Aroulette wheel has 15 red slots, 15 black slots, and 2 green slots. when it is spun, a metal ball has an equal chance to land in each slot. a bet on red pays even money, i. e., if the ball lands in a red slot you win an amount equal to your bet and if the ball does not land in a red slot you lose the amount you bet. you come to the roulette wheel with only $1, which you bet on red. you continue to bet all of your money on red each time the wheel is spun, until you lose. let x be the number of spins up to and including the time that you lose. what is var(x)?

Orly uses 2 cups of raisins for every 12 cups of trail mix she makes. how many cups of trail mix will she make if she uses 8 cups of raisins?

An automobile assembly line operation has a scheduled mean completion time, μ, of 12 minutes. the standard deviation of completion times is 1.6 minutes. it is claimed that, under new management, the mean completion time has decreased. to test this claim, a random sample of 33 completion times under new management was taken. the sample had a mean of 11.2 minutes. assume that the population is normally distributed. can we support, at the 0.05 level of significance, the claim that the mean completion time has decreased under new management? assume that the standard deviation of completion times has not changed.

Which equation can be solved to find x the measure of jk in the apex