{"id":1582,"date":"2021-12-02T19:38:37","date_gmt":"2021-12-03T00:38:37","guid":{"rendered":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/back-matter\/answer-key-1-6\/"},"modified":"2024-01-09T17:01:51","modified_gmt":"2024-01-09T22:01:51","slug":"answer-key-1-6","status":"publish","type":"back-matter","link":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/back-matter\/answer-key-1-6\/","title":{"raw":"Answer Key 1.6","rendered":"Answer Key 1.6"},"content":{"raw":"
    \r\n \t
  1. [latex]7\\text{ mi}=7\\cancel{\\text{mi}}\\times \\dfrac{1760\\text{ yd}}{\\cancel{\\text{mi}}}[\/latex]\r\n[latex]\\phantom{7\\text{ mi}}=12,320\\text{ yd}[\/latex]<\/li>\r\n \t
  2. [latex]234\\text{ oz}=234\\cancel{\\text{oz}}\\times \\dfrac{1\\cancel{\\text{lb}}}{16\\cancel{\\text{oz}}}\\times \\dfrac{1\\text{ ton}}{2000\\cancel{\\text{lb}}}[\/latex]\r\n[latex]\\phantom{234\\text{ oz}}=0.0073\\text{ tons}[\/latex]<\/li>\r\n \t
  3. [latex]11.2\\text{ mg}=11.2\\cancel{\\text{mg}}\\times \\dfrac{1\\text{ g}}{1000\\cancel{\\text{mg}}}[\/latex]\r\n[latex]\\phantom{11.2\\text{ mg}}=0.0112\\text{ g}[\/latex]<\/li>\r\n \t
  4. [latex]1.35\\text{ km}=1.35\\cancel{\\text{km}}\\times \\dfrac{1000\\cancel{\\text{m}}}{1\\cancel{\\text{km}}}\\times \\dfrac{100\\text{ cm}}{1\\cancel{\\text{m}}}[\/latex]\r\n[latex]\\phantom{1.35\\text{ km}}=135,000\\text{ cm}[\/latex]<\/li>\r\n \t
  5. [latex]9,800,000\\text{ mm}=9,800,000\\cancel{\\text{mm}}\\times \\dfrac{1\\cancel{\\text{m}}}{1000\\cancel{\\text{mm}}}\\times \\dfrac{1\\cancel{\\text{km}}}{1000\\cancel{\\text{m}}}\\times \\dfrac{1\\text{ mi}}{1.61\\cancel{\\text{km}}}[\/latex]\r\n[latex]\\phantom{9,800,000\\text{ mm}}=6.09\\text{ mi (rounded)}[\/latex]<\/li>\r\n \t
  6. [latex]4.5\\text{ ft}^2=4.5\\cancel{\\text{ ft}^2}\\times \\dfrac{(1\\text{ yd})^2}{(3\\cancel{\\text{ft}})^2}[\/latex]\r\n[latex]\\phantom{4.5\\text{ ft}^2}=0.5\\text{ yd}^2[\/latex]<\/li>\r\n \t
  7. [latex]435,000\\text{ m}^2=435,000\\cancel{\\text{ m}^2}\\times \\dfrac{(1\\text{ km}^2)}{(1000\\cancel{\\text{m}})^2}[\/latex]\r\n[latex]\\phantom{435,000\\text{ m}^2}=0.435\\text{ km}^2[\/latex]<\/li>\r\n \t
  8. [latex]8\\text{ km}^2=8\\cancel{\\text{ km}^2}\\times \\dfrac{1\\cancel{\\text{ mi}^2}}{(1.61\\cancel{\\text{km}})^2}\\times \\dfrac{(5280 \\text{ ft})^2}{(1\\cancel{\\text{mi}})^2}[\/latex]\r\n[latex]\\phantom{8\\text{ km}^2}=86,000,000\\text{ ft}^2\\text{ (rounded)}[\/latex]<\/li>\r\n \t
  9. [latex]0.0065\\text{ km}^3=0.0065 \\cancel{\\text{ km}^3}\\times \\dfrac{(1000\\text{ m})^3}{(1\\cancel{\\text{km}})^3}[\/latex]\r\n[latex]\\phantom{0.0065\\text{ km}^3}=6,500,000\\text{ m}^3[\/latex]<\/li>\r\n \t
