Answer Key 1.6
- \(\begin{array}{rrl}
\\ \\
7\text{ mi} &=& 7 \times \dfrac{1760\text{ yd}}{1\text{ mi}} \\ \\
&=& 12,320\text{ yd}
\end{array}\) - \(\begin{array}{rrl}
\\ \\
234\text{ oz} &=& 234 \times \dfrac{1\text{ lb}}{16\text{ oz}} \times \dfrac{1\text{ ton}}{2000\text{ lb}} \\ \\
&=& 0.0073\text{ tons}
\end{array}\) - \(\begin{array}{rrl}
\\ \\
11.2\text{ mg} &=& 11.2 \times \dfrac{1\text{ g}}{1000\text{ mg}} \\ \\
&=& 0.0112\text{ g}
\end{array}\) - \(\begin{array}{rrl}
\\ \\
1.35\text{ km} &=& 1.35 \times \dfrac{1000\text{ m}}{1\text{ km}} \times \dfrac{100\text{ cm}}{1\text{ m}} \\ \\
&=& 135{,}000\text{ cm}
\end{array}\) - \(\begin{array}{rrl}
\\ \\
9{,}800{,}000\text{ mm} &=& 9{,}800{,}000 \times \dfrac{1\text{ m}}{1000\text{ mm}} \times \dfrac{1\text{ km}}{1000\text{ m}} \times \dfrac{1\text{ mi}}{1.61\text{ km}} \\ \\
&=& 6.09\text{ mi (rounded)}
\end{array}\) - \(\begin{array}{rrl}
\\ \\
4.5\text{ ft}^2 &=& 4.5 \times \dfrac{(1\text{ yd})^2}{(3\text{ ft})^2} \\ \\
&=& 0.5\text{ yd}^2
\end{array}\) - \(\begin{array}{rrl}
\\ \\
435,000\text{ m}^2 &=& 435,000 \times \dfrac{(1\text{ km})^2}{(1000\text{ m})^2} \\ \\
&=& 0.435\text{ km}^2
\end{array}\) - \(\begin{array}{rrl}
\\ \\
8\text{ km}^2 &=& 8 \times \dfrac{1\text{ mi}^2}{(1.61\text{ km})^2} \times \dfrac{(5280 \text{ ft})^2}{1\text{ mi}^2} \\ \\
&=& 86,000,000\text{ ft}^2\text{ (rounded)}
\end{array}\) - \(\begin{array}{rrl}
\\ \\
0.0065\text{ km}^3 &=& 0.0065 \times \dfrac{(1000\text{ m})^3}{1\text{ km}^3} \\ \\
&=& 6,500,000\text{ m}^3
\end{array}\) - \(\begin{array}{rrl}
\\ \\
14.62\text{ in}^2 &=& 14.62 \times \dfrac{(2.54\text{ cm})^2}{(1\text{ in})^2} \\ \\
&=& 94.3\text{ cm}^2
\end{array}\) - \(\begin{array}{rrl}
\\ \\
5500\text{ cm}^3 &=& 5500 \times \dfrac{(1\text{ in})^3}{(2.54\text{ cm})^3} \times \dfrac{(1\text{ yd})^3}{(36\text{ in})^3} \\ \\
&=& 0.0072\text{ yd}^3
\end{array}\) - \(\begin{array}{rrl}
\\ \\
3.5\text{ mi/h} &=& \dfrac{3.5\text{ mi}}{1\text{ h}} \times \dfrac{5280\text{ ft}}{1\text{ mi}} \times \dfrac{1\text{ h}}{3600\text{ s}} \\ \\
&=& 5.13\text{ ft/s}
\end{array}\) - \(\begin{array}{rrl}
\\ \\
185\text{ yd/min} &=& \dfrac{185\text{ yd}}{1\text{ min}} \times \dfrac{1\text{ mi}}{1760\text{ yd}} \times \dfrac{60\text{ min}}{1\text{ h}} \\ \\
&=& 6.31\text{ mi/h}
