Below is a two-column proof incorrectly proving that the three angles of δpqr sum to 180°: statements reasons ∠qry ≅ ∠pqralternate interior angles theorem draw line zy parallel to segment pq construction m∠zrp + m∠prq + m∠qry = m∠zry angle addition postulate ∠zrp ≅ ∠rpq alternate interior angles theorem m∠rpq + m∠prq + m∠pqr = m∠zry substitution m∠zry = 180° definition of a straight angle m∠rpq + m∠prq + m∠pqr = 180° substitution which statement will accurately correct the two-column proof? a.) the measure of angle zry equals 180° by definition of supplementary angles. b.) angles qry and pqr should be proven congruent after the construction of line zy. c.) the three angles of δpqr equal 180° according to the transitive property of equality. d.) line zy should be drawn parallel to segment qr.

The graph below shows the amount of money left in the school’s desk fund, f, after d desks have been purchased. for each new desk that is purchased, by how much does the amount of money left in the school’s desk fund decrease?

Which ordered pair is a solution of the equation? y + 5 = 2(2+1) choose 1 answer ® only (5,10 ® only (-1,-5) © both (5, 10) and (-1,-5) 0 neither

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.