  10. [latex]14.62\\text{ in.}^2=14.62\\cancel{\\text{ in.}^2}\\times \\dfrac{(2.54\\text{ cm})^2}{(1\\cancel{\\text{in.}})^2}[\/latex]\r\n[latex]\\phantom{14.62\\text{ in.}^2}=94.3\\text{ cm}^2[\/latex]<\/li>\r\n \t
  11. [latex]5500\\text{ cm}^3=5500\\cancel{\\text{ cm}^3}\\times \\dfrac{(1\\cancel{\\text{in}})^3}{(2.54\\cancel{\\text{cm}})^3}\\times \\dfrac{(1\\text{ yd})^3}{(36\\cancel{\\text{in}})^3}[\/latex]\r\n[latex]\\phantom{5500\\text{ cm}^3}=0.0072\\text{ yd}^3[\/latex]<\/li>\r\n \t
  12. [latex]3.5\\text{ mi\/h}=\\dfrac{3.5\\cancel{\\text{mi}}}{\\cancel{\\text{h}}}\\times \\dfrac{5280\\text{ ft}}{1\\cancel{\\text{mi}}}\\times \\dfrac{1\\cancel{\\text{h}}}{3600\\text{ s}}[\/latex]\r\n[latex]\\phantom{3.5\\text{ mi\/h}}=5.13\\text{ ft\/s}[\/latex]<\/li>\r\n \t
  13. [latex]185\\text{ yd\/min.}=\\dfrac{185 \\cancel{\\text{yd}}}{\\cancel{\\text{min.}}}\\times \\dfrac{1\\text{ mi}}{1760\\cancel{\\text{yd}}}\\times \\dfrac{60\\cancel{\\text{min.}}}{1\\text{ h}}[\/latex]\r\n[latex]\\phantom{185\\text{ yd\/min.}}=6.31\\text{ mi\/h}[\/latex]<\/li>\r\n \t
  14. [latex]153\\text{ ft\/s}=\\dfrac{153\\cancel{\\text{ft}}}{\\text{s}}\\times \\dfrac{1\\text{ mi}}{5280\\cancel{\\text{ft}}}\\times \\dfrac{3600\\cancel{\\text{s}}}{1\\text{ h}}[\/latex]\r\n[latex]\\phantom{153\\text{ ft\/s}}=104.3\\text{ mi\/h}[\/latex]<\/li>\r\n \t
  15. [latex]248\\text{ mi\/h}=\\dfrac{248\\cancel{\\text{mi}}}{\\cancel{\\text{h}}}\\times \\dfrac{1.61\\cancel{\\text{km}}}{1\\cancel{\\text{mi}}}\\times \\dfrac{1000\\text{ m}}{1\\cancel{\\text{km}}}\\times \\dfrac{1\\cancel{\\text{h}}}{3600\\text{ s}}[\/latex]\r\n[latex]\\phantom{248\\text{ mi\/h}}=111\\text{ m\/s}[\/latex]<\/li>\r\n \t
  16. [latex]186,000\\text{ mi\/h}=\\dfrac{186,000\\cancel{\\text{mi}}}{\\cancel{\\text{h}}}\\times \\dfrac{1.61\\text{ km}}{1\\cancel{\\text{mi}}}\\times \\dfrac{24\\cancel{\\text{h}}}{1\\cancel{\\text{day}}}\\times \\dfrac{365\\cancel{\\text{days}}}{1\\text{ yr}}[\/latex]\r\n[latex]\\phantom{186,000\\text{ mi\/h}}=2,620,000,000\\text{ km\/yr (rounded)}[\/latex]<\/li>\r\n \t
  17. [latex]7.50\\text{ t\/yd}^2=\\dfrac{7.50\\cancel{\\text{t}}}{\\cancel{\\text{yd}^2}}\\times\\dfrac{2000\\text{ lb}}{1\\cancel{\\text{t}}}\\times\\dfrac{(1\\cancel{\\text{yd}})^2}{(36\\text{ in})^2}[\/latex]\r\n[latex]\\phantom{7.50\\text{ t\/yd}^2}=11.57\\text{ lb\/in}^2[\/latex]<\/li>\r\n \t