\end{array}\) - \(\begin{array}{rrl}
\\ \\
153\text{ ft/s} &=& \dfrac{153\text{ ft}}{1\text{ s}} \times \dfrac{1\text{ mi}}{5280\text{ ft}} \times \dfrac{3600\text{ s}}{1\text{ h}} \\ \\
&=& 104.3\text{ mi/h}
\end{array}\) - \(\begin{array}{rrl}
\\ \\
248\text{ mi/h} &=& \dfrac{248\text{ mi}}{1\text{ h}} \times \dfrac{1.61\text{ km}}{1\text{ mi}} \times \dfrac{1000\text{ m}}{1\text{ km}} \times \dfrac{1\text{ h}}{3600\text{ s}} \\ \\
&=& 111\text{ m/s}
\end{array}\) - \(\begin{array}{rrl}
\\ \\
186,000\text{ mi/h} &=& \dfrac{186,000\text{ mi}}{1\text{ h}} \times \dfrac{1.61\text{ km}}{1\text{ mi}} \times \dfrac{24\text{ h}}{1\text{ day}} \times \dfrac{365\text{ days}}{1\text{ yr}} \\ \\
&=& 2,620,000,000\text{ km/yr (rounded)}
\end{array}\) - \(\begin{array}{rrl}
\\ \\
7.50\text{ t/yd}^2 &=& \dfrac{7.50\text{ t}}{1\text{ yd}^2} \times \dfrac{2000\text{ lb}}{1\text{ t}} \times \dfrac{(1\text{ yd})^2}{(36\text{ in})^2} \\ \\
&=& 11.57\text{ lb/in}^2
\end{array}\) - \(\begin{array}{rrl}
\\ \\
16\text{ ft/s}^2 &=& \dfrac{16\text{ ft}}{1\text{ s}^2} \times \dfrac{1\text{ mi}}{5280\text{ ft}} \times \dfrac{1.61\text{ km}}{1\text{ mi}} \times \dfrac{(3600\text{ s})^2}{(1\text{ h})^2} \\ \\
&=& 63,200\text{ km/h}^2 \text{ (rounded)}
\end{array}\) - \(\phantom{1}\)
\(\text{mpg: }\dfrac{260\text{ mi}}{8\text{ gal}}\Rightarrow 32.5\text{ mpg} \\ \)
\(\begin{array}{rrl}
32.5\text{ mi/gal} &=& \dfrac{32.5\text{ mi}}{1\text{ gal}} \times \dfrac{1.602\text{ km}}{1\text{ mi}} \times \dfrac{1\text{ gal}}{3.785\text{ litres}} \\ \\
&=& 13.8\text{ km/litre} \\ \\
32.5\text{ mpg} &=& 13.8\text{ km/l}
\end{array}\) - \(\begin{array}{ccccccl}
\\ \\ \\
12\text{ pg/min} &=& \dfrac{12\text{ pg}}{1\text{ min}} & \times & \dfrac{60\text{ min}}{1\text{ hr}} & \Rightarrow & 720\text{ pg/hr} \\ \\
720\text{ pg/hr} &=& \dfrac{720\text{ pg}}{1\text{ hr}} & \times & \dfrac{24\text{ hr}}{1\text{ d}} & \Rightarrow & 17,280\text{ pg/d}
\end{array}\) - \(\begin{array}{rrl}
\\ \\ \\ \\
60\text{ beats/min} &=& \dfrac{60\text{ beats}}{1\text{ min}} \times \dfrac{60\text{ min}}{1\text{ hr}} \times \dfrac{24\text{ hr}}{1\text{ day}} \times \dfrac{365.24\text{ days}}{1\text{ yr}} \times \dfrac{86\text{ yr}}{1\text{ life}} \\ \\
&=& 2,713,879,296\text{ beats/life} \\ \\
&=& 2.71\text{ billion beats}
\end{array}\) - \(\begin{array}{rrl}
