Suppose an online electronics retailer is running two different specials. One deal will get you 10% off your total purchase, and the other deal is worth $20 off a purchase
of $100 or more. Assuming you spend at least $100, if you are allowed to use both
deals, in which order do you want to apply them? Try the calculation both ways with
a few different prices, or write a formula to represent each option.

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.

Can you divide 25 into 4 equal groups? explain why or why not.

If the equation of a line containing the midsegment of a triangle is y = -1/4x -11, what is the slope of the triangle side that is opposite the midsegment (the one not touching it). explain how you know.