{"id":192911,"date":"2025-02-18T10:35:22","date_gmt":"2025-02-18T10:35:22","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=192911"},"modified":"2025-02-18T10:35:24","modified_gmt":"2025-02-18T10:35:24","slug":"converting-units-there-are-4-quarts-in-1-gallon-4-cups-in-1-quart-and-16-tablespoons-in-1-cup","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/02\/18\/converting-units-there-are-4-quarts-in-1-gallon-4-cups-in-1-quart-and-16-tablespoons-in-1-cup\/","title":{"rendered":"Converting Units There are 4 quarts in 1 gallon, 4 cups in 1 quart, and 16 tablespoons in 1 cup"},"content":{"rendered":"\n<p>Converting Units There are 4 quarts in 1 gallon, 4 cups in 1 quart, and 16 tablespoons in 1 cup. (a) Write a function Q that converts x gallons to quarts.<\/p>\n\n\n\n<p>(b) Write a function C that converts x quarts to cups.<\/p>\n\n\n\n<p>(c) Write a function T that converts x cups to tablespoons.<\/p>\n\n\n\n<p>(d) Express a function F that converts x gallons to tablespoons as a composition of three functions. (e) Write a formula for F.<\/p>\n\n\n\n<p><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-ast-global-color-6-color\"><strong>The Correct Answer and Explanation is :<\/strong><\/mark><\/p>\n\n\n\n<p>Let&#8217;s break down the problem step by step.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">(a) Function Q that converts gallons to quarts:<\/h3>\n\n\n\n<p>We know that there are 4 quarts in 1 gallon. So, the function ( Q(x) ) that converts ( x ) gallons to quarts is:<\/p>\n\n\n\n<p>[<br>Q(x) = 4x<br>]<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">(b) Function C that converts quarts to cups:<\/h3>\n\n\n\n<p>We know that there are 4 cups in 1 quart. So, the function ( C(x) ) that converts ( x ) quarts to cups is:<\/p>\n\n\n\n<p>[<br>C(x) = 4x<br>]<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">(c) Function T that converts cups to tablespoons:<\/h3>\n\n\n\n<p>We know that there are 16 tablespoons in 1 cup. So, the function ( T(x) ) that converts ( x ) cups to tablespoons is:<\/p>\n\n\n\n<p>[<br>T(x) = 16x<br>]<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">(d) Function F that converts gallons to tablespoons as a composition of three functions:<\/h3>\n\n\n\n<p>To express a function ( F ) that converts ( x ) gallons to tablespoons, we need to compose the functions we\u2019ve created. First, we convert gallons to quarts, then quarts to cups, and finally cups to tablespoons.<\/p>\n\n\n\n<p>The composition of functions will look like:<\/p>\n\n\n\n<p>[<br>F(x) = T(C(Q(x)))<br>]<\/p>\n\n\n\n<p>Where:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>( Q(x) ) converts gallons to quarts,<\/li>\n\n\n\n<li>( C(x) ) converts quarts to cups, and<\/li>\n\n\n\n<li>( T(x) ) converts cups to tablespoons.<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">(e) Formula for F:<\/h3>\n\n\n\n<p>Now, let\u2019s write out the full formula for ( F(x) ). We already know the formulas for ( Q(x) ), ( C(x) ), and ( T(x) ):<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>( Q(x) = 4x )<\/li>\n\n\n\n<li>( C(x) = 4x )<\/li>\n\n\n\n<li>( T(x) = 16x )<\/li>\n<\/ul>\n\n\n\n<p>So, plugging in each function step by step:<\/p>\n\n\n\n<p>[<br>F(x) = T(C(Q(x))) = T(C(4x)) = T(16x) = 16(16x) = 256x<br>]<\/p>\n\n\n\n<p>Thus, the formula for ( F(x) ) is:<\/p>\n\n\n\n<p>[<br>F(x) = 256x<br>]<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Explanation:<\/h3>\n\n\n\n<p>In this problem, we are asked to convert units of volume. To do so, we use simple multiplication based on conversion factors:<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li>Gallons to quarts: There are 4 quarts in 1 gallon, so multiplying the number of gallons by 4 converts it to quarts.<\/li>\n\n\n\n<li>Quarts to cups: Similarly, there are 4 cups in 1 quart, so multiplying the number of quarts by 4 converts it to cups.<\/li>\n\n\n\n<li>Cups to tablespoons: Finally, there are 16 tablespoons in 1 cup, so multiplying the number of cups by 16 converts it to tablespoons.<\/li>\n<\/ol>\n\n\n\n<p>For part (d), we used a composition of these functions to create a new function that converts directly from gallons to tablespoons. By composing the functions ( Q ), ( C ), and ( T ), we multiplied the factors together to get the final conversion factor, which in this case is 256 (since ( 4 \\times 4 \\times 16 = 256 )).<\/p>\n\n\n\n<p>This approach shows how to convert between units by systematically applying conversion factors in sequence.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Converting Units There are 4 quarts in 1 gallon, 4 cups in 1 quart, and 16 tablespoons in 1 cup. (a) Write a function Q that converts x gallons to quarts. (b) Write a function C that converts x quarts to cups. (c) Write a function T that converts x cups to tablespoons. (d) Express [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"default","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","ast-disable-related-posts":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"footnotes":""},"categories":[25],"tags":[],"class_list":["post-192911","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/192911","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/comments?post=192911"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/192911\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=192911"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=192911"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=192911"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}