<span>65 = number of different arrangements of 2 and 3 card pages such that the total number of card slots equals 18. 416,154,290,872,320,000 = number of different ways of arranging 18 cards on the above 65 different arrangements of page sizes. ===== This is a rather badly worded question in that some assumptions aren't mentioned. The assumptions being: 1. The card's are not interchangeable. So number of possible permutations of the 18 cards is 18!. 2. That all of the pages must be filled. Since the least common multiple of 2 and 3 is 6, that means that 2 pages of 3 cards can only be interchanged with 3 pages of 2 cards. So with that said, we have the following configurations. 6x3 card pages. Only 1 possible configuration. 4x3 cards and 3x2 cards. These pages can be arranged in 7!/4!3! = 35 different ways. 2x3 cards and 6x2 cards. These pages can be arranged in 8!/2!6! = 28 ways 9x2 card pages. These can only be arranged in 1 way. So the total number of possible pages and the orders in which that they can be arranged is 1+35+28+1 = 65 possible combinations. Now for each of those 65 possible ways of placing 2 and 3 card pages such that the total number of card spaces is 18 has to be multiplied by the number of possible ways to arrange 18 cards which is 18! = 6402373705728000. So the total amount of arranging those cards is 6402373705728000 * 65 = 416,154,290,872,320,000</span>
Answer:
the answer would be 90
Step-by-step explanation:
100 giants fills 5/8 (100/160) of the theater leaving 3/8 of the theater for the elves.
3/8 times 240 elves is 90 elves.
If there were 150 elves that would also be 5/8 filled plus the original 5/8 filled with 100 giants! Some elves might suffer!!!
The question does not make sense.
The commutative property applies to addition and multiplication, not addition and subtraction.
The commutative property does not apply to subtraction or division because in those operations, the order of the numbers makes a difference, whereas in addition and subtraction the order does not make a difference.
For example:
Addition
5 + 4 = 9
4 + 5 = 9
5 + 4 = 4 + 5
Changing the order of the 4 and the 5 gives the same answer.
The commutative property does apply to addition.
Multiplication
5 * 4 = 20
4 * 5 = 20
5 * 4 = 4 * 5
Changing the order of the 4 and the 5 gives the same answer.
The commutative property does apply to multiplication.
Subtraction
5 - 4 = 1
4 - 5 = -1
5 - 4 is not equal to 4 - 5
Changing the order of the 4 and the 5 gives a different answer.
The commutative property does not apply to subtraction.
Division
5/4 = 1.25
4/5 = 0.8
1.25 is not equal to 0.8.
Changing the order of the 4 and the 5 gives a different answer.
The commutative property does not apply to division.
Answer:
(x) = x - 5
Step-by-step explanation:
Let y = f(x) and make x the subject
y = x + 5 ( subtract 5 from both sides )
y - 5 = x
Change y back into terms of x, thus
(x) = x - 5