Answer:
see below
Step-by-step explanation:
![f(x)=2/x\\\\g(x)=2/x\\\\f(g(x))=f(2/x)\\\\f(2/x)=2/(2/x)\\\\f(g(x))=2x/2\\\\f(g(x))=x\\\\](https://tex.z-dn.net/?f=f%28x%29%3D2%2Fx%5C%5C%5C%5Cg%28x%29%3D2%2Fx%5C%5C%5C%5Cf%28g%28x%29%29%3Df%282%2Fx%29%5C%5C%5C%5Cf%282%2Fx%29%3D2%2F%282%2Fx%29%5C%5C%5C%5Cf%28g%28x%29%29%3D2x%2F2%5C%5C%5C%5Cf%28g%28x%29%29%3Dx%5C%5C%5C%5C)
and since f(x)=g(x) the same process applies to g(f(x))
Answer:
B. 5/21 chance
Step-by-step explanation:
The probability he gets the black marker first is 5/7. The probability he gets a blue marker after his black marker not replaced is 2/6 or 1/3. 1/3*5/7 is 5/21
By the binomial theorem,
![\displaystyle \left(x^2-\frac1x\right)^6 = \sum_{k=0}^6 \binom 6k (x^2)^{6-k} \left(-\frac1x\right)^k = \sum_{k=0}^6 \binom 6k (-1)^k x^{12-3k}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cleft%28x%5E2-%5Cfrac1x%5Cright%29%5E6%20%3D%20%5Csum_%7Bk%3D0%7D%5E6%20%5Cbinom%206k%20%28x%5E2%29%5E%7B6-k%7D%20%5Cleft%28-%5Cfrac1x%5Cright%29%5Ek%20%3D%20%5Csum_%7Bk%3D0%7D%5E6%20%5Cbinom%206k%20%28-1%29%5Ek%20x%5E%7B12-3k%7D)
I assume you meant to say "independent", not "indecent", meaning we're looking for the constant term in the expansion. This happens for k such that
12 - 3k = 0 ===> 3k = 12 ===> k = 4
which corresponds to the constant coefficient
![\dbinom 64 (-1)^4 = \dfrac{6!}{4!(6-4)!} = \boxed{15}](https://tex.z-dn.net/?f=%5Cdbinom%2064%20%28-1%29%5E4%20%3D%20%5Cdfrac%7B6%21%7D%7B4%21%286-4%29%21%7D%20%3D%20%5Cboxed%7B15%7D)
Patrick has a total of 600 meters skein of yarn.
He used 248.9 meters of yarn to make a hat.
Now, If he has used 248.9 meters of yarn, we need to find how much yarn has he left.
We need to subtract the amount of yarn used from the total length. That is, 248.9 from 600.
![600-248.9=351.1](https://tex.z-dn.net/?f=600-248.9%3D351.1)
So, now Patrick has left 351.1 meters of yarn.
Patrick needs to make a scarf that needs 354.03 meters of yarn but after making a hat he has left with only 351.1 meters of yarn. Therefore, Patrick does not have enough yarn to make a scarf.
To determine the fourth term, plug 4 into the equation;