Q1 (a)0.5 kg of water is contained in a rigid vessel at a temperature of 125oC and a pressure of 232.1 kPa. The specific enthalpy is 1050 kJ•kg-1. Which of the following could also be correct?

(A) v = 0.001065 m3 •kg-1 (B) v = 0.7706 m3 •kg-1 (C) x = 0.24 (D) x = 0.5

(b).0.020 kg of air, initially at 20oC is compressed in a perfectly insulated and sealed cylinder which is fitted with a moveable piston. A mean force of 1000 N was applied to the piston as it moved through a displacement of 100 mm to compress the gas. The final temperature of the gas after compression will be?

(A) 27oC (B) 20oC (C) 30oC (D) 13oC

(c). 0.8857 m3 of H2O is stored in a rigid vessel at 200 kPa, 125oC. Is this?

(A) Sub-cooled liquid ? (B) Saturated liquid ? (C) Saturated vapour ? (D) Superheated vapour ?

1.8. Problem. (Sections 2.2-2.4) Three fair, six-sided dice colored red, green and blue are rolled. Calculate each of the following probabilities:

(a) The probability all three dice show the same face (“triples”).

(b) The probability that the red die shows a larger number than the green die.

(c) The probability that the red die shows a larger number than the green die and the green die shows a larger number than the blue die.

(d) The probability that the sum of the pips on all three dice is exactly 10.

(e) The probability that the sum of the pips on all three dice is less than 10.

(f) The probability that the sum of the pips on all three dice is greater than 10.

Assume that random guesses are made for seven multiple choice questions on an SAT​ test, so that there are

equals ​trials, each with probability of success​ (correct) given by

p =0.45

.

Find the indicated probability for the number of correct answers.

Find the probability that the number x of correct answers is fewer than

4

.

Spurious correlation refers to the apparent relationship between variables that either have no true relationship or are related to other variables that have not been measured. One widely publicized stock market indicator that is an example of spurious correlation is the relationship between the winner of a major sports championship and the performance of a stock index in that year. The​ "indicator" states that when a team from a particular conference wins the​ championship, the stock index will increase in that year. Since the first championship was​ held, the indicator has been correct 44 out of 56 times. Assuming that this indicator is a random event with no predictive​ value, you would expect that the indicator would be correct​ 50% of the time.

a. What is the probability that the indicator would be correct 44 or more times in 56 years?

b. What does this tell you about the usefulness of this indicator?

A person bets his remaining savings on a horse race based on the large payoff if his horse wins. Which of the following decision-making criteria does this typify?

Choose one answer.

Jake woke up late in the morning on the day that he has to go to school to take an important test. He can either take the shuttle bus which is usually running late 20% of the time or ride his unreliable motorcycle which breaks down 40% of the time. He decides to toss a fair coin to make his choice. If Jake, in fact, gets to the test on time, what is the probability that he took the bus?

Choose one answer.

A coin with probability p>0 of turning up heads is tossed 4 times. Let X be the number of times heads are tossed.

(a) Find the probability function of X in terms of p.

(b) The result above can be extended to the case of n independent tosses (that is, for a generic number of tosses), and the probability function in this case receives a very specific name. Find the name of this particular probability function.

Notice that the probability of turning up tails in one toss is 1−p.

A high performance 4 stroke supercharged gasoline engine is being designed. The target specifications are as follows:

1. IMEP: 25 bar at peak power
2. bsfc:    237 g/kWh
3. isfc:     211 g/kWh
4. Bore to stroke ratio:    1.1
5. Number of cylinders: 4
6. Maximum mean piston speed: 21 m/s
7. Compression ratio: 10.5:1
8. Simulation results indicate that the indicated work per cylinder per cycle needs to be 1550 J/cyl/cyc.

Based on the provided information, finalize the engine design for the following parameters:

1. Bore and stroke (mm)
2. Engine displacement (litre)
3. Engine Speed at peak power (rpm)
4. Peak brake power (kW)
5. Fuel flow rate at peak power (kg/hr)
6. The minimum cylinder volume (cm³)

A roulette wheel has 38 slots, 18 of which are black, 18 red, and 2 green. When the wheel is spun, the ball is equally likely to land in any of the 38 slots. Gamblers can place a number of different bets in roulette. One of the simplest wagers chooses red or black. A bet of $1 on red will pay off an additional dollar if the ball lands in a red slot. Otherwise, the player loses the original dollar. When gamblers bet on red or black, the two green slot belong to the house.

a. A gambler’s winnings on a $1 bet are either $1 or -$1. Give the probabilities of each of these outcomes. Find the mean and standard deviation of a gambler’s winnings on one such bet.

b. Explain briefly what the law of large numbers tells us about what will happen in the long run if the gambler makes a very large number of bets on red.

c. The central limit theorem tells us the approximate distribution of the gambler’s mean winnings in 50 bets. What is this distribution? Be sure to specify the values of all necessary parameters.

d. If a gambler makes 50 bets on red, find a range into which there is roughly a 95% chance that the gambler’s mean winnings will fall. Multiply this result by 50 to get the middle 95% of the distribution of the gambler’s winnings on nights when he places 50 bets.

e. What is the probability that the gambler will win money if he places 50 bets on red? (This is simply the probability that the mean winnings are greater than 0.)

f. The casino takes the other side of these bets. If 100,000 bets are placed on red in a week at the casino, what is the distribution of the mean winnings of gamblers on these 100,000 bets? What range covers the middle 95% of the distribution of mean winnings in 100,000 bets? Multiply by 100,000 to get the range of gambler’s losses. What is the approximate probability that the casino will lose money on 100,000 bets?

(Note that the gamblers’ losses are the casino’s winnings. Parts (d) and (e) indicate that an individual gambler has a pretty decent chance of winning money on any given night – which creates excitement and keeps people gambling. However, part (f) indicates that in the long run, the casino essentially always wins.)

Dior Company purchased an 8-floor building as an investment on January 3, 2016 for $2,000,000 cash. The building is intended to earn rentals and for capital appreciation in the future. In addition to the purchase price, the company also paid $90,000 legal fees for acquisition of property, $10,000 taxes for title transfer and $30,000 to paint the whole building. On the date of acquisition, all eight floors were leased and the company received $150,000 for tenant deposits obligations.

Based on independent appraisal, land accounted for approximately 40% of the value of the property. In valuing the property, it was also determined that the fair value of the elevator in its present condition is $180,000. The elevator is expected to have a useful life of 10 years, zero residual value and it will have to be replaced at the end of the useful life. The building is expected to have a useful life of 20 years and a residual value of $260,000.

Assume the company uses the fair value model, prepare the journal entry to record the acquisition of the property on January 3, 2016. The purchase was made in cash.

Problem 1.1: Making Sense of the Trade Deficit

a) Explain the difference between the current account and the capital and financial account in the balance of payments.

b) What is a trade deficit?

c) Assume a U.S. firm buys (imports) $5 million (in U.S. dollars) of foreign goods. That transaction by itself increases the trade deficit by $5 million. But, the $5 million will flow back to the United States to purchase either (i) U.S. goods and services or (ii) U.S. assets.

1. How does the way the $5 million comes back to the United States determine whether there will be balanced trade or a trade deficit?
2. How does the U.S. economy benefit from either transaction (the foreign purchase of U.S. goods and services [exports] or the purchase of U.S. assets)?

d) How does the “global savings glut” help explain the trade deficit?

e) Write a short "elevator conversation" in which you explain clearly to less informed people (on the elevator, in a few minutes) what a "trade deficit" really is.