Answer Key 1.6
- [latex]7\text{ mi}=7\cancel{\text{mi}}\times \dfrac{1760\text{ yd}}{\cancel{\text{mi}}}[/latex]
[latex]\phantom{7\text{ mi}}=12,320\text{ yd}[/latex] - [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]
[latex]\phantom{234\text{ oz}}=0.0073\text{ tons}[/latex] - [latex]11.2\text{ mg}=11.2\cancel{\text{mg}}\times \dfrac{1\text{ g}}{1000\cancel{\text{mg}}}[/latex]
[latex]\phantom{11.2\text{ mg}}=0.0112\text{ g}[/latex] - [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]
[latex]\phantom{1.35\text{ km}}=135,000\text{ cm}[/latex] - [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]
[latex]\phantom{9,800,000\text{ mm}}=6.09\text{ mi (rounded)}[/latex] - [latex]4.5\text{ ft}^2=4.5\cancel{\text{ ft}^2}\times \dfrac{(1\text{ yd})^2}{(3\cancel{\text{ft}})^2}[/latex]
[latex]\phantom{4.5\text{ ft}^2}=0.5\text{ yd}^2[/latex] - [latex]435,000\text{ m}^2=435,000\cancel{\text{ m}^2}\times \dfrac{(1\text{ km}^2)}{(1000\cancel{\text{m}})^2}[/latex]
[latex]\phantom{435,000\text{ m}^2}=0.435\text{ km}^2[/latex] - [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]
[latex]\phantom{8\text{ km}^2}=86,000,000\text{ ft}^2\text{ (rounded)}[/latex] - [latex]0.0065\text{ km}^3=0.0065 \cancel{\text{ km}^3}\times \dfrac{(1000\text{ m})^3}{(1\cancel{\text{km}})^3}[/latex]
[latex]\phantom{0.0065\text{ km}^3}=6,500,000\text{ m}^3[/latex] - [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]
[latex]\phantom{14.62\text{ in.}^2}=94.3\text{ cm}^2[/latex] - [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]
[latex]\phantom{5500\text{ cm}^3}=0.0072\text{ yd}^3[/latex] - [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]
[latex]\phantom{3.5\text{ mi/h}}=5.13\text{ ft/s}[/latex] - [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]
[latex]\phantom{185\text{ yd/min.}}=6.31\text{ mi/h}[/latex] - [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]
[latex]\phantom{153\text{ ft/s}}=104.3\text{ mi/h}[/latex] - [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]
[latex]\phantom{248\text{ mi/h}}=111\text{ m/s}[/latex] - [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]
[latex]\phantom{186,000\text{ mi/h}}=2,620,000,000\text{ km/yr (rounded)}[/latex] - [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]
[latex]\phantom{7.50\text{ t/yd}^2}=11.57\text{ lb/in}^2[/latex] - [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]
[latex]\phantom{16\text{ ft/s}^2}=63,200\text{ km/h}^2\text{ (rounded)}[/latex] - [latex]\text{mpg: }\dfrac{260\text{ mi}}{8\text{ gal}}\Rightarrow 32.5\text{ mpg}[/latex]
[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] - [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]
[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] - [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]
[latex]60\text{ beats/min}=2,713,879,296\text{ beats/life}[/latex]
[latex]\phantom{60\text{ beats/min}}=2.71\text{ million beats}[/latex] - [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]
[latex]128\text{ mg/dL}=1.28\text{ g/L}[/latex] - [latex]\phantom{a}[/latex]
[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] - [latex]\phantom{a}[/latex]
[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] - [latex]\phantom{a}[/latex]
[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] - [latex]\phantom{a}[/latex]
[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] - [latex]\phantom{a}[/latex]
[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]