  18. [latex]16\\text{ ft\/s}^2=\\dfrac{16\\cancel{\\text{ft}}}{\\cancel{\\text{s}^2}}\\times \\dfrac{1\\cancel{\\text{mi}}}{5280\\cancel{\\text{ft}}}\\times \\dfrac{1.61\\text{ km}}{1\\cancel{\\text{mi}}}\\times \\dfrac{(3600 \\cancel{\\text{s}})^2}{(1\\text{ h})^2}[\/latex]\r\n[latex]\\phantom{16\\text{ ft\/s}^2}=63,200\\text{ km\/h}^2\\text{ (rounded)}[\/latex]<\/li>\r\n \t
  19. [latex]\\text{mpg: }\\dfrac{260\\text{ mi}}{8\\text{ gal}}\\Rightarrow 32.5\\text{ mpg} [\/latex]\r\n[latex]\\begin{array}{rrl}\r\n32.5\\text{ mi\/gal}&=&\\dfrac{32.5\\cancel{\\text{mi}}}{\\cancel{\\text{gal}}}\\times \\dfrac{1.602\\text{ km}}{1\\cancel{\\text{mi}}}\\times \\dfrac{1\\cancel{\\text{gal}}}{3.785\\text{ litres}} \\\\ \\\\\r\n&=&13.8\\text{ km\/litre} \\\\ \\\\\r\n32.5\\text{ mpg}&=&13.8\\text{ km\/l}\r\n\\end{array}[\/latex]<\/li>\r\n \t
  20. [latex]12\\text{ pg\/min}=\\dfrac{12\\text{ pg}}{\\cancel{\\text{min}}}\\times\\dfrac{60\\cancel{\\text{min}}}{1\\text{ hr}}\\Rightarrow 720\\text{ pg\/hr}[\/latex]\r\n[latex]720\\text{ pg\/hr}=\\dfrac{720\\text{ pg}}{\\cancel{\\text{hr}}}\\times \\dfrac{24\\cancel{\\text{hr}}}{1\\text{ d}}\\Rightarrow 17,280\\text{ pg\/d}[\/latex]<\/li>\r\n \t
  21. [latex]60\\text{ beats\/min}=\\dfrac{60\\text{ beats}}{\\cancel{\\text{min}}}\\times \\dfrac{60\\cancel{\\text{min}}}{1\\cancel{\\text{hr}}}\\times \\dfrac{24\\cancel{\\text{hr}}}{1\\cancel{\\text{day}}}\\times \\dfrac{365.24\\cancel{\\text{days}}}{\\cancel{\\text{yr}}}\\times \\dfrac{86\\cancel{\\text{yrs}}}{\\text{life}}[\/latex]\r\n[latex]60\\text{ beats\/min}=2,713,879,296\\text{ beats\/life}[\/latex]\r\n[latex]\\phantom{60\\text{ beats\/min}}=2.71\\text{ million beats}[\/latex]<\/li>\r\n \t
  22. [latex]128\\text{ mg\/dL}=\\dfrac{128\\cancel{\\text{mg}}}{\\cancel{\\text{dL}}}\\times \\dfrac{1\\text{ g}}{1000\\cancel{\\text{mg}}}\\times \\dfrac{10\\cancel{\\text{dL}}}{\\text{L}} [\/latex]\r\n[latex]128\\text{ mg\/dL}=1.28\\text{ g\/L}[\/latex]<\/li>\r\n \t
  23. [latex]\\phantom{a}[\/latex]\r\n[latex]\\begin{array}[t]{ccccccl}\r\n38\\text{ ft}&=&38\\cancel{\\text{ft}}&\\times&\\dfrac{1\\text{ yd}}{3\\cancel{\\text{ft}}}&\\Rightarrow &12\\dfrac{2}{3}\\text{ yd} \\\\ \\\\\r\n40\\text{ ft}&=&40\\cancel{\\text{ft}}&\\times &\\dfrac{1\\text{ yd}}{3\\cancel{\\text{ft}}}&\\Rightarrow &13\\dfrac{1}{3}\\text{ yd} \\\\ \\\\\r\n\\text{Area}&=&12\\dfrac{2}{3}\\text{ yd}&\\times &13\\dfrac{1}{3}\\text{ yd}&\\Rightarrow &168\\dfrac{8}{9}\\text{ yd}^2 \\\\ \\\\\r\n\\text{Cost}&=&\\$18\\text{\/yd}^2&\\times &168\\dfrac{8}{9}\\text{ yd}^2&\\Rightarrow &\\$3040\r\n\\end{array}\r\n[\/latex]<\/li>\r\n \t
