{"id":1095,"date":"2019-05-16T16:32:23","date_gmt":"2019-05-16T20:32:23","guid":{"rendered":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/?post_type=back-matter&p=1095"},"modified":"2019-10-24T12:32:41","modified_gmt":"2019-10-24T16:32:41","slug":"answer-key-1-6","status":"publish","type":"back-matter","link":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/back-matter\/answer-key-1-6\/","title":{"raw":"Answer Key 1.6","rendered":"Answer Key 1.6"},"content":{"raw":"[latexpage]\r\n
    \r\n \t
  1. \\(\\begin{array}{rrl}\r\n\\\\ \\\\\r\n7\\text{ mi}&=&7\\text{ \\cancel{mi}}\\times \\dfrac{1760\\text{ yd}}{\\text{ \\cancel{mi}}} \\\\ \\\\\r\n&=&12,320\\text{ yd}\r\n\\end{array}\\)<\/li>\r\n \t
  2. \\(\\begin{array}{rrl}\r\n\\\\ \\\\\r\n234\\text{ oz}&=&234\\text{ \\cancel{oz}}\\times \\dfrac{1\\text{ \\cancel{lb}}}{16\\text{ \\cancel{oz}}}\\times \\dfrac{1\\text{ ton}}{2000\\text{ \\cancel{lb}}} \\\\ \\\\\r\n&=&0.0073\\text{ tons}\r\n\\end{array}\\)<\/li>\r\n \t
  3. \\(\\begin{array}{rrl}\r\n\\\\ \\\\\r\n11.2\\text{ mg}&=&11.2\\text{ \\cancel{mg}}\\times \\dfrac{1\\text{ g}}{1000\\text{ \\cancel{mg}}} \\\\ \\\\\r\n&=&0.0112\\text{ g}\r\n\\end{array}\\)<\/li>\r\n \t
  4. \\(\\begin{array}{rrl}\r\n\\\\ \\\\\r\n1.35\\text{ km}&=&1.35\\text{ \\cancel{km}}\\times \\dfrac{1000\\text{ \\cancel{m}}}{1\\text{ \\cancel{km}}}\\times \\dfrac{100\\text{ cm}}{1\\text{ \\cancel{m}}} \\\\ \\\\\r\n&=&135,000\\text{ cm}\r\n\\end{array}\\)<\/li>\r\n \t
  5. \\(\\begin{array}{rrl}\r\n\\\\ \\\\\r\n9,800,000\\text{ mm}&=&9,800,000\\text{ \\cancel{mm}}\\times \\dfrac{1\\text{ \\cancel{m}}}{1000\\text{ \\cancel{mm}}}\\times \\dfrac{1\\text{ \\cancel{km}}}{1000\\text{ \\cancel{m}}}\\times \\dfrac{1\\text{ mi}}{1.61\\text{ \\cancel{km}}} \\\\ \\\\\r\n&=&6.09\\text{ mi (rounded)}\r\n\\end{array}\\)<\/li>\r\n \t
  6. \\(\\begin{array}{rrl}\r\n\\\\ \\\\\r\n4.5\\text{ ft}^2&=&4.5\\cancel{\\text{ ft}^2}\\times \\dfrac{(1\\text{ yd})^2}{(3\\text{ \\cancel{ft}})^2} \\\\ \\\\\r\n&=&0.5\\text{ yd}^2\r\n\\end{array}\\)<\/li>\r\n \t
  7. \\(\\begin{array}{rrl}\r\n\\\\ \\\\\r\n435,000\\text{ m}^2&=&435,000\\cancel{\\text{ m}^2}\\times \\dfrac{(1\\text{ km}^2)}{(1000\\text{ \\cancel{m}})^2} \\\\ \\\\\r\n&=&0.435\\text{ km}^2\r\n\\end{array}\\)<\/li>\r\n \t
