A roulette wheel is divided into 38 labeled pockets, 18 of which are red, 18 are black, and 2 are green. Each round, you can place a $1 bet on one specific red or black pocket with odds of 35 : 1. That is, if you are correct you receive $35 in addition to the dollar you bet, and if you are incorrect, you get nothing. Your friend has developed what he describes as a "foolproof system" for winning. It involves him repeatedly betting $1 on red pocket number 7. You try to discourage him, but he is insistent. (a) What are your friend’s expected winnings after one spin of the wheel? What are his expected winnings after 36 spins of the wheel? (b) Despite showing him the outcome of the above calculation, he is unwavering in his opinion, so you decide to at least try to make some money for yourself. You bet your friend $20 that at the end of 36 spins he will have lost money, i. e. have less money than he began with. What are your expected winnings in this bet? What are your friend’s expected winnings after 36 spins taking this side-bet into account as well? (c) Explain what went wrong.

Atrain traveled for 1.5 hours to the first station, stopped for 30 minutes, then traveled for 4 hours to the final station where it stopped for 1 hour. the total distance traveled is a function of time. which graph most accurately represents this scenario? a graph is shown with the x-axis labeled time (in hours) and the y-axis labeled total distance (in miles). the line begins at the origin and moves upward for 1.5 hours. the line then continues upward at a slow rate until 2 hours. from 2 to 6 hours, the line continues quickly upward. from 6 to 7 hours, it moves downward until it touches the x-axis a graph is shown with the axis labeled time (in hours) and the y axis labeled total distance (in miles). a line is shown beginning at the origin. the line moves upward until 1.5 hours, then is a horizontal line until 2 hours. the line moves quickly upward again until 6 hours, and then is horizontal until 7 hours a graph is shown with the axis labeled time (in hours) and the y-axis labeled total distance (in miles). the line begins at the y-axis where y equals 125. it is horizontal until 1.5 hours, then moves downward until 2 hours where it touches the x-axis. the line moves upward until 6 hours and then moves downward until 7 hours where it touches the x-axis a graph is shown with the axis labeled time (in hours) and the y-axis labeled total distance (in miles). the line begins at y equals 125 and is horizontal for 1.5 hours. the line moves downward until 2 hours, then back up until 5.5 hours. the line is horizontal from 5.5 to 7 hours