For three consecutive years, sam invested some money at the start of the year. the first year, he invested x dollars. the second year, he invested $2,000 less than 5/2 times the amount he invested the first year. the third year, he invested $1,000 more than 1/5 of the amount he invested the first year.

during the same three years, sally also invested some money at the start of every year. the first year, she invested $1,000 less than 3/2 times the amount sam invested the first year. the second year, she invested $1,500 less than 2 times the amount sam invested the first year. the third year, she invested $1,400 more than 1/4 of the amount sam invested the first year.

if sam and sally invested the same total amount at the end of three years, the amount sam invested the first year is $ and the amount sally invested the last year is $ .

Someone this asap for a group of students attends a basketball game. * the group buys x hot dogs at the concession stand for $2 each. * the group buys y drinks at the concession stand for $3 each. the group buys 29 items at the concession stand for a total of $70. how many hot dogs did the group buy?

15 points! write the slope-intercept form of the equation of the line through the given point with the given slope. use y-y = m(x-x) to solve. through (2,5) slope= undefined

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.