A shopping center project is proposed to the city council. It cannot be built unless a zoning change is approved by the council. The planning board must first make a recommendation, for or against the zoning change, to the council.
Let A1 = city council approves the zoning change A2 = city council disapproves the change

The prior is: Pr(A1) = .7,   Pr(A2) = .3

Let B denote the event of a negative recommendation by the planning board.

Past history with the planning board and the city council indicates the following

Pr(B|A1) = .2, Pr(B|A2) = .9

3. ____ The planning board has recommended against the zoning change. What is the posterior probability that the city council will approve the zoning change? a) 0.2 b) 0.22 c) 0.3 d) 0.34 e) 0.43


4. ____ You own a local store in the downtown of the city. If the shopping center project is not allowed, your revenue will be $3,000. If allowed, your revenue will be $1,000. The cost of operation is $2,000. Then, you will choose to ______ because your expected profit (or loss if you choose to exit) is ____.

a) Stay, $140 b) Stay, $320 c) Stay, $400 d) Exit, $140 e) Exit, $320

There are three students (Alice, Bill and Roby) applying the scholarships which are evaluated by four professors. Each professor (P1, P2, P3 and P4) gives a score (between 0 and 10) which is then combined into an overall score for each student.
Here are the scores given by the four professors:
P1 gives 8, 6, 3 to Alice, Bill and Roby, respectively;
P2 gives 7, 6, 3 to Alice, Bill and Roby, respectively;
P3 gives 6, 4, 7 to Alice, Bill and Roby, respectively;
P4 gives 4, 9, 7 to Alice, Bill and Roby, respectively.
(1) If each judge's score has equal importance, which student(s) get(s) the highest overall score based on the arithmetic mean?
(2) If the importance for the four professors P1, P2, P3 and P4 are 0.4, 0.3, 0.2 and 0.1, respectively. Which student(s) get(s) the highest overall weighted score based on the weighted arithmetic mean?
(3) If using Borda count, such that a student awards 3 points for first place, 1 point for second place and 0 points for third place, what are the overall scores for the three students?

Consider a three-factor APT model. The factors and associated risk premiums are: Factor Risk Premium (%) Change in gross national product (GNP) +5.7 Change in energy prices 0.3 Change in long-term interest rates +2.7 Calculate expected rates of return on the following stocks. The risk-free interest rate is 5.5%. A stock whose return is uncorrelated with all three factors. (Enter your answer as a percent rounded to 1 decimal place.) A stock with average exposure to each factor (i.e., with b = 1 for each). (Enter your answer as a percent rounded to 1 decimal place.) A pure-play energy stock with high exposure to the energy factor (b = 2.1) but zero exposure to the other two factors. (Enter your answer as a percent rounded to 2 decimal places.) An aluminum company stock with average sensitivity to changes in interest rates and GNP, but negative exposure of b = –1.6 to the energy factor. (The aluminum company is energy-intensive and suffers when energy prices rise.) (Enter your answer as a percent rounded to 2 decimal places.) a. Expected rate of return % b. Expected rate of return % c. Expected rate of return % d. Expected rate of return %

true or fulse

q1

In a regression model it is given that the estimate of intercept is 5 and the estimate of slope is 4 , then the value of dependent variable y for x = 2 is 14.

True

False

q2

When looking at the waiting line at SEU daam system, we can assume that calling population is limited. True

False

q3

A coffee machine can serve customers at the rate of 20 per hour . The customers arrive at the rate of 10 per hour. The probability of more than one customer in the system is 0.25.

True

False

q4

If the coefficient of determination for some data is 0.3, then the correlation coefficient is

True

False

q5

If we make changes in the technological coefficient from 3x +2y ≤ 50 to 6x + 2y ≤ 50, it may cause a change in the optimal solution.

True

False

q6

The customer who arrives at a bank , sees a long line , and leaves to return another time is called balking.

True

False

q7

A vendor selling vegetables on a street corner is an example of a multi-channel, single-phase system.

True

False

q8

  The Graphical Method in Linear programming Problem can also work when there are more than two decision variables.