  24. [latex]\\phantom{a}[\/latex]\r\n[latex]\\begin{array}[t]{ccccl}\r\n\\text{Volume}&=&50\\text{ ft}\\times 10\\text{ ft}\\times 8\\text{ ft}&\\Rightarrow&4000\\text{ ft}^3 \\\\ \\\\\r\n4000\\text{ ft}^3&=&4000\\cancel{\\text{ ft}^3}\\times \\dfrac{1\\text{ yd}^3}{(3\\text{ \\cancel{ft}})^3}&\\Rightarrow &148\\text{ yd}^3 \\\\ \\\\\r\n148\\text{ yd}^3&=&148\\cancel{\\text{ yd}^3}\\times \\dfrac{(0.9144\\text{ m})^3}{1\\cancel{\\text{ yd}^3}}&\\Rightarrow &113\\text{ m}^3\\end{array}\r\n[\/latex]<\/li>\r\n \t
  25. [latex]\\phantom{a}[\/latex]\r\n[latex]\\begin{array}[t]{rcccl}\r\n\\text{Area of lot}&\\Rightarrow&\\dfrac{1}{3}\\left(43,560\\text{ ft}^2\\right)&\\Rightarrow &14,520\\text{ ft}^2 \\\\ \\\\\r\n\\text{Now }\\dfrac{1}{4}\\text{ of this is}&\\Rightarrow &\\dfrac{1}{4}\\left(14,520\\text{ ft}^2\\right)&\\Rightarrow &3630\\text{ ft}^2 \\\\ \\\\\r\n\\text{Convert to square metres}&\\Rightarrow&3630\\cancel{\\text{ ft}^2}\\times \\dfrac{(1\\text{ yd})^2}{(3\\cancel{\\text{ft}})^2}&\\Rightarrow &403\\dfrac{1}{3}\\text{ yd}^2\r\n\\end{array}[\/latex]<\/li>\r\n \t
  26. [latex]\\phantom{a}[\/latex]\r\n[latex]\\begin{array}[t]{rcccl}\r\n\\text{Car speed}&\\Rightarrow &\\dfrac{23\\text{ km}}{15\\cancel{\\text{min}}}\\times \\dfrac{60\\cancel{\\text{min}}}{1\\text{ h}}&\\Rightarrow& \\dfrac{92\\text{ km}}{\\text{h}} \\\\ \\\\\r\n\\text{Convert to m\/s}&\\Rightarrow &\\dfrac{92\\cancel{\\text{km}}}{\\cancel{\\text{h}}}\\times \\dfrac{1000\\text{ m}}{1\\cancel{\\text{km}}}\\times \\dfrac{1\\cancel{\\text{h}}}{3600\\text{ s}}&\\Rightarrow &25.6\\text{ m\/s}\r\n\\end{array}[\/latex]<\/li>\r\n \t
  27. [latex]\\phantom{a}[\/latex]\r\n[latex]\\begin{array}[t]{rcccl}\r\n3106\\text{ carats}&=&3106\\cancel{\\text{carats}}\\times \\dfrac{0.20\\text{ g}}{1\\cancel{\\text{carat}}}&\\Rightarrow &621.2\\text{ g} \\\\ \\\\\r\n621.2\\text{ g}&=&621.2\\cancel{\\text{g}}\\times \\dfrac{1000\\text{ mg}}{1\\cancel{\\text{g}}}&\\Rightarrow &621,200\\text{ mg} \\\\ \\\\\r\n621.2\\text{ g}&=&621.2\\cancel{\\text{g}}\\times \\dfrac{0.0022005\\text{ lbs}}{1\\cancel{\\text{g}}}&\\Rightarrow &1.37\\text{ lbs}\r\n\\end{array}[\/latex]<\/li>\r\n<\/ol>","rendered":"
      \n
    1. [latex]7\\text{ mi}=7\\cancel{\\text{mi}}\\times \\dfrac{1760\\text{ yd}}{\\cancel{\\text{mi}}}[\/latex]
      \n[latex]\\phantom{7\\text{ mi}}=12,320\\text{ yd}[\/latex]<\/li>\n
    2. [latex]234\\text{ oz}=234\\cancel{\\text{oz}}\\times \\dfrac{1\\cancel{\\text{lb}}}{16\\cancel{\\text{oz}}}\\times \\dfrac{1\\text{ ton}}{2000\\cancel{\\text{lb}}}[\/latex]
      \n[latex]\\phantom{234\\text{ oz}}=0.0073\\text{ tons}[\/latex]<\/li>\n
