Boran Stockbrokers, Inc., selects four stocks for the purpose of developing its own index of stock market behavior. Prices per share for a 2007 base period, January 2009, and March 2009 follow. Base-year quantities are set on the basis of historical volumes for the four stocks.

$$\begin{matrix} \text{ } & \text{ } & \text{ } & \text{ } & \text{Price per Share (\$)}\\ \text{ } & \text{ } & \text{2007} & \text{2007} & \text{January} & \text{March}\\ \text{Stock} & \text{Industry} & \text{Quantity} & \text{Base} & \text{2009} & \text{2009}\\ \hline \text{A} & \text{Oil} & \text{100} & \text{31.50} & \text{22.75} & \text{22.50}\\ \text{B} & \text{Computer} & \text{150} & \text{65.00} & \text{49.00} & \text{47.50}\\ \text{C} & \text{Steel} & \text{75} & \text{40.00} & \text{32.00} & \text{29.50}\\ \text{D} & \text{Real Estate} & \text{50} & \text{18.00} & \text{6.50} & \text{3.75}\\ \end{matrix}$$

Use the 2007 base period to compute the Boran index for January 2009 and March 2009. Comment on what the index tells you about what is happening in the stock market.

Convert decimal degrees to degrees, minutes, seconds, and convert degrees, minutes, seconds to decimal degrees. Round to the nearest second or the nearest thousandth of a degree, as appropriate. Use a calculator as necessary. $119^{\circ} 8^{ \prime} 3^{\prime \prime}$

A 20-ft^3 rigid tank initially contains saturated refrigerant- 134a vapor at 160 psia. As a result of heat transfer from the refrigerant, the pressure drops to 50 psia. Show the process on a P-v diagram with respect to saturation lines and determine (a) the final temperature, (b) the amount of refrigerant that has condensed, and (c) the heat transfer.

Determine whether each statement is true or false. ff the statement is false, make the necessary change(s) to produce a true statement. In using the quadratic formula to solve the quadratic equation

$$5x^2 = 2x - 7,$$

we have a = 5, b = 2, and c = -7.

Under the last-in first-out (LIFO) inventory valuation method, a price index for inventory must be established for tax purposes. The quantity weights are based on year-ending inventory levels. Use the beginning-of-the-year price per unit as the base-period price and develop a weighted aggregate index for the total inventory value at the end of the year. What type of weighted aggregate price index must be developed for the LIFO inventory valuation?

$$\begin{matrix} \text{ } & \text{Ending} & \text{Unit} & \text{Price (\$)}\\ \hline \text{Product} & \text{Inventory} & \text{Beginning} & \text{Ending}\\ \hline \text{A} & \text{500} & \text{.15} & \text{.19}\\ \text{B} & \text{50} & \text{1.60} & \text{1.80}\\ \text{C} & \text{100} & \text{4.50} & \text{4.20}\\ \text{D} & \text{40} & \text{12.00} & \text{13.20}\\ \end{matrix}$$

Use prime factorization to find the greatest common divisor. $6m^3n,8mn^2$

The response to a question has three alternatives: A, B, and C. A sample of 120 responses provides 60 A, 24 B, and 36 C. Show the frequency and relative frequency distributions.

Investigate the one-parameter family of functions. Assume that a is positive. (a) Graph f(x) using three different values for a. (b) Using your graph in part (a), describe the critical points of f and how they appear to move as a increases. (c) Find a formula for the x-coordinates of the critical point(s) of f in terms of a. $f ( x ) = ( x - a ) ^ { 2 }$

A cat's crinkle ball toy of mass 15 g is thrown straight up with an initial speed of 3 m/s. Assume in this problem that air drag is negligible. (a) What is the kinetic energy of the ball as it leaves the hand? (b) How much work is done by the gravitational force during the ball's rise to its peak? (c) What is the change in the gravitational potential energy of the ball during the rise to its peak? (d) If the gravitational potential energy is taken to be zero at the point where it leaves your hand, what is the gravitational potential energy when it reaches the maximum height? (e) What if the gravitational potential energy is taken to be zero at the maximum height the ball reaches, what would the gravitational potential energy be when it leaves the hand? (f) What is the maximum height the ball reaches?

Think of a student behavior that exists at your school and that a teacher or the principal might want to change. Then devise a way to change that behavior by using behavior modification techniques. Write out your plan in a short paper.

Shipments of product from manufacturer to the retailer are tracked by the U.S. Census Bureau. The value of shipments for computer and electronic products in September 2009, 2010, and 2011 are shown in the table below, along with the CPI and PPI for each of these months.

a. Use the CPI to deflate the value of the shipped computer and electronics products.

b. Use the PPI to deflate the value of the shipped computer and electronics products.

c. Which index, the CPI or PPI, do you feel is more appropriate for deflating these shipment values? Why

Solve the equation.

$$6 ^ { x - 2 } = 36$$

Solve each equation. $\log _{4} x=\frac{3}{2}$

Each of exercises refers to the Euler phi function denoted

$$\phi$$

, which is defined as follows: For each integer

$$n \geq 1 , \phi ( n )$$

is the number of positive integers less than or equal to n that have no common factors with n except

$$\pm 1$$

. For example,

$$\phi ( 10 ) = 4$$

because there are four positive integers less than because there are four positive integers less than

$$\pm 1$$

; namely, 1, 3, 7, and 9. Prove that there are infinitely many integers n for which

$$\phi ( n )$$

is a perfect square.