Find each sum. Express your answer in simplest form. $34 \frac { 5 } { 6 } + \left( - 10 \frac { 2 } { 9 } \right)$

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.

Create a chart that illustrates the skills that you will need to have to provide good customer service at a restaurant.

A sample of an alpha emitter having an activity of 0.18 Ci is stored in a 25.0-mL sealed co ntainer at $22 ^ { \circ } \mathrm { C }$ for 245 days. How many alpha particles are formed during this time?

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:

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

Simplify: 4.315 ÷ 5