When ringing up a customer, a cashier needs 10 seconds to process payment as well as 2 second to scan each item being purchased. if it takes 42 seconds to ring up a customer, how many items are being purchased?

The total number of dental clinics total for the last 12 months was recorded

Tamar is measuring the sides and angles of tuv to determine whether it is congruent to the triangle below. which pair of measurements would eliminate the possibility that the triangles are congruent

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.