James is fencing off a triangular region for his cats to play in. from the first fence post, he walks 13 meters in a straight line and plants the second fence post. from there, james heads in another direction for 5 meters and places the third fence post. if the distance between the first and third fence posts is 9 meters, find the area of the enclosed region. round the answer to the nearest tenth.

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What would be the reasons for lines 3 and 4? a. addition property; subtraction property b. addition property; solve c. substitution property; subtraction property d. substitution property; prove

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.)