Mark works at a grocery store where employees make one and a half times their regular hourly wage when they work on a Saturday or a Sunday. Mark works an 8 hour shift 5 days per week, sometimes including weekends. His regular hourly wage is $8.50. What is the maximum amount that he could earn in one week? Explain your reasoning.

You work full time for a local department store as a manager. For three days a week, you work a standard nine-to-five shift. For two days a week, you work a split shift. Your pay is $20 per hour. However, on the two days you work a split shift, you receive an 8-percent pay differential, which makes your pay$21.60 per hour for those two 8-hour days. What is your average rate of pay for the 40-hour week?

A company that builds homes advertises that, by choosing from its upgrade options, each of its new homes is available in 256 different variations. How many upgrade options does the company offer?

Write a matrix equation to model the system. Then use the matrix equation to solve the system.

$$\left\{ \begin{array} { l } { 3 x + 2 y - 7 z = - 29 } \\ { 4 x - 6 y + 5 z = - 19 } \\ { 8 x + y - 4 z = - 30 } \end{array} \right.$$

The table gives annual US emissions, H(t), of hydrofluorocarbons, or "super greenhouse gases," in millions of metric tons of carbon-dioxide equivalent. Let t be in years since 2000. (a) What are the units and meaning of $\int _ { 0 } ^ { 12 } H ( t ) d t ?$ (b) Estimate $\int _ { 0 } ^ { 12 } H ( t ) d t .$

$$\begin{matrix} \text{Year} & \text{2000} & \text{2002} & \text{2004} & \text{2006} & \text{2008} & \text{2010} & \text{2012}\\ \text{H(t)} & \text{158.9} & \text{154.4} & \text{152.1} & \text{153.9} & \text{162.7} & \text{167.0} & \text{173.6}\\ \end{matrix}$$

Use the following table to estimate the area between f(x) and the x-axis on the interval $0 \leq x \leq 20$.

$$\begin{array}{|c|ccccc|} \hline x & {0} & {5} & {10} & {15} & {20} \\ \hline f(x) & {15} & {18} & {20} & {16} & {12} \\ \hline \end{array}$$

Simplify the expression.

$$\log _ { 3 } 3^{2 x}$$

Evaluate the integrals. If the integral diverges, answer “diverges.” $\int_{0}^{\infty} x e^{-x} d x$

An animal shelter has 200 calendars to sell at a fair as a fundraiser. Each of the calendars costs $3 to make. The shelter hopes to sell all the calendars and make a total profit of$1800. a. What should the selling price of each calendar be? b. If the shelter hopes to make a profit of $2000, what should the selling price of each calendar be? Explain your reasoning.

Find the real or imaginary solutions of each equation by factoring. 2x³ - 250 = 0

Let A and B be $3 \times 3$ matrices, with det A=-3 and det B=4. Use properties of determinants to compute: det AB.

Fill in each blank so that the resulting statement is true. In the formula

$$P = \frac { A } { \left( 1 + \frac { r } { n } \right) ^ { n i } }$$

the variable ____ represents the amount that needs to be invested now in order to have ____ dollars accumulated in ____ years in an account that pays rate ____ compounded ____ times per year.

Find the total area between the graph and the x-axis between x=-2 and x=1.

A worldwide rental car company receives about 10,000 calls at its European call center. These calls typically involve customer issues with the level of service or the billing/invoice process. Management conducted a thorough study of the call center's procedures to reduce the number of problems that were not resolved on the customer’s first call. The results were published in the International Journal of Productivity and Performance Management (Vol. 59, 2010). After making significant changes at the call center, management constructed a p-chart to monitor the process improvements. Assume that 18 calls to the center were sampled each day for 60 consecutive days. The article reported that the proportion of all calls in the sample that had unresolved issues at the end of the call was .107. (This significantly improved over the previous unresolved-first-call rate of .845.)

a. What is the centerline for the p-chart?