Let c ∈ (a, b) and let d ∈ r. define f : [a, b] → r as ( d if x = c, f (x) : = 0 if x = c. prove that f ∈ r[a, b] and compute r b a f using the definition of the integral (but feel free to use the propositions of this section).

At least two people have the same birthday in a school of 150 students

When you have 25 numbers, and jake picks 3 random numbers and puts them back, what is the chance bob has of picking those 3 numbers when he picks 6 random numbers (without putting them back)? explain.

Apoll is being conducted at a mall nothingto obtain a sample of the population of an entire country. what is the frame for this type of​ sampling? who would be excluded from the survey and how might this affect the results of the​ survey? what is the frame for this type of​ sampling? a. the frame is people who need new clothes. b. the frame is people who shop at the mall. c. the frame is people who like to shop. d. the frame is the entire population of the country. who would be excluded from the survey and how might this affect the results of the​ survey? a. any person that does not need new clothes is excluded. this could result in sampling bias due to undercoverage. b. any person who does not shop at the mall is excluded. this could result in sampling bias due to undercoverage. c. any person who does not shop at the mall is excluded. this could result in nonresponse bias due to people not participating in the poll. d. there is nobody that is being excluded from the survey.