Final answer:
For temporary spare tires, it is usually recommended not to exceed 50-70 miles. For the survey scenario, you'd need to perform a hypothesis test to determine if the data is inconsistent with the tire's lifespan claim. For the revolutions made by tires over a given distance, the formula involving the circumference of the tire's circle is used.
Step-by-step explanation:
You should not drive on a spare tire for more than 50-70 miles. Spare tires are designed for short-term use to get you to a safe location or a service station after experiencing a flat tire. They are not built for long distances or high speeds.
In the brand of tires claiming an average lifespan of 50,000 miles, with a typical standard deviation of 8,000 miles, a survey of 28 tires yielded a mean lifespan of 46,500 miles and a standard deviation of 9,800 miles. To determine if this data is highly inconsistent with the claim, a hypothesis test can be conducted using the alpha level of 0.05.
For the question about the number of revolutions a tire makes during its lifecycle, if a car with tires of 0.260 meters radius travels 80,000 kilometers, you can calculate the number of revolutions by converting the distance to meters (80,000 kilometers = 80,000,000 meters) and then using the formula for the circumference of a circle (Circumference = 2 π × radius). The total number of revolutions is then the total distance traveled divided by the circumference of one tire revolution.