Which statement best compares the value of the 4 in each of these numbers? a: 16.942 b: 9.214 a) (40 < 400) the value of the 4 in a is 40, and the value of the 4 in b is 400. b) (.4 < .004) the value of the 4 in a is .4, and the value of the 4 in b is .004. c) (.04 > .004) the value of the 4 in a is .04, and the value of the 4 in b is .004. d) (.004 > .04) the value of the 4 in a is .004, and the value of the 4 in b is .04.

This week, conrad will work 1 3/4 times longer than last week. giovanni will work 1 1/3 times longer than last week. sally will work 2/3 the number of hours she worked last week. match each employee's name to the number of hours he or she will work this week

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.

50 points and will mark brainlest if you were constructing a triangular frame, and you had wood in the length of 4inches, 4 inches, and 7 inches, would it make a triangle? would you be able to create a frame from these pieces of wood? yes or no? = explain your mathematical thinking: