(12x+6x-30x-10)/(x-3)=
=(-12x-10)/(x-3)
=-12x*+36- 10x+30=
=-22x+56
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)
WEEKLY Earning Full time = 40 h x $15 = $600/week
Over time = 3 h 25 min or 3h + 25/60 h
WEEKLY Earning Over time = (3 h)x $30 + (25/60) x $30 = $115
TOTAL WEEKLY INCLUDING OVERTIME: = $715
TOTAL SEMI MONTHLY INCLUDING OVERTIME =$715 X2 = $1,430
BIWEEKLY = SEMI MONTHLY = $1,430
TOTAL MONTHLY INCLUDING OVERTIME =$715 x 4 = $2,860
Answer:
The objective of the confidence interval is to give a range in which the real mean of the population is placed, with a degree of confidence given by the level of significance.
The conclusion we can make is that there is 95% of probability that the mean of the population (professor's average salary) is within $99,881 and $171,172.
Step-by-step explanation:
This is a case in which, from a sample os size n=16, a confidence interval is constructed.
The objective of the confidence interval is to give a range in which the real mean of the population is placed, with a degree of confidence given by the level of significance. In this case, the probability that the real mean is within the interval is 95%.