Let v be the vector from initial point

$$P_1$$

to terminal point

$$P_2.$$

Write v in terms of i and j.

$$P _ { 1 } = ( - 3,4 ) , P _ { 2 } = ( 6,4 )$$

Sketch the vector as a position and find its magnitude. v= 5i+4j

Solve the inequality. |5.2+x|<7.3

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.

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

Find (a) the mean, (b) the median, and (c) the mode (if it exists) of each set of data.

$$21, 25, 43, 36$$

Evaluate the expression. Write your answer in scientific notation and standard form.

$$\frac { \left( 6.4 \times 10 ^ { 7 } \right) } { \left( 1.6 \times 10 ^ { 5 } \right) }$$

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)

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

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

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?

Solve the given initial-value problem.

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

Find the position function $x(t)$ of a moving particle with the given acceleration $a(t)$, initial position $x_0=x(0)$, and initial velocity $v_0=v(0)$.

$$a ( t ) =50\sin 5t,\: v _ { 0 } = - 10,\: x _ { 0 } = 8$$

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

Three sides of a trapezoid are congruent. The fourth side is 4 in. longer than each of the other three. The perimeter is 49 in. What is the length of each side?