Order numbers from greatest to least -4.55, -4.556,- 4 5/8, 4 5/8

Triangle xyz, with vertices x(-2, 0), y(-2, -1), and z(-5, -2), undergoes a transformation to form triangle x? y? z? , with vertices x? (4, -2), y? (4, -3), and z? (1, -4). the type of transformation that triangle xyz undergoes is a . triangle x? y? z? then undergoes a transformation to form triangle x? y? z? , with vertices x? (4, 2), y? (4, 3), and z? (1, 4). the type of transformation that triangle x? y? z? undergoes is a .

If the car had not hit the fence, how much farther would it have skidded? solve the skid-distance formula to find the extra distance that the car would have traveled if it had not hit the fence. round your answer to two decimal places. note that unit conversion is built into the skid distance formula, so no unit conversions are needed.

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.