    3. [latex]11.2\\text{ mg}=11.2\\cancel{\\text{mg}}\\times \\dfrac{1\\text{ g}}{1000\\cancel{\\text{mg}}}[\/latex]
      \n[latex]\\phantom{11.2\\text{ mg}}=0.0112\\text{ g}[\/latex]<\/li>\n
    4. [latex]1.35\\text{ km}=1.35\\cancel{\\text{km}}\\times \\dfrac{1000\\cancel{\\text{m}}}{1\\cancel{\\text{km}}}\\times \\dfrac{100\\text{ cm}}{1\\cancel{\\text{m}}}[\/latex]
      \n[latex]\\phantom{1.35\\text{ km}}=135,000\\text{ cm}[\/latex]<\/li>\n
    5. [latex]9,800,000\\text{ mm}=9,800,000\\cancel{\\text{mm}}\\times \\dfrac{1\\cancel{\\text{m}}}{1000\\cancel{\\text{mm}}}\\times \\dfrac{1\\cancel{\\text{km}}}{1000\\cancel{\\text{m}}}\\times \\dfrac{1\\text{ mi}}{1.61\\cancel{\\text{km}}}[\/latex]
      \n[latex]\\phantom{9,800,000\\text{ mm}}=6.09\\text{ mi (rounded)}[\/latex]<\/li>\n
    6. [latex]4.5\\text{ ft}^2=4.5\\cancel{\\text{ ft}^2}\\times \\dfrac{(1\\text{ yd})^2}{(3\\cancel{\\text{ft}})^2}[\/latex]
      \n[latex]\\phantom{4.5\\text{ ft}^2}=0.5\\text{ yd}^2[\/latex]<\/li>\n
    7. [latex]435,000\\text{ m}^2=435,000\\cancel{\\text{ m}^2}\\times \\dfrac{(1\\text{ km}^2)}{(1000\\cancel{\\text{m}})^2}[\/latex]
      \n[latex]\\phantom{435,000\\text{ m}^2}=0.435\\text{ km}^2[\/latex]<\/li>\n
    8. [latex]8\\text{ km}^2=8\\cancel{\\text{ km}^2}\\times \\dfrac{1\\cancel{\\text{ mi}^2}}{(1.61\\cancel{\\text{km}})^2}\\times \\dfrac{(5280 \\text{ ft})^2}{(1\\cancel{\\text{mi}})^2}[\/latex]
      \n[latex]\\phantom{8\\text{ km}^2}=86,000,000\\text{ ft}^2\\text{ (rounded)}[\/latex]<\/li>\n
    9. [latex]0.0065\\text{ km}^3=0.0065 \\cancel{\\text{ km}^3}\\times \\dfrac{(1000\\text{ m})^3}{(1\\cancel{\\text{km}})^3}[\/latex]
      \n[latex]\\phantom{0.0065\\text{ km}^3}=6,500,000\\text{ m}^3[\/latex]<\/li>\n
    10. [latex]14.62\\text{ in.}^2=14.62\\cancel{\\text{ in.}^2}\\times \\dfrac{(2.54\\text{ cm})^2}{(1\\cancel{\\text{in.}})^2}[\/latex]
      \n[latex]\\phantom{14.62\\text{ in.}^2}=94.3\\text{ cm}^2[\/latex]<\/li>\n
    11. [latex]5500\\text{ cm}^3=5500\\cancel{\\text{ cm}^3}\\times \\dfrac{(1\\cancel{\\text{in}})^3}{(2.54\\cancel{\\text{cm}})^3}\\times \\dfrac{(1\\text{ yd})^3}{(36\\cancel{\\text{in}})^3}[\/latex]
      \n[latex]\\phantom{5500\\text{ cm}^3}=0.0072\\text{ yd}^3[\/latex]<\/li>\n
    12. [latex]3.5\\text{ mi\/h}=\\dfrac{3.5\\cancel{\\text{mi}}}{\\cancel{\\text{h}}}\\times \\dfrac{5280\\text{ ft}}{1\\cancel{\\text{mi}}}\\times \\dfrac{1\\cancel{\\text{h}}}{3600\\text{ s}}[\/latex]
      \n[latex]\\phantom{3.5\\text{ mi\/h}}=5.13\\text{ ft\/s}[\/latex]<\/li>\n
    13. [latex]185\\text{ yd\/min.}=\\dfrac{185 \\cancel{\\text{yd}}}{\\cancel{\\text{min.}}}\\times \\dfrac{1\\text{ mi}}{1760\\cancel{\\text{yd}}}\\times \\dfrac{60\\cancel{\\text{min.}}}{1\\text{ h}}[\/latex]
