Consider the following two-player game. There are two piles of matches. Initially each pile contains n matches. Players alternate moves. A move consists of choosing one of the two piles and removing some nonzero number of matches from it. The player who removes the last match wins. Using strong induction, show that the second player always has a winning strategy.

Arrange these numbers from least to greatest 3/5 5/7 2/9

Four airplanes carrying a total of 400 passengersarrive at the detroit airport. the airplanes carry, respectively,50, 80, 110, and 160 passengers.a) one of the 400 passengers is selected uniformly at random.let x denote the number of passengers that were on theairplane carrying the randomly selected passenger. find var(x)for x as given in the problemb) one of the 4 airplane drivers is also selected uniformly atrandom. let y denote the number of passengers on the chosen driver’s airplane. find var(y) for y as given in the problem

Point r divides in the ratio 1 : 3. if the x-coordinate of r is -1 and the x-coordinate of p is -3, what is the x-coordinate of q? a. b. 3 c. 5 d. 6 e. -9