Total fish = 100
Carp = 30
Number of fish caught = 20
The random variable X follows hyper-geometric distribution.
Mean = 30 *20 / 100 = 600/100 = 6
Variance = 30*20/100 * ((20-1)*(30-1)/100-1 + 1-30*20/100)
Variance = 600/100 * 56/99
Variance = 112/33
Assumptions: Is that X follows hyper-geometric distribution with the given information.
Answer:
1. x=69/40
2. x=3/4
Step-by-step explanation:
#1 steps
1. Convert the decimals to fractions
x/9/20 = 23/100/3/50
2. Simplify the fractions
20x/9 = 23/6
3. Simplify the equation using cross multiplication
6 * 20x = 23 * 9
120x = 207
4. Divide both sides by 120
x = 69/40
#2 steps
1. Simplify the fractions
1/3/1/6 = 3/2/x
2 = 3/2/x
2 = 3/2x
2. Multiply both sides by the equation 2x
4x = 3
3. Divide both sides by 4
x = 3/4
The answer is $44.10. You times 42 by 0.05 and then add that answer to 42 and you get 44.10
Answer:
![\displaystyle y'=-\frac{9}{2}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20y%27%3D-%5Cfrac%7B9%7D%7B2%7D)
Step-by-step explanation:
<u>Differentiation</u>
We have a relationship between x and y as follows:
![x^2+y^2=25](https://tex.z-dn.net/?f=x%5E2%2By%5E2%3D25)
Both variables depend on time t for t≥0.
Differentiating with respect to time:
![(x^2)'+(y^2)'=(25)'](https://tex.z-dn.net/?f=%28x%5E2%29%27%2B%28y%5E2%29%27%3D%2825%29%27)
Applying the derivative of a power function:
![2xx'+2yy'=0](https://tex.z-dn.net/?f=2xx%27%2B2yy%27%3D0)
Recall the derivative of a constant is 0.
Dividing by 2:
![xx'+yy'=0](https://tex.z-dn.net/?f=xx%27%2Byy%27%3D0)
Solving for y':
![\displaystyle y'=-\frac{xx'}{y}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20y%27%3D-%5Cfrac%7Bxx%27%7D%7By%7D)
At some specific time, we have:
x=3, y=4, dx/dt = x' = 6. Substituting:
![\displaystyle y'=-\frac{3\cdot 6}{4}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20y%27%3D-%5Cfrac%7B3%5Ccdot%206%7D%7B4%7D)
Operating:
![\displaystyle y'=-\frac{18}{4}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20y%27%3D-%5Cfrac%7B18%7D%7B4%7D)
Simplifying:
![\mathbf{\displaystyle y'=-\frac{9}{2}}](https://tex.z-dn.net/?f=%5Cmathbf%7B%5Cdisplaystyle%20y%27%3D-%5Cfrac%7B9%7D%7B2%7D%7D)