Easoning and proofs 7. let a, b, c be a pythagorean triple. prove that if any two of a, b, and c are relatively prime, then all three numbers are pairwise relatively prime.

Acommunity group sells 2,000 tickets for its raffle. the grand prize is a car. neil and 9 of his friends buy 10 tickets each. when the winning ticket number is announced, it is found to belong to neil's group. given this information, what is the probability that the ticket belongs to neil? a.1/5 b.1/10 c.1/200 d.1/4

An automated water dispenser fills packets with one liter of water on average, with a standard deviation of 5 milliliter. the manual says that after a year of operation the dispenser should be tested to see if it needs recalibration. a year later a number of filled packets are set aside and measured separately. it is found that the average packet now contains about 0.995 liters. does the dispenser need calibration? explain your answer.

Acircular garden with radius of 8 feet is surrounded by a circular path with a width of 3 feet. what is the approximate area of the path alone? use 3.14 for π