Suppose that every student in a discrete mathematics class of 25 students is a freshman, a sophomore, or a junior. a) show that there are at least nine freshmen, at least nine sophomores, or at least nine juniors in the class. b) show that there are either at least three freshmen, at least 19 sophomores, or at least five juniors in the class.

Two spray paint machines are used to paint different portions of a large wall. the first machine (nicknamed "paint pro") is used for two hours. the second machine (nicknamed "goldilocks") is used for an hour and a half. when they are working at the same time, they can paint 55 square feet per minute. together they painted 5850 square feet of wall. how many square feet of wall per minute can each machine paint? e used to paint different portions of a large wall. the first machine (nicknamed "paint pro") is used for two hours. the second machine (nicknamed "goldilocks") is used for an hour and a half. when they are working at the same time, they can paint 55 square feet per minute. together they painted 5850 square feet of wall. how many square feet of wall per minute can each machine paint?