Find an expression, in terms of n, for the coefficient of x in the expansion $(1+4 x)+(1+4 x)^{2}+(1+4 x)^{3}+\ldots+(1+4 x)^{n}$.

Suppose that

$$f_{X, Y}(x, y)=\lambda^{2} e^{-\lambda(x+y)}, 0 \leq x, 0 \leq y$$

Find E(X + Y).

From 2000 through 2009, the population of Kentucky grew more slowly than that of South Carolina. Models that represent the populations of the two states are given by

$$\left\{\begin{array}{ll} P=30.8 t+4035 & \mathrm { Kentucky } \\ P=61.6 t+3985 & \mathrm { South Carolina } \end{array}\right.$$

where P represents the population (in thousands) and t represents the year, with t=0 corresponding to 2000. Use a graphing utility to estimate the year when the population of South Carolina first exceeded that of Kentucky.

Compute $-2 \ln \lambda$ for the nightmare data, and use it to test the hypothesis that $p_{X}=p_{Y} .$ Let $\alpha=0.01$

A restaurant offers a choice of four appetizers, four-teen entrees, six desserts, and five beverages. How many different meals are possible if a diner intends to order only three courses? (Consider the beverage to be a “course.”)

Find P(X < 2Y) if

$$f_{X, Y}(x, y)=x+y$$

for X and Y each defined over the unit interval.

Brass waveguides are often silver plated to reduce losses. If the thickness of silver $\left(\mu=\mu_{\mathrm{o}}, \varepsilon=\varepsilon_{\mathrm{o}}, \sigma=6.1 \times 10^{7} \mathrm{S} / \mathrm{m}\right)$ must be $5 \delta$, find the minimum thickness required for a waveguide operating at 12 GHz.

Will the CountKeywords program work if lines 33–34 are changed to Set keywordSet = new LinkedHashSet<>(Arrays.asList(keywordString));

What are $A_{\text {mid }}$ in $\mathrm{dB}, f_{H}, f_{L}$, and the BW in Hz for the amplifier described by $A_{v}(s) = \frac{4 \pi^{2} \times 10^{14} s^{2}}{(s+20 \pi)(s+50 \pi)\left(s+2 \pi \times 10^{5}\right)\left(s+2 \pi \times 10^{6}\right)}$ What type of amplifier is this?

Which energy source does not originate from the Sun? (a) coal (b) solar (c) oil (d) nuclear

What does the following statement do? for ( ; ; ) { // Do something }

Suppose a Normal model is useful for describing weights of the yearling Angus steers. Remember, the mean and standard deviation of the weights were 1152 lbs and 84 lbs. Which would be more unusual, a steer weighing 1000 pounds or one weighing 1250 pounds?

Find the natural domain and corresponding range of each of the following functions. (a) $f: x \mapsto x^{2}$ (b) $\mathbf{f}: x \mapsto \cos x^{\circ}$ (c) $f: x \mapsto \sqrt{x-3}$ (d) $\mathrm{f}: x \mapsto x^{2}+5$ (e) $\mathrm{f}: x \mapsto \frac{1}{\sqrt{x}}$ (f) $f: x \mapsto x(4-x)$ (g) $f: x \mapsto \sqrt{x(4-x)}$ (h) $\mathrm{f}: x \mapsto x^{2}+4 x+10$ (i) $f: x \mapsto(1-\sqrt{x-3})^{2}$

Choose the best answer. Which is used to reduce the impact of timber harvesting? (a) tree plantations (b) selective cutting (c) prescribed burns (d) mechanized logging