Two circles with centers p and q touch at point t. a line through t meets the first circle again at b and the second at c. show the side bp is parallel to side cq

The difference of three and the reciprocal of a number is equal to the quotient of 20 and the number. find the number.

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.

Will’s boss has asked him to compile the credit scores of everyone in his department. the data that will collected is shown in the table below. what is the mode of the credit scores in will’s department? (round to the nearest whole point, if applicable.) 634 667 644 892 627 821 857 703 654 a. 667 b. 722 c. 627 d. there is no mode in this group.