Ethan, Alexis and Daniel keep money in metal banks. Ethan, Alexis and Daniel count the money in their metal banks. Ethan has twenty-six dimes in his bank. Daniel has twenty-six pennies in his bank. Alexis has twenty-six one-dollar bills in her bank. Daniel thinks they have the same amount of money because they all have the same number of coins or bills in their banks. Ethan says Alexis has ten times what Ethan has in his bank and that Daniel has one-tenth what Ethan has in his bank. Alexis is not sure Ethan is correct. Alexis thinks Ethan has one-tenth of what she has in her bank and ten times what Daniel has in his bank. Who is correct? Show all your mathematical thinking.

Richard save $32 in march he saved $48 in april and $38 in may then richard spent $113 on a keyboard how much money does richard have left

(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.)

Aprisoner is trapped in a cell containing three doors. the first door leads to a tunnel that returns him to his cell after two days of travel. the second leads to a tunnel that returns him to his cell after three days of travel. the third door leads immediately to freedom. (a) assuming that the prisoner will always select doors 1, 2 and 3 with probabili- ties 0.5,0.3,0.2 (respectively), what is the expected number of days until he reaches freedom? (b) assuming that the prisoner is always equally likely to choose among those doors that he has not used, what is the expected number of days until he reaches freedom? (in this version, if the prisoner initially tries door 1, for example, then when he returns to the cell, he will now select only from doors 2 and 3.) (c) for parts (a) and (b), find the variance of the number of days until the prisoner reaches freedom. hint for part (b): define ni to be the number of additional days the prisoner spends after initially choosing door i and returning to his cell.