Find div $\mathbf{F}$ and curl $\mathbf{F}$ for the vector field $\mathbf{F}$ at the given point.

$$\begin{array}{l}{\mathbf{F}(x, y, z)=\left(e^{-x} \sin y\right) \mathbf{i}+\left(e^{-x} \cos y\right) \mathbf{j}+\mathbf{k} \text { at }} \\ {(1,3,-2)}\end{array}$$

Decide whether the following statements are true or false. Explain your answer. a. If X has a normal distribution with $\mu = 8,$ then $P(X \geq 8.21)=P(X \leq 7.79).$ b. If X has a normal distribution, then the probability is about 0.87 that its value will be within 1.5 standard deviations of the mean.

How many 2-person groups can be chosen from 7 people?

How could more young women be convinced of the importance of regular breast exams?

Identify the coordinates of any local and absolute extreme points and inflection points. Graph the function. y = -x^4 + 6x^2 - 4 = x^2(6 - x^2) - 4

In a product liability case, a company can settle out of court for a loss of $350,000, or go to trial, losing$700,000 if found guilty and nothing if found not guilty. Lawyers for the company estimate the probability of a not-guilty verdict to be 0.8. a. Find the expected value of the amount the company can lose by taking the case to court. b. Should the company settle out of court?

A large mountain can slightly affect the direction of “down” as determined by a plumb line. Assume that we can model a mountain as a sphere of radius R = 2.00 km and density (mass per unit volume) 2.6 × 10³ kg/m³. Assume also that we hang a 0.50 m plumb line at a distance of 3R from the sphere’s center and such that the sphere pulls horizontally on the lower end. How far would the lower end move toward the sphere?

solve 240= 6z + c for c.

Name the bones of the thigh, leg, ankle, and foot.

Suppose that $Z \sim N(0, 1)$. Find:

$$\begin{align*} &\mathbf{(a)}\, P(Z \le −0.77)\\ &\mathbf{(b)}\, P(Z \ge 0.32)\\ &\mathbf{(c)}\, P(−3.09 \le Z \le −1.59)\\ &\mathbf{(d)}\, P(−0.82 \le Z \le 1.80)\\ &\mathbf{(e)}\, P(|Z| \ge 0.91)\\ &\mathbf{(f)}\,\text{The value of } x \text{ for which } P(Z \le x) = 0.23\\ &\mathbf{(g)}\,\text{The value of } x \text{ for which } P(Z \ge x) = 0.51\\ &\mathbf{(h)}\,\text{The value of } x \text{ for which } P(|Z| \ge x) = 0.42\\ \end{align*}$$

Describe how your muscles work to help you kick a ball.

Do the ratios in each pair form a proportion? 3.5/35, 2.04/204

A plant’s response to gravity is an example of a a.Dormancy b.Hormone c.Tropism d.Critical night length

Find the derivative of each function. $f(x)=\tanh x^{2}$