<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>
<u>Complete Question</u>
The circle is inscribed in triangle PRT. A circle is inscribed in triangle P R T. Points Q, S, and U of the circle are on the sides of the triangle. Point Q is on side P R, point S is on side R T, and point U is on side P T. The length of R S is 5, the length of P U is 8, and the length of U T is 6. Which statements about the figure are true?
Answer:
(B)TU ≅ TS
(D)The length of line segment PR is 13 units.
Step-by-step explanation:
The diagram of the question is drawn for more understanding,
The theorem applied to this problem is that of tangents. All tangents drawn to a circle from the same point are equal.
Therefore:
|PQ|=|PU|=8 Units
|ST|=|UT| =6 Units
|RS|=|RQ|=5 Units
(b)From the above, TU ≅ TS
(d)Line Segment |PR|=|PQ|+|QR|=8+5=`13 Units
Answer: The slope is 3
Step-by-step explanation:
For each unit of run in the x-values, there is an increase of 3 in the y-values. Slope is Rise over Run so 3/1 = 3
You find 7% of $45.79 and then add that on to $45.79
7% of $45.79 = $3.21
45.79 + 3.21 = 49
The new price is $49
