Juan wants to deposit $700 into savings accounts at three different banks: Bank of Chance, Merchant Bank, and Utopian Financing. He will deposit four times as much into Merchant Bank as Bank of Chance because they offer a higher interest rate. He also expects the Utopian Financing deposit to be only 25% of the total of the other two deposits. How much will Juan deposit into the Utopian Financing savings account? a $112 b $140 c $175 d $448

Describe the possible echelon forms of the standard matrix for a linear transformation t where t: set of real numbers is onto.

Write a fraction less than 1, which has a denominator of 6 and is greater than 3/4 plz answer !

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.