Environmentalists have found that in some climates, there are some animals whose rate of population can be modeled by a sinusoidal function. For example, the beetle population in Alaska can be predicted by the function (Function in the picture)

where B(t) represents the total number of beetles over t months starting with December. How many beetles are expected to be in Alaska in the month of May?

(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?

Is the number 128.439 a rational number

At the beginning of the year, adrian's savings account balance was \$28$28. each week, he deposits another \$15$15 into that account, and he doesn't spend any of his savings. is his savings account balance proportional to the number of weeks since the start of the year?