Amilkshake vendor sells shakes in three different flavors: mango, strawberry, and chocolate. this table gives the number of shakes of each flavor sold during three shifts on one day. mango strawberry chocolate shift 1 16 13 29 shift 2 26 19 45 shift 3 6 11 0 total sales were $419 in the first shift, $649 in the second shift, and $96 in the third shift. if you form a linear system representing the data in the table and create a matrix from it, the determinant is 578. what is the price of one chocolate shake?

(20 points) a bank has been receiving complaints from real estate agents that their customers have been waiting too long for mortgage confirmations. the bank prides itself on its mortgage application process and decides to investigate the claims. the bank manager takes a random sample of 20 customers whose mortgage applications have been processed in the last 6 months and finds the following wait times (in days): 5, 7, 22, 4, 12, 9, 9, 14, 3, 6, 5, 15, 10, 17, 12, 10, 9, 4, 10, 13 assume that the random variable x measures the number of days a customer waits for mortgage processing at this bank, and assume that x is normally distributed. 2a. find the sample mean of this data (x ě…). 2b. find the sample variance of x. find the variance of x ě…. for (c), (d), and (e), use the appropriate t-distribution 2c. find the 90% confidence interval for the population mean (îľ). 2d. test the hypothesis that îľ is equal to 7 at the 95% confidence level. (should you do a one-tailed or two-tailed test here? ) 2e. what is the approximate p-value of this hypothesis?