Nthe “folklore” of mathematics, g. h. hardy, a twentieth-century mathematician, remarked to a colleague that the number 1,729 was “rather a dull number.” his colleague responded, “no, hardy! it is a very interesting number. it is the smallest number expressible as the sum of 2 cubes in 2 different ways.” which of the following are those 2 ways?

i. 1^3 + 12^3
ii. 2^3 + 11^3
iii. 4^3 + 8^3
iv. 9^3 + 10^3

select your answer.

i and ii

i and iii

i and iv

ii and iii

iii and iv

Which graph represents the equation y =4x

What is the least common multiple for 6 and 8? what is the least common multiple for 4 and 12 ? what is the least common multiple for 11 and 12? what is the least common multiple for 3 and 6?

(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?