Given the data below for the reaction, 2 A + 2 B + 4 C => D + E + 3 F,

Calculate the value of k to 3 significant figures.

Using the following information, which investment would be most preferred using Roy's safety first criterion, if R_L=7%.

1) The number of cracks in a section of interstate highway that are significant enough to require repair is assumed to follow a Poisson distribution with mean of three cracks every five miles. What is the probability that there are exactly two cracks that require repair in 3 miles of highway?

2) The volume of a shampoo filled into a container is a continuous random variable uniformly distributed with 240 and 260 milliliters. What is the probability that the container is filled with MORE THAN the advertised target of 255 milliliters?

3) The time between arrivals of taxis at a busy intersection is exponentially distributed with a mean of 10 minutes. What is the probability that you wait between 10 and 20 minutes for a taxi?

1). A group of students plans a tour. The charge per student is $66 if 25 students go on a trip. If more that 25 students participated, the charge per student is reduced by $2 times the number of students over 25. Find the number of students that will furnish the maximum revenue. The number of students that will furnish the maximum revenue is ______? The maximum revenue is $_______?

2) A motorboat is capable of traveling at a speed of 15 miles per hour in still water. On a particular​ day, it took 30 minutes longer to travel a distance of 18 miles upstream than it took to travel the same distance downstream. What was the rate of current in the stream on that​ day?

Larry offered to sell Stanley his car and told Stanley that the car had been driven only 25,000 miles and had never been in an accident. Stanley hired Cohen, a mechanic, to appraise the condition of the car, and Cohen said that the car probably had at least 50,000 miles on it and probably had been in an accident. In spite of this information, Stanley still thought the car would be a good buy for the price, so he purchased it. Later, when the car developed numerous mechanical problems, Stanley sought to rescind the contract on the basis of Larry's fraudulent misrepresentation of the auto's condition. Will Stanley be able to rescind his contract? Discuss.

The maintenance manager at a trucking company wants to build a regression model to forecast the time (in years) until the first engine overhaul based on four explanatory variables: (1) annual miles driven (in 1,000s of miles), (2) average load weight (in tons), (3) average driving speed (in mph), and (4) oil change interval (in 1,000s of miles). Based on driver logs and onboard computers, data have been obtained for a sample of 25 trucks. A portion of the data is shown in the accompanying table.

a. For each explanatory variable, discuss whether it is likely to have a positive or negative causal effect on time until the first engine overhaul.

b. Estimate the regression model. (Negative values should be indicated by a minus sign. Round your answers to 4 decimal places.)

c. Based on part (a), are the signs of the regression coefficients logical?

d. What is the predicted time before the first engine overhaul for a particular truck driven 56,000 miles per year with an average load of 21 tons, an average driving speed of 59 mph, and 22,000 miles between oil changes. (Round coefficient estimates to at least 4 decimal places and final answer to 2 decimal places.)

1.         Corey is the city sales manager for “RIBS,” a national fast food franchise. Every working day, Corey drives his car as follows:

                                                Miles

Home to office                           20

Office to RIBS No. 1                 15

RIBS No. 1 to No. 2                    8

RIBS No. 2 to No. 3                    3

RIBS No. 3 to office                  10

Office to home                           20

Corey’s deductible daily mileage is:

a.         0 miles.

b.         36 miles.

c.         46 miles.

d.         56 miles.

e.         76 miles.

2.         Which of the following trips, if any, will qualify for the travel expense deduction?

a.         Dr. Jones, a general dentist, attends a two-day seminar on financial planning.

b.         Dr. Brown, an undergraduate pre-med student, attends a two-day seminar on developing a medical practice.

c.         Paul, a romance language high school teacher, spends summer break in France, Portugal, and Spain improving his language skills.

d.         Myrna went on a two-week vacation in Boston. While there, she visited her employer’s home office to have lunch with former co-workers.

e.         Mary, a CPA, attends a three-day seminar on state income taxation.

3.         Tax advantages of being self-employed (rather than being an employee) include:

a.         The self-employment tax is always lower than the Social Security tax.

b.         The overall limitation (50%) on meals does not apply.

c.         An office in the home deduction from AGI is available without having to meet the “convenience of the employer” test.

d.         Job-related expenses are deductions for AGI.

e.         Both (c) and (d) are advantages.

4.         When using the automatic mileage method, which of the following expenses, if any, also can be claimed?

a. Engine tune-up.

b. Parking.

c. Interest on automobile loan.

d. MACRS depreciation.

e. None of these.

5.         Which, if any, of the following is subject to a 50% cutback adjustment for the cost of meals in 2019?

a.         An airline pilot for an executive jet rental company who pays his own travel expenses while away from home on flights she pilots.

b.         Meals provided at cost to employees by a cafeteria funded by the employer/taxpayer.

c.         A Fourth of July company picnic for employees of the employer/taxpayer.

d.         A vacation trip to Bermuda awarded to the employer/taxpayer’s top salesperson, where the cost (including meals) is treated as a taxable bonus to the employee.

e.         None of these is subject to the 50% cutback.

1) Let   x be a continuous random variable that follows a normal distribution with a mean of 321 and a standard deviation of 41.

(a) Find the value of   x > 321 so that the area under the normal curve from 321 to x is 0.2224.

Round your answer to the nearest integer.
The value of   x is_______

(b) Find the value of x so that the area under the normal curve to the right of x is 0.3745.

Round your answer to the nearest integer.
The value of   x is ______

2) A study has shown that 24% of all college textbooks have a price of $80 or higher. It is known that the standard deviation of the prices of all college textbooks is $10.00. Suppose the prices of all college textbooks have a normal distribution. What is the mean price of all college textbooks?

Round your answer to the nearest integer.

μ=

3) Use a table, calculator, or computer to find the specified area under a standard normal curve.

Round your answers to 4 decimal places.

a) More than a z-score of 2.48; area = _____________

b) More than a z-score of 1.7; area =_____________

c) More than a z-score of -0.41; area = _____________

d) More than a z-score of 00; area = _____________

4)

The highway police in a certain state are using aerial surveillance to control speeding on a highway with a posted speed limit of 55 miles per hour. Police officers watch cars from helicopters above a straight segment of this highway that has large marks painted on the pavement at  1-mile intervals. After the police officers observe how long a car takes to cover the mile, a computer estimates that cars speed. Assume that the errors of these estimates are normally distributed with a mean of  0 and a standard deviation of  3.58 miles per hour.

a. The state police chief has directed his officers not to issue a speeding citation unless the aerial units estimate of speed is at least 66 miles per hour. What is the probability that a car travelling at 61 miles per hour or slower will be cited for speeding?

Round your answer to four decimal places.

The probability that a car travelling at 61 miles per hour or slower will be cited for speeding is ______

b. Suppose the chief does not want his officers to cite a car for speeding unless they are 99% sure that it is travelling at 61 miles per hour or faster. What is the minimum estimate of speed at which a car should be cited for speeding?

Round your answer to the nearest integer.

The minimum estimate of speed is __