Bob, Peter and Paul travel together. Peter and Paul are good
hikers; each walks p miles per hour. Bob has a bad foot and drives
a small car in which two people can ride, but not three; the car
covers c miles per hour. The threee friends adopted the following
scheme: They start together, Paul rides in the car with Bob, Peter
walks. After a while, Bob drops Paul who walks on; Bob returns to
pick up Peter, and then Bob and Peter ride in the car till they
overtake paul. At this point, they change: Paul rides and Peter
walks just as they started and the whole procedure is repeated as
often as necessary.
A. How much progress (how many miles) does the company make per
hour?
In: Advanced Math
Marc Lusebrink, sole proprietor of Oak Company, bought a used automobile and drove it 13,326 miles for business during 2017 and a total (including business miles) of 16,250 miles. His total expenses for his automobile for the year are:
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The automobile cost $15,000 on January 1, and depreciation expense for the year, including business use, was $3,000. His business parking and toll fees for business amount to $327.
Calculate Marc's transportation expense deduction for the year under each method listed below.
Round business use to the nearest whole percentage. If required, round your answers to the nearest dollar.
Standard Mileage Method: $
Actual Cost Method:
In: Accounting
Your small remodeling business has two work vehicles. One is a small passenger car used for job-site visits and for other general business purposes. The other is a heavy truck used to haul equipment. The car gets 25 miles per gallon (mpg). The truck gets 10 mpg. You want to improve gas mileage to save money, and you have enough money to upgrade one vehicle. The upgrade cost will be the same for both vehicles. An upgraded car will get 40 mpg; an upgraded truck will get 12.5 mpg. The cost of gasoline is $3.70 per gallon.
Suppose you drive the truck 12,000 miles per year. How many miles would you have to drive the car before upgrading the car would be the better choice?
In: Finance
Determine an approximate sample size required to construct a 90% confidence interval for the mean number of miles on four-year -old Honda Civics, with a margin of error of 1000 miles. Assume that a preliminary study showed that the standard deviation is estimated to be 19,700 miles.
A random sample of 32 washing machines had a mean replacement time of 10.6 years and a population standard deviation of 2.1 years. Find the margin of error that corresponds to 99% confidence level.
A football coach randomly selected ten players and timed below long each player took to perform a certain drill. The times (in minutes) were:
7.6 10.4 9.7 8.4 11.8
7.0 6.5 11.1 10.4 12.4
Construct a 95% confidence interval for the mean time for all players
In: Statistics and Probability
According to a recent government survey, the daily one-way commuting distance
of U. S. workers averages 13 miles. An investigator wishes to determine whether the
national average describes the mean commute distance for all workers in the Chicago area.
Commute distances are obtained for a random sample of 100 workers from this area, and the
mean distance is found to be 12.25 miles with a standard deviation of 2.5 miles. Test the null
hypothesis at the .05 level of significance.
A. State H 0 : ______________________
B. State H A : ______________________
C. Is this a one- or two-tail test? Why? ______________________________________
D. What is(are) the critical value(s)? ______________________
E. What is the decision rule? _______________________________________________
F. Calculate the t statistic:
t = x̄- µm/ s/√n
G. What is your decision regarding H 0 and why? _______________________________
H. Interpretation of the results: _____________________________________________
In: Statistics and Probability
Moana (an expert sailor) is sailing from her home to a nearby island which is 125 miles north and 125 miles west. There is a constant ocean current of 0.50 knots (kn) moving from west to east. Moana can sail her boat at a cruising speed of 5.5 miles per hour in still water.
1. What angle should Moana sail to get to the island?
2. How long will it take her to get there?
3. Moana’s friend Maui is floating on a raft that is moving with the ocean current (meaning, he is not traveling with respect to the water). Would Maui see Moana’s boat traveling with a speed faster than, slower than, or equal to what an observer standing on the shore would see? Explain your reasoning
In: Physics
In: Statistics and Probability
Answer all questions. Show all of your work. Turn in all relevant computer STATA printouts.
Problem 1 (20 points). Show work
Consider the following regression on the average miles per gallon achieved by a random sample of 500 automobiles:
MPGi = 20.4 + 2.5 FOREIGNi – 3.1 WEIGHTi + 1.2 (FOREIGNi*WEIGHTi)
Where:
MPGi is the average miles per gallon achieved by the ith car
FOREIGNi is a dummy variable equal to 1 if the ith car is made outside the United States, zero otherwise.
WEIGHTi is the weight of the ith car, in thousands of pounds.
FOREIGNi*WEIGHTi is the interaction between FOREIGN and WEIGHT
a. Interpret the meaning of the coefficient on FOREIGN*WEIGHT.
b. If the weight of a foreign car increases 3000 pounds, what is the change in miles per gallon?
In: Economics
Suppose that you are interested in estimating the average number of miles per gallon of gasoline your car can get. You calculate the miles per gallon for each of the next twenty-five times you fill the tank. Suppose that in truth, the values for your car are bell-shaped, with a mean of 20 miles per gallon and a standard deviation of 1. Find the possible sample means you are likely to get based on your sample of twenty-five observations. Consider the intervals into which 68%, 95%, and almost all of the potential sample means will fall, using the Empirical Rule. (Round all answers to the nearest thousandth.)
About 68% of possible sample means will be in the range between ___ and ____ .
About 95% of possible sample means will be in the range between ____ and ____ .
About 99.7% of possible sample means will be in the range between ____ and ____.
In: Math
In: Civil Engineering