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Time (minutes) amount of water (gallons) practice 1. jin fills up a 510-gallon pool in the backyard for her children. she fills it with the garden hose at a rate of 17 gallons per minute. after it is filled, she lets it sit for 30 minutes in order to let the water temperature rise. the children then get in and have fun for an hour. the pool loses about 5 gallon of water each minute due to their splashing and playing. at the end of the hour, they tear the pool while getting out, which causes a leak the pool then begins to lose water at a rate of 2 gallons per minute. a. complete the table to show the amount of water in the pool after each minute. b. create a graph to model the problem situation. include when the pool will be empty. c. write a piecewise function that models this problem situation. explain your reasoning for each piece of the function. d. identify the x- and y-intercept. explain what they mean in terms of the problem situation, atamantha a cul 80 100 120 150 200 ning, inc

Acone is placed inside a cylinder. the cone has half the radius of the cylinder, but the height of each figure is the same. the cone is tilted at an angle so its peak touches the edge of the cylinder’s base. what is the volume of the space remaining in the cylinder after the cone is placed inside it?

Amanufacturing firm has been averaging 16.8 orders per week for several years. however, during a recession, orders appeared to slow. suppose the firm’s production manager randomly samples 31 weeks and finds an average of 15.6 orders with a standard deviation of 2.3 orders. using a 0.025 significance level, test whether the mean number of orders has decreased. type the full 5 step procedure into the answer box, then for multiple choice practice, answer the following: 1. what is the name and symbol of the parameter that you are testing? 2. what is the symbol and value of the point estimate of that parameter? 3. what distribution are you using to test this parameter? 4. what is the critical value? 5. what is the test statistic value? 6. what is the p-value?