<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>
Find min
min is 1.5-0.2=1.3cm
max is 0.2+1.5=1.7cm
so it would be a graph from 1.3cm to 1.7cm
like below
I'm assuming that the full statement is ΔABC is congruent to ΔDEF.
Given:
m∠A = 70
m∠B = 47
m∠C = 63
Since both triangles are congruent, the corresponding angles in ΔDEF also has the same measure as those in ΔABC.
m∠D = 70
m∠E = 47
m∠F = 63
The measure of angle F is 63.
(5x^3 + 4)(25x^6 - 20x3 +16) remember factoring the cubes?
The answer is:
But if x2 was supposed to be x^2 then the answer is:
