Answer:
![P(X=7)](https://tex.z-dn.net/?f=%20P%28X%3D7%29)
And using the probability mass function we got:
Step-by-step explanation:
Let X the random variable of interest, on this case we now that:
The probability mass function for the Binomial distribution is given as:
Where (nCx) means combinatory and it's given by this formula:
And we want to find the following probability:
![P(X=7)](https://tex.z-dn.net/?f=%20P%28X%3D7%29)
And using the probability mass function we got:
First calculate the distance covered going down:
d_down = (16 m / s) * 8 s = 128 m
Then the distance going up is:
d_up = 71 m
So the distance from the ledge to the nest is:
d = 128 m – 71 m = 57 m
Therefore the elevation is:
<span>elevation = 1364 m + 57 m = 1421 m</span>
ANSWER
![x = 4](https://tex.z-dn.net/?f=x%20%3D%20%204)
and
![y = - 1](https://tex.z-dn.net/?f=y%20%3D%20%20%20-%201)
EXPLANATION
Line s has equation:
y=x-5
And line t has equation:
![y = - \frac{3}{4}x + 2](https://tex.z-dn.net/?f=y%20%3D%20%20-%20%20%5Cfrac%7B3%7D%7B4%7Dx%20%20%2B%202)
We equate the two equations to get:
![x - 5 = - \frac{3}{4} x + 2](https://tex.z-dn.net/?f=x%20-%205%20%3D%20%20-%20%20%5Cfrac%7B3%7D%7B4%7D%20x%20%2B%202)
Multiply through by 4
![4x - 20 = - \frac{3}{4} x \times 4 + 2 \times 4](https://tex.z-dn.net/?f=4x%20-%2020%20%20%3D%20%20-%20%20%5Cfrac%7B3%7D%7B4%7D%20x%20%5Ctimes%204%20%2B%202%20%5Ctimes%204)
![4x - 20 = - 3 x + 8](https://tex.z-dn.net/?f=4x%20-%2020%20%20%3D%20%20-%203%20x%20%20%2B%208)
![4x + 3x = 8 + 20](https://tex.z-dn.net/?f=4x%20%2B%203x%20%20%20%3D%20%208%20%2B%2020)
7x=28
![x = \frac{28}{7} = 4](https://tex.z-dn.net/?f=x%20%3D%20%20%5Cfrac%7B28%7D%7B7%7D%20%20%3D%204)
![y = 4 - 5 = - 1](https://tex.z-dn.net/?f=y%20%3D%20%204%20%20-%205%20%3D%20%20-%201)
The formula of a midpoint:
![M_{AB}\left(\dfrac{x_A+x_B}{2},\ \dfrac{y_A+y_B}{2}\right)](https://tex.z-dn.net/?f=M_%7BAB%7D%5Cleft%28%5Cdfrac%7Bx_A%2Bx_B%7D%7B2%7D%2C%5C%20%5Cdfrac%7By_A%2By_B%7D%7B2%7D%5Cright%29)
We have:
![M(1.5,\ 1.5)\to x_M=1.5,\ y_M=1.5\\A(5,\ 7)\to x_A=5,\ y_A=7](https://tex.z-dn.net/?f=M%281.5%2C%5C%201.5%29%5Cto%20x_M%3D1.5%2C%5C%20y_M%3D1.5%5C%5CA%285%2C%5C%207%29%5Cto%20x_A%3D5%2C%5C%20y_A%3D7)
Substitute
![\dfrac{5+x_B}{2}=1.5\qquad|\cdot2\\\\5+x_B=3\qquad|-5\\\\x_B=-2\\\\\dfrac{7+y_B}{2}=1.5\qquad|\cdot2\\\\7+y_B=3\qquad|-7\\\\y_B=-4](https://tex.z-dn.net/?f=%5Cdfrac%7B5%2Bx_B%7D%7B2%7D%3D1.5%5Cqquad%7C%5Ccdot2%5C%5C%5C%5C5%2Bx_B%3D3%5Cqquad%7C-5%5C%5C%5C%5Cx_B%3D-2%5C%5C%5C%5C%5Cdfrac%7B7%2By_B%7D%7B2%7D%3D1.5%5Cqquad%7C%5Ccdot2%5C%5C%5C%5C7%2By_B%3D3%5Cqquad%7C-7%5C%5C%5C%5Cy_B%3D-4)
<h3>Answer: (-2, -4)</h3>
Step-by-step explanation:
5×a×5×a
collect like terms
5×5×a×a
25×a^2
25a^2