Three cards are randomly selected from a deck of 52 cards. After every draw, the card is NOT replaced back in the deck. Find the probability of drawing a King, followed by two Aces in a row.

An instructor gives a pop quiz consisting of 10 multiple choice questions, where each question has 5 choices, (a) through (e). What is the probability of passing the pop quiz if you guess the answers and you have to get 8 questions correct?

The probability of event A is 0.5 and probability of event B is 0.2. Given that A and B are independent, then the probability of A and B (A intersection B) is:

How many different ways can a 9-player baseball team be selected for an informal game if there are 25 available players? Which counting method do you use?

You are tossing a coin, then rolling a die, then drawing a card from a deck of cards. What is the probability that you will get: a tail AND an even number on the die AND a card less than 5 (assume the ace is equal to 1) from the deck?

In a club there are 11 women and 7 men. A committee of 5 women and 3 men is to be chosen. How many different ways are there to select the committee?

If a distribution follows the binomial distribution with n = 50 and probability of success of 0.25, calculate the mean and variance.

At a raffle, 1500 tickets are being sold for $2 each. There is one prize of $500, one prize of $250, one prize of $150, and one prize of $75. If you buy one ticket, what is the expected value of your gain?

Probability is:

Choose one • 10 points

The measure of how likely an event is to occur.

The ratio of total possible outcomes to desired outcomes.

Not conveyed as a decimal or a percent.

None of the above.

Monica Britt has enjoyed sailing small boats since she was 7 years old, when her mother started sailing with her. Today, Monica is considering the possibility of starting a company to produce small sailboats for the recreational market. Unlike other mass-produced sailboats, however, these boats will be made specifically for children between the ages of 10 and 15. The boats will be of the highest quality and extremely stable, and the sail size will be reduced to prevent problems of capsizing. Her basic decision is whether to build a large manufacturing facility, a small manufacturing facility, or no facility at all. With a favorable market, Monica can expect to make $90,000 from the large facility or $60,000 from the smaller facility. If the market is unfavorable, however, Monica estimates that she would lose $30,000 with a large facility, and she would lose only $20,000 with the small facility. Because of the expense involved in developing the initial molds and acquiring the necessary equipment to produce fiberglass sailboats for young children, Monica has decided to conduct a pilot study to make sure that the market for the sailboats will be adequate. She estimates that the pilot study will cost her $10,000. Furthermore, the pilot study can be either favorable or unfavorable. Monica estimates that the probability of a favorable market given a favorable pilot study is .8. The probability of an unfavorable market given an unfavorable pilot study result is estimated to be .9. Monica feels that there is a .65 chance that the pilot study will be favorable. Of course, Monica could bypass the pilot study and simply make the decision as to whether to build a large plant, small plant, or no facility at all. Without doing any testing in a pilot study, she estimates that the probability of a favorable market is .6. What do you recommend? compute EVSI

For each of the following processes, use a calculation to predict whether or not it will
occur spontaneously. (For some cases you may need to use data from Appendix A in
your textbook.)
a) A piston with radius of 15.6 cm containing 2.86 L of an ideal gas (Cv,m = 3/2 R) at
1.00 atm, 298.15 K undergoes isothermal compression by the addition of a 5.64
kg weight.
b) The combustion reaction for methanol CH4O(l) at 298.15 K carried out in a bomb
calorimeter.
c) Evaporation of 10.00oC liquid water under standard conditions, given that ΔHo
vap
= 44.120 kJ/mol at 298.15 K. Temperature-independent heat capacity for water:
Cp,m(H2O(l)) =75.327 kJ mol-1; Cp,m(H2O(g))=33.651 kJ mol-1

The particulars of a 20 TR R 22 food freezer are as follows:

Evaporator temperature – 30°C

Condenser temperature 40°C

Temperature of vapor leaving evaporator – 25°C

Subcooling of liquid with vapor in heat exchanger 5°C

Polytropic index of compressor 1.15

Superheating of suction vapor after passing through suction valve 15°C

Compressor clearance factor 0.05

Pressure drop in valves 0.2 bar suction

0.5 bar discharge

The compressor has 6 cylinders with bore equal to stroke. Its rpm is 1500, and mechanical efficiency is 0.75. Determine

(i) Mass flow rate of refrigerant.

