ail Delivery A local postal carrier distributes first-class letters, advertisements, and magazines. For a certain day, she distributed the following numbers of each type of item. Delivered to First-class letters Ads Magazines Home 302 382 179 Business 711 1005 82 Send data to Excel If an item of mail is selected at random, find the probability for the following. Round your answers to at least three decimal places

Data are collected to see how many ice-cream cones are sold at a ballpark in a week. day 1 is sunday and day 7 is the following saturday. use the data from the table to create a scatter plot.

The graph of y=x3 is transformed as shown in the graph below. which equation represents the transformed function?

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.