Consider a first-price, sealed-bid auction in which a bidder’s valuation can take one of three values: 5, 7, and 10, occurring with probabilities .2, .5, and .3, respectively. there are two bidders, whose valuations are independently drawn by nature. after each bidder learns her valuation, they simultane- ously choose a bid that is required to be a positive integer. a bidder’s payoff is zero if she loses the auction and is her valuation minus her bid if she wins it. a. determine whether it is a symmetric bne for a bidder to bid 4 when her valuation is 5, 5 when her valuation is 7, and 6 when her valuation is 10. b. determine whether it is a symmetric bne for a bidder to bid 4 when her valuation is 5, 6 when her valuation is 7, and 9 when her valuation is 10.

The table shows population statistics for the ages of best actor and best supporting actor winners at an awards ceremony. the distributions of the ages are approximately bell-shaped. compare the z-scores for the actors in the following situation. best actor best supporting actor muequals42.0 muequals49.0 sigmaequals7.3 sigmaequals15 in a particular year, the best actor was 59 years old and the best supporting actor was 45 years old. determine the z-scores for each. best actor: z equals best supporting actor: z equals (round to two decimal places as needed.) interpret the z-scores. the best actor was (more than 2 standard deviations above more than 1 standard deviation above less than 1 standard deviation above less than 2 standard deviations below) the mean, which (is not, is) unusual. the best supporting actor was (less than 1 standard deviation below more than 1 standard deviation above more than 2 standard deviations below more than 1 standard deviation below) the mean, which (is is not) unusual.

Awoman has 14 different shirts: 10 white shirts and 4 red shirts. if she randomly chooses 2 shirts to take with her on vacation, then what is the probability that she will choose two white shirts? show your answer in fraction and percent, round to the nearest whole percent.

Write a similarity statement for the similar triangles. afgh ~ a