Emily rows six miles downstream in 1 hour and her friend Ashley, rowing 1 mile per hour faster, completes the return trip in 2 hours.

Find the speed of the current (c) and each girls rowing speed.

The Toyota Prius is a​ gasoline-electric hybrid car that gets 54 miles to the gallon. An article in the Wall Street Journal notes that sales of the Prius have been hurt by low gasoline prices and​ that: "Americans are now more likely to trade in a hybrid or an electric vehicle for an​ SUV...."

Does the article indicate that​ gasoline-powered cars and gasoline are substitutes or​ complements? Briefly explain.

A.

​Substitutes, because the more consumers buy of one​ good, the more they will buy of the other good.

B.

​Substitutes, because the more consumers buy of one​ good, the less they will buy of the other good.

C.

​Complements, because they are used for the same purpose.

D.

​Complements, because they are used together.

Does it indicate that​ gasoline-powered cars and hybrids are substitutes or​ complements?

A.

​Complements, because they are used for the same purpose.

B.

​Substitutes, because the more consumers buy of one​ good, the less they will buy of the other good.

C.

​Substitutes, because the more consumers buy of one​ good, the more they will buy of the other good.

D.

​Complements, because they are used together.

A company has a policy of retiring company cars; this policy looks at number of miles driven, purpose of trips, style of car and other features. The distribution of the number of months in service for the fleet of cars is bell-shaped and has a mean of 55 months and a standard deviation of 8 months. Using the empirical rule (as presented in the book), what is the approximate percentage of cars that remain in service between 39 and 47 months?

Do not enter the percent symbol.
ans =  %

A large university claims that the average cost of housing within 5 miles of the campus is $8900 per scholl year. A high shcool student is preparing her budget for her freshman year at the university. She is concerned that the university's esimate is too low. She obtained a random sample of 81 records and computes the average cost is $9050. Based on earlier data, the population stand deviation is $760. Use a=0.01 level of significance.

Step 1. State the null and alternative hypothese.

Step 2. Write doown the appropriate test statistic (formula) and the rejection region of your test (repot z critical(s)

Step 3. Compute the value of the test statistic (z observed)

Step 4. State your conclusin (in one sentence, state whether of not the test reject the null hypothesis and in another sentence apply the result to the problem).

Step 5. Compute the p-value for this test. Is this evidence strong or weak in spporting the alternative hypothesis.

A consumer group conducts a study to compare the average mileages (in units of miles per gallon, mpg) of two popular car brands achieved in road tests. A random sample of 5 cars from Brand 1 were tested, yielding mean mileage xbar1= 29.5 mpg and sample standard deviation s₁ = 7.4 mpg. A random sample of 8 cars from Brand 2 were tested, yielding mean mileage xbar2= 31.6 mpg and s₂ = 8.4 mpg. Assume that two populations from which the samples are drawn are normally distributed. At the 5 percent significance level, do the data provide sufficient evidence to conclude that there is no difference between average mileages of Brand 1 cars and Brand 2 cars?

Water is drawn from a reservoir and pumped an equivalent length of 2 miles through a horizontal, circular duct of 10-in. i.d. (wall roughness k = 0.01 ft). At the end of this duct, the flow is divided into a 4- and a 3-in. schedule 40 steel pipe. The 4-in. line has an equivalent length of 200 ft. and discharges to the atmosphere at a point 50 ft. above the surface of the water in the reservoir. This flow must be maintained at 1000 gal/min. The 3-in. line discharges to the atmosphere at a point 700 ft. from the junction at the reservoir level. The pump you are considering has an efficiency of 70. Kinetic energy effects can be ignored. Determine how much horsepower is needed for the system.

A company has a policy of retiring company cars; this policy looks at number of miles driven, purpose of trips, style of car and other features. The distribution of the number of months in service for the fleet of cars is bell-shaped and has a mean of 47 months and a standard deviation of 5 months. Using the 68-95-99.7 rule, what is the approximate percentage of cars that remain in service between 57 and 62 months?

Suppose that a category of world class runners are known to run a marathon (26 miles) in an average of 145 minutes with a standard deviation of 15 minutes. Consider 49 of the races.

Let

X = the average of the 49 races.

• Part (a)

  Give the distribution of

  X.

  (Round your standard deviation to two decimal places.)

  X~  

• Part (b)

  Find the probability that the runner will average between 143 and 148 minutes in these 49 marathons. (Round your answer to four decimal places.)
  

• Part (c)

  Find the 80th percentile for the average of these 49 marathons. (Round your answer to two decimal places.)
    min

• Part (d)

  Find the median of the average running times.
    min

World class marathon runners are known to run that distance (26.2 miles) in an average of 146 minutes with a standard deviation of 15 minutes.

If we sampled a group of world class runners from a particular race, find the probability of the following:

**(use 4 decimal places)**

a.) The probability that one runner chosen at random finishes the race in less than 140 minutes.

b.) The probability that 10 runners chosen at random have an average finish time of less than 140 minutes.  

c.) The probability that 50 runners chosen at random have an average finish time of less than 140 minutes.