Tell whether the sampling strategy will result in a random sample from the population under consideration. If it is not random, explain why it is not. A talk-show hostess wants to give free automobiles to ten random members of her audience. She instructs the ushers to go into the theater before the show and place special stickers under ten seats of their choice.

For the following exercises, rewrite the given equation in standard form, and then determine the vertex (V), focus (F), and directrix (d) of the parabola. $(x+1)^{2}=2(y+4)$

Define a parabola in terms of its focus and directrix.

For the following exercises, identify the conic with a focus at the origin, and then give the directrix and eccentricity. $r(7+8 \cos \theta)=7$

A function is given. Determine whether it is one-to-one. f(x) = 2x - 3

Describe ethers by completing the following sentence. Ethers are similar to ______ as they are compounds in which oxygen is bonded to ________. Ethers are different from alcohols because the oxygen atom bonds with ____ carbon atoms. Ethers are much less ____ in water than alcohol because they have no ____ to donate to a hydrogen bond.

Match the equation with the degenerate conic section dint would describe its graph. The matching is one-to-one. $y^{2}-4=0$. A. A single point. B. Two intersecting lines. C. Two parallel lines. D. The empty set.

Identify three common polymers described in the text. Include their uses.

Consumer Price Index The Consumer Price Index for food and beverages in 2007 was 203.3 after a hefty 3.9% increase from the previous year. What was the Consumer Price Index for food and beverages in 2006?

Write a proof of the following theorem. If two angles are supplementary to the same angle, then they are equal in measure to each other.

Use the method of your choice to find the solution of the following initial value problem. $y^{\prime}(x)=\frac{x}{y}, y(2)=4$

Evaluate each expression when a=-5 and b=4. $a^{3}-b$

For the following exercises, use the matrices below to perform scalar multiplication.

$$A=\left[\begin{array}{rr} 4 & 6 \\ 13 & 12 \end{array}\right], B=\left[\begin{array}{rr} 3 & 9 \\ 21 & 12 \\ 0 & 64 \end{array}\right], C=\left[\begin{array}{cccc} 16 & 3 & 7 & 18 \\ 90 & 5 & 3 & 29 \end{array}\right], D=\left[\begin{array}{rrr} 18 & 12 & 13 \\ 8 & 14 & 6 \\ 7 & 4 & 21 \end{array}\right]$$

100D

For the following exercises, find the multiplicative inverse of each matrix, if it exists.

$$\left[\begin{array}{rr} 0.5 & 1.5 \\ 1 & -0.5 \end{array}\right]$$