(ii) Piston displacement of compressor.

(iii) Cylinder diameter.

(iv) Motor horse power.

(v) Cooling requirement of compressor in kW.

A railway buffer consists of a pair of cylinders placed parallel side-by-side. Oil is present in each cylinder and is arranged to bypass through ports, thereby producing a damping resistance, which is proportional to the velocity of the piston within the cylinder. The magnitude of this resistance is 50 kN at a velocity of 0.25 m/s. Each cylinder also contains a compression spring, initially with negligible compression, of stiffness 65 kN/m. A rigid train of mass 250 tons is moving at a speed of 1.6 m/s and collides with the buffer. Determine the distance taken by the train before first coming to rest. Assuming that the train comes into contact and then become attached to the free end of the buffer. Determine the time it takes the train to come to a complete stop. Solution for this problem should show the position and velocity of the train.

1. If a closed system loses 2200 J of heat (to the surrounding environment) and 800 J of work is done on the system then what was the change in the internal energy of the system.

2. An ideal gas (inside a cylinder fitted with a movable piston) is heated and slowly expands at constant pressure of 5 atm from 1.5 L to 5.5 L.  How much work is done by the gas in this process?

3. If 1,700 J of heat was added to the gas in problem 3, then how much did the internal energy of the system change?

4. What is the efficiency of an automobile engine that has a heat input of 60.0 kJ and a heat output of 25.0 kJ?

5. If the exhaust temperature of the engine in problem 5 is 250° C, then what is the intake temperature?    (The exhaust and intake temperatures are the low and high operating temperatures of the engine, T_L and T_H)

Harry is a HS student with too much time on his hand when he was homebound during the COVID-19 pandemic. He designed a method how he can throw pebbles over the 2.1-m fence in his backyard such that they land in a pot on the ground of his neighbor’s property: he stands 6.7 m in front of the fence and throws a pebble from 1.7-m height such that the highest point is at 1.5 m right above the fence.

a) We use t1 for the time for the pebble to travel from Harry’s hand to the highest point and t2 for the time for the pebble to travel from the highest point until it falls into the pot. Find the ratio t1/t2!

b) Find the distance D of the pot from the fence!

c) Find the launch speed of the pebble!

d) Find the direction in which he throws the pebble!

The osmotic pressure of blood is 7.65 atm at 37 °C. What mass of glucose (C6H12O6, molar mass = 180.2 g/mol) is needed to prepare 2.50 L of solution for intravenous injection? The osmotic pressure of the glucose solution must equal the osmotic pressure of blood. (R = 0.08206 L×atm/mol×K)

4.17E-3 g

1.14E3 g

0.751 g

11.1 g

136 g

Match the following aqueous solutions with the appropriate letter from the column on the right.

Which of the following investments would have the highest future value at the end of 10 years? Which has the highest present value today? Rank the choices below from highest to lowest present value. Assume that the effective annual interest rate for all investments is the same and is greater than zero.

1. Investment A pays $250,000 at the beginning of every year for the next 10 years (a total of 10 payments).

2. Investment B pays $125,000 at the end of every 6-month period for the next 10 years (a total of 20 payments).

3. Investment C pays $125,000 at the beginning of every 6-month period for the next 10 years (a total of 20 payments).

4. Investment D pays $2.5 million at the end of 10 years (just one payment).

5. Investment E pays $250,000 at the end of every year for the next 10 years (a total of 10 payments).

The following data are collected to study unemployment in a particular region in upstate New York. The first column shows the number of months unemployed and the second column shows the count of people in the study with the corresponing unemployment length.

Let X be a random variable indicating the number of months a person is unemployed.

a)Use the data to develop the probability mass function for X.

b)Find the cumulative distribution function for X.

c)Calculate the mean and standard deviation of X.