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Answer:
1/14
Step-by-step explanation:
The total number of coins in the bag is 10+6+5, or 21.
You reach into the bag and take ONE coin. The chances of that being a nickel is 6/21, or 2/7, since nickels compose 6 of the 21 coins in the bag.
You don't replace the nickel.
Now you have 20 coins in the bag, including 5 nickels.
The chances of your next draw being a dime is 5/20, or 1/4, since there are 5 dimes in the bag.
The joint probability of drawing a nickel and then a dime is then the product of these two probabilities:
(2/7)(1/4) = 2/28 = 1/14
Start with
![\dfrac{2x-1}{2x+1}-\dfrac{2x+1}{2x-1}](https://tex.z-dn.net/?f=%5Cdfrac%7B2x-1%7D%7B2x%2B1%7D-%5Cdfrac%7B2x%2B1%7D%7B2x-1%7D)
Observe that this implies that the domain is
![2x+1,\ 2x-1\neq 0 \implies x \neq \pm\dfrac{1}{2}](https://tex.z-dn.net/?f=2x%2B1%2C%5C%202x-1%5Cneq%200%20%5Cimplies%20x%20%5Cneq%20%5Cpm%5Cdfrac%7B1%7D%7B2%7D)
The least common denominator is
![\dfrac{2x-1}{2x+1}-\dfrac{2x+1}{2x-1} = \dfrac{(2x-1)^2-(2x+1)^2}{(2x+1)(2x-1)}=\dfrac{-8x}{4x^2-1}](https://tex.z-dn.net/?f=%5Cdfrac%7B2x-1%7D%7B2x%2B1%7D-%5Cdfrac%7B2x%2B1%7D%7B2x-1%7D%20%3D%20%5Cdfrac%7B%282x-1%29%5E2-%282x%2B1%29%5E2%7D%7B%282x%2B1%29%282x-1%29%7D%3D%5Cdfrac%7B-8x%7D%7B4x%5E2-1%7D)
In the right hand side, we have
![-2\dfrac{2}{3}=-\left(2+\dfrac{2}[3}\right)=-\left(\dfrac{6}{3}+\dfrac{2}{3}\right)=-\dfrac{8}{3}](https://tex.z-dn.net/?f=-2%5Cdfrac%7B2%7D%7B3%7D%3D-%5Cleft%282%2B%5Cdfrac%7B2%7D%5B3%7D%5Cright%29%3D-%5Cleft%28%5Cdfrac%7B6%7D%7B3%7D%2B%5Cdfrac%7B2%7D%7B3%7D%5Cright%29%3D-%5Cdfrac%7B8%7D%7B3%7D)
So, the equation becomes
![-\dfrac{8x}{4x^2-1}=-\dfrac{8}{3} \iff \dfrac{x}{4x^2-1}=\dfrac{1}{3}](https://tex.z-dn.net/?f=-%5Cdfrac%7B8x%7D%7B4x%5E2-1%7D%3D-%5Cdfrac%7B8%7D%7B3%7D%20%5Ciff%20%5Cdfrac%7Bx%7D%7B4x%5E2-1%7D%3D%5Cdfrac%7B1%7D%7B3%7D)
Multiply both sides by 3:
![\dfrac{3x}{4x^2-1}=1 \iff 3x=4x^2-1 \iff 4x^2-3x-1=0](https://tex.z-dn.net/?f=%5Cdfrac%7B3x%7D%7B4x%5E2-1%7D%3D1%20%5Ciff%203x%3D4x%5E2-1%20%5Ciff%204x%5E2-3x-1%3D0)
This equation has solutions
![x=-\dfrac{1}{4},\quad x=1](https://tex.z-dn.net/?f=x%3D-%5Cdfrac%7B1%7D%7B4%7D%2C%5Cquad%20x%3D1)
Which are compliant with the domain of the equation
P=2
X=4
D=3
Y=4.5
You’re welcome
6x-24=48
+24 +24
6x=72
72/6
X=12