(a) Prove that the sequence defined by x1 = 3 and xn+1 = 1 4 − xn converges. 60 Chapter 2. Sequences and Series (b) Now that we know lim xn exists, explain why lim xn+1 must also exist and equal the same value. (c) Take the limit of each side of the recursive equation in part (a) to explicitly compute lim xn.

Abox of chocolates costs $7. which equation relates the number of boxes sold (x) and total cost of the boxes sold (y)?

Meg constructed triangle poq and then used a compass and straightedge to accurately construct line segment os, as shown in the figure below, which could be the measures of angles pos and angle poq?

(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?