Consider the weighted voting system {60: 4, 56, 58}. a. Compute the Banzhaf power index for each voter in this system. b. Voter B has a weight of 56 compared with only 4 for voter A, yet the results of part a show that voter A and voter B both have the same Banzhaf power index. Explain why it seems reasonable, in this voting system, to assign voters A and B the same Banzhaf power index.

In each item you are to compare a quantity in Column $1$ with a quantity in Column $2$. Write the letter of the correct answer from these choices: A. The quantity in Column $1$ is greater than the quantity in Column $2$ . B. The quantity in Column $2$ is greater than the quantity in Column $1$ . C. The quantity in Column $1$ is equal to the quantity in Column $2$ . D. The relationship cannot be determined from the given information. Notes: Information centered over both columns refers to one or both of the quantities being compared. A symbol that appears in both columns has the same meaning in each column. All variables represent real numbers. Most figures are not drawn to scale.

$$\begin{array}{} \text{Column 1}& &\text{Column 2}\\ &\text{amplitude}\\ f(x)=2 \sin 3 x && g(x)=4 \cos 2 x \end{array}$$

A triangular crown glass prism is surrounded by air. If light inside the prism strikes one of its facets, what is the critical angle of incidence a for total reflection? (The refractive index for crown glass is 1.52, and the refractive index for air is 1.00.)

Write a C++ program that accepts both a string and a single character from the user. The program should determine how many times the character is contained in the string. (Hint: Search the string by using the find(str, ind) function. This function should be used in a loop that starts the index value at 0 and then changes the index value to one past the index of where the char was last found.)

A diving board oscillates with simple harmonic motion of frequency $3.5$ cycles per second. What is the maximum amplitude with which the end of the board can vibrate in order that a pebble placed there not lose contact with the board during the oscillation?

What performance problem can result from using function templates and class templates?

A board of mass $m$ and length $l$ is placed on a horizontal tabletop. The coefficient of static friction between the board and the table is $\mu$.How far from the edge of the tabletop can one extend the board before it falls off?

Sketch the graph of a function f that is cotinuous on [1, 5] and has the given properties. Absolute maximum at 4, absolute minimum at 5, local maximum at 2, local minimum at 3

A 124-g sample of a pure liquid, liquid A, with a density of $3.00 \mathrm{~g} / \mathrm{mL}$ is mixed with a $40.8-\mathrm{mL}$ sample of a pure liquid, liquid B, with a density of $2.00 \mathrm{~g} / \mathrm{mL}$. What is the total volume of the mixture? (Assume there is no reaction upon the mixing of $\mathrm{A}$ and $\mathrm{B}$, and volumes are additive.)

The following table gives the values of the Lorenz function for the market income distribution in the United States for the year 2007.

$$\begin{matrix} \text{x} & \text{0.0} & \text{0.1} & \text{0.2} & \text{0.3} & \text{0.4} & \text{0.5} & \text{0.6} & \text{0.7} & \text{0.8} & \text{0.9} & \text{1.0}\\ \text{f(x)} & \text{0.00} & \text{0.01} & \text{0.02} & \text{0.05} & \text{0.09} & \text{0.15} & \text{0.21} & \text{0.31} & \text{0.40} & \text{0.56} & \text{1.00}\\ \end{matrix}$$

Use the Trapezoidal Rule with n = 10 to estimate the Gini Index for the market income distribution in the United States for the year 2007.

Compute the formal adjoint of the given linear differential operator $L$. \

$$L[y](x)=x y^{\prime \prime}(x)+\left(2-x^2\right) y^{\prime}(x)+3 y(x)$$

Woodworking Scarlet measures two sides of a board of wood as 14 inches and 7 inches. If she wants to find out the perimeter of the board, what formula should she use? What is the perimeter of the board?

Jeffrey Bruner, CFA, uses the capital asset pricing model (CAPM) to help identify mispriced securities. A consultant suggests Bruner use arbitrage pricing theory (APT) instead. In comparing CAPM and APT, the consultant made the following arguments:

a. Both the CAPM and APT require a mean-variance efficient market portfolio.

b. The CAPM assumes that one specific factor explains security returns but APT does not. State whether each of the consultant’s arguments is correct or incorrect. Indicate, for each incorrect argument, why the argument is incorrect.

Write a program that meets the following requirements:

• Creates an array with 100 randomly chosen integers.
• Prompts the user to enter the index of the array, then displays the corresponding element value. If the specified index is out of bounds, display the message Out of Bounds.