\\ \\
128\text{ mg/dL} &=& \dfrac{128\text{ mg}}{1\text{ dL}} \times \dfrac{1\text{ g}}{1000\text{ mg}} \times \dfrac{10\text{ dL}}{1\text{ L}} \\ \\
&=& 1.28\text{ g/L}
\end{array}\) - \(\begin{array}{ccccccl}
\\ \\ \\ \\ \\ \\ \\ \\
38\text{ ft} &=& 38\text{ ft} &\times& \dfrac{1\text{ yd}}{3\text{ ft}} &\Rightarrow & 12\dfrac{2}{3}\text{ yd} \\ \\
40\text{ ft} &=& 40\text{ ft} &\times & \dfrac{1\text{ yd}}{3\text{ ft}} &\Rightarrow & 13\dfrac{1}{3}\text{ yd} \\ \\
\text{Area} &=& 12\dfrac{2}{3}\text{ yd} &\times & 13\dfrac{1}{3}\text{ yd} &\Rightarrow & 168\dfrac{8}{9}\text{ yd}^2 \\ \\
\text{Cost} &=& \$18\text{/yd}^2 &\times & 168\dfrac{8}{9}\text{ yd}^2 &\Rightarrow & \$3040
\end{array}\) - \(\begin{array}{ccccl}
\\ \\ \\ \\ \\ \\
\text{Volume} &=& 50\text{ ft} \times 10\text{ ft} \times 8\text{ ft} &\Rightarrow& 4000\text{ ft}^3 \\ \\
4000\text{ ft}^3 &=& 4000\text{ ft}^3 \times \dfrac{1\text{ yd}^3}{(3\text{ ft})^3} &\Rightarrow & 148\text{ yd}^3 \\ \\
148\text{ yd}^3 &=& 148\text{ yd}^3 \times \dfrac{(0.9144\text{ m})^3}{1\text{ yd}^3} &\Rightarrow & 113\text{ m}^3
\end{array}\) - \(\begin{array}{rcccl}
\\ \\ \\ \\ \\ \\
\text{Area of lot} &\Rightarrow& \dfrac{1}{3}\left(43,560\text{ ft}^2\right) &\Rightarrow& 14,520\text{ ft}^2 \\ \\
\text{Now } \dfrac{1}{4} \text{ of this is} &\Rightarrow& \dfrac{1}{4}\left(14,520\text{ ft}^2\right) &\Rightarrow& 3630\text{ ft}^2 \\ \\
\text{Convert to square yards} &\Rightarrow& 3630\text{ ft}^2 \times \dfrac{(1\text{ yd})^2}{(3\text{ ft})^2} &\Rightarrow& 403\dfrac{1}{3}\text{ yd}^2
\end{array}\) - \(\begin{array}{rcccl}
\\ \\
\text{Car speed} &\Rightarrow& \dfrac{23\text{ km}}{15\text{ min}} \times \dfrac{60\text{ min}}{1\text{ h}} &\Rightarrow& \dfrac{92\text{ km}}{\text{h}} \\ \\
\text{Convert to m/s} &\Rightarrow& \dfrac{92\text{ km}}{\text{h}} \times \dfrac{1000\text{ m}}{1\text{ km}} \times \dfrac{1\text{ h}}{3600\text{ s}} &\Rightarrow& 25.6\text{ m/s}
\end{array}\) - \(\begin{array}{rcccl}
\\ \\ \\ \\ \\ \\
3106\text{ carats} &=& 3106 \times \dfrac{0.20\text{ g}}{1} &\Rightarrow& 621.2\text{ g} \\ \\
621.2\text{ g} &=& 621.2 \times \dfrac{1000\text{ mg}}{1\text{ g}} &\Rightarrow& 621,200\text{ mg} \\ \\
621.2\text{ g} &=& 621.2 \times \dfrac{0.0022005\text{ lbs}}{1\text{ g}} &\Rightarrow& 1.37\text{ lbs}
\end{array}\)
