Question

Mathematics

1 answer:

Taya2010 [7]3 years ago

5 0

Answer:

the ratio of Jan's average walking rate to Bev's average walking rate is 3/4 or 3 : 4

Step-by-step explanation:

Let x and y represent jan and Bev's average walk rate.

Also t represent the time taken for Bev to walk 4 miles, so it will take jan 2t time to walk 6 miles

Given that;

It takes Jan twice as many hours to walk 6 miles as it takes Bev to walk 4 miles

For Bev;

y = 4/t

For Jan;

x = 6/(2t) = 3/t

the ratio of Jan's average walking rate to Bev's average walking rate is;

x/y = (3/t)/(4/t) = 3/4

the ratio of Jan's average walking rate to Bev's average walking rate is 3/4 or 3 : 4

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

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Answer:

9.11*10^-4 %

Step-by-step explanation:

To find the probability, you simply need to find the possible outcomes that allows no rooks to be in danger, and the possible amount of ways to place the rooks.

For the first outcome, you start by putting 1 rook in the first columns, you have 8 possible rows to do this. The next rook in the next column will only have 7 possible rows, as you have to exclude the one where the previous rook is located. The next rook, 6 possibilities, the next 5, and so on. So we conclude that the total amount of ways so that none of the rooks can capture any of the other rooks is 8*7*6*5*4*3*2*1 = 8! = 40320

In order to find the total amount of ways to place the rooks, you can just use a combinatoric:

$\left[\begin{array}{ccc}64\\8\end{array}\right]= \frac{64!}{8!(64-8)!} = 4.43*10^9$