xy<\/em>(<em>y<\/em> + 12):<br><em>xy<\/em>(<em>y<\/em> + 12) = <em>xy<\/em><sup>2<\/sup> + 12<em>xy<\/em>.<br>2. Expand <em>y<\/em>(<em>x<\/em> \u2212 8):<br><em>y<\/em>(<em>x<\/em> \u2212 8) = <em>xy<\/em> \u2212 8<em>y<\/em>.<br>3. Add the two expressions:<br><em>xy<\/em><sup>2<\/sup> + 12<em>xy<\/em> + <em>xy<\/em> \u2212 8<em>y<\/em>.<br>4. Combine like terms:<br>~ Combine 12<em>xy<\/em> + <em>xy<\/em> = 13<em>xy<\/em>,<br>~ Keep <em>xy<\/em><sup>2<\/sup> and \u22128<em>y<\/em> as they are.<br>Thus, the numerator simplifies to:<br><em>xy<\/em><sup>2<\/sup> + 13<em>xy<\/em> \u2212 8<em>y<\/em>.<br><br><strong>Step 6: Final simplified fraction<\/strong><br>The expression becomes:<br>Numerator =     <strong> <em>xy<\/em><sup>2<\/sup> + 13<em>xy<\/em> \u2212 8<em>y<\/em><\/strong><sub><br><\/sub><strong><sup>                                <sub>________________________<\/sub><\/sup><br><\/strong>Denominator =      <strong> x<sup>2<\/sup><em>y &#8211;<\/em> 8<em>xy<\/em><\/strong><br><br>This is the final simplified form of the expression.<br><br><strong>Final Answer: Option C<\/strong>.<\/p>\n<\/div><\/details><\/div>\n\n\n\n<div class=\"wp-block-coblocks-accordion-item\"><details><summary class=\"wp-block-coblocks-accordion-item__title\"><strong>21th Question<\/strong><\/summary><div class=\"wp-block-coblocks-accordion-item__content\">\n<p class=\"is-style-warning\" style=\"font-size:0.9em\">I. <em>f<\/em>(<em>x<\/em>) = \u22126(3)<sup>x<\/sup> \u2212 3<br>II. <em>g<\/em>(<em>x<\/em>) = \u22123(6)<sup>x<\/sup><br><strong>Question:<\/strong> Which of the following functions has(have) a minimum value at \u22123?<br>A) I only<br>B) II only<br>C) I and II<br>D) Neither I nor II<\/p>\n\n\n\n<p class=\"is-style-success\" style=\"font-size:0.9em\"><strong>Choice D<\/strong> is correct. A function of the form <em>f<\/em>(x) = <em>a<\/em>(<em>b<\/em>)<sup>x<\/sup> + <em>c<\/em>, where <em>a<\/em> &lt; 0 and <em>b<\/em> &gt; 1, is a decreasing function. Both of the given functions are of this form; therefore, both are decreasing functions. If a function <em>f<\/em> is decreasing, as the value of <em>x<\/em> increases, the corresponding value of <em>f<\/em>(<em>x<\/em>) decreases; therefore, the function doesn\u2019t have a minimum value. Thus, neither of the given functions has a minimum value.<\/p>\n\n\n\n<p class=\"is-style-error\" style=\"font-size:0.9em\">Choice A is incorrect and may result from conceptual or calculation errors.<\/p>\n\n\n\n<p class=\"is-style-error\" style=\"font-size:0.9em\">Choice B is incorrect and may result from conceptual or calculation errors.<\/p>\n\n\n\n<p class=\"is-style-error\" style=\"font-size:0.9em\">Choice C is incorrect and may result from conceptual or calculation errors.<\/p>\n\n\n\n<p class=\"is-style-info\" style=\"font-size:0.9em\"><strong>Step 1: Analyze the structure of <em>f<\/em>(<em>x<\/em>) = \u22126(3)<sup>x<\/sup> \u2212 3<\/strong><br>~ (3)<strong><sup>x<\/sup><\/strong> is an <strong>exponential function<\/strong> with a base of 3. Exponential functions with positive bases (3 &gt; 1) are <strong>increasing<\/strong> as <em>x<\/em> increases.<br>For (3)<strong><sup>x<\/sup><\/strong>, as <strong><em>x<\/em> \u2192 \u2212\u221e<\/strong>, the function (3)<strong><sup>x<\/sup><\/strong> \u2192 0, and as <em>x<\/em> \u2192 \u221e, (3)<strong><sup>x<\/sup><\/strong> \u2192 \u221e.<br><br>~ Multiplying by \u22126: \u22126(3)<strong><sup>x<\/sup><\/strong> reverses the behavior. Now, \u22126(3)<strong><sup>x<\/sup><\/strong> \u2192 0 as <strong><em>x<\/em> \u2192 \u2212\u221e<\/strong>, and \u22126(3)<strong><sup>x<\/sup><\/strong> \u2192 <strong>\u2212\u221e<\/strong> as <em>x<\/em> \u2192 \u221e.<br><br>~ Adding \u22123: The term \u22123 shifts the graph of \u22126(3)<strong><sup>x<\/sup><\/strong> down by 3 units. This does not affect the increasing or decreasing nature of the function.<br>Thus, <em>f<\/em>(<em>x<\/em>) is a <strong>decreasing function<\/strong> overall, and there is no minimum at <em>x<\/em> = \u22123 because the function decreases indefinitely as <em>x<\/em> \u2192 \u221e.