  8. \\(\\begin{array}{rrl}\r\n\\\\ \\\\\r\n8\\text{ km}^2&=&8\\cancel{\\text{ km}^2}\\times \\dfrac{1\\cancel{\\text{ mi}^2}}{(1.61\\text{ \\cancel{km}})^2}\\times \\dfrac{(5280 \\text{ ft})^2}{(1\\text{ \\cancel{mi}})^2} \\\\ \\\\\r\n&=&86,000,000\\text{ ft}^2\\text{ (rounded)}\r\n\\end{array}\\)<\/li>\r\n \t
  9. \\(\\begin{array}{rrl}\r\n\\\\ \\\\\r\n0.0065\\text{ km}^3&=&0.0065 \\cancel{\\text{ km}^3}\\times \\dfrac{(1000\\text{ m})^3}{(1\\text{ \\cancel{km}})^3} \\\\ \\\\\r\n&=&6,500,000\\text{ m}^3\r\n\\end{array}\\)<\/li>\r\n \t
  10. \\(\\begin{array}{rrl}\r\n\\\\ \\\\\r\n14.62\\text{ in}^2&=&14.62\\cancel{\\text{ in}^2}\\times \\dfrac{(2.54\\text{ cm})^2}{(1\\text{ \\cancel{in}})^2} \\\\ \\\\\r\n&=&94.3\\text{ cm}^2\r\n\\end{array}\\)<\/li>\r\n \t
  11. \\(\\begin{array}{rrl}\r\n\\\\ \\\\\r\n5500\\text{ cm}^3&=&5500\\cancel{\\text{ cm}^3}\\times \\dfrac{(1\\text{ \\cancel{in}})^3}{(2.54\\text{ \\cancel{cm}})^3}\\times \\dfrac{(1\\text{ yd})^3}{(36\\text{ \\cancel{in}})^3} \\\\ \\\\\r\n&=&0.0072\\text{ yd}^3\r\n\\end{array}\\)<\/li>\r\n \t
  12. \\(\\begin{array}{rrl}\r\n\\\\ \\\\\r\n3.5\\text{ mi\/h}&=&\\dfrac{3.5\\text{ \\cancel{mi}}}{\\cancel{\\text{h}}}\\times \\dfrac{5280\\text{ ft}}{1\\text{ \\cancel{mi}}}\\times \\dfrac{1\\text{ \\cancel{h}}}{3600\\text{ s}} \\\\ \\\\\r\n&=&5.13\\text{ ft\/s}\r\n\\end{array}\\)<\/li>\r\n \t
  13. \\(\\begin{array}{rrl}\r\n\\\\ \\\\\r\n185\\text{ yd\/min.}&=&\\dfrac{185 \\text{ \\cancel{yd}}}{\\text{\\cancel{min.}}}\\times \\dfrac{1\\text{ mi}}{1760\\text{ \\cancel{yd}}}\\times \\dfrac{60\\text{ \\cancel{min.}}}{1\\text{ h}} \\\\ \\\\\r\n&=&6.31\\text{ mi\/h}\r\n\\end{array}\\)<\/li>\r\n \t
  14. \\(\\begin{array}{rrl}\r\n\\\\ \\\\\r\n153\\text{ ft\/s}&=&\\dfrac{153\\text{ \\cancel{ft}}}{\\text{s}}\\times \\dfrac{1\\text{ mi}}{5280\\text{ \\cancel{ft}}}\\times \\dfrac{3600\\text{ \\cancel{s}}}{1\\text{ h}} \\\\ \\\\\r\n&=&104.3\\text{ mi\/h}\r\n\\end{array}\\)<\/li>\r\n \t
  15. \\(\\begin{array}{rrl}\r\n\\\\ \\\\\r\n248\\text{ mi\/h}&=&\\dfrac{248\\text{ \\cancel{mi}}}{\\cancel{\\text{h}}}\\times \\dfrac{1.61\\text{ \\cancel{km}}}{1\\text{ \\cancel{mi}}}\\times \\dfrac{1000\\text{ m}}{1\\text{ \\cancel{km}}}\\times \\dfrac{1\\text{ \\cancel{h}}}{3600\\text{ s}} \\\\ \\\\\r\n&=&111\\text{ m\/s}\r\n\\end{array}\\)<\/li>\r\n \t
