In the following diagram line C intersects line D. Figure may not be drawn to scale.

Using complete sentences, classify the relationship between ∠7 and ∠8 created by the intersection of lines C and D.
Use complete sentences to explain how the special angles created by the intersection of lines C and D can be used to solve for y.
Solve for y and find the measures of ∠7 and ∠8

Aschool had an election where the candidates received votes in the ratio 1: 2: 3. if the winning candidate received 210 votes, how many total people voted in the election?

Question 4 of 102 pointsjuliana had $96, which is eight times as much money as al had. how mucmoney did al have? select the correct solution method below, representingals money with x.

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.