Answer:
Step-by-step explanation:
Given that:
P(Y) = ky
where;
y =1,2,...7
To find the value of c or k (constant)
![\sum P(Y) = 1](https://tex.z-dn.net/?f=%5Csum%20P%28Y%29%20%3D%201)
![\sum \limits_{y \to 1}^7 k*y = 1](https://tex.z-dn.net/?f=%5Csum%20%5Climits_%7By%20%5Cto%201%7D%5E7%20k%2Ay%20%3D%201)
= k(1+2+3+4+5+6+7) = 1
28k = 1
![k = \dfrac{1}{28}](https://tex.z-dn.net/?f=k%20%3D%20%5Cdfrac%7B1%7D%7B28%7D)
b) The required probability is P ( X ≤ 3)
![P(X \le 3) = \sum \limits^3_{y=1 } P(y)](https://tex.z-dn.net/?f=P%28X%20%5Cle%203%29%20%3D%20%5Csum%20%5Climits%5E3_%7By%3D1%20%7D%20P%28y%29)
![P(X \le 3) = \sum \limits^3_{y=1 } \dfrac{1}{28}(y)](https://tex.z-dn.net/?f=P%28X%20%5Cle%203%29%20%3D%20%5Csum%20%5Climits%5E3_%7By%3D1%20%7D%20%5Cdfrac%7B1%7D%7B28%7D%28y%29)
![P(X \le 3) = \dfrac{1}{28} (1 +2+3)](https://tex.z-dn.net/?f=P%28X%20%5Cle%203%29%20%3D%20%5Cdfrac%7B1%7D%7B28%7D%20%281%20%2B2%2B3%29)
![P(X \le 3) = \dfrac{6}{28}](https://tex.z-dn.net/?f=P%28X%20%5Cle%203%29%20%3D%20%5Cdfrac%7B6%7D%7B28%7D)
P ( X ≤ 3) = 0.2143
c) The required probability P(2 ≤ Y ≤ 4)
![P(2 \le Y \le 4) = \sum \limits ^4_{y=2} P(Y)](https://tex.z-dn.net/?f=P%282%20%5Cle%20Y%20%5Cle%204%29%20%3D%20%5Csum%20%5Climits%20%5E4_%7By%3D2%7D%20P%28Y%29)
![P(2 \le Y \le 4) = \sum \limits ^4_{y=2} \dfrac{1}{28}(Y)](https://tex.z-dn.net/?f=P%282%20%5Cle%20Y%20%5Cle%204%29%20%3D%20%5Csum%20%5Climits%20%5E4_%7By%3D2%7D%20%5Cdfrac%7B1%7D%7B28%7D%28Y%29)
![P(2 \le Y \le 4) = \dfrac{1}{28}(2+3+4)](https://tex.z-dn.net/?f=P%282%20%5Cle%20Y%20%5Cle%204%29%20%3D%20%5Cdfrac%7B1%7D%7B28%7D%282%2B3%2B4%29)
![P(2 \le Y \le 4) = 0.3214](https://tex.z-dn.net/?f=P%282%20%5Cle%20Y%20%5Cle%204%29%20%3D%200.3214)
d) The required probability:
![P(X) = \dfrac{x^2}{50} ; \ \ \ \ where; \ x= 1,2,...5](https://tex.z-dn.net/?f=P%28X%29%20%3D%20%5Cdfrac%7Bx%5E2%7D%7B50%7D%20%3B%20%5C%20%20%5C%20%5C%20%5C%20%20where%3B%20%5C%20x%3D%201%2C2%2C...5)
![\sum \limits ^5_{y =1} P(Y)= \sum \limits ^5_{y =1} \dfrac{1}{50}(x)^2](https://tex.z-dn.net/?f=%5Csum%20%5Climits%20%5E5_%7By%20%3D1%7D%20P%28Y%29%3D%20%5Csum%20%5Climits%20%5E5_%7By%20%3D1%7D%20%5Cdfrac%7B1%7D%7B50%7D%28x%29%5E2)
![\sum \limits ^5_{y =1} P(Y)= \sum \limits ^5_{y =1} \dfrac{1}{50}(1+4+9+16+25)](https://tex.z-dn.net/?f=%5Csum%20%5Climits%20%5E5_%7By%20%3D1%7D%20P%28Y%29%3D%20%5Csum%20%5Climits%20%5E5_%7By%20%3D1%7D%20%5Cdfrac%7B1%7D%7B50%7D%281%2B4%2B9%2B16%2B25%29)
![\sum \limits ^5_{y =1} P(Y)=1.1](https://tex.z-dn.net/?f=%5Csum%20%5Climits%20%5E5_%7By%20%3D1%7D%20P%28Y%29%3D1.1)
Answer:
D.
Step-by-step explanation:
Order of operation states that in order for the addition to be done first, it must be in a set of parenthesis. Then, 4 multiplied by the sum would mean the addition has to be done first. so, yeah.
Don't know if that helps. I hope it does. Have a great day
Answer:
56
Step-by-step explanation:
Answer:
25
Step-by-step explanation:
because you have to divide by 15's
Answer:
1176 squared units
Step-by-step explanation:
You need to use the formula for finding area (Length x Width) to find the surface area of each face. For example, 7 times 21 is 147, so that face by itself is 147 squared units