Answer:
The probability is
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,
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 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
Hey there!
<u>Solve </u><u>the </u><u>equation</u><u>:</u>
x = -10 ✅
2(x + 3) = x - 4
<em><u>Distributive property:</u></em> A(B + C) = AB + AC
<em>></em><em>></em><em> </em><em>Substitute </em><em>2</em><em> </em><em>for</em><em> </em><em>A</em><em> , </em><em>x</em><em> </em><em>for </em><em>B</em><em> </em><em>and </em><em>3</em><em> </em><em>for</em><em> </em><em>C</em><em> : </em>
2(x) + 2(3) = x - 4
2x + 6 = x - 4
<em>></em><em>></em><em> </em><em>Subtract </em><em>6</em><em> </em><em>from </em><em>each </em><em>side </em><em>:</em>
2x + 6 - 6 = x - 4 - 6
2x = x - 10
<em>></em><em>></em><em> </em><em>Subtract </em><em>x </em><em>from </em><em>both </em><em>sides </em><em>:</em>
2x - x = x - 10 - x
x = -10
▪️Let's check our work :
2(-10 + 3) ⇔ 2(-7) ⇔ -14
-10 - 4 ⇔-14
Therefore, your answer is x = -10
Learn more about first-degree equations :
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Answer:
50
Step-by-step explanation:
5 x 7+5 x 3
5 x 7= 35+5 x 3
35+5 x 3
5 x 3=15
35+15=
50
Answer:
D.44
Step-by-step explanation:
i hope its help for you po