There are
![\dbinom{2n}2 = \dfrac{(2n)!}{2! (2n-2)!}](https://tex.z-dn.net/?f=%5Cdbinom%7B2n%7D2%20%3D%20%5Cdfrac%7B%282n%29%21%7D%7B2%21%20%282n-2%29%21%7D)
ways of pairing up any 2 members from the pool of
contestants. Note that
![(2n)! = 1\times2\times3\times4\times\cdots\times(2n-2)\times(2n-1)\times(2n) = (2n-2)! \times(2n-1) \times(2n)](https://tex.z-dn.net/?f=%282n%29%21%20%3D%201%5Ctimes2%5Ctimes3%5Ctimes4%5Ctimes%5Ccdots%5Ctimes%282n-2%29%5Ctimes%282n-1%29%5Ctimes%282n%29%20%3D%20%282n-2%29%21%20%5Ctimes%282n-1%29%20%5Ctimes%282n%29)
so that
![\dbinom{2n}2 = \dfrac{(2n)\times(2n-1)\times(2n-2)!}{2! (2n-2)!} = \boxed{n(2n-1)}](https://tex.z-dn.net/?f=%5Cdbinom%7B2n%7D2%20%3D%20%5Cdfrac%7B%282n%29%5Ctimes%282n-1%29%5Ctimes%282n-2%29%21%7D%7B2%21%20%282n-2%29%21%7D%20%3D%20%5Cboxed%7Bn%282n-1%29%7D)
Answer:
562.5
Step-by-step explanation:
i=?
p=3750
r=3*1/100=3/100
t=5 years
I=P*R*T
3750*5*3/100
=5625/100
=562.5
Answer:
60%
Step-by-step explanation:
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Answer:
The irrational number is 4.37124...
Step-by-step explanation:
This is because the number is non-terminating and non-repeating; as in the numbers don't repeat in the same order and they never end.
Answer:
D: 2/4
Step-by-step explanation:
Usually when we talk about a point partitioning a segment, we are interested in the ratio of the first segment to the second:
BC : CD = 2 : 2 = 1 : 1
Since this is not an answer choice, we need to "reverse engineer" the answer list to see if we can find an answer that corresponds to a reasonable interpretation of the question.
__
None of the segments is 3 units long, so neither of answer choices A or B makes any sense.
While segment BD is 4 units long, there is no segment that is 1 unit long, so answer choice C makes no sense, either.
There are segments that are 2 units long and a segment that is 4 units long, so if we interpret the question to be "what is the ratio of BC to BD?" then answer choice D is appropriate.