{"id":221894,"date":"2025-05-30T17:17:26","date_gmt":"2025-05-30T17:17:26","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=221894"},"modified":"2025-05-30T17:17:28","modified_gmt":"2025-05-30T17:17:28","slug":"a-tree-is-67-inches-tall","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/05\/30\/a-tree-is-67-inches-tall\/","title":{"rendered":"A tree is 67 inches tall."},"content":{"rendered":"\n

a tree is 67 inches tall. how tall is it in feet and inches?<\/p>\n\n\n\n

    \n
  1. If in a bit\u2019s string of {0,1}, of length 4, such that no two ones are together. Then the total number of such possible strings are?<\/li>\n<\/ol>\n\n\n\n

    a) 1
    b) 5
    c) 7
    d) 4<\/p>\n\n\n\n

    The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n

    Part 1: Converting 67 Inches into Feet and Inches<\/h3>\n\n\n\n

    To convert 67 inches<\/strong> into feet and inches<\/strong>:<\/p>\n\n\n\n

      \n
    • There are 12 inches<\/strong> in a foot.<\/li>\n\n\n\n
    • Divide 67 by 12:<\/li>\n<\/ul>\n\n\n\n

      67\u00f712=5 remainder 767 \\div 12 = 5\\text{ remainder }7<\/p>\n\n\n\n

      So, 67 inches = 5 feet and 7 inches<\/strong>.<\/p>\n\n\n\n

      \n\n\n\n

      Part 2: Binary Strings of Length 4 with No Two Adjacent 1s<\/h3>\n\n\n\n

      We are asked to find how many bit strings of length 4 made up of {0,1} do not<\/strong> have two 1s next to each other.<\/p>\n\n\n\n

      Step-by-step Explanation:<\/h4>\n\n\n\n

      We need to count all strings of length 4 such that no two 1s are adjacent<\/strong>.<\/p>\n\n\n\n

      Let\u2019s define:<\/p>\n\n\n\n

        \n
      • ana_n: number of valid strings of length nn with no two consecutive 1s<\/strong>.<\/li>\n<\/ul>\n\n\n\n

        This is a classic recurrence relation<\/strong> problem. The recurrence relation is: an=an\u22121+an\u22122a_n = a_{n-1} + a_{n-2}<\/p>\n\n\n\n

        Where:<\/p>\n\n\n\n

          \n
        • a1=2a_1 = 2: “0”, “1”<\/li>\n\n\n\n
        • a2=3a_2 = 3: “00”, “01”, “10”<\/li>\n<\/ul>\n\n\n\n

          Using the recurrence:<\/p>\n\n\n\n

            \n
          • a3=a2+a1=3+2=5a_3 = a_2 + a_1 = 3 + 2 = 5<\/li>\n\n\n\n
          • a4=a3+a2=5+3=8a_4 = a_3 + a_2 = 5 + 3 = 8<\/li>\n<\/ul>\n\n\n\n

            So there are 8<\/strong> such strings of length 4 in total<\/strong> that do not have consecutive 1s.<\/p>\n\n\n\n

            But wait! The question is more specific \u2014 it wants strings that contain 1s<\/strong>, but no two 1s are together<\/strong>. So we need to exclude<\/strong> the string with no 1s at all<\/strong> (i.e., “0000”).<\/p>\n\n\n\n

            From the 8 valid strings with no adjacent 1s:<\/p>\n\n\n\n

              \n
            • Valid strings: 0000<\/code>, 0001<\/code>, 0010<\/code>, 0100<\/code>, 0101<\/code>, 1000<\/code>, 1001<\/code>, 1010<\/code><\/li>\n<\/ul>\n\n\n\n

              Only 7<\/strong> of these contain at least one ‘1’ and no adjacent 1s.<\/p>\n\n\n\n

              \n\n\n\n

              \u2705 Final Answer: (c) 7<\/strong><\/h3>\n\n\n\n

              There are 7 valid bit strings of length 4<\/strong> that contain at least one \u20181\u2019 and no two 1s are adjacent<\/strong>.<\/p>\n\n\n\n

              \"\"<\/figure>\n","protected":false},"excerpt":{"rendered":"

              a tree is 67 inches tall. how tall is it in feet and inches? a) 1b) 5c) 7d) 4 The Correct Answer and Explanation is: Part 1: Converting 67 Inches into Feet and Inches To convert 67 inches into feet and inches: 67\u00f712=5 remainder 767 \\div 12 = 5\\text{ remainder }7 So, 67 inches = 5 feet […]<\/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-221894","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/221894","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=221894"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/221894\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=221894"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=221894"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=221894"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}