At a raffle 100 tickets are sold for 1 prize of $100 and 3 consolation prizes of $20. What price should the ticket be sold for if the goal is to make the raffle a fair game?

You are in charge of the customer service phone line with many employees. at the end of each phone callthe customers are asked to rate their service from 1 to 5 stars, with 5 being the best. you find the averagerating for 20 randomly selected employees and decide you want to improve the ratings so you require thoseemployees to go through a new training program. you then wait a week and find the new average rating foreach employee. the average change is an increase in 1.3 stars with a standard devation of .9 stars.(a) is this data paired or not paired? (b) what are the null and alternative hypothesis being tested? (c) what is the t-statistic you would use? write the general formula and the final calculation.(d) sketch a t-distribution, label your t-statistic and the probability you would be interested in:

Mr. chen is parking in a lot downtown. the graph shows the relationship between the time and the total cost of parking. evaluate the function for and input of 10.

Find an equation for the line that is perpendicular to the graph of 5x-3y=9 if the two lines intersect at x=30