Four Nigerians (A, B, C, D), three Chinese (#,* &), and three Greeks $(\alpha, \beta, \gamma)$ are lined up at the box office, waiting to buy tickets for the World's Fair. (a) How many ways can they position themselves if the Nigerians are to hold the first four places in line; the Chinese, the next three; and the Greeks, the last three? (b) How many arrangements are possible if members of the same nationality must stay together? (c) How many different queues can be formed? (d) Suppose a vacationing Martian strolls by and wants to photograph the ten for her scrapbook. A bit myopic, the Martian is quite capable of discerning the more obvious differences in human anatomy but is unable to distinguish one Nigerian (N) from another, one Chinese (C) from another, or one Greek (G) from another. Instead of perceiving a line to be $B * \beta A D \# \& C \alpha \gamma,$ for example, she would see NCGNNCCNGG. From the Martian's perspective, in how many different ways can the ten funny-looking Earthlings line themselves up?

Identical amounts of thermal energy are added to each of three isolated , equal-mass samples A, B, and C of unknown substances. If their temperature changes are ordered as $\Delta T_{\mathrm{B}}>\Delta T_{\mathrm{C}}>\Delta T_{\mathrm{A}}$, which sample has the largest specific heat?

Evaluate each function for the given value. $H(a)=4 \log \frac{2 a}{5}-8 ; a=25$

Write a letter about yourself that will help your teacher get to know you as an individual. Address each of the general topics below (in bold). Choose a few of the suggested questions to get you started. About You: By what name do you like to be called? What are your interests, talents, and hobbies? What are you proud of? With whom do you live? What languages do you speak? When is your birthday? What are you like as a member of a team? In what ways are you excited about working in a team? In what ways are you nervous about it? You as a Math Student: Describe your memories as a math student from kindergarten until now. What experiences in math have you liked? Why? How do you feel about taking this math class? Have you ever worked in a team in a math class before? What kinds of math do you imagine yourself doing in this class?

Find the limit. $\lim _{x \rightarrow 5} 4$

Solve each logarithmic equation. $\log x=3-\log (100 x900)$

Discuss the validity of each statement. If the statement is always true, explain why. If not, give a counterexample. If f(x)=C is a constant function, then $f^{\prime}(x)=0$.

Describe how the graphs of g(x) and f(x) are related. f(x)=arcsin x and $g(x)=\frac{1}{2} \arcsin (x 2)$

Twenty batteries have been sitting in a drawer for 2 yr. There are 4 dead batteries among the 20. If three batteries are selected at random, determine the number of ways in which a. 3 dead batteries can be selected. b. 3 good batteries can be selected. c. 2 good batteries and 1 dead battery can be selected.

Evaluate the function for the given values of x.

$$f(x)=-3 x \quad g(x)=|x-2| \quad h(x)=\frac{1}{x+1}$$

$\left(\frac{g}{h}\right)(-5)$

A Poisson random variable has pdf

$$p_{X}(k)=e^{-\lambda} \frac{\lambda^{k}}{k !}, k=0,1,2, \ldots$$

and $\lambda>0$ . Also, $E(X)=\lambda$ Suppose the Poisson random variable U is the number of calls for technical assistance received by a computer company during the firm's nine normal workday hours, with the average number of calls per hour equal 7.0. Also suppose each call costs the company $50. Let V be a Poisson random variable representing the number of calls for technical assistance received during a day's remaining fifteen hours. Assume the average number of calls per hour is four for that time period and that each such call costs the company$60. Find the expected cost and the variance of the cost associated with the calls received during a twenty-four-hour day.

(a) Design a pseudo NMOS inverter to operate from $V_{DD} = 3.0 V$ with $V_L = 0.3 V$ and a power of $200 \mu \mathrm{W}$. (b) Find the noise margins for your design.

Some factories have added filtering systems called scrubbers to their smokestacks in order to reduce pollution emissions. The percent of pollution P removed after f feet of length of a particular scrubber can be modeled by $P=\frac{0.9}{1+70 e^{-0.28 f}}$. Graph the percent of pollution removed as a function of scrubber length.

Find the exact value of each expression. If undefined, write undefined. $\csc 5400^{\circ}$