Noa was walking in the forest and measured the circumference of two trees that he found. The first tree measured 37 and StartFraction 5 over 8 EndFraction inches around, and the second tree measured 45 and one-third inches around. Noa wanted to find the difference of the circumferences of the two trees. He recorded his steps in the table. Steps Noa’s work Step 1 45 and one-third minus 37 and StartFraction 5 over 8 EndFraction Step 2 45 and StartFraction 8 over 24 EndFraction minus 37 and StartFraction 15 over 24 EndFraction Step 3 44 and StartFraction 32 over 24 EndFraction minus 37 and StartFraction 15 over 24 EndFraction Step 4 44 and StartFraction 32 over 24 EndFraction minus 37 and StartFraction 15 over 24 EndFraction = 8 and StartFraction 17 over 24 EndFraction In which step did Noa first make an error? Step 1 Step 2 Step 3 Step 4

What is the remainder when 2872 is divided by 76? a) 51 b) 57 c) 60 d) 63

Write the equation of a line that is perpendicular to the given line and that passes through the given point. –3x – 6y = 17; (6, 3) y = x – 9 y = 2x – 9 y = –2x – 9 y = x + 0 3. is the relationship shown by the data linear? if so, model the data with an equation. x y 1 5 5 10 9 15 13 20 the relationship is linear; y – 5 = (x – 1). the relationship is not linear. the relationship is linear; y – 5 = (x – 1). the relationship is linear; y – 1 = (x – 5). write an equation in point-slope form for the line through the given point with the given slope. (–10, –1); m = y + 10 = (x + 1) y – 1 = (x – 10) y – 1 = (x + 10) y + 1 = (x + 10) 5. write an equation for each translation of . 6.5 units up y + 6.5 = | x | y = | 6.5 x | y = | x | + 6.5 y = | x | – 6.5 6. write an equation for each translation of . 5.5 units right y = | x | + 5.5 y = | x – 5.5 | y = | x | – 5.5 y = | x + 5.5 | 7. which equation translates y = | x | by 8 units to the left? y = | x | – 8 y = | x | + 8 y = | x – 8| y = | x + 8|

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.