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krazyapril4601
25.11.2021 •
Mathematics
Diesel fuel for automobiles and trucks is a mixture of hydrocarbons that can be modeled by C16H34. How many grams of O2 are needed to react with 0.500 mol C16H34
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Ответ:
a. 336
b. 14.01%
c. 0.2%
Step-by-step explanation:
a. We have that the number of zinfandel bottles is 8 and that the number of zinfandel served is 3, therefore:
n = 8 and r = 3
we can calculate it by means of permutation:
nPr = n! / (n-r)!
replacing:
8P3 = 8! / (8-3)!
8P3 = 336
Which means there are 336 ways.
b. First we must calculate the ways to choose 2 bottles of each variety, through combinations:
nCr = n! / (r! * (n-r)!
We know that there are 8 bottles zinfandel, 10 of merlot, and 12 of cabernet, and we must choose 2 of each, therefore it would be:
8C2 * 10C2 * 12C2
8! / (2! * (8-2)! * 10! / (2! * (10-2)! * 12! / (2! * (12-2)!
28 * 45 * 66 = 83160
Now we must calculate the total number of ways, that is, choose 6 bottles of the 30 total (8 + 10 + 12)
30C6 = 30! / (6! * (30-6)! = 593775
Thus:
83160/593775 = 0.1401
In other words, the probability is 14.01%
c. In this case, we must calculate the number of ways of 8 bottles zinfandel, 10 of merlot, and 12 of cabernet choose 6, that is to say that they are all of the same variety, therefore:
8C6 + 10C6 + 12C6
8! / (6! * (8-6)! + 10! / (6! * (10-6)! + 12! / (6! * (12-6)!
28 + 210 + 924 = 1162
And that divide it by the total amount that we calculated the previous point, 30C6 = 593775
Thus:
1162/593775 = 0.002
In other words, the probability 0.2%