Evelyn has $524.96 in her checking account. She must maintain a $500 balance to avoid a fee. She wrote a check for $32.50 today. Write an inequality that would be used to solve for the least amount of money she needs to deposit to avoid a fee. 524.96 − 32.50 + x ≥ 500 524.96 − 32.50 + x ≤ 500 524.96 + 32.50 − x ≥ 500 524.96 + 32.50 − x ≤ 500

A. 127 cm^2 b. 144.5 cm^2 c. 172 cm^2 d. 50 cm^2

At the beginning of year 1, carlos invests $600 at an annual compound interest rate of 4%. he makes no deposits to or withdrawals from the account. which explicit formula can be used to find the account's balance at the beginning of year 5? what is, the balance?

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.