Answer:120
Step-by-step explanation:
Volume of box=length x width x height
Volume of box=4x2.5x1.5
Volume of box=15
Cube length=1/2=0.5
Volume of cube=0.5x0.5x0.5
Volume of cube=0.125
Number of cube that can be packed inside the box=15 ➗ 0.125=120
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
Mean is the average number in the data set.
To get the average we first add all the numbers.
After we add all these numbers we then divide by the number of numbers in the data set.
So we do 22+18+38+6+24+18 which is equal to 126 there are six numbers so we divide 126 by 6. This gives us a mean of 21.
ANOTHER EXAMPLE:
Another example of this is the data set (4,65,7,34,5)
We first add all the numbers and get 115 then we divide by 5 and get 23 as the mean.
Answer:
y = x-3 is the equation
Step-by-step explanation:
If two lines are perpendicular, the product of their slopes is -1
The general equation form of a straight line is;
y = mx + b
Fro the equation;
y = -1x + 2
The slope is -1
So the equation of the perpendicular line is as follows;
-1 * m = -1
m = 1
so we can use the point-slope equation form
That would be:
y-y1 = m(x-x1)
y-3 = 1(x-6)
y-3 = x-6
y = x-6+3
y = x-3
Factorized: (a + b + 2) ^2