A ship X sailing with velocity (21 km/h, 052°) observes a light from the lighthouse due North. The bearing of the lighthouse from the ship, 20 minutes later, is found to be 312°, calculate correct to three significant figures: (i) the original distance, in kilometres, when the lighthouse is due west of the ship from the time when it is due North of the ship.
(ii) the time, in minutes, when the lighthouse is due West of the ship from the time when it is due North of the ship.
(iii) the distance, in km, of the ship from the lighthouse when the lighthouse is due West of the ship.

(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?