Unfortunately, robbery is an all-too-frequent crime. Bank robberies tend to be the most lucrative for criminals. In most cases banks do not report the size of the loss. However, several researchers were able to gain access to bank robberies in England. Here are the variables recorded:

Bank raid successful from the point of view of the robbers (2 = yes and 1 = no)

Amount stolen (for successful raids only)

Number of bank staff present

Number of customers present.

If these data can be considered a random sample of British bank robberies estimate with 95% confidence the following parameters. Proportion of all bank robberies that are successful

A printer can print 8 pages per minute. Identify the dependent and independent variables for the situation. Write an equation in function notation.

Given that λ = 1 is a three-times repeated eigenvalue of the matrix

$$A=\left[ \begin{array}{rrr}{-3} & {-7} & {-5} \\ {2} & {4} & {3} \\ {1} & {2} & {2}\end{array}\right]$$

using the concept of rank, determine how many linearly independent eigenvectors correspond to this value of λ. Determine a corresponding set of linearly independent eigenvectors.

The viscosities of chemical infusions obtained from a specific production technique are normally distributed with a standard deviation $\sigma = 3.9$. If a chemist is able to measure the viscosities of 15 independent samples of the infusions, what is the probability that the resulting point estimate of the mean $\mu$ will be within 0.5 of the true value? How does this probability change if a sample of 40 independent infusions is obtained?

Find two linearly independent Frobenius series solutions (for $x > 0$) of the differential equation.

$$2 x y ^ { \prime \prime } + 3 y ^ { \prime } - y = 0$$

Determine if the following systems are consistent and independent, consistent and dependent, or inconsistent.

$$\begin{aligned} &y=2x+5\\ &y-2x=1 \end{aligned}$$

Identify the independent variable and the dependent variable in situation: The amount of time, t, to finish a race and the number of laps, l , around a track

Dawson purchased a diesel-powered car that averages 41 miles per gallon. Suppose Dawson is interested in how far the car travels on a given amount of gas. a. Identify the independent and dependent quantities.b. Define variables for each quantity and identify which is the independent variable and which is the dependent variable. c. Write an equation to represent the relationship between the two variables.

evaluate (if possible) the function at each specified value of the independent variable and simplify. q(t) = (2t^2 + 3)/t^2 , q(2)

For each of the following, give the appropriate nonparametric test to apply: a. Comparing two populations with independent samples. b. Making an inference about a population median. c. Comparing three or more populations with independent samples. d. Making an inference about rank correlation. e. Comparing two populations with matched pairs. f. Comparing three or more populations with a block design.

Fill each blank with the word from the list below that best fits the context.

$$\begin{array}{lllll}\text { abound } & \text { appendix } & \text { desolate } & \text { dissimilar } & \text { manipulate } \\ \text { manual } & \text { manuscript } & \text { pending } & \text { redundant } & \text { resolution } \\ \text { resolve } & \text { revise } & \text { simulate } & \text { simile } & \text { sole } \\ \text { soliloquy } & \text { solitude } & \text { veracity } & \text { verdict } & \text { video }\end{array}$$

Othello thinks Iago is his true friend. However, in a(n) ________ later in the play, Iago reveals that his friendship for Othello is ________ d.

Under what conditions should you use the $x^2$ test to determine whether there is a difference between the proportions of two independent populations?

The following arguments were abstracted from newspaper articles, editorials, and letters to the editor. Use the method presented in this section to construct argument patterns. If a statement is redundant or plays no role in the argument, do not include it in the pattern. 1 Unscrupulous for-profit colleges are not only cheating their students but 2 they are also ripping off the American taxpayer to the tune of billions of dollars. 3 Ninety-six percent of the students who attend these colleges are forced to take out loans. 4 Most of these students leave without degrees. 5 And the students then default on their loans, leaving a $32 billion annual debt to the taxpayer.

In your own words, describe what it means to say that the cross-product operation is “coordinate independent," and state why this fact is significant.