  16. \\(\\begin{array}{rrl}\r\n\\\\ \\\\\r\n186,000\\text{ mi\/h}&=&\\dfrac{186,000\\text{ \\cancel{mi}}}{\\cancel{\\text{h}}}\\times \\dfrac{1.61\\text{ km}}{1\\text{ \\cancel{mi}}}\\times \\dfrac{24\\text{ \\cancel{h}}}{1\\text{ \\cancel{day}}}\\times \\dfrac{365\\text{ \\cancel{days}}}{1\\text{ yr}} \\\\ \\\\\r\n&=&2,620,000,000\\text{ km\/yr (rounded)}\r\n\\end{array}\\)<\/li>\r\n \t
  17. \\(\\begin{array}{rrl}\r\n\\\\ \\\\\r\n7.50\\text{ t\/yd}^2&=&\\dfrac{7.50\\text{ \\cancel{t}}}{\\cancel{\\text{yd}^2}}\\times \\dfrac{2000\\text{ lb}}{1\\text{ \\cancel{t}}}\\times \\dfrac{(1\\text{ \\cancel{yd}})^2}{(36\\text{ in})^2} \\\\ \\\\\r\n&=&11.57\\text{ lb\/in}^2\r\n\\end{array}\\)<\/li>\r\n \t
  18. \\(\\begin{array}{rrl}\r\n\\\\ \\\\\r\n16\\text{ ft\/s}^2&=&\\dfrac{16\\text{ \\cancel{ft}}}{\\cancel{\\text{s}^2}}\\times \\dfrac{1\\text{ \\cancel{mi}}}{5280\\text{ \\cancel{ft}}}\\times \\dfrac{1.61\\text{ km}}{1\\text{ \\cancel{mi}}}\\times \\dfrac{(3600 \\text{ \\cancel{s}})^2}{(1\\text{ h})^2} \\\\ \\\\\r\n&=&63,200\\text{ km\/h}^2\\text{ (rounded)}\r\n\\end{array}\\)<\/li>\r\n \t
  19. \\(\\phantom{1}\\)\r\n\\(\\text{mpg: }\\dfrac{260\\text{ mi}}{8\\text{ gal}}\\Rightarrow 32.5\\text{ mpg} \\\\ \\)\r\n\\(\\begin{array}{rrl}\r\n32.5\\text{ mi\/gal}&=&\\dfrac{32.5\\text{ \\cancel{mi}}}{\\text{\\cancel{gal}}}\\times \\dfrac{1.602\\text{ km}}{1\\text{ \\cancel{mi}}}\\times \\dfrac{1\\text{ \\cancel{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}\\)<\/li>\r\n \t
  20. \\(\\begin{array}{ccccccl}\r\n\\\\ \\\\ \\\\\r\n12\\text{ pg\/min}&=&\\dfrac{12\\text{ pg}}{\\cancel{\\text{min}}}&\\times&\\dfrac{60\\text{ \\cancel{min}}}{1\\text{ hr}}&\\Rightarrow &720\\text{ pg\/hr} \\\\ \\\\\r\n720\\text{ pg\/hr}&=&\\dfrac{720\\text{ pg}}{\\cancel{\\text{hr}}}&\\times &\\dfrac{24\\text{ \\cancel{hr}}}{1\\text{ d}}&\\Rightarrow &17,280\\text{ pg\/d}\r\n\\end{array}\\)<\/li>\r\n \t
  21. \\(\\begin{array}{rrl}\r\n\\\\ \\\\ \\\\ \\\\\r\n60\\text{ beats\/min}&=&\\dfrac{60\\text{ beats}}{\\cancel{\\text{min}}}\\times \\dfrac{60\\text{ \\cancel{min}}}{1\\text{ \\cancel{hr}}}\\times \\dfrac{24\\text{ \\cancel{hr}}}{1\\text{ \\cancel{day}}}\\times \\dfrac{365.24\\text{ \\cancel{days}}}{\\cancel{\\text{yr}}}\\times \\dfrac{86\\text{ \\cancel{yrs}}}{\\text{life}} \\\\ \\\\\r\n60\\text{ beats\/min}&=&2,713,879,296\\text{ beats\/life} \\\\ \\\\\r\n&=&2.71\\text{ million beats}\r\n\\end{array}\\)<\/li>\r\n \t
