Suppose an investor is concerned about a business choice in which there are three prospects-the probability and returns are given below:

$$\begin{array}{|cr|} \hline \text { PROBABILITY } & \text { RETURN } \\ \hline .4 & \$ 100 \\ \hline 3 & 30 \\ \hline 3 & -30 \\ \hline \end{array}$$

What is the expected value of the uncertain investment? What is the variance?

Write the phrase as an algebraic expression. Use the variable $x$ to represent the unknown number.

A number divided by eleven.

Solve the inequality $\left\vert 10-x\right \vert >4$ and sketch the graph of the solution on the real number line.

Find the indicated velocities and accelerations.

A package of relief supplies is dropped and moves according to the parametric equations $x=45t$ and $y=-4.9t^2$ ( $x$ and $y$ in m, $t$ in s). Find the velocity and acceleration when $t=3.0$ s.

The $1 \mathrm{~N} 5160$ is conducting. If we allow $0.7 \mathrm{~V}$ across the diode at the drop-out point, what is the value of $V$ when the diode opens?

Solve the inequality $\frac{|2 w+8|}{5} \geq 3$ . Sketch the graph of the solution set on a number line.

At what point does the curve $x=t\left(t^2-3\right), y=3\left(t^2-3\right)$ cross itself? Find equations of both tangents at that point.

Water $\left(\right.$ at $\left.50^{\circ} \mathrm{F}\right)$ flows in the horizontal bend at a rate of 12 $\mathrm{cfs}$ and discharges into the atmosphere past the downstream flange. The pipe diameter is $1\ \mathrm{ft}$. What force must be applied at the upstream flange to hold the bend in place? Consider that the volume of water downstream of the upstream flange is $4\ \mathrm{ft}^3$ and that the bend and pipe weigh $100\ \mathrm{lbf}$. Suppose the pressure at the inlet section is $\mathrm{4\ psig}$.

Recognizing Interjections. Rewrite each of the following sentences, using an appropriate interjection in place of the feeling shown in parentheses. Relief) I thought that lecture would never end.

Circle the phrase or clause that modifies the underlined word or words in each sentence.

Who are the $\underline{\text{people}}$ whom you invited along?

Determine the area above the $n^{t h}$ bend of $y=x \sin x$ which liesbelow the $x$ axis. See the earlier fig.

Write the sentence as an inequality. Graph the inequality.

A number d is less than -2 or greater than or equal to 2.

Solve the inequality and graph the solution on the real number line. $\frac{x+6}{x+1}-2<0$

Read the paragraph below and answer the questions. Plumbers often use a non-metallic pipe called PVC pipe for sink and toilet drain lines. The four most common diameters of PVC pipe are $1 \frac{1}{2}$ in., 2 in., 3 in., and 4 in. When plumbers need to combine pipes with diameters of difference sizes, they use a bushing or reducer coupling. Elbows or "bends" help make turns when connecting pipes. There are three different sizes of elbows and two common fittings that are used. A "wye" is a straight fitting with a $45^{\circ}$ elbow attached to one end, and a "tee" is a straight fitting with a $90^{\circ}$ elbow attached to one end. Pipes are connected by cleaning and priming the ends and then fitting them together. Liquid cement is applied to each piece and the pieces are twisted together slightly to ensure an even coating of cement on the pieces.

If a plumber only has $\frac{1}{16}$ bends,state the angle he needs to create 90$^{\circ}$.