For a short time after a wave is created by wind, the height of the wave can be modeled using y = a sin 2πt/t , where a is the amplitude and t is the period of the wave in seconds.

part 1: write an equation for the given function given the amplitude, period, phase shift, and vertical shift.
amplitude = 4 , period = 4π , phase shift = -4/3 π , vertical shift = -2

part 2: write an equation for the given function given the period, phase shift, and vertical shift.
cotangent function, period = π , phase shift = -1/3 π , vertical shift = 2

What are the equivalent ratios for 24/2= /3= /5.5=108/ = /15

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.

Marking brainliest rewrite the equation x = 65 - 60p by factoring the side that contains the variable p.