The chs baseball team was on the field and the batter popped the ball up. the equation b(x)=80t-16t^2+3.5 represents the height of the ball above the ground in feet as a function of time in seconds. how long will the catcher have to get in position to catch the ball before it hits the ground? round to the nearest second.

Select the correct answer. what is the exact value of sin (157.5°)? a. 'sqrt(2 - sqrt(2))/2 b. *"-"'sqrt(2 + sqrt(2))/29 c.'sqrt(2 + sqrt(2))/4" d. "-"sqrt(2 + sqrt(2))/4)

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.

F. a fair coin is thrown in the air four times. if the coin lands with the head up on the first three tosses, what is the probability that the coin will land with the head up on the fourth toss? a. 0 b. 1/16 c. 1/8 d. 1/2