The entire company went together to buy lottery tickets. Inside to save are two different types of lottery tickets. The mega million ticket cost five dollars each and the scratch off ticket cost two dollars each. There are 60 tickets totaling $246. How many of each lottery tickets at the company purchase

Solve the following simultaneous equation by using an algebraic method (either substitution or elimination) 2x + 3y=-4 4x-y=11

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.

Which of these angles are complementary? a. 45o and 45o b. 63o and 117o c. 45o and 135o d. 90o and 45o