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Subtract both sides from 6x, leaving you with the equation:
-2y=-6x+12
Now, you divide all of the sides by -2, therefore leabing you with the equation:
y=3x-6
Answer:
D. 314 yds
Step-by-step explanation:
Given:
Diameter = 100 yds
Required;
Circumference of the circle
Solution:
Circumference of circle = πd
Plug in the value
Circumference = π × 100
= 314 yds (nearest whole number)
Answer:
![P(B' \cup A') = P((A \cap B)') = 1-P(A \cap B)= 1-0.32=0.68](https://tex.z-dn.net/?f=P%28B%27%20%5Ccup%20A%27%29%20%3D%20P%28%28A%20%5Ccap%20B%29%27%29%20%3D%201-P%28A%20%5Ccap%20B%29%3D%201-0.32%3D0.68)
See explanation below.
Step-by-step explanation:
For this case we define first some notation:
A= A new training program will increase customer satisfaction ratings
B= The training program can be kept within the original budget allocation
And for these two events we have defined the following probabilities
![P(A) = 0.8, P(B) = 0.2](https://tex.z-dn.net/?f=%20P%28A%29%20%3D%200.8%2C%20P%28B%29%20%3D%200.2)
We are assuming that the two events are independent so then we have the following propert:
![P(A \cap B ) = P(A) * P(B)](https://tex.z-dn.net/?f=%20P%28A%20%5Ccap%20B%20%29%20%3D%20P%28A%29%20%2A%20P%28B%29)
And we want to find the probability that the cost of the training program is not kept within budget or the training program will not increase the customer ratings so then if we use symbols we want to find:
![P(B' \cup A')](https://tex.z-dn.net/?f=%20P%28B%27%20%5Ccup%20A%27%29%20)
And using the De Morgan laws we know that:
![(A \cap B)' = A' \cup B'](https://tex.z-dn.net/?f=%20%28A%20%5Ccap%20B%29%27%20%3D%20A%27%20%5Ccup%20B%27)
So then we can write the probability like this:
![P(B' \cup A') = P((A \cap B)')](https://tex.z-dn.net/?f=%20P%28B%27%20%5Ccup%20A%27%29%20%3D%20P%28%28A%20%5Ccap%20B%29%27%29)
And using the complement rule we can do this:
![P(B' \cup A') = P((A \cap B)')= 1-P(A \cap B)](https://tex.z-dn.net/?f=%20P%28B%27%20%5Ccup%20A%27%29%20%3D%20P%28%28A%20%5Ccap%20B%29%27%29%3D%201-P%28A%20%5Ccap%20B%29)
Since A and B are independent we have:
![P(A \cap B )=P(A)*P(B) =(0.8*0.4) =0.32](https://tex.z-dn.net/?f=%20P%28A%20%5Ccap%20B%20%29%3DP%28A%29%2AP%28B%29%20%3D%280.8%2A0.4%29%20%3D0.32)
And then our final answer would be:
![P(B' \cup A') = P((A \cap B)') = 1-P(A \cap B)= 1-0.32=0.68](https://tex.z-dn.net/?f=P%28B%27%20%5Ccup%20A%27%29%20%3D%20P%28%28A%20%5Ccap%20B%29%27%29%20%3D%201-P%28A%20%5Ccap%20B%29%3D%201-0.32%3D0.68)
Joe is 15, 45-15=30 30/2=15