Find the exact circumference of a circle with a radius of 31.9 meters. Give answers as a fraction and not a decimal.

Acircular city park has a sidewalk directly through the middle that is 111 - feet long. if each bag of fertilizer covers 50 square feet, then determine how many bags of fertilizers the parks and recreation department needs to use to cover the circular park. ignore all the sidewalks around and through the park.

1- what do you think the product of a nonzero rational number and an irrational number is? is it rational or irrational? make use of variables, the closure property of integers, and possibly a proof by contradiction to prove your hypothesis.2- why do we have to specify that the rational number must be nonzero when we determine what the product of a nonzero rational number and an irrational number is? if the rational number were 0, would it give us the same result we found in the first question?

Peter applied to an accounting firm and a consulting firm. he knows that 30% of similarly qualified applicants receive job offers from the accounting firm, while only 20% of similarly qualified applicants receive job offers from the consulting firm. assume that receiving an offer from one firm is independent of receiving an offer from the other. what is the probability that both firms offer peter a job?