A runaway train speeds horizontally off a 500.0-m-high cliff. Ignore air resistance for all parts. (a) How long does the train spend in the air? (b) How fast did the train leave the cliff top to land on level ground below, 900.0 m from the base of the cliff? Give your answer in miles per hour. (c) What is the velocity (magnitude and direction) of the train 5 seconds after leaving the cliff? Give your answer with respect to the positive x-axis.

to estimate the fuel efficiency of a new compact automobile, an engineer performed n=16 test runs and recorded the miles per gallon (mpg) for each run. the sample mean was 42.2 mpg with standard deviation 8.8.

a) construct a 99% confidence interval for the true mean mileage for this automobile.

- Lower limit= ?

-upper limit= ?

(please round your answers to 1 decimal place)

b) the manufacturer of this automobile claims that it gets 50mpg. Based on the confidence interval, do you think this is a reasonable claim? why or why not?

David is driving his prius on the freeway and reaches his exit. The exit has a radius of curvature of 25 m and is banked at 38 degrees. How fast can David travel around the curve on a dry day (where the coefficient of friction between his tires and the road is 1)? How fast can he travel around the curve on a rainy day (when the coefficient of friction between his tires and a wet road is 0.75)? Give your in miles per hour. Show all work and explain each step.

A westbound section of freeway currently has three 12-ft wide lanes, a 6-ft right shoulder, and no ramps within 3 miles upstream and downstream of the segment midpoint. It is on rolling terrain with 10% heavy vehicles and is operating at capacity with a peak-hour factor of 0.9. If the road is expanded to four 11-foot lanes with a 2-foot right shoulder, and traffic after the expansion is projected to increase by 10% with the same heavy vehicle percentage and peak-hour factor, what is the new LOS and estimated density?

Suppose you manage a local grocery store and yo have learn that a popular national grocery chain is about to open a store in your town a few miles away. Use model of monopolistic competition to analyze the impact of this new store on quantity of output should produce and your store should charge . Explain how opening of this new store affect your business, be asure to address what happen to your customers, supply demand and prices. what will happen to your profiyts. show graphically and explain reasoning in detail

Choose a cost in your organization (or personal life). Now identify what drives that cost. Keep in mind that the cost driver is something that can be counted!

For instance, if I choose gasoline cost, my cost driver is the number of miles I drive to meet at clients' offices. At home, the cost driver for my electric bill is the number of people-days at my house - i.e. some months everyone is gone (low bill), and other times many houseguests makes for a high electric bill. What are your examples?

A sociologist was hired by a large city hospital to investigate the relationship between the number of unauthorized days that employees are absent per year and the distance (miles) between home and work for the employees. A sample of 10 employees was chosen, and the following data were collected. Distance to Work Number of Days Absent 2 9 4 6 4 9 7 8 9 7 11 4 13 7 15 3 15 6 19 3 Which of the following scatter diagrams accurately represents these data? Scatter Diagram #1 Scatter Diagram #2 Scatter Diagram #3 Consider the following three scatter diagrams of the residuals against the independent variable. Which of the following accurately represents the data? Scatter Diagram #1 Scatter Diagram #2 Scatter Diagram #3 Develop the least squares estimated regression equation (to 3 decimals). Days Absent = + Distance Is there a significant relationship between the two variables? Use = .05. Compute the value of the F test statistic (to 2 decimals). The p-value is What is your conclusion? What is the value of r2 (to 3 decimals)? Note: report r2 between 0 and 1. Did the estimated regression equation provide a good fit? Use the estimated regression equation developed in part (c) to develop a 95% confidence interval for the expected number of days absent for employees living 5 miles from the company (to 1 decimal). ( , )