How to solve 2/3:x::4.5:2 and 2/3%:1/5::50:x

Mathematics

1 answer:

solong [7]3 years ago

7 0

A) x = 0.296

B) x= 15

Step-by-step explanation:

Step 1:

(2/3) : x :: 4.5 :2

By using expansion method,

(2/3) × 2 = 4.5 x

x= (2/3) × 2 / 4.5

x = 0.296

Step 2:

(2/3) : (1/5) :: 50 :x

By using expansion method,

(2/3) x = (1/5) × 50

x= (1/5) × 50 / (2/3)

x = 15

You might be interested in

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

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