Aperson flips a fair coin until the first head appears. if flips the coin n times, they win 2^n dollars. if x denotes the player’s winnings, show that e[x] = +∞. (a) would you pay $1 million to play this game? (b) would you pay $1 million for each game and only need to settle your debt after you decide to stop playing?

Carmen begins her next painting on a rectangular canvas that is 82.7 cm long and has a area of 8,137.68 cm2. will the painting fit in a frame with an opening that is 82.7 cm long and 95 cm wide? explain

Which of the following is the best first step in solving the equation below? 4+2㏒³x=17

Aking and his army will attempt to capture a fortress. the left and right flanks break off from the main group to attack the west and east guard towers. suppose the left flank has a 60% chance of success and the right flank has a 75% chance of success, independently of one another. if both flanks capture their respective targets, then the king has a 98% chance of successfully taking the fort. if, however, only the left flank captures its tower, the king has an 80% chance of success; if only the right flank succeeds, the king has a 50% chance. if both flanks fail, then the king's chance of capturing the fort drops to 20%. it turns out the king captures the fort. what is the probability that one, and only one, flank was successful (either the left, or the right, but not both)? (round your answer to 3 decimal places)