Use words to write 4.02.

A woman has n keys, of which one will open her door. (a) If she tries the keys at random, discarding those that do not work, what is the probability that she will open the door on her kth try? (b) What if she does not discard previously tried keys?

Name the property shown by the statement.

$$14 \times 0 \times 3 = 0$$

Let

$$\mathbf { u } = \left[ \begin{array} { l } { 1 } \\ { 1 } \\ { 2 } \end{array} \right] , \mathbf { v } = \left[ \begin{array} { l } { 0 } \\ { 1 } \\ { 2 } \end{array} \right]$$

, and

$$\mathbf { w } = \left[ \begin{array} { r } { 1 } \\ { 0 } \\ { - 1 } \end{array} \right]$$

. In each case, find numbers a, b, and c such that x=au+bv+cw. (a)

$$\mathbf { x } = \left[ \begin{array} { r } { 2 } \\ { - 1 } \\ { 6 } \end{array} \right]$$

, (b)

$$\mathbf { x } = \left[ \begin{array} { l } { 1 } \\ { 3 } \\ { 0 } \end{array} \right]$$

A newspaper article about an opinion poll says that "43% of American approve of the president's overall job performance," Toward the end of the article, you read: "The poll is based on telephone interviews with 1210 adults from around the United States, excluding Alaska and Hawaii." What variable did this poll measure? What population do you think the newspaper wants information about? What was the sample? Are there any sources of bias in the sampling method used?

Explain why most metals are malleable and ductile but ionic crystals are not.

Solve the given initial-value problem.

$$y ^ { \prime } = y ^ { 3 } \sin x , \quad y ( 0 ) = 0$$

use the matrix capabilities of a graphing utility to solve (if possible) the system of linear equations. {x - 3y - 2z = 8 , -2x + 7y + 3z = -19 , x - y - 3z = 3

Find the period of each function. Then graph the function.

$$y = \cot 2 \theta$$

Write the first five terms of each geometric sequence.

$$a _ { n } = - 3 a _ { n - 1 } , \quad a _ { 1 } = 10$$

Determine whether each sequence is arithmetic or geometric. Then find the specified term of the sequence. 5, -1, -7, ...;

$$t_{15}$$

Simplify the product. -b²(b - 10)

Plot the point in a coordinate plane. Describe the location of the point. J(- 3, 8)

Find the following average values. The average z-coordinate of points on and within a hemisphere of radius 4 centered at the origin with its base in the xy-plane