Use the geometric series f(x)equalsStartFraction 1 Over 1 minus x EndFraction equalsSummation from k equals 0 to infinity x Superscript k, for StartAbsoluteValue x EndAbsoluteValueless than1, to find the power series representation for the following function (centered at 0). Give the interval of convergence of the new series. f(9x)equalsStartFraction 1 Over 1 minus 9 x EndFraction Which of the following is the power series representation for f(9x)? A. Summation from k equals 0 to infinity StartFraction 1 Over 1 minus (9 x )Superscript k EndFraction B. Summation from k equals 0 to infinity (9 x )Superscript k C. Summation from k equals 0 to infinity x Superscript 9 k D. Summation from k equals 0 to infinity 9 x Superscript k The interval of convergence is nothing.

In dire need~! describe how to use area models to find the quotient 2/3 divided by 1/5. check your work by also finding the quotient 2/3 divided by 1/5 using numerical operations only.

Atown has a population of 12000 and grows at 3.5% every year. what will be the population after 7 years, to the nearest whole number?

Afriend of mine is giving a dinner party. his current wine supply includes 10 bottles of zinfandel, 8 of merlot, and 11 of cabernet (he only drinks red wine), all from different wineries. (a) if he wants to serve 3 bottles of zinfandel and serving order is important, how many ways are there to do this? ways (b) if 6 bottles of wine are to be randomly selected from the 29 for serving, how many ways are there to do this? ways (c) if 6 bottles are randomly selected, how many ways are there to obtain two bottles of each variety? ways (d) if 6 bottles are randomly selected, what is the probability that this results in two bottles of each variety being chosen? (round your answer to three decimal places.) (e) if 6 bottles are randomly selected, what is the probability that all of them are the same variety? (round your answer to three decimal places.)