Between the years of 1947 and 1956, earthenware jars containing what are known as the Dead Sea Scrolls were found in caves along the coast of Jerusalem in the Dead Sea. Upon radiometric testing, it was found that the scrolls were wrapped in material that contained about 79 percent of the original carbon-14. Archaeologists estimated that the scrolls are about 1,900 years old. Are they right? Using the half-life of carbon-14 (5,730 years), prove or disprove this estimate age. Describe how you are testing this hypothesis.

Atemperature of 1.64◦f corresponds to answer in units of ◦c.

Common binomial factor of 6x(3x+7)+5(3x+7)

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.)