Which of the following steps is needed to inscribe a circle in a triangle

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.

30 points! here is a you are the new manager at trusty goods wholesale produce. you need to figure out how to adjust the amount of produce in your notes after the events of the day: you got 5 more crates of bananas someone returned 2 crates of apples a worker dropped a crate of grapes (oh no! , you had to throw them out) you sold a crate of bananas you sold 5 crates of apples can you write an expression to describe your day using: "a" for crates of apples "b" for crates of bananas and "g" for crates of grapes? make sure the expression is in simplest form question 2 (3 points) explain your steps using sentences.

Consider the enlargement of the pentagon. what is the value of x, rounded to the nearest tenth? 2.1 centimeters 3.3 centimeters 7.0 centimeters 15.0 centimeters