Answer:
1) 
2) 
3) 
And the variance would be given by:
![Var (M)= E(M^2) -[E(M)]^2 = 207.1 -(13.9^2)= 13.89](https://tex.z-dn.net/?f=Var%20%28M%29%3D%20E%28M%5E2%29%20-%5BE%28M%29%5D%5E2%20%3D%20207.1%20-%2813.9%5E2%29%3D%2013.89)
And the deviation would be:
4) 
And the variance would be given by:
![Var (J)= E(J^2) -[E(J)]^2 = 194.8 -(11.8^2)= 55.56](https://tex.z-dn.net/?f=Var%20%28J%29%3D%20E%28J%5E2%29%20-%5BE%28J%29%5D%5E2%20%3D%20194.8%20-%2811.8%5E2%29%3D%2055.56)
And the deviation would be:
Step-by-step explanation:
For this case we have the following distributions given:
Probability M J
0.3 14% 22%
0.4 10% 4%
0.3 19% 12%
Part 1
The expected value is given by this formula:

And replacing we got:

Part 2

Part 3
We can calculate the second moment first with the following formula:

And the variance would be given by:
![Var (M)= E(M^2) -[E(M)]^2 = 207.1 -(13.9^2)= 13.89](https://tex.z-dn.net/?f=Var%20%28M%29%3D%20E%28M%5E2%29%20-%5BE%28M%29%5D%5E2%20%3D%20207.1%20-%2813.9%5E2%29%3D%2013.89)
And the deviation would be:
Part 4
We can calculate the second moment first with the following formula:

And the variance would be given by:
![Var (J)= E(J^2) -[E(J)]^2 = 194.8 -(11.8^2)= 55.56](https://tex.z-dn.net/?f=Var%20%28J%29%3D%20E%28J%5E2%29%20-%5BE%28J%29%5D%5E2%20%3D%20194.8%20-%2811.8%5E2%29%3D%2055.56)
And the deviation would be:
Answer:
180 - 61 = 119
Step-by-step explanation:
So from A to D it is 180 degrees so just have to subtract 61 from 180 for an answer.
Answer:
150/250
Step-by-step explanation:
24/42, 75/135, 150/250, and 75/150 I believe is what you're asking. We know 75/135 is better than 75/150 so 75/150 is out of the equation. If we multiple 75/135 by 2 we get 150/270 which is more than 150/250, so 75/135 is out of the equation. Now to compare 24/42 and 150/250 we can divide their fractions, if we divide 24/42 we get 0.57, so 57%. If we did 150/250 we get 0.6 or 60%. So 150/250 is the best score.
Answer:
Beth can make 9 2 1/3 foot steps
Step-by-step explanation:
21/2.3=9.1
round to 9
If the length of a rectangle is a two-digit number with identical digits and the width is 1/10 the length and the perimeter is 2 times the area of the rectangle, what is the the length and the width
Solution:
Let the length of rectangle=x
Width of rectangle=x/10
Perimeter is 2(Length+Width)
= 2(x+x/10)
Area of Rectangle= Length* Width=x*x/10
As, Perimeter=2(Area)
So,2(x+x/10)=2(x*x/10)
Multiplying the equation with 10, we get,
2(10x+x)=2x²
Adding Like terms, 10x+x=11x
2(11x)=2x^2
22x=2x²
2x²-22x=0
2x(x-11)=0
By Zero Product property, either x=0
or, x-11=0
or, x=11
So, Width=x/10=11/10=1.1
Checking:
So, Perimeter=2(Length +Width)=2(11+1.1)=2*(12.1)=24.2
Area=Length*Width=11*1.1=12.1
Hence, Perimeter= 2 Area
As,24.2=2*12.1=24.2
So, Perimeter=2 Area
So, Answer:Length of Rectangle=11 units
Width of Rectangle=1.1 units