A cookie baker has an automatic mixer that turns out a sheet of dough in
the shape of a square 12 inches wide. His cookie cutter cuts 3-inch
diameter circular cookies as shown at right. The supervisor complained
that too much dough was being wasted and ordered the baker to find out
what size cookie would have the least amount of waste.

Analyze this situation and determine how much cookie dough is “wasted” when 3-inch cookies are cut. Write a note to the supervisor explaining your results. Justify your conclusion.

Select the correct answer. what is the exact value of sin (157.5°)? a. 'sqrt(2 - sqrt(2))/2 b. *"-"'sqrt(2 + sqrt(2))/29 c.'sqrt(2 + sqrt(2))/4" d. "-"sqrt(2 + sqrt(2))/4)

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.

F. a fair coin is thrown in the air four times. if the coin lands with the head up on the first three tosses, what is the probability that the coin will land with the head up on the fourth toss? a. 0 b. 1/16 c. 1/8 d. 1/2