Answer:
a) ![P(A \cup B) = P(A) +P(B) - P(A\cap B)](https://tex.z-dn.net/?f=%20P%28A%20%5Ccup%20B%29%20%3D%20P%28A%29%20%2BP%28B%29%20-%20P%28A%5Ccap%20B%29)
And if we solve for
we got:
![P(A \cap B) = P(A) + P(B) -P(A\cup B)= 0.7+0.3-0.9 = 0.1](https://tex.z-dn.net/?f=%20P%28A%20%5Ccap%20B%29%20%3D%20P%28A%29%20%2B%20P%28B%29%20-P%28A%5Ccup%20B%29%3D%200.7%2B0.3-0.9%20%3D%200.1)
b) False
The reason is because we don't satisfy the following relationship:
![P(A\cup B) = P(A) + P(B)](https://tex.z-dn.net/?f=%20P%28A%5Ccup%20B%29%20%3D%20P%28A%29%20%2B%20P%28B%29)
We have that:
![0.9 \neq 0.3+0.7 =1](https://tex.z-dn.net/?f=%200.9%20%5Cneq%200.3%2B0.7%20%3D1)
c) False
In order to satisfy independence we need to have the following condition:
![P(A \cap B) = P(A) *P(B)](https://tex.z-dn.net/?f=%20P%28A%20%5Ccap%20B%29%20%3D%20P%28A%29%20%2AP%28B%29)
And for this case we don't satisfy this relation since:
![0.1 \neq 0.7*0.3 = 0.21](https://tex.z-dn.net/?f=%200.1%20%5Cneq%200.7%2A0.3%20%3D%200.21)
Step-by-step explanation:
For this case we have the following probabilities given:
![P(A) = 0.7, P(B) =0.7, P(A \cup B) =0.9](https://tex.z-dn.net/?f=%20P%28A%29%20%3D%200.7%2C%20P%28B%29%20%3D0.7%2C%20P%28A%20%5Ccup%20B%29%20%3D0.9)
Part a
We want to calculate the following probability: ![P(A \cap B)](https://tex.z-dn.net/?f=%20P%28A%20%5Ccap%20B%29)
And we can use the total probability rule given by:
![P(A \cup B) = P(A) +P(B) - P(A\cap B)](https://tex.z-dn.net/?f=%20P%28A%20%5Ccup%20B%29%20%3D%20P%28A%29%20%2BP%28B%29%20-%20P%28A%5Ccap%20B%29)
And if we solve for
we got:
![P(A \cap B) = P(A) + P(B) -P(A\cup B)= 0.7+0.3-0.9 = 0.1](https://tex.z-dn.net/?f=%20P%28A%20%5Ccap%20B%29%20%3D%20P%28A%29%20%2B%20P%28B%29%20-P%28A%5Ccup%20B%29%3D%200.7%2B0.3-0.9%20%3D%200.1)
Part b
False
The reason is because we don't satisfy the following relationship:
![P(A\cup B) = P(A) + P(B)](https://tex.z-dn.net/?f=%20P%28A%5Ccup%20B%29%20%3D%20P%28A%29%20%2B%20P%28B%29)
We have that:
![0.9 \neq 0.3+0.7 =1](https://tex.z-dn.net/?f=%200.9%20%5Cneq%200.3%2B0.7%20%3D1)
Part c
False
In order to satisfy independence we need to have the following condition:
![P(A \cap B) = P(A) *P(B)](https://tex.z-dn.net/?f=%20P%28A%20%5Ccap%20B%29%20%3D%20P%28A%29%20%2AP%28B%29)
And for this case we don't satisfy this relation since:
![0.1 \neq 0.7*0.3 = 0.21](https://tex.z-dn.net/?f=%200.1%20%5Cneq%200.7%2A0.3%20%3D%200.21)
Answer:
540 ft^2.
Step-by-step explanation:
The area of the trapezoid = h/2 (10 + 18) = 14h.
By Pythagoras the height h = √(5^2 - 4^2) = 3.
So the area of the 2 trapezoidal bases = 2 * 14*3
= 84 ft^2.
Now we calculate the area of the four lateral rectangular sides:
= 10*12 + 18*12 + 2*5*12
= 456 ft^2.
Total area = 456 + 54
= 540 ft^2.
Answer:
16
Step-by-step explanation:
Not the correct website go to a. dating website you idi0t
You can see the distance, or the absolute value. For example, -2, and 2, have the same absolute value because they are the same distance from 0, and if you look at a number line, it shows that.
I hope this helps! :D