  22. \\(\\begin{array}{rrl}\r\n\\\\ \\\\\r\n128\\text{ mg\/dL}&=&\\dfrac{128\\text{ \\cancel{mg}}}{\\cancel{\\text{dL}}}\\times \\dfrac{1\\text{ g}}{1000\\text{ \\cancel{mg}}}\\times \\dfrac{10\\text{ \\cancel{dL}}}{\\text{L}} \\\\ \\\\\r\n128\\text{ mg\/dL}&=&1.28\\text{ g\/L}\r\n\\end{array}\\)<\/li>\r\n \t
  23. \\(\\begin{array}{ccccccl}\r\n\\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\\r\n38\\text{ ft}&=&38\\text{ \\cancel{ft}}&\\times&\\dfrac{1\\text{ yd}}{3\\text{ \\cancel{ft}}}&\\Rightarrow &12\\dfrac{2}{3}\\text{ yd} \\\\ \\\\\r\n40\\text{ ft}&=&40\\text{ \\cancel{ft}}&\\times &\\dfrac{1\\text{ yd}}{3\\text{ \\cancel{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}\\)<\/li>\r\n \t
  24. \\(\\begin{array}{ccccl}\r\n\\\\ \\\\ \\\\ \\\\ \\\\ \\\\\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\r\n\\end{array}\\)<\/li>\r\n \t
  25. \\(\\begin{array}{rcccl}\r\n\\\\ \\\\ \\\\ \\\\ \\\\ \\\\\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\\text{ \\cancel{ft}})^2}&\\Rightarrow &403\\dfrac{1}{3}\\text{ yd}^2\r\n\\end{array}\\)<\/li>\r\n \t
  26. \\(\\begin{array}{rcccl}\r\n\\\\ \\\\\r\n\\text{Car speed}&\\Rightarrow &\\dfrac{23\\text{ km}}{15\\text{ \\cancel{min}}}\\times \\dfrac{60\\text{ \\cancel{min}}}{1\\text{ h}}&\\Rightarrow& \\dfrac{92\\text{ km}}{\\text{h}} \\\\ \\\\\r\n\\text{Convert to m\/s}&\\Rightarrow &\\dfrac{92\\text{ \\cancel{km}}}{\\text{ \\cancel{h}}}\\times \\dfrac{1000\\text{ m}}{1\\text{ \\cancel{km}}}\\times \\dfrac{1\\text{ \\cancel{h}}}{3600\\text{ s}}&\\Rightarrow &25.6\\text{ m\/s}\r\n\\end{array}\\)<\/li>\r\n \t
  27. \\(\\begin{array}{rcccl}\r\n\\\\ \\\\ \\\\ \\\\ \\\\ \\\\\r\n3106\\text{ carats}&=&3106\\text{ \\cancel{carats}}\\times \\dfrac{0.20\\text{ g}}{1\\text{ \\cancel{carat}}}&\\Rightarrow &621.2\\text{ g} \\\\ \\\\\r\n621.2\\text{ g}&=&621.2\\text{ \\cancel{g}}\\times \\dfrac{1000\\text{ mg}}{1\\text{ \\cancel{g}}}&\\Rightarrow &621,200\\text{ mg} \\\\ \\\\\r\n621.2\\text{ g}&=&621.2\\text{ \\cancel{g}}\\times \\dfrac{0.0022005\\text{ lbs}}{1\\text{ \\cancel{g}}}&\\Rightarrow &1.37\\text{ lbs}\r\n\\end{array}\\)<\/li>\r\n<\/ol>","rendered":"
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      \n\"\text{mpg: }\dfrac{260\text{ mi}}{8\text{ gal}}\Rightarrow 32.5\text{ mpg} \\\"
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