$10 bet between you and me. At any time during the game, I can ask to double it. If you accept we both put in another $10 and if you win, you win the $20 and if you lose, you lose it all. If you reject, you lose the initial $10. What is the minimum probability you would take to accept the double

Arecipe uses 2 cups of sugar to make 32 brownies. how many cups of sugar are needed to make 72 brownies?

(b) suppose that consolidated power decides to use a level of significance of α = .05, and suppose a random sample of 100 temperature readings is obtained. if the sample mean of the 100 temperature readings is x⎯⎯ = 60.990, test h0 versus ha and determine whether the power plant should be shut down and the cooling system repaired. perform the hypothesis test by using a critical value and a p-value. assume σ = 5. (round your z to 2 decimal places and p-value to 4 decimal places.)

Use the ratio test to determine whether ∑n=14∞n+2n! converges or diverges. (a) find the ratio of successive terms. write your answer as a fully simplified fraction. for n≥14, limn→∞∣∣∣an+1an∣∣∣=limn→∞.