Tell whether the two ratios form a proportion. Explain.

$$\frac { 3 } { 4 } \text { and } \frac { 12 } { 15 }$$

Factor the polynomial completely. Solve:

$$x ^ { 2 } = \frac { 1 } { 2 } ( x + 1 )$$

find the inverse of the matrix (if it exists). [-8 0 0 0 , 0 1 0 0 , 0 0 4 0 , 0 0 0 -5]

Choose the letter of the correct term or concept below to complete the sentence. a. personality b. contingencies of reinforcement c. trait d. defense mechanism e. inferiority complex f. self-actualization g. positive regard h. conditions of worth i. extravert j. introvert. According to Carl Rogers, people require __________, or approval, from other people in order to acquire a self.

The number of new home sales (in thousands) in the United States as of March 24, 2010, is given in the table below.

$$\left[\begin{array}{lllll} & \text{Northeast} & \text{Midwest} & \text{South} & \text{West} \\ \hline\text{Feb-Mar 2009} & 47 & 94 & 402 & 143\\ \text{April-Jun 2009} & 82 & 607 & 607 & 278\\ \text{Jul-Sep 2009} & 114 & 179 & 623 & 302\\ \text{Oct-Dec 2009} & 102 & 174 & 578 & 253\\ \text{Jan-Feb 2010} & 67 & 91 & 299 & 170 \end{array}\right]$$

Use the information in the table above. Round your answers to three decimal places. What is the probability a home selected at random was sold in the Midwest from Oct–Dec 2009?

Complete the chart using the additive inverse and the multiplicative inverse of each number.

$$\begin{matrix} & \text{Additive Inverses (opposites)} & \text{Multiplicative Inverses (reciprocals)}\\ -5 \\ \end{matrix}$$

Some skin creams claim that they are “pH balanced" and yet do not have a pH of 7. What do the manufacturers mean when they say “pH balanced"?

Solve these percent problems using proportions. Make a ratio box for the problem. Seventy percent of the team members played in the game. If 21 team members played, how many team members did not play?

find the rational zeros of the function. h(x) = x^3 - 9x^2 + 20x - 12

If 68 is 25% of a number, what is 600% of the number?

Divide.

$$5 \overline{)64.5}$$

Solve each equation below for the indicated variable. Show all steps. a. Solve for x: 2x+22=12, b. Solve for y: 2x-y=3, c. Solve for x: 2x+15=2x-15, d. Solve for y: 6x+2y=10

About 41% of twelfth graders participated in school performing arts last year. A high school had 1800 students, one-fourth of which were twelfth graders. About how many twelfth graders participated in school performing arts?

(a) identify the claim and state

$$H _ { 0 }$$

and

$$H _ { a }$$

, (b) use technology to find the P-value, (c) decide whether to reject or fail to reject the null hypothesis, and (d) interpret the decision in the context of the original claim. Assume the population is normally distributed. A repair shop believes that people travel more than 3500 miles between oil changes. A random sample of 8 cars getting an oil change has a mean distance of 3375 miles since having an oil change with a standard deviation of 225 miles. At

$$\alpha = 0.05$$

, do you have enough evidence to support the shop’s claim?