      \n[latex]\\phantom{185\\text{ yd\/min.}}=6.31\\text{ mi\/h}[\/latex]<\/li>\n
    14. [latex]153\\text{ ft\/s}=\\dfrac{153\\cancel{\\text{ft}}}{\\text{s}}\\times \\dfrac{1\\text{ mi}}{5280\\cancel{\\text{ft}}}\\times \\dfrac{3600\\cancel{\\text{s}}}{1\\text{ h}}[\/latex]
      \n[latex]\\phantom{153\\text{ ft\/s}}=104.3\\text{ mi\/h}[\/latex]<\/li>\n
    15. [latex]248\\text{ mi\/h}=\\dfrac{248\\cancel{\\text{mi}}}{\\cancel{\\text{h}}}\\times \\dfrac{1.61\\cancel{\\text{km}}}{1\\cancel{\\text{mi}}}\\times \\dfrac{1000\\text{ m}}{1\\cancel{\\text{km}}}\\times \\dfrac{1\\cancel{\\text{h}}}{3600\\text{ s}}[\/latex]
      \n[latex]\\phantom{248\\text{ mi\/h}}=111\\text{ m\/s}[\/latex]<\/li>\n
    16. [latex]186,000\\text{ mi\/h}=\\dfrac{186,000\\cancel{\\text{mi}}}{\\cancel{\\text{h}}}\\times \\dfrac{1.61\\text{ km}}{1\\cancel{\\text{mi}}}\\times \\dfrac{24\\cancel{\\text{h}}}{1\\cancel{\\text{day}}}\\times \\dfrac{365\\cancel{\\text{days}}}{1\\text{ yr}}[\/latex]
      \n[latex]\\phantom{186,000\\text{ mi\/h}}=2,620,000,000\\text{ km\/yr (rounded)}[\/latex]<\/li>\n
    17. [latex]7.50\\text{ t\/yd}^2=\\dfrac{7.50\\cancel{\\text{t}}}{\\cancel{\\text{yd}^2}}\\times\\dfrac{2000\\text{ lb}}{1\\cancel{\\text{t}}}\\times\\dfrac{(1\\cancel{\\text{yd}})^2}{(36\\text{ in})^2}[\/latex]
      \n[latex]\\phantom{7.50\\text{ t\/yd}^2}=11.57\\text{ lb\/in}^2[\/latex]<\/li>\n
    18. [latex]16\\text{ ft\/s}^2=\\dfrac{16\\cancel{\\text{ft}}}{\\cancel{\\text{s}^2}}\\times \\dfrac{1\\cancel{\\text{mi}}}{5280\\cancel{\\text{ft}}}\\times \\dfrac{1.61\\text{ km}}{1\\cancel{\\text{mi}}}\\times \\dfrac{(3600 \\cancel{\\text{s}})^2}{(1\\text{ h})^2}[\/latex]
      \n[latex]\\phantom{16\\text{ ft\/s}^2}=63,200\\text{ km\/h}^2\\text{ (rounded)}[\/latex]<\/li>\n
    19. [latex]\\text{mpg: }\\dfrac{260\\text{ mi}}{8\\text{ gal}}\\Rightarrow 32.5\\text{ mpg}[\/latex]
      \n[latex]\\begin{array}{rrl} 32.5\\text{ mi\/gal}&=&\\dfrac{32.5\\cancel{\\text{mi}}}{\\cancel{\\text{gal}}}\\times \\dfrac{1.602\\text{ km}}{1\\cancel{\\text{mi}}}\\times \\dfrac{1\\cancel{\\text{gal}}}{3.785\\text{ litres}} \\\\ \\\\ &=&13.8\\text{ km\/litre} \\\\ \\\\ 32.5\\text{ mpg}&=&13.8\\text{ km\/l} \\end{array}[\/latex]<\/li>\n
    20. [latex]12\\text{ pg\/min}=\\dfrac{12\\text{ pg}}{\\cancel{\\text{min}}}\\times\\dfrac{60\\cancel{\\text{min}}}{1\\text{ hr}}\\Rightarrow 720\\text{ pg\/hr}[\/latex]
      \n[latex]720\\text{ pg\/hr}=\\dfrac{720\\text{ pg}}{\\cancel{\\text{hr}}}\\times \\dfrac{24\\cancel{\\text{hr}}}{1\\text{ d}}\\Rightarrow 17,280\\text{ pg\/d}[\/latex]<\/li>\n
