The three straight paths, , , and , meet each other at three points, A, B, and C. How do these points of intersection differ from each other? Explain the differences in terms of the angles that you see. Also look at the length of the side opposite each angle. What pattern do you see regarding the measurements? In what situation would all the points of intersection resemble one another?

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.

Here is another math questions. i will keep asking different questions. 4^2x=6

Pranav and molly are selling pies for a school fundraiser. customers can buy blueberry pies and pumpkin pies. pranav sold 6 blueberry pies and 4 pumpkin pies for a total of $106. molly sold 6 blueberry pies and 3 pumpkin pies for a total of $90. find the cost of each of one blueberry pie and one pumpkin pie