Suppose s is a set of 10 integers (any integers at all). prove that there are a pair of numbers in s whose difference is a multiple of 9; i. e. prove that there exists a, b ∈ s and an integer k ∈ z such that a − b = 9k. (hint: apply the pigeonhole principle to the potential remainders of elements of s with respect to division by 9).

Seth practice piano for 1 1/3 hours on saturday and 5/6 hour on sunday for much longer did he practice on saturday than on sunday?

Find the value of x that will make l ll m

Aball is thrown from a height of 139 feet with an initial downward velocity of 15 ft/s. the ball's height h (in feet) after t seconds is given by the following. h=139-15t-16t^2 how long after the ball is thrown does it hit the ground? round your answer(s) to the nearest hundredth. (if there is more than one answer, use the "or" button.) t =