    21. [latex]60\\text{ beats\/min}=\\dfrac{60\\text{ beats}}{\\cancel{\\text{min}}}\\times \\dfrac{60\\cancel{\\text{min}}}{1\\cancel{\\text{hr}}}\\times \\dfrac{24\\cancel{\\text{hr}}}{1\\cancel{\\text{day}}}\\times \\dfrac{365.24\\cancel{\\text{days}}}{\\cancel{\\text{yr}}}\\times \\dfrac{86\\cancel{\\text{yrs}}}{\\text{life}}[\/latex]
      \n[latex]60\\text{ beats\/min}=2,713,879,296\\text{ beats\/life}[\/latex]
      \n[latex]\\phantom{60\\text{ beats\/min}}=2.71\\text{ million beats}[\/latex]<\/li>\n
    22. [latex]128\\text{ mg\/dL}=\\dfrac{128\\cancel{\\text{mg}}}{\\cancel{\\text{dL}}}\\times \\dfrac{1\\text{ g}}{1000\\cancel{\\text{mg}}}\\times \\dfrac{10\\cancel{\\text{dL}}}{\\text{L}}[\/latex]
      \n[latex]128\\text{ mg\/dL}=1.28\\text{ g\/L}[\/latex]<\/li>\n
    23. [latex]\\phantom{a}[\/latex]
      \n[latex]\\begin{array}[t]{ccccccl} 38\\text{ ft}&=&38\\cancel{\\text{ft}}&\\times&\\dfrac{1\\text{ yd}}{3\\cancel{\\text{ft}}}&\\Rightarrow &12\\dfrac{2}{3}\\text{ yd} \\\\ \\\\ 40\\text{ ft}&=&40\\cancel{\\text{ft}}&\\times &\\dfrac{1\\text{ yd}}{3\\cancel{\\text{ft}}}&\\Rightarrow &13\\dfrac{1}{3}\\text{ yd} \\\\ \\\\ \\text{Area}&=&12\\dfrac{2}{3}\\text{ yd}&\\times &13\\dfrac{1}{3}\\text{ yd}&\\Rightarrow &168\\dfrac{8}{9}\\text{ yd}^2 \\\\ \\\\ \\text{Cost}&=&\\$18\\text{\/yd}^2&\\times &168\\dfrac{8}{9}\\text{ yd}^2&\\Rightarrow &\\$3040 \\end{array}[\/latex]<\/li>\n
    24. [latex]\\phantom{a}[\/latex]
      \n[latex]\\begin{array}[t]{ccccl} \\text{Volume}&=&50\\text{ ft}\\times 10\\text{ ft}\\times 8\\text{ ft}&\\Rightarrow&4000\\text{ ft}^3 \\\\ \\\\ 4000\\text{ ft}^3&=&4000\\cancel{\\text{ ft}^3}\\times \\dfrac{1\\text{ yd}^3}{(3\\text{ \\cancel{ft}})^3}&\\Rightarrow &148\\text{ yd}^3 \\\\ \\\\ 148\\text{ yd}^3&=&148\\cancel{\\text{ yd}^3}\\times \\dfrac{(0.9144\\text{ m})^3}{1\\cancel{\\text{ yd}^3}}&\\Rightarrow &113\\text{ m}^3\\end{array}[\/latex]<\/li>\n
    25. [latex]\\phantom{a}[\/latex]
      \n[latex]\\begin{array}[t]{rcccl} \\text{Area of lot}&\\Rightarrow&\\dfrac{1}{3}\\left(43,560\\text{ ft}^2\\right)&\\Rightarrow &14,520\\text{ ft}^2 \\\\ \\\\ \\text{Now }\\dfrac{1}{4}\\text{ of this is}&\\Rightarrow &\\dfrac{1}{4}\\left(14,520\\text{ ft}^2\\right)&\\Rightarrow &3630\\text{ ft}^2 \\\\ \\\\ \\text{Convert to square metres}&\\Rightarrow&3630\\cancel{\\text{ ft}^2}\\times \\dfrac{(1\\text{ yd})^2}{(3\\cancel{\\text{ft}})^2}&\\Rightarrow &403\\dfrac{1}{3}\\text{ yd}^2 \\end{array}[\/latex]<\/li>\n
    26. [latex]\\phantom{a}[\/latex]
