Write the ratio in lowest terms.

$\$ 1.20$ to $75 \%$

Write equations for the lines. The line through $(2,0,0)$ and $(0,1,0)$.

Let x be a random variable that represents the average daily temperature (in degrees Fahrenheit) in January for the town of Hana, Maui. The x variable has a mean $\mu$ of approximately $68^{\circ} \mathrm{F}$ and standard deviation $\sigma$ of approximately $4^{\circ} \mathrm{F}$. A 20-year study (620 January days) gave the entries in the rightmost column of the following table. $$ \scriptscriptstyle\begin{array}{lccc} \hline \mathrm{I} & \mathrm{II} & \mathrm{III} & \mathrm{IV} \\ \hline \text { Region Under } & & \text { Expected % from } & \text { Observed } \\ \text { Normal Curve } & x^{\circ} \mathrm{F} & \text { Normal Curve } & \text { Number of Days } \\ & & & \text { in 20 Years } \\ \hline \mu-3 \sigma \leq x<\mu-2 \sigma & 56 \leq x<60 & 2.35 \% & 14 \\ \mu-2 \sigma \leq x<\mu-\sigma & 60 \leq x<64 & 13.5 \% & 86 \\ \mu-\sigma \leq x<\mu & 64 \leq x<68 & 34 \% & 207 \\ \mu \leq x<\mu+\sigma & 68 \leq x<76 & 34 \% & 215 \\ \mu+\sigma \leq x<\mu+2 \sigma & 72 \leq x<76 & 13.5 \% & 83 \\ \mu+2 \sigma \leq x<\mu+3 \sigma & 76 \leq x<80 & 2.35 \% & 15 \\ \hline \end{array} $$ (i) Remember that $\mu=68$ and $\sigma=4$. Write a brief explanation for Columns I, II, and III in the context of this problem. (ii) Use a 1% level of significance to test the claim that the average daily January temperature follows a normal distribution with $\mu=68$ and $\sigma=4$. Find or estimate the P-value of the sample test statistic.

The volume, in cubic inches, of the following solid can be calculated by $V(x)=x^3+3 x^2$.

Use the Remainder Theorem to determine the volume of the solid if

a. $x=7$ inches

b. $x=11$ inches

Consider $\pi \displaystyle\int_0^{\pi / 2}\left[(1+\cos x)^2-1^2\right] d x$. This integral represents the volume of a solid. Describe the solid.

Write the ratio in lowest term.

20 hours to 5 days

Write the ratio in lowest term.

30 inches to five yards

$4 p$ electrons in an atom of Ge;

On a trip from Tucson to Phoenix via Interstate 10, you used your cruise control to travel at a constant speed for the entire trip. Since your speedometer was broken, you decided to use your watch and the mile markers to determine your speed. At mile marker 219 you noticed that the time on your digital watch just advanced to 9:22 am. At mile marker 197 your digital watch advanced to 9:46 am. a. Compute the constant speed at which you traveled over the time period from 9:22am to 9:46 am. b. As you were passing mile marker 219 you also passed a truck. The same truck sped by you exactly at mile marker 197. i. Construct a distance-time graph of your car. On the same graph, construct one possible distance-time graph for the truck. Be sure to label the axes. ii. Compare the speed of the truck to the speed of the car between 9:22 am and 9:45 am. iii. Compare the distance that your car traveled over this part of the trip with the distance that the truck traveled over this same part of the trip. Compare the time that it took the truck to travel this distance with the time that it took your car to travel this distance. What do you notice? iv. "Why are the average speed of the car and the average speed of the truck the same? v. Phoenix is another 53 miles past mile marker 197. Assuming you continued at the constant speed, at what time should you arrive in Phoenix?

Use the procedures developed in this chapter to find the general solution of each differential equation. $y^{\prime \prime \prime}-y^{\prime \prime}=6$

A square steel bar, $25 \mathrm{~mm}$ on a side and $650 \mathrm{~mm}$ long, is subjected to a torque of $230 \mathrm{~N} \cdot \mathrm{m}$. Compute the shear stress and the angle of twist for the bar.

a. Suppose that $\vec{E}=\overrightarrow{0}$ throughout some region of space. Can you conclude that V = 0 V in this region? Explain. b. Suppose that V = 0 V throughout some region of space. Can you conclude that $\vec{E}=\overrightarrow{0}$ in this region? Explain.

Refer to the results from the 150 subjects given below.

$$\begin{array} {c c c } &{ \text { Spent the Money } } & { \text { Kept the Money } } \\ \hline \text{Women Given a Single 100-Yuan Bill}&60 & { 15 } \\ \hline \text{Women Given 100 Yuan in Smaller Bills}&68 & { 7 } \\ \hline \end{array}$$

Find the probability that if 1 of the 150 subjects is randomly selected, the result is a woman who spent the money or was given a single 100-yuan bill.

Write the ratio in simplest form.

$$15: 25$$