The pressure of a fluid flowing through a closed system, P, after t seconds can be modeled by the function P(t) = 100 + 30 sin (12 pi/5 t). Answer parts (a) through (c) below.
(a) In the interval [0, 1], determine the times at which the pressure of the fluid is 100 mmHg. The solution set is {}.
(b) In the interval [0, 1], determine the times at which the pressure of the fluid is 130 mmHg. The solution set is {}.
(c) In the interval [0, 1], determine the times at which the pressure of the fluid is between 100 and 105 mmHg. Interval endpoints are rounded to the nearest hundredth.
A. (0, 0.21) U(0.42, 0.44) U (0.81, 0.83)
B. (0, 0.02)U(0.39, 0.42)U(0.83, 0.86)
C. (0, 0.83)U(0.86, 1)
D. (0, 0.22)
E. (0.02, 0.21) U (0.42, 0.44)U(0.86, 1)
F. (0, 0.21)

3. a sum of $2700 is to be given in the form of 63 prizes. if the prize is of either $100 or $25, find the number of prizes of each type.

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.

Abag contains pieces of paper numbered from 5 to 9. a piece of paper is drawn at random. what is the theoretical probability of drawing a number less than 8?