Given sin y = -4/5, where π < y < 3π/2, and cos x = 12/13, where 0 < x < π/2. Find the exact value of sin (x - y). Please show all the exact steps in order I am really lost on how to solve this.

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.

Given a normal distribution with µ =50 and σ =4, what is the probability that 5% of the values are less than what x values? between what two x values (symmetrically distributed around the mean) are 95 % of the values? instructions: show all your work as to how you have reached your answer. don’t simply state the results. show graphs where necessary.

If you do this you are getting 20+ points so can you hurry plsphil is riding his bike. he rides 29 miles in 2 hours, 43.5 miles in 3 hours, and 58 miles in 4 hours. find the constant of proportionality and write an equation to describe the situation. let x represent the number of hours.