In the bottom of the 9th inning in a tie game, the leadoff batter for the home team hitsa double. According to researcher Tom Tango, teams in this situation have a win probability of 0.807. Because the home team only needs one run to win the game, some managers will choose to have the next player attempt a sacrifice bunt, which allows the runner on second base to reach third base while the hitter is thrown out. If the sacrifice bunt is successful, then the home team has a runner on third base with 1 out and a win probability of 0.830. However, if the sacrifice is unsuccessful and the runner is thrown out at third, there is a runner at first with one out (win probability of 0.637), What is the minimum probability of a successful bunt that would warrant using the bunt? Enter your answer as a decimal (not a percent) with 3 decimal places.

step-by-step explanation:

most likely the answer is a.

alice wins if a total of 5 is rolled. finn wins if a total of 9 is rolled.

2x + 8

step-by-step explanation:

step-by-step explanation:

part a. the differences are decreasing, so we know the sequence is not arithmetic. the ratios are constant (=3/4), so we know the sequence is geometric.

part b. from part a, we know the common ratio is 3/4, so each term is 3/4 of the one before. the initial term is the number of gallons at h=1.

g[h] = (3/4)·g[h-1]

g[1] = 384 . . . . initial value required for a recursive definition

part c. the general formula for a geometric sequence is

a[n] = a[1]·r^(n-1)

we have a[1] = 384, r = 3/4, and the term number given by h. the formula that follows is

g[h] = 384·(3/4)^(h-1)

part d. filling in the value and doing the arithmetic, we have

g[12] = 384·(3/4)^11 ≈ 384·0.042235136 ≈ 16.2183 . . gallons

part e. each gallon is 4 quarts, so

16.2183 gal × 4 qt/gal = 64.8732 qt