A team's best hitter has a lifetime batting average of $.320 .$ He has been at bat 325 times. a. How many hits has he made?b. The same player goes into a slump and doesn't get any hits at all in his next ten times at bat. What is his current batting average to the nearest thousandth?

A basketball player has made 24 points out of 30 free throws. She hopes to make all her next free throws until her free-throw percentage is 85 or better. How many consecutive free throws will she have to make?

Points $B$ and $C$ lie on $\overline{A D}$ . Find $A C$ if $\frac{A B}{B D}=\frac{3}{4}, \frac{A C}{C D}=\frac{5}{6},$ and $B D=66$

$$\begin{aligned} \text { Find the ratio of } x \text { to } y : \frac{4}{y}+\frac{3}{x} &=44 \\ & \frac{12}{y}-\frac{2}{x}=44 \end{aligned}$$

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What is the ratio of the measure of an interior angle to the measure of an exterior angle in a regular hexagon? A regular decagon? A regular $n$ -gon?

$720 \cdot 360=2 : 1$$1440 : 350=4 : 1$$180(n-2) : 360$

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MODELING WITH MATHEMATIGSe loor of the gazebo shown is shaped like a regular decagon.Find the measure of each interior angle of the regular decagon. Then I nd the measure of each exterior angle.

In Exercises $27-30,$ ind the measure of each interior angle and each exterior angle of the indicated regular polygon. (See Example $6 .$ )90 -gon

The measure of each interior angle of a regular polygon is eleven times that of an exterior angle. How many sides does the polygon have?

In Exercises $27-30,$ ind the measure of each interior angle and each exterior angle of the indicated regular polygon. (See Example $6 .$ )

Prove that there is no regular polygon with an interior angle whose measure is $155 .$

If two resistors with resistances $ R_1 $ and $ R_2 $ are connected in parallel, as in the figure, then the total resistance $ R, $ measured in ohms $ (\Omega), $ is given by$ \frac {1}{R} = \frac {1}{R_1} + \frac {1}{R_2} $If $ R_1 $ and $ R_2 $ are increasing at rates of $ 0.3 \Omega/s $ and $ 0.2 \Omega/s, $ respectively, how fast is $ R $ changing when $ R_1 = 80 \Omega $ and $ R_2 = 100 \Omega? $

The circuit of Fig. $27-75$ shows a capacitor, two ideal batteries, two resistors, and a switch S. Initially S has been open for a long time. If it is then closed for a long time, what is thechange in the charge on the capacitor?Assume $C=10 \mu \mathrm{F},$ $\mathscr{E}_{1}=1.0 \mathrm{V}, \mathscr{E}_{2}=3.0$$\mathrm{V}, R_{1}=0.20 \Omega,$ and $R_{2}=0.40 \Omega$

The perimeter of a rectangle is 24 feet.a. If $x$ is the measure of one side of the rectangle, represent the measure of an adjacent side in terms of $x .$b. If $y$ is the area of the rectangle, express the area in terms of $x$ .c. Draw the graph of the function written in b.d. What are the dimensions of the rectangle with the largest area?

Convert each angle in degrees to radians. Write the answer as a multiple of $\pi$.$$15^{\circ}$$

Can you neutralize a strong acid solution by adding an equal volume of a weak base having the same molarity as the acid? Support your position.

Analyze the solution $ y=\phi(x) $ to the initial value problem$$ \frac{d y}{d x}=y^{2}-3 y+2, \quad y(0)=1.5 $$using approximation methods and then compare with its exact form as follows.(a) Sketch the direction field of the differential equation and use it to guess the value of $ \lim _{x \rightarrow \infty} \phi(x) $(b) Use Euler's method with a step size of 0.1 to find an approximation of $ \phi(1) $.(c) Find a formula for $ \phi(x) $ and graph $ \phi(x) $ on the direction field from part (a).(d) What is the exact value of $ \phi(1) ? $ Compare with your approximation in part (b).(e) Using the exact solution obtained in part (c), determine $ \lim _{x \rightarrow \infty} \phi(x) $ and compare with your guess in part (a).

Mass Find the mass of the solid region bounded by the parabolic surfaces $z=16-2 x^{2}-2 y^{2}$ and $z=2 x^{2}+2 y^{2}$ if the density of the solid is $\delta(x, y, z)=\sqrt{x^{2}+y^{2}}$

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MODELING WITH MATHEMATIGSe loor of the gazebo shown is shaped like a regular decagon.

Find the measure of each interior angle of the regular decagon. Then I nd the measure of each exterior angle.

In Exercises $27-30,$ ind the measure of each interior angle and each exterior angle of the indicated regular polygon. (See Example $6 .$ )

90 -gon

The measure of each interior angle of a regular polygon is eleven times that of an exterior angle. How many sides does the polygon have?

In Exercises $27-30,$ ind the measure of each interior angle and each exterior angle of the indicated regular polygon. (See Example $6 .$ )

Prove that there is no regular polygon with an interior angle whose measure is $155 .$

If two resistors with resistances $ R_1 $ and $ R_2 $ are connected in parallel, as in the figure, then the total resistance $ R, $ measured in ohms $ (\Omega), $ is given by

$ \frac {1}{R} = \frac {1}{R_1} + \frac {1}{R_2} $

If $ R_1 $ and $ R_2 $ are increasing at rates of $ 0.3 \Omega/s $ and $ 0.2 \Omega/s, $ respectively, how fast is $ R $ changing when $ R_1 = 80 \Omega $ and $ R_2 = 100 \Omega? $

The circuit of Fig. $27-75$ shows a capacitor, two ideal batteries, two resistors, and a switch S. Initially S has been open for a long time. If it is then closed for a long time, what is the

change in the charge on the capacitor?

Assume $C=10 \mu \mathrm{F},$ $\mathscr{E}_{1}=1.0 \mathrm{V}, \mathscr{E}_{2}=3.0$

$\mathrm{V}, R_{1}=0.20 \Omega,$ and $R_{2}=0.40 \Omega$

The perimeter of a rectangle is 24 feet.

a. If $x$ is the measure of one side of the rectangle, represent the measure of an adjacent side in terms of $x .$

b. If $y$ is the area of the rectangle, express the area in terms of $x$ .

c. Draw the graph of the function written in b.

d. What are the dimensions of the rectangle with the largest area?

Convert each angle in degrees to radians. Write the answer as a multiple of $\pi$.

$$15^{\circ}$$

Can you neutralize a strong acid solution by adding an equal volume of a weak base having the same molarity as the acid? Support your position.

Analyze the solution $ y=\phi(x) $ to the initial value problem

$$ \frac{d y}{d x}=y^{2}-3 y+2, \quad y(0)=1.5 $$

using approximation methods and then compare with its exact form as follows.

(a) Sketch the direction field of the differential equation and use it to guess the value of $ \lim _{x \rightarrow \infty} \phi(x) $

(b) Use Euler's method with a step size of 0.1 to find an approximation of $ \phi(1) $.

(c) Find a formula for $ \phi(x) $ and graph $ \phi(x) $ on the direction field from part (a).

(d) What is the exact value of $ \phi(1) ? $ Compare with your approximation in part (b).

(e) Using the exact solution obtained in part (c), determine $ \lim _{x \rightarrow \infty} \phi(x) $ and compare with your guess in part (a).

Mass Find the mass of the solid region bounded by the parabolic surfaces $z=16-2 x^{2}-2 y^{2}$ and $z=2 x^{2}+2 y^{2}$ if the density of the solid is $\delta(x, y, z)=\sqrt{x^{2}+y^{2}}$