6,500,000 65,000 complete the pattern

Pepe is going to spin the following spinner 800 times. the spinner is divided into equal sections. a. exactly 160 timesb. clost to 160 times but probably not exactly 160 timesc. exactly 640 timesd. close to 640 times but not probably not exactly 640 times. me

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.

Sanjay solved the equation below. which property did he use to determine that 7x+42=42 is equivalent to 7(x+6)=42 7x+42=42 7x=0 x=0