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Mathematics

2 answers:

zalisa [80]3 years ago

8 0

Answer:

$200

Step-by-step explanation:

2.5 % commission on sales

he sold 8000

his commission will be sales * 2.5%

commission = 8000 * .025

= 200

mart [117]3 years ago

3 0

Answer:

200

Step-by-step explanation:

Start by changing 2.5% into a decimal. A percent means divide by 100

2.5 / 100 = 0.025

Now multiply the percent by the actual sales.

Sales = 8000 dollars.

Pay = Sales * %

Pay = 8000 * 0.025

Pay = 200 dollars

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Eights rooks are placed randomly on a chess board. What is the probability that none of the rooks can capture any of the other r

erastova [34]

Answer:

The probability is $\frac{56!}{64!}$

Step-by-step explanation:

We can divide the amount of favourable cases by the total amount of cases.

The total amount of cases is the total amount of ways to put 8 rooks on a chessboard. Since a chessboard has 64 squares, this number is the combinatorial number of 64 with 8, $64 \choose 8 .$

For a favourable case, you need one rook on each column, and for each column the correspondent rook should be in a diferent row than the rest of the rooks. A favourable case can be represented by a bijective function $f : A \rightarrow A ,$ with A = {1,2,3,4,5,6,7,8}. f(i) = j represents that the rook located in the column i is located in the row j.

Thus, the total of favourable cases is equal to the total amount of bijective functions between a set of 8 elements. This amount is 8!, because we have 8 possibilities for the first column, 7 for the second one, 6 on the third one, and so on.

We can conclude that the probability for 8 rooks not being able to capture themselves is

$\frac{8!}{64 \choose 8} = \frac{8!}{\frac{64!}{8!56!}} = \frac{56!}{64!}$