<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.
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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>
The total monthly bill of the gym = $53
The cost of membership of a month = $25
Let 'n' be extra the number of hours Bella worked on.
The cost for working on extra hours = $4
So, we have to determine the equation, Bella worked out after hours.
We will determine the equation by:
(Monthly cost of membership) + ( cost for extra hours
number of hours extra worked on ) = Total monthly bill received
So, we get

$25+4n = $53 is the required equation.
Therefore, $25+4n = $53 equation can be used to determine how many times Bella worked out after hours.
Answer:
See the attached figure for better explanation :
Step-by-step explanation :
1. By the unique line postulate, you can draw only one line segment : <u>BC</u>
Since only one line can be drawn between two distinct points.
2. Using the definition of <u>reflection</u>, reflect BC over l.
To find line segment which reflects BC over l, we will use the definition of reflection.
3. By the definition of reflection, C is the image of itself and <u>A</u> is the image of B.
Definition of reflection says the figure about a line is transformed to form the mirror image. Now, CD is perpendicular bisector of AB so A and B are equidistant from D forming the mirror image of each other.
4. Since reflections preserve <u>length</u>, AC = BC
In Reflection the figure is transformed to form a mirror image, Hence the length will be preserved in case of reflection.
All we need to do here is divide the circumference by 2.
104.48 / 2 = 52.24
The new circumference is 52.24 mm.