Jeffrey is saving up for a down payment on a car. he plans to invest $2,000 at the end of every year for 4 years. if the interest rate on the account is 2.15% compounding annually, what is the present value of the investment?

The sixth grade art students are making a mosaic using tiles in the shape of right triangles. each tile has leg measures of 3 centimeters and 5 centimeters. i f there are 200 tiles in the mosaic what is the area of the mosaic.

What ia the sum if the first 7 terms of the geometric series

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.