<br><br><strong>Conclusion for <em>f<\/em>(<em>x<\/em>):<\/strong><br><em>f<\/em>(<em>x<\/em>) does <strong>not<\/strong> have a minimum at <em>x<\/em> = \u22123.<br><br><strong>Step 2: Analyze the structure of <em>g<\/em>(<em>x<\/em>) = \u22123(6)<\/strong><sup><strong>x<\/strong><\/sup><br>~ (6)<strong><sup>x<\/sup><\/strong> is another <strong>exponential function<\/strong>, with base 6. Like (3)<strong><sup>x<\/sup><\/strong>, it is increasing for <em>x<\/em> &gt; 0, but as <strong><em>x<\/em> \u2192 \u2212\u221e<\/strong>, (6)<strong><sup>x<\/sup><\/strong> \u2192 0, and as <em>x<\/em> \u2192 \u221e, (6)<strong><sup>x<\/sup><\/strong> \u2192 \u221e.<br><br>~ Multiplying by \u22123: \u22123(6)<strong><sup>x<\/sup><\/strong> reverses the trend. Now, \u22123(6)<strong><sup>x<\/sup><\/strong> \u2192 0 as <strong><em>x<\/em> \u2192 \u2212\u221e<\/strong>, and \u22123(6)<strong><sup>x<\/sup><\/strong> \u2192 \u2212\u221e as <em>x<\/em> \u2192 \u221e.<br>Like <em>f<\/em>(<em>x<\/em>), <em>g<\/em>(<em>x<\/em>) is also a <strong>decreasing function<\/strong> and has no minimum at <em>x<\/em> = \u22123.<br><br><strong>Conclusion for <em>g<\/em>(<em>x<\/em>):<\/strong><br><em>g<\/em>(<em>x<\/em>) does <strong>not<\/strong> have a minimum at <em>x<\/em> = \u22123.<br><br><strong>Step 3: Verify by substitution<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"701\" height=\"674\" src=\"https:\/\/us.mrenglishkj.com\/sat\/sat\/wp-content\/uploads\/2024\/12\/image-34.png\" alt=\"Step-by-step math learning for the SAT Test\" class=\"wp-image-4892\" srcset=\"https:\/\/us.mrenglishkj.com\/sat\/wp-content\/uploads\/sites\/2\/2024\/12\/image-34.png 701w, https:\/\/us.mrenglishkj.com\/sat\/wp-content\/uploads\/sites\/2\/2024\/12\/image-34-300x288.png 300w\" sizes=\"auto, (max-width: 701px) 100vw, 701px\" \/><\/figure>\n\n\n\n<p class=\"is-style-info\" style=\"font-size:0.9em\">Again, this is just a value of the function at <em>x<\/em> = \u22123, not a minimum, as <em>g<\/em>(<em>x<\/em>) also keeps decreasing.<br><br><strong>Verification:<\/strong><br>~ Graphing the functions confirms that both are decreasing functions.<br>~ Substituting values verifies that neither function exhibits a minimum at <em>x<\/em> = \u22123.<br><br><strong>Step 4: Final Decision<\/strong><br>Since neither <em>f<\/em>(<em>x<\/em>) nor <em>g<\/em>(<em>x<\/em>) has a minimum at <em>x<\/em> = \u22123, the answer is: <strong>D)&nbsp;Neither&nbsp;I&nbsp;nor&nbsp;II<\/strong>.<\/p>\n<\/div><\/details><\/div>\n\n\n\n<div class=\"wp-block-coblocks-accordion-item\"><details><summary class=\"wp-block-coblocks-accordion-item__title\"><strong>22th Question<\/strong><\/summary><div class=\"wp-block-coblocks-accordion-item__content\">\n<p class=\"is-style-warning\" style=\"font-size:0.9em\"><strong>Question:<\/strong> The result of increasing the quantity <em>x<\/em> by 400% is 60. What is the value of <em>x<\/em> ?<br>A) 12<br>B) 15<br>C) 240<br>D) 340<\/p>\n\n\n\n<p class=\"is-style-success\" style=\"font-size:0.9em\"><strong>Choice A<\/strong> is correct. It\u2019s given that the result of increasing the quantity <em>x<\/em> by 400% is 60. This can be written as <em>x<\/em> + (400\/100)<em>x<\/em> = 60, which is equivalent to <em>x<\/em> + 4<em>x<\/em> = 60, or 5<em>x<\/em> = 60. Dividing each side of this equation by 5 yields <em>x<\/em> = 12. Therefore, the value of <em>x<\/em> is 12.<\/p>\n\n\n\n<p class=\"is-style-error\" style=\"font-size:0.9em\">Choice B is incorrect. The result of increasing the quantity 15 by 400% is 75, not 60.<\/p>\n\n\n\n<p class=\"is-style-error\" style=\"font-size:0.9em\">Choice C is incorrect. The result of increasing the quantity 240 by 400% is 1,200, not 60.<\/p>\n\n\n\n<p class=\"is-style-error\" style=\"font-size:0.9em\">Choice D is incorrect. The result of increasing the quantity 340 by 400% is 1,700, not 60.<\/p>\n\n\n\n<p class=\"is-style-info\" style=\"font-size:0.9em\"><strong>Step 1: Understand what &#8220;increased by 400%&#8221; means.<\/strong><br>~ To increase <em>x<\/em> by 400%, we add 400% of <em>x<\/em> to <em>x<\/em>.<br>~ In mathematical terms:<br>Result = <em>x<\/em> + 4<em>x<\/em> = 5<em>x<\/em>.