Answer:
The probability that the pitcher throws exactly 8 strikes out of 15 pitches is approximately 0.199
Step-by-step explanation:
The given probability that the pitcher throws a strike, p = 0.507
The number of pitches thrown by the pitcher = 15 pitches
The probability that the pitcher does not throw a strike, q = 1 - P
∴ q = 1 - 0.507 = 0.493
By binomial theorem, we have;
When X = r = 8, and n = 15, we get;
The probability that the pitcher throws exactly 8 strikes out of 15 pitches, P(8), is given as follows
P(8) = ₁₅C₈ × 0.507⁸ × (1 - 0.507)⁽¹⁵ ⁻ ⁸⁾ = 6,435 × 0.507⁸ × 0.493⁷ ≈ 0.199
If you have two vectors A and B,
Dot product is a scalar quantity dealing with how much of one vector is in the same direction as the other vector, or the projection of one onto the other. You can see that from the cosine part of this form-
![A~*~B = [A][B]cos(\theta)](https://tex.z-dn.net/?f=A~%2A~B%20%3D%20%5BA%5D%5BB%5Dcos%28%5Ctheta%29)
The cross product is a vector perpendicular to both A and B. It deals with how much of one vector is perpendicular to the other vector. You can see that in the sine part of this form -
![A ~x ~B= [A][B]sin(\theta)](https://tex.z-dn.net/?f=A%20~x%20~B%3D%20%5BA%5D%5BB%5Dsin%28%5Ctheta%29)
3 cards
1/4 = x/12 1/4 = 3/12
4 * 3 = 12
1 * 3 = 3
x = 3
Answer:
y=9-7x
If x= -1, y=16
If x= 0, y=9
If x=2, y= -5
Step-by-step explanation:
Because you are solving the equation for y, you want to have y by itself on one side. The only way to do that in this problem is by subtracting the 7x on both sides.
y+7x=9
-7x -7x ---> y=9-7x
The next part of the question says to find the value of Y for each value of X. Using the given X values, we plug them into the equation we just got in order to find Y.
y=9-7(-1) ----> y=16
y=9-7(0) ----> y=9
y=9-7(2) ----> y=-5
Answer:
1
Step-by-step explanation:
The absolute value of 4 is 4 and the absolute value of -3 is 3 so the difference between 4 and 3 is 1.