True

False

The accounting department needs to forecast the profit for a subsidiary. The data for several months is supplied below. Be careful since the data is listed beginning with the most recent. The forecasting method to be used here is exponential smoothing with trend accounting for seasonality given a smoothing constant (alpha) of 0.69, a trend smoothing constant (delta) of 0.3, a previous trend amount, seasonally adjusted, of 65, and a previous seasonal forecast of 582. Please round your forecast to the nearest whole number.

A cylindrical pressure vessel with flat ends of length 6 ft and inner diameter of 35 in. is subjected to an internal gauge pressure of 150 psi. Neglect the end effects and the mass of ends of the pressure vessel in your design. Take the factor of safety as 1.95:

Examine the following book-value balance sheet for Toys INC. The preferred stock currently sells for $30 per share and pays a dividend of $3 a share. The common stock sells for $20 per share and has a beta of 0.6. There are 3 million common shares outstanding. The market risk premium is 9%, the risk-free rate is 5%, and the firm’s tax rate is 40%.

a. What is the market debt-to-value ratio of the firm? (Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places.)

b. What is Toys WACC? (Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places.)

§Problem 1: Two meters of fill (=2.04 Mg/m3) are compacted over a large area (thus 100% of its influence is felt throughout the depth). Above the compacted fill, a 3*4m spread footing loaded with 5000 kN is placed. Assume that the average density of the soil is 1.68 Mg/m3, and the water table is very deep. Then it is required to (a) compute and plot the profile of effective vertical stresses at the middles of five 2m intervals or layers of depth, prior to fill placement. (b) compute and plot the stresses at the same intervals due to adding the fill. (c) compute and plot the stresses with depth due to the addition of 3*4 m footing, using the equations below, for the increase in stresses below the corner of a rectangular area of width B and Length L. (assume that, the weight of footing plus backfill equals weight of soil removed).

§Problem 2 For the previous problem. It was assumed that the settlement of the footing would occur from settlement in the 2m fill below the footing and the 10m layers of medium sand. Consider that, the values of E and ν are 20 MPa and 0.3, respectively, (for both materials). Assuming a linear, isotropic, elastic material behaviour, calculate and plot The Total Elastic Settlement Profile.

Direct Labor Variances

Ada Clothes Company produced 40,000 units during April. The Cutting Department used 12,800 direct labor hours at an actual rate of $16.50 per hour. The Sewing Department used 19,600 direct labor hours at an actual rate of $19.25 per hour. Assume there were no work in process inventories in either department at the beginning or end of the month. The standard labor rate is $18.00. The standard labor time for the Cutting and Sewing departments is 0.3 hour and 0.5 hour per unit, respectively.

a. Determine the direct labor rate, direct labor time, and total direct labor cost variance for the (1) Cutting Department and (2) Sewing Department. Enter a favorable variance as a negative number using a minus sign and an unfavorable variance as a positive number.

b. The two departments have opposite results. The Cutting Department has a(n)   rate variance and a(n)   time variance, resulting in a total   cost variance. In contrast, the Sewing Department has a(n)   rate variance but has a(n)   time variance, resulting in a total   cost variance.

A capacitor C1 =1F is connected to a 1V battery using a wire with a total resistance R = 1Ohm

Suppose after the charging is complete the capacitor C1 is connected to another capacitor C2 = 2 F using a wire with a total resistance of R =0.3 Ohm. Now the first capacitor discharges while the second one charges.

2.8 [1pt] How much charge was transferred through the resistor R during the discharge?

ANSWER

2.9 [1pt] How much energy was dissipated in the resistor R during the discharge

ANSWER

Let’s derive the differential equation describing the discharge in this 2-capacitor circuit. Let’s label the charge on the capacitor C1 as q1(t) and the charge on the capacitor C2 as q2(t).

2.10 [1pt] Sketch the circuit diagram, label the charges and their signs at the capacitors plate, and link q1(t) and q2(t).

Hint, what is q1(t=0) and q2(t=0) (t=0 is the instant the connection was made)?

ANSWER

2.11 [1pt] Express the current through the resistor in terms of the charge derivative and write down the voltages across both capacitors and the resistor add up to zero. From the resulting equation, deduce the characteristic charging time without solving it.

ANSWER