<br>Thus, increasing <em>x<\/em> by 400% gives 5<em>x<\/em>.<br><br><strong>Step 2: Write an equation based on the given information.<\/strong><br>We are told that the result of this increase is 60:<br>5<em>x<\/em> = 60.<br><br><strong>Step 3: Solve for <em>x<\/em>.<\/strong><br>Divide both sides of the equation by 5:<br><em>x<\/em> = 60\/5 = 12.<br><br><strong>Step 4: Verify the solution.<\/strong><br>1. Start with <em>x<\/em> = 12.<br>2. Increase <em>x<\/em> by 400%:<br>~ 400% of 12 is 4 \u00d7 12 = 48.<br>~ Add this to <em>x<\/em>: 12 + 48 = 60.<br>3. The result matches the given condition. Hence, <em>x<\/em> = 12 is correct.<br><br><strong>Final Answer: A) 12.<\/strong><\/p>\n<\/div><\/details><\/div>\n<\/div>\n\n\n\n<div style=\"height:70px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<p>Did you try all the features and get comfortable using them? You should work on using the calculator and seeing references and directions. So be prepared for everything before taking the final SAT exam. The explanation of answers makes it easy to learn and progress. You must try to work on your speed and spend less time on the beginning and more on the later questions. This is the 5th Practice Test of SAT Math Module 1st.<\/p>\n\n\n\n<p>Either you can take the 6th Practice Test of SAT Math or the 5th Practice Test of SAT Math Module 2nd.<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><a href=\"https:\/\/us.mrenglishkj.com\/sat\/sat-math-test-5-module-2nd-lessons\/\" target=\"_blank\" rel=\"noopener\" title=\"\">SAT Test 5th (Math Module 2nd)<\/a><\/li>\n\n\n\n<li><a href=\"https:\/\/us.mrenglishkj.com\/sat\/sat-test-6-module-1st-math-problem-solution\/\" target=\"_blank\" rel=\"noopener\" title=\"\">SAT Test 6th (Math Module 1st)<\/a><\/li>\n\n\n\n<li><a href=\"https:\/\/us.mrenglishkj.com\/sat\/sat-reading-and-writing-test-5-module-1st\/\" target=\"_blank\" rel=\"noopener\" title=\"\">SAT Test 5th (Reading and Writing Module 1st)<\/a><\/li>\n<\/ul>\n\n\n\n<p>The best way to become a master in Math is to find the correct answer and understand why other options are incorrect. I wish you luck in your bright career.<\/p>\n\n\n\n<p><\/p>\n","protected":false},"excerpt":{"rendered":"<p>SAT Math Free Test 5 (Module 1st Examination Questions Hack: Prepare for the SAT Final Exam, learn by taking the free SAT Tests, and understand their answer and step-by-step solutions. You will also learn tricks and tips<\/p>\n","protected":false},"author":1,"featured_media":4743,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"googlesitekit_rrm_CAowmvTFDA:productID":"","_coblocks_attr":"","_coblocks_dimensions":"","_coblocks_responsive_height":"","_coblocks_accordion_ie_support":"","footnotes":""},"categories":[12],"tags":[27,28],"class_list":["post-4739","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-1st-module","tag-sat-math","tag-sat-module-1st"],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/us.mrenglishkj.com\/sat\/wp-json\/wp\/v2\/posts\/4739","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/us.mrenglishkj.com\/sat\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/us.mrenglishkj.com\/sat\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/us.mrenglishkj.com\/sat\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/us.mrenglishkj.com\/sat\/wp-json\/wp\/v2\/comments?post=4739"}],"version-history":[{"count":1,"href":"https:\/\/us.mrenglishkj.com\/sat\/wp-json\/wp\/v2\/posts\/4739\/revisions"}],"predecessor-version":[{"id":8825,"href":"https:\/\/us.mrenglishkj.com\/sat\/wp-json\/wp\/v2\/posts\/4739\/revisions\/8825"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/us.mrenglishkj.com\/sat\/wp-json\/wp\/v2\/media\/4743"}],"wp:attachment":[{"href":"https:\/\/us.mrenglishkj.com\/sat\/wp-json\/wp\/v2\/media?parent=4739"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/us.mrenglishkj.com\/sat\/wp-json\/wp\/v2\/categories?post=4739"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/us.mrenglishkj.com\/sat\/wp-json\/wp\/v2\/tags?post=4739"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}