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?

Set up the payoff matrix. You must decide whether to attack your opponent by sea or air, and your opponent must simultaneously decide whether to mount an all-out air defense, an all-out coastal defense (against an attack from the sea) or a combined air and coastal defense. If there is no defense for your mode of attack, you win 100 points. If your attack is met by a shared air and coastal defense, you win 50 points. If your attack is met by an all-out defense, you lose 200 points.

Imagine that you are out of school and have started working and saving. You want to keep from using credit cards or unnecessary loans as much as possible, so you make savings plans for major purchases and expenses.

Why is saving up for major purchases and expenses better than using credit cards or taking out loans?

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.

Mai needs to be at the auditorium by $\underline{6:00}$ P.M. for rehearsal.

GENERAL: Airplane Flight Delays For flights from U.S. airports, the "taxi-out" time (the number of minutes between leaving the gate and takeoff) can be approximated by an exponential random variable with mean 20 . Find the probability that for a given flight the taxi-out time is more than:

a. 1 hour ( 60 minutes)

b. 3 hours ( 180 minutes)

a) Find a recurrence relation for the number of ways to lay out a walkway with slate tiles if the tiles are red, green, or gray, so that no two red tiles are adjacent and tiles of the same color are considered indistinguishable. b) What are the initial conditions for the recurrence relation in part (a)? c) How many ways are there to lay out a path of seven tiles as described in part (a)?

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 $r(t)=F^{\prime}(t)$ ?

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

Consider a bivariate normal distribution with $\mu 1=1, \mu 2=3, \sigma 11=2, \sigma 22=1$ and $\rho 12=-.8$. (a) Write out the bivariate normal density. (b) Write out the squared statistical distance expression $(x-\mu)^{\prime} \Sigma-1(x-\mu)$ as a quadratic function of $x_{1}$ and $x_{2}$.

For each sentence, if the underlined pronoun is correct write C above it. If it is not correct, cross it out and write the correct form of the pronoun above it.

Example 1. My choice for the student delegate will be $\overset{\textit{\color{#c34632}{she}}}{{\underline{\sout{\text{her}}}}}$.

It wasn’t $\underline{\text{I}}$ who left the baseball equipment out on the field.

The human eye has about 137 million _(s).

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 temperature should not drop below $\underline{32}$ degrees tonight.

A box contains four white and eight black balls. You pick out a ball with your left hand and don’t look at it. Then you pick out a ball with your right hand and don’t look at it.

Next, you look at the ball in your right hand and it is black. Now what is the probability that the ball in your left hand is white?

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.