What is the sine value of pi over 6?

In the past, professional baseball was played at the astrodome in houston, texas. the astrodome has a maximum height of 63.4 m. the height of a baseball t seconds after it is hit straight up in the air with a velocity of 45 ft/s is given by h = -9.8t2 + 45t + 1. will a baseball hit straight up with this velocity hit the roof of the astrodome? use the discriminant to explain your answer.

Abag contains 3 red marbles 4 white marbles and 5 blue marbles if one marble is drawn from the bag what is the probability that the marble will be blue

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.