Consider a coordinate system in which the positive x axis is directed upward vertically. What are the positions of a particle (a) 5.0 m directly above the origin and (b) 2.0 m below the origin?

Solve the equation. Check your solution. 5 = 8x - 5

Simplify by combining like terms. $5+10 s-8 s$

Explain how to find the slope of a line when given two points.

Evaluate the function at each specified value of the independent variable and simplify. $q(t)=\frac{2 t^{2}+3}{t^{2}}$. (a) q(2), (b) q(0), (c) q(−x).

The formula for converting Fahrenheit temperature, F, to Celsius temperature , C, is

$$C = \frac { 5 } { 9 } ( F - 32 )$$

If Celsius temperature ranges from

$$15 ^ { \circ } \text { to } 35 ^ { \circ }$$

inclusive, what is the range for the Fahrenheit temperature ?

If

$$A = \left[ \begin{array} { r r r } { 4 } & { 5 } & { 6 } \\ { 0 } & { - 1 } & { - 3 } \\ { 2 } & { - 3 } & { 7 } \end{array} \right] \text { and } B = \left[ \begin{array} { r r r } { 3 } & { 9 } & { 1 } \\ { - 3 } & { 5 } & { - 3 } \\ { 1 } & { 2 } & { 6 } \end{array} \right]$$

, find the product. -2B

A box full of charged plastic balls sits on a table. The electric force exerted on a ball near one upper corner of the box has components $1.2 \times 10 ^ { - 3 } \mathrm { N }$ directed north, $5.7 \times 10 ^ { - 4 } \mathrm { N }$ directed east, and $2.2 \times 10 ^ { - 4 } \mathrm { N }$ directed vertically upward. The charge on this ball is 120 nC. If this ball were replaced with one that has a charge of -50 nC, what would be the force components exerted on the replacement ball?

The following crosstabulation shows household income by educational level of the head of household (Statistical Abstract of the United States, 2008).

$$\begin{matrix} & & \text{Household } & \text{Income} & \text{ (\$1000s)}\\ \text{Education Level} & \text{Under 25.0} & \text{25.0– 49.9} & \text{50.0– 74.9} & \text{75.0– 99.9} & \text{100 or more} & \text{Total}\\ \text{Not H.S. Graduate} & \text{4207} & \text{3459} & \text{1389} & \text{539} & \text{367} & \text{9961}\\ \text{H.S. Graduate} & \text{4917} & \text{6850} & \text{5027} & \text{2637} & \text{2668} & \text{22099}\\ \text{ College College} & \text{2807} & \text{5258} & \text{4678} & \text{3250} & \text{4074} & \text{20067}\\ \text{Bachelor’s Degree} & \text{885} & \text{2094} & \text{2848} & \text{2581} & \text{5379} & \text{13787}\\ \text{Beyond Bach. Deg.} & \text{290} & \text{829} & \text{1274} & \text{1241} & \text{4188} & \text{7822}\\ \text{Total} & \text{13106} & \text{18490} & \text{15216} & \text{10248} & \text{16676} & \text{73736}\\ \end{matrix}$$

a. Develop a joint probability table.
b. What is the probability of a head of household not being a high school graduate?
c. What is the probability of a head of household having a bachelor’s degree or more education?
d. What is the probability of a household headed by someone with a bachelor’s degree earning $100,000 or more?
e. What is the probability of a household having income below$25,000?
f. What is the probability of a household headed by someone with a bachelor’s degree earning less than $25,000?
g. Is household income independent of educational level?

The area in square centimeters of a square mat is $25 x^{2}-10 x+1.$ Find the dimensions of the mat in terms of x.

Write an equation in slope-intercept form for the line described.

$$\text { slope } 4 , \text { passes through } ( 6,9 )$$

Two electrons initially repel each other with an electric force of magnitude $2.5 \times 10 ^ { - 20 } \mathrm { N }$. What is the magnitude of the electric field at one electron due to the other?

Evaluate the expression.

$$- 125 ^ { 1 / 3 }$$