      \n[latex]\\begin{array}[t]{rcccl} \\text{Car speed}&\\Rightarrow &\\dfrac{23\\text{ km}}{15\\cancel{\\text{min}}}\\times \\dfrac{60\\cancel{\\text{min}}}{1\\text{ h}}&\\Rightarrow& \\dfrac{92\\text{ km}}{\\text{h}} \\\\ \\\\ \\text{Convert to m\/s}&\\Rightarrow &\\dfrac{92\\cancel{\\text{km}}}{\\cancel{\\text{h}}}\\times \\dfrac{1000\\text{ m}}{1\\cancel{\\text{km}}}\\times \\dfrac{1\\cancel{\\text{h}}}{3600\\text{ s}}&\\Rightarrow &25.6\\text{ m\/s} \\end{array}[\/latex]<\/li>\n
    27. [latex]\\phantom{a}[\/latex]
      \n[latex]\\begin{array}[t]{rcccl} 3106\\text{ carats}&=&3106\\cancel{\\text{carats}}\\times \\dfrac{0.20\\text{ g}}{1\\cancel{\\text{carat}}}&\\Rightarrow &621.2\\text{ g} \\\\ \\\\ 621.2\\text{ g}&=&621.2\\cancel{\\text{g}}\\times \\dfrac{1000\\text{ mg}}{1\\cancel{\\text{g}}}&\\Rightarrow &621,200\\text{ mg} \\\\ \\\\ 621.2\\text{ g}&=&621.2\\cancel{\\text{g}}\\times \\dfrac{0.0022005\\text{ lbs}}{1\\cancel{\\text{g}}}&\\Rightarrow &1.37\\text{ lbs} \\end{array}[\/latex]<\/li>\n<\/ol>\n","protected":false},"author":90,"menu_order":13,"template":"","meta":{"pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":"cc-by-nc-sa"},"back-matter-type":[],"contributor":[],"license":[56],"class_list":["post-1582","back-matter","type-back-matter","status-publish","hentry","license-cc-by-nc-sa"],"_links":{"self":[{"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/pressbooks\/v2\/back-matter\/1582","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/pressbooks\/v2\/back-matter"}],"about":[{"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/wp\/v2\/types\/back-matter"}],"author":[{"embeddable":true,"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/wp\/v2\/users\/90"}],"version-history":[{"count":4,"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/pressbooks\/v2\/back-matter\/1582\/revisions"}],"predecessor-version":[{"id":2299,"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/pressbooks\/v2\/back-matter\/1582\/revisions\/2299"}],"metadata":[{"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/pressbooks\/v2\/back-matter\/1582\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/wp\/v2\/media?parent=1582"}],"wp:term":[{"taxonomy":"back-matter-type","embeddable":true,"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/pressbooks\/v2\/back-matter-type?post=1582"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/wp\/v2\/contributor?post=1582"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/wp\/v2\/license?post=1582"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}