Trace the shuffle algorithm for the input 5, 51, 2, 44, 96. Assume that the values of rand are rand(1,5)=1, rand(2,5)=3, rand(3,5)=5, rand(4,5)=5.

By recognizing the series as a Taylor series evaluated at a particular value of x, find the sum of each of the following convergent series. $1+\frac{2}{1 !}+\frac{4}{2 !}+\frac{8}{3 !}+\dots+\frac{2^{n}}{n !}+\cdots$

Prove the following identities, where C is a simple closed smooth oriented curve. $\oint _ { C } f ( x ) d x + g ( y ) d y = 0$, where f and g have continuous derivatives on the region enclosed by C

A company sales manager, after careful analysis, presents two sales plans. It is estimated that plan A will net $10 million if successful (probability .8) and lose$2 million if not (probability .2); plan B will net $12 million if successful (probability .7) and lose$2 million if not (probability .3). What is the expected return for each plan? Which plan should be chosen based on the expected return?

Use a calculator to tell how many nickels and how many dimes in problem. 900c, 4 times more dimes than nickels

Select the best answer. The General Social Survey (GSS), conducted by the National Opinion Research Center at the University of Chicago, is a major source of data on social attitudes in the United States. Once each year, 1500 adults are interviewed in their homes all across the country. The subjects are asked their opinions about sex and marriage, attitudes toward women, welfare, foreign policy, and many other issues. The GSS begins by selecting a sample of counties from the 3000 counties in the country. The counties are divided into urban, rural, and suburban; a separate sample is chosen at random from each group. This is a (a) simple random sample. (b) systematic random sample. (c) cluster sample. (d) stratified random sample. (e) voluntary response sample.

Along with dimensional analysis, to approximately convert the given unit to the unit indicated. Where necessary, round answers to two decimal places.

$$\begin{matrix} \text{2 pints (pt)=1 quart (qt)}\\ \text{4 quarts=1 gallon (gal)}\\ \text{1 gallon=128 fluid ounces (fl oz)}\\ \text{1 cup (c)=8 fluid ounces}\\ \text{Volume in cubic Units} & \text{Capactiy}\\ \text{1 cubic yard} & \text{about 200 gallons}\\ \text{1 cubic foot} & \text{about 7.48 gallons}\\ \text{231 cubic inches} & \text{about 1 gallon}\\ \end{matrix}$$

10,000 $\mathrm{ft}^{3}$ to gal

Use synthetic division. Divide $-2 x^{5}+30 x^{3}-140$ by x + 4.

What do you do first if you are asked to solve a triangle and are given one side and two angles?

How can 20 balls, 10 white and 10 black, be put into two urns so as to maximize the probability of drawing a white ball if an urn is selected at random and a ball is drawn at random from it?

At what point(s) is the tangent line to the curve $y ^ { 2 } = 2 x ^ { 3}$ perpendicular to the line $4 x - 3 y + 1 = 0 ?$

Newton’s method fails. Explain why the method fails and, if possible, find a root by correcting the problem. $4 x^{3}-7 x^{2}+1=0, x_{0}=1$

In a probability model, which of the following numbers could be the probability of an outcome? $0 \quad 0.01 \quad 0.35 \quad-0.4 \quad 1 \quad 1.4$

What forbade women to vote in New Jersey after 1801?