Your company, Sonic Video, Inc., has conducted research that shows the following probability distribution, where X is the number of video arcades in a randomly chosen city with more than 500,000 inhabitants.

$$\begin{matrix} \text{x} & \text{0} & \text{1} & \text{2} & \text{3} & \text{4} & \text{5} & \text{6} & \text{7} & \text{8} & \text{9}\\ \text{P(X=x)} & \text{.07} & \text{.09} & \text{.35} & \text{.25} & \text{.15} & \text{.03} & \text{.02} & \text{.02} & \text{.01} & \text{.01}\\ \end{matrix}$$

a. Compute $\mu=E(X)$ and interpret the result. b. Which is larger, $P(X<\mu)$ or $P(X>\mu)$? Interpret the result.

A student has grades on three examinations of 88, 90, and 84. What must the student earn on a fourth examination in order to have an average of at least 90?

A market survey shows that 40% of the population used Brand X laundry detergent last year, 5% of the population gave up doing its laundry last year, and 4% of the population used Brand X and then gave up doing laundry last year. Are the events of using Brand X and giving up doing laundry independent? Is a user of Brand X detergent more or less likely to give up doing laundry than a randomly chosen person?

Describe the sample space S of the experiment and list the elements of the given event. (Assume that the coins are distinguishable and that what is observed are the faces or numbers that face up.) A sequence of two different digits is randomly chosen from the digits 0-4; the first digit is larger than the second.

Simplify each sum or difference. $\frac{x(x+4)}{x-2}+\frac{x-1}{x^{2}-4}$

Suppose that the electron in the hydrogen atom obeyed classical mechanics rather than quantum mechanics. Why should such a hypothetical atom emit a continuous spectrum rather than the observed line spectrum?

At the band's peak of popularity, a personally signed Black Diamond poster sold for $\$500$. Three years later the band was almost forgotten and the poster was worth only $\$10$. What were the annual multiplier and annual percent of decrease?

The following figures show the price of silver per ounce, in dollars, for the 10-business day period Feb. 2-Feb. 13, 2009: 12.4, 12.4, 12.4, 12.8, 12.9, 13.0, 13.0, 13.4, 13.3, 13.4 Find the sample mean, median, and mode(s). What do your answers tell you about the price of silver?

In November 2008 the probability that a randomly selected subprime home mortgage in Texas was current in its payments was .67. Choose 10 subprime home mortgages at random. a. What is the probability that exactly four of them were current? b. Use technology to generate the probability distribution for the associated binomial random variable. c. Fill in the blank: If 10 subprime home mortgages were chosen at random, the number of them most likely to have been current was ______.

The random variable X has the probability distribution table shown below:

$$\begin{matrix} \text{x} & \text{-2} & \text{-1} & \text{0} & \text{1} & \text{2}\\ \text{P(X=x)} & \text{-} & \text{-} & \text{.4} & \text{.1} & \text{.1}\\ \end{matrix}$$

a. Calculate $P(X \geq 0)$ and P(X<0). b. Assuming P(X=-2)=P(X=-1), find each of the missing values.

Identify the error in this statement. $\frac{\sqrt[3]{x}}{\sqrt[3]{y}} \cdot \frac{\sqrt[3]{y}}{\sqrt[3]{y}}=\frac{\sqrt[3]{x y}}{y}$

Sketch the voltage across a $33 \Omega$ resistor over the range $0<t<2 \pi \mathrm{s},$ if the current is given by 2.8 cos(t) A. Assume both the current and voltage are defined according to the passive sign convention.

For a school fair, Donny is going to design a spinner with red, white, and blue regions. Since he has a certain proportion of three types of prizes, he wants the P(red) = $40\%$ and P(white) = $10\%$. a. If the spinner only has red, white, and blue regions, then what is P(blue)? Explain how you know. b. Find the central angles of this spinner if it has only three sections. Then draw a sketch of the spinner. Be sure to label the regions accurately. c. Is there a different spinner that has the same probabilities? If so, sketch another spinner that has the same probabilities. If not, explain why there is no other spinner with the same probabilities .

Graph each inequality. $y<-x+4$