Find the exact value of the given expression.

$\sin 15^{\circ} \cos 15^{\circ}$.

Solve. Sam wants to buy a new wakeboard that costs $\$ 434$. If he makes $\$ 7.75$ per hour, how many hours must he work to earn enough money for the wakeboard?

For the following exercises, identify the conic with a focus at the origin, and then give the directrix and eccentricity. $r=\frac{3}{4-4 \sin \theta}$

A charity sells raffle tickets for $\$ 1$ each. First prize is $\$ 500$, second prize is $\$ 100$, third prize is $\$ 10$. If you buy one of the $1000$ tickets sold, what are your expected winnings?

Solve $d=550+450 \cos \left(\frac{\pi}{50} t\right)$ for $t$, where $t$ is in the interval $[0,50]$.

For each plane curve, find a rectangular equation. State the appropriate interval for x or y.

$x=3 t, y=t-1$, for $t$ in $(-\infty, \infty)$

Using Pronouns In the Nominative Case. Complete each of the following sentences by writing a nominative pronoun. Then write how ench pronoun is used in the sentence. The first person in line to buy tickets to the concert was ______ .

One apartment is directly above the second apartment. The resident living downstairs calls his neighbor living above him and states, "If one of you is willing to come downstairs, we'll have the same number of people in both apartments." The upstairs resident responds, "We're all too tired to move. Why don't one of you come up here? Then we'll have twice as many people up here as you've got down there." How many people are in each apartment?

For the equation of each parabola, find the coordinates of the vertex and focus, and the equations of the directrix and axis of symmetry. Then graph the equation. $x^{2}=-4(y-3)$

Account Tom Tupper wants to buy a $\$ 30,000$ car. He has saved $\$ 27,000$. Find the number of years (to the nearest tenth) it will take for his $\$ 27,000$ to grow to $\$ 30,000$ at $2.3 \%$ interest compounded quarterly.

Solve the inequality. Express the solution using interval notation, and graph the solution set on the real number line.

$$|x-1|< |x-3|$$

[Hint: Interpret the quantities as distances.]

How many grams of acetic acid $\left(\mathrm{C}_2 \mathrm{H}_4 \mathrm{O}_2\right)$ would you use to make $10 \mathrm{~L}$ of a $0.1 \mathrm{M}$ aqueous solution of acetic acid? (Note: The atomic masses, in daltons, are approximately 12 for carbon, 1 for hydrogen, and 16 for oxygen.) a. $10 \mathrm{~g}$ $\hspace{0.5cm}$ b. $0.1 \mathrm{~g}$ $\hspace{0.5cm}$ c. $6.0 \mathrm{~g}$ $\hspace{0.5cm}$ d. $60 \mathrm{~g}$ $\hspace{0.5cm}$ e. $0.6 \mathrm{~g}$

Find the exact function value.

$$\cot \left(\frac{5 \pi}{4}\right)$$

Find polar equations for and graph the conic section with focus (0, 0) and the given directrix and eccentricity. Directrix y=-2, e=0.9