10. In list T, consists of 30 positive decimals. None of which are integers. The sum of the 30 decimals is S. The estimated sum of the 30 decimals is E. The estimated sum is calculated as follows: Each decimal in T whose tenth digit is even is rounded up to nearest integer, and each decimal in T whose tenth digit is odd is rounded down to nearest integer. E is sum. If 1/3 of decimals in T have even tenth digit that is even, what is a possible value of E-S? I. -16 II. 6 III. 10 A. I only B. I and II only C. I and III only D. II and III only E. I, II, and III

Jude is making cement for a driveway. the instructions show the amount of each ingredient to make 1 batch of cement. complete each statement to adjust the ingredients for each new situation if jude uses these instructions.

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.

Aclothing designer is selecting models to walk the runway for her fashion show. the clothes she designed require each model’s height to be no more than y inches from 5 feet 10 inches, or 70 inches. which graph could be used to determine the possible variance levels that would result in an acceptable height, x?