As you are going through family records, you notice that your great-grandfather purchased 500 shares at $2.10 a share for a company called Bubba Gump Shrimp. When you search the internet for this company, you found that they list the value of their stock at $154.16 per share. You decide to sell all the shares and invest this into a retirement fund paying 9% annual interest. If you were to sell all your great-grandfathers shares, how much would you have to invest in your retirement?

Find the length of the diagonal of the rectangle. round your answer to the nearest tenth. || | | 8 m | | | | 11 m

Hich equation can pair with x + 2y = 5 to create an inconsistent system? 2x + 4y = 3 5x + 2y = 3 6x + 12y = 30 3x + 4y = 8

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.