For an extra $49 you can buy extended warranty protection on your new HDTV for three years. If the set requires maintenance during that lime, it will be free You estimate that there is a 5% chance that you might need a$300 repair within three years and a 1% chance that you will need a $500 repair, but the chances arc 94% that you will need no repair at all. Based on expected values, should you purchase the extended coverage?

Write the standard form equation of a hyperbola with foci at (1, 0) and (1, 6), and a vertex at (1, 2).

The stem-and-leaf plot records the number of CDs each of fifteen friends owns.

$$\begin{array}{c|ccccccc} \text { Stems } & {\text { Leaves }} \\ & 2 & & 6 & 9 & 9 & & & \\ & 3 & & 0 & 4 & 5 & 7 & 9 & & \\ & 4 & & 2 & 3 & 3 & 3 & 6 & 6 & 8 \end{array}$$

2|6 represents 26 CDs. Find the mode of the data.

Analyze the data as indicated. The salaries of the workers in one department of the Garcia Brothers Company (given in thousands of dollars) are as follows:

$$\begin{matrix} \text{33.5} & \text{35.3} & \text{33.8} & \text{29.3} & \text{36.7} & \text{32.8} & \text{31.7} & \text{36.3} & \text{33.5} & \text{28.2} & \text{34.8}\\ \text{33.5} & \text{35.3} & \text{29.7} & \text{38.5} & \text{32.7} & \text{34.8} & \text{34.2} & \text{31.6} & \text{35.4}\\ \end{matrix}$$

Explain why a bar graph will not work for these data.

For the following exercises, convert the polar equation of a conic section to a rectangular equation. $r=\frac{4}{2+2 \sin \theta}$

Find the domain of the function.

$$f(x)=\frac{\cos x}{1-\sin x}$$

Find the complement and supplement of each angle. $m \angle C D E=27^{\circ}$

Can any two matrices of the same size be multiplied? If so, explain why, and if not, explain why not and give an example of two matrices of the same size that cannot be multiplied together.

Rewrite $\ln \left(\frac{1}{x^{5}}\right)$ as a product.

The estrogens (estrone and estradiol) are easily separated from the androgens (androsterone and testosterone) on the basis of one of their chemical properties. What is that property, and how could such a separation be accomplished?

Use trigonometric identities and assume $0<0<\frac{\pi}{2}$. Given that $\cot 2 \theta=8 / 15,$ find $\cos 2 \theta$

Write the converse of this statement. If two angles are vertical angles, then they are equal in measure. Are the given statement and its converse true or false?

For the following exercises, solve the system of inequalities. Use a calculator to graph the system to confirm the answer.

$$\begin{array}{r} x^{2}+y<3 \\ y>2 x \end{array}$$

When benzaldehyde reacts with a peroxy acid, the product is benzoic acid. The mechanism for this reaction is analogous to the one just given for the oxidation of acetophenone, and the outcome illustrates the greater migratory aptitude of a hydrogen atom compared to phenyl. Outline all the steps involved.