Two cars start driving from the same point. One travels north at 30 miles per hour, and the other travels east at 45 miles per hour. At what rate is the distance between the cars increasing two hours later?
(a) Draw a diagram, label quantities.
(b) Write rates as derivatives.
(c) Find an equation involving the quantities; differentiate on both sides with respect to t.
(d) Plug in known information and solve for the unknown. [As usual, numeric simplification not required.]

1. Suppose two automobiles leave from the same point at the same time. If one travels north at 60 miles per hour and the other travels east at 45 miles per hour, how fast will the distance between them be changing after 3 hours?

2. Find the critical values of , find the intervals on which f(x)is increasing and decreasing, and any local maximum or minimum values.

Critical values?

Increasing on?

Decreasing on?

Max?

Min?

Please show all work.

A transportation company is suspicious of the claim that the average useful life of certain tires is at least 28,000 miles. To verify that, 40 tires are placed in trucks and an average useful life of 27,463 is obtained with a standard deviation of 13,48 miles. Test this hypothesis with a level of significance of 1%.

Fail to reject the null hypothesis

Reject the null hypothesis

If the population mean under the alternative hypothesis is 27,230, calculate the probability of Type II Error.

A. 5%

B. 85%

C. 5%

D. 99%

A. The Sunshine Skyway Bridge is 131 m high. A truck crossing the bridge loses a piece of cargo, launching it horizontally and perpendicularly off the bridge at 75 miles per hour. How far does the object travel horizontally before it hits the water?

B.The Sunshine Skyway Bridge is 131 m high. A truck crossing the bridge loses a piece of cargo, launching it horizontally and perpendicularly off the bridge at 75 miles per hour. How fast is it going when it hits the water?

A tire manufacturer has been producing tires with an average life expectancy of 26,000 miles. Now the company is advertising that its new tires' life expectancy has increased. In order to test the legitimacy of the advertising campaign, an independent testing agency tested a sample of 6 of their tires and has provided the following data. The p-value is equal to

Select one:

a. 0.102

b. 0.072

c. 0.203

d. 1.46

On Myth Busters it was determined that a penny dropped from the top of the Empire State Building would reach a terminal velocity of 64.4 miles per hour before hitting the ground. What is the height of the building in feet needed for a penny with a mass of 2.5 grams to reach a velocity of 46.7 miles per hour? Assume that no energy is lost from frictional drag. For the acceleration of gravity on the Earth us 9.81 meters per second squared or 32.2 feet per second squared.

A tow truck company suspects that the lifespan of certain tires is less than the 28,000 miles they were offered. To verify if its suspicion is true, the company purchases 40 tires, places them in its trucks and measures the life of each one. The results are presented in the rate below. Presumed known standard deviation = 1300 miles

If we perform a hypothesis test with α = 0.1,

to. What can we conclude? Is the company correct in its suspicions? Respond based on evidence - Clearly define hypotheses, areas of acceptance and rejection, test statistic and CONCLUDE in complete sentence

b. If we wanted to construct a confidence interval for µ with an error of not more than 25 miles, what sample size should we use?

c. If the actual average is 27,800 miles, what would be the probability of making a type II error? What would it mean in this case to make a type II error?

A tow truck company suspects that the lifespan of certain tires is less than the 28,000 miles they were offered. To verify if its suspicion is true, the company purchases 40 tires, places them in its trucks and measures the life of each one. The results are presented in the rate below.

Presumed known standard deviation = 1300 miles

26579 27965 26868 25070 26488
25834 27355 28039 32237 25523
28331 29103 24439 32850 28942
27474 27618 25645 27497 28183
27475 27697 28524 27704 26873
27232 31633 29363 26857 28017
27396 26982 28007 26293 25828
28256 25679 22594 31000 24208

If we perform a hypothesis test with α = 0.1,

a) What can we conclude? Is the company correct in its suspicions? Respond based on evidence - Clearly define hypotheses, areas of acceptance and rejection, test statistic, and CONCLUDE in full sentence

b) If we wanted to construct a confidence interval for µ with an error not greater than 25 miles, what sample size should we use?

c) If the real average is 27,800 miles, what would be the probability of making a type II error? What would it mean in this case to make a type II error?

A tow truck company suspects that the lifespan of certain tires is less than the 28,000 miles they were offered. To verify if its suspicion is true, the company purchases 40 tires, places them in its trucks and measures the life of each one. The results are presented in the rate below.

Presumed known standard deviation = 1200 miles

28965 27531 30211 27700 29191
27218 31246 26151 28453 28753
27613 28560 27106 29395 28852
28164 26220 30894 25910 26247
26767 29664 31536 30671 26811
29516 29096 30185 29537 28135
27768 25767 28601 27726 28601
30598 28196 28939 26414 24601

If we perform a hypothesis test with α = 0.1,

a. What can we conclude? Is the company correct in its suspicions? Respond based on evidence - Clearly define hypotheses, areas of acceptance and rejection, test statistic and CONCLUDE in full sentence

b. If we wanted to construct a confidence interval for µ with an error of not more than 25 miles, what sample size should we use?

c. If the actual average is 27,800 miles, what would be the probability of making a type II error? What would it mean in this case to make a type II error?

A tow truck company suspects that the useful life of certain tires is less than the 28,000 miles they were offered. To verify if its suspicion is true, the company purchases 40 tires, places them in its trucks and measures the life of each one. The results are presented in the rate below.

Presumed known standard deviation = 1200 miles

28965 27531 30211 27700 29191
27218 31246 26151 28453 28753
27613 28560 27106 29395 28852
28164 26220 30894 25910 26247
26767 29664 31536 30671 26811
29516 29096 30185 29537 28135
27768 25767 28601 27726 28601
30598 28196 28939 26414 24601

If we perform a hypothesis test with α = 0.1,

a. What can we conclude? Is the company correct in its suspicions? Respond based on evidence - Clearly define hypotheses, areas of acceptance and rejection, test statistic and CONCLUDE in full sentence

b. If we wanted to construct a confidence interval for µ with an error of not more than 25 miles, what sample size should we use?

c. If the actual average is 27,800 miles, what would be the probability of making a type II error? What would it mean in this case to make a type II error?