A) Factorise a^2 - b^2

B) simplify fully (x^2+3)^3 - (x^2-1)^2

Aculture started with 4,000 bacteria. after 5 hours, it grew to 5,200 bacteria. predict how many bacteria will be present after 19 hours. round your answer to the nearest whole number.

Due to a packaging error, 4 cans labeled diet soda were accidentally filled with regular soda and placed in a 12 pack carton of diet soda. two cans were randomly selected from this 12 pack. what is the probability that both cans were regular soda?

(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?