A manufacturer of lightbulbs wants to produce bulbs that last about $700$ hours but, of course, some bulbs burn out faster than others. Let $F(t)$ be the fraction of the company's bulbs that burn out before $t$ hours, so $F(t)$ always lies between $0$ and $1$ .

What is the meaning of the derivative $r(t)=F^{\prime}(t)$ ?

Answer the next two questions based on the following scenario. Bank #1 receives a $\$20,000$ deposit from a customer. Bank #1 then loans out all its excess reserves of $\$18,000$, which are deposited into Bank #2. Bank #2 loans out all its excess reserves, as does Bank #3, and so on.

If the process described previously continues throughout the banking system until all excess reserves are loaned out, the total change in the money supply resulting from the $\$20,000$ deposit would be

a. $\$18,000$.

b. $\$20,000$.

c. $\$38,000$.

d. $\$200,000$.

An urn contains four green and three blue balls. You take one ball out of the urn, note its color, and replace it. You then take a second ball out of the urn, note its color, and replace it. If A denotes the event that the first ball is green and B denotes the event that the second ball is green, determine whether A and B are independent.

Assume all variables are binomial. (Note: If values are not found in Previous Table . use the binomial formula.)
High School Dropouts Approximately $10.3\%$ of American high school students drop out of school before graduation. Choose $10$ students entering high school at random. Find the probability that
No more than $2$ drop out

Show that a directed multigraph having no isolated vertices has an Euler path but not an Euler circuit if and only if the graph is weakly connected and the in-degree and out-degree of each vertex are equal for all but two vertices, one that has in-degree one larger than its outdegree and the other that has out-degree one larger than its in-degree.

A shunt-connected dc motor has zero rotational losses and $R_A = 0$ Assume that $R_F + R_{adj}$ is constant [except in part (d)] and that $\phi$ is directly proportional to field current. For $V_T = 200 \ \text{V}$ and $P_{out} = 2 \ \text{hp}$ the speed is 1200 rpm. What is the effect on $I_A$ and speed if: $\textbf{a.}$ the load torque doubles; $\textbf{b.}$ the load power doubles; $\textbf{c.}$ $V_T$ is changed to 100 V and $P_{out}$ remains constant; $\textbf{d.}$ $R_F + R_{adj}$ is doubled in value and $P_{out}$ remains constant?

After a collision with a power pole, you are trapped in your car, with a high-voltage line (with frayed insulation) in contact with the hood of the car. If you must get out before help arrives, is it safer to step out of the car one foot at a time or to jump with both feet leaving the car at the same time? Explain your reasoning.

Consider a room air conditioner using a Carnot cycle at maximum theoretical efficiency and operating between the temperatures of $18.0^{\circ} \mathrm{C}$ (indoors) and $35.0^{\circ} \mathrm{C}$ (outdoors). For each $1.00 \mathrm{~J}$ of heat flowing out of the room into the air conditioner: a) How much heat flows out of the air conditioner to the outdoors?

Read each sentence and decide if the underlined number should be spelled out. If it should, write the spelled-out form above it. If the number is already correct, write $C$ above it.

Example 1. $\underline{152}$ (One hundred fifty-two) students auditioned for the marching band.

The next rest area is $\underline{100}$ miles away.

Remember to use the largest common factor and to check by multiplying. Factor out a negative factor if the first coefficient is negative.

$$8 x+24$$

A piston $/$ cylinder has $15\ \mathrm{ft}$ of liquid $70 \mathrm{~F}$ water on top of the piston $(m=0)$ with a cross-sectional area of $1\ \mathrm{ft}^2$. Air let in under the piston rises and pushes the water out over the top edge. Determine the work needed to push all the water out and plot the process in a $P-V$ diagram.

Write an equivalent expression by factoring out the greatest common factor.

$$15 m^4 n+30 m^5 n^2+25 m^3 n^3$$

According to the American Red Cross, about one out of nine people in the U.S. have Type B blood. Suppose the blood types of people arriving at a blood drive are independent. In this case, the number of Type B blood types that arrive roughly follows the Poisson distribution.

What is the probability that over 10 people out of these 100 have type B blood?

In paragraphs 24-27, the second woman rips the embroidered man completely out of her embroidery because -

A. she did not want the other women to be jealous of her fine stitching B. she was angry and afraid C. she knew she could do better D. she was not paying attention and tore too much of the man out