You have two summer jobs. You mow lawns for $20 per lawn. You also work at a restaurant for$7.50 per hour. Write an equation for the total amount of money you earn. Then find three different ways to earn $300 during one week.

You are in charge of buying food for a school picnic. You have $45 to spend on ground beef and chicken. Ground beef costs$1.80 per pound and chicken costs $1.00 per pound. Write an equation representing the situation. You want to buy equal amounts of ground beef and chicken. How much of each can you buy? Show how you found your answer.

Let

$$\sin t = a , \cos t = b , \text { and } \tan t = c.$$

Write each expression in terms of a, b, and c.

$$4 \cos ( - t ) - \cos t$$

Solve the initial value problem. Confirm your answer by checking that it conforms to the slope field of the differential equation. dy/dx = (x+2) sin x and y = 2 when x = 0

Use the factor theorem to determine whether the binomial is a factor of the given polynomial.

$$z - i ; P ( z ) = z ^ { 7 } + z ^ { 6 } + z ^ { 5 } + z ^ { 4 } + z ^ { 3 } + z ^ { 2 } + z + 1$$

Tell whether each expression is completely factored. If not, factor it. (2x+3)(3x-5)

The heights of young men follow a Normal distribution with mean 69.3 inches and standard deviation 2.8 inches. The heights of young women follow a Normal distribution with mean 64.5 inches and standard deviation 2.5 inches. Suppose we select independent SRSs of 16 young men and 9 young women and calculate the sample mean heights

$$\overline{x}_M$$

and

$$\overline{x}_W.$$

Find the standard deviation of the sampling distribution. Show your work.

Find the prime factorization of each composite number.

$$1575$$

Name an everyday situation that requires problem-solving skills.

Solve the equation.

$$w ( w - 6 ) ^ { 2 } = 0$$

At time $t = 0$, a 3.0 kilogram particle with velocity ${\hat{v}} = (5.0\ \text{~m/s}){\hat{i}}\ -\ (6.0\ \text{~m/s}){\hat{j}}$ is at $x = 3.0\text{~m}, y = 8.0\text{~m}$. It is pulled by a $7.0 \text{~N}$ force in the negative x direction. About the origin, what is the particle’s angular momentum?

Circle the letter of each simple sugar. a. glucose b. sucrose c. fructose d. starch

Rationalize the following lattice energy values:

$$\begin{matrix} \text{Compound} & & \text{Lattice Energy (kJ/mol)}\\ \hline \\ \begin{array} { l } { \text { CaSe } } \\ { \mathrm { Na } _ { 2 } \mathrm { Se } } \\ { \text { CaTe } } \\ { \mathrm { Na } _ { 2 } \mathrm { Te } } \end{array} & & \begin{array} { l } { - 2862 } \\ { - 2130 } \\ { - 2721 } \\ { - 2095 } \end{array} \end{matrix}$$

Use elimination to solve the system of equation. 8x + 3y = -7, 7x + 2y = -3