A plane begins its takeoff at 2:00 pm on a 2500-mile flight. The plane arrives at its destination at 7:30 pm. Use the Mean Value Theorem to show that there were at least two times during the flight when the speed of the plane was exactly 400 mi/hr.
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- Dave is driving on an American Interstate highway which has a speed limit of 55 mph. At 2 pm he is at milepost 110 and at 5 pm he is at milepost 290. Is this enough evidence to prove that Dave was speeding? Prove using the Mean Value Theorem.express the null hypotehsis and the alternative hypothesis in symbolic form. the manufacturer of a refrigerator system for beer kegs produces refrigerators that are supposed to mantain a true mean temperature, u, of 43 F, ideal ofr a certain type of German pilsner. the owner of the brewery does not agree with the refrigerator manufacturer, and claims he can prove that the true mean temperature is incorrectsuppose that the mean time for a certain car to go from 0 to 60 miles per hour was 8.6 seconds. Suppose that you want to test the claim that the average time to accelerate from 0 to 60 miles per hour is longer than 8.6 secons. What would you use for the alternative hypothesis?
- If W denotes the weight (in pounds) of an individual and t denotes time (in weeks), then dW/dt is the rate of weight gain or loss (in lb/wk). Suppose that a person weighed 220 pounds 10 weeks ago, and now weighs 198 pounds. Using the Mean Value Theorem, show that their rate of rate loss must have exceeded 2 lb/wk at some point during this 10 week period.Assume that a car drove for two hours and traversed 120 miles. The average rate of change is clearly 60 miles per hour. Was it possible for the car to have gone over 60 mph at some point in the interval? Explain how. Was it possible for the car to have stayed under 60 mph the whole time? Explain how. Was it possible for the car never to have gone exactly 60 mph?Explain how. The truth of this statement is an example of the Mean Value Theorem from CalculusExplain why not all of the hypotheses for the Mean Value Theorem hold for f(x)=1−|x|on [−1, 2].
- For what values of a, b, c and d does the function given below satisfy the hypotheses of the Mean Value Theorem on the interval [−1, 2]Suppose that the speed at which cars go on the freeway is normally distributed with mean 80 mph and standard deviation 8 miles per hour. Let X be the speed for a randomly selected car. Round all answers to 4 decimal places where possible. d. 74% of all cars travel at least how fast on the freeway? ____ mph.A state wildlife service wants to estimate the mean number of days that each licensed hunter actually hunts during a given season, with a bound on the error of estimation equal to 3 hunting days. If data collected in earlier surveys have shown a to be approximately equal to 12, how many hunters must be included in the survey?
- A research worker wants to determine the mean time it takes a mechanic to rotate the tires ofa car, and she wants to be able to assert with 95% confidence that the average of her sample isoff by at most 0.50 minutes. If she can presume from past experience that σ2 = 2:56 minutes,how large a sample will she have to take?Suppose that we have two attributes, gender and programs and, we observe the values of bothvariables through a random sample as given below: a. selected student is male or from the Computing Engineering b. selected student is female given that she is from Electronics and Instrumentation c. selected student is not from the Computing Engineering T =28Does satisfy the hypotheses of the Mean Value Theorem on the interval [0, 5]? If so, find a value c that satisfies the conclusion of the Mean Value Theorem on that interval. (If an answer does not exist) (I inputed c=2/5)