Answer:
Step-by-step explanation:
16
Answer and explanation:
Given : At Tech Express, 40% of the customers purchases small coffee and 60% purchases medium. Of those customers purchasing small coffee, 30% prefer decaf. Of those purchasing medium coffee, 50% prefer decaf.
Let
customer purchase small coffee.
i.e. ![P(A_1)=40\%=0.4](https://tex.z-dn.net/?f=P%28A_1%29%3D40%5C%25%3D0.4)
customer purchase medium coffee.
i.e. ![P(A_2)=60\%=0.6](https://tex.z-dn.net/?f=P%28A_2%29%3D60%5C%25%3D0.6)
Let B be the customer purchase prefer decaf.
So, ![P(B|A_1)=30\%=0.3](https://tex.z-dn.net/?f=P%28B%7CA_1%29%3D30%5C%25%3D0.3)
![P(B|A_2)=50\%=0.5](https://tex.z-dn.net/?f=P%28B%7CA_2%29%3D50%5C%25%3D0.5)
(a) What is the probability that the next customer will request medium and decaf coffee?
i.e. ![P(A_2\cap B)=P(A_2)\times P(B|A_2)](https://tex.z-dn.net/?f=P%28A_2%5Ccap%20B%29%3DP%28A_2%29%5Ctimes%20P%28B%7CA_2%29)
![P(A_2\cap B)=0.6\times 0.5](https://tex.z-dn.net/?f=P%28A_2%5Ccap%20B%29%3D0.6%5Ctimes%200.5)
![P(A_2\cap B)=0.3](https://tex.z-dn.net/?f=P%28A_2%5Ccap%20B%29%3D0.3)
(b) What is the probability that the next customer prefers decaf?
i.e. ![P(B)=P(A_1\cap B)+P(A_2\cap B)](https://tex.z-dn.net/?f=P%28B%29%3DP%28A_1%5Ccap%20B%29%2BP%28A_2%5Ccap%20B%29)
![P(B)=P(A_1)\times P(B|A_1)+P(A_2)\times P(B|A_2)](https://tex.z-dn.net/?f=P%28B%29%3DP%28A_1%29%5Ctimes%20P%28B%7CA_1%29%2BP%28A_2%29%5Ctimes%20P%28B%7CA_2%29)
![P(B)=0.4\times 0.3+0.6\times 0.5](https://tex.z-dn.net/?f=P%28B%29%3D0.4%5Ctimes%200.3%2B0.6%5Ctimes%200.5)
![P(B)=0.12+0.3](https://tex.z-dn.net/?f=P%28B%29%3D0.12%2B0.3)
![P(B)=0.42](https://tex.z-dn.net/?f=P%28B%29%3D0.42)
(c) If the next customer prefers decaf, what is the probability that small is requested?
i.e. ![P(A_1|B)=\frac{P(A_1\cap B)}{P(B)}](https://tex.z-dn.net/?f=P%28A_1%7CB%29%3D%5Cfrac%7BP%28A_1%5Ccap%20B%29%7D%7BP%28B%29%7D)
![P(A_1|B)=\frac{0.12}{0.42}](https://tex.z-dn.net/?f=P%28A_1%7CB%29%3D%5Cfrac%7B0.12%7D%7B0.42%7D)
![P(A_1|B)=0.28](https://tex.z-dn.net/?f=P%28A_1%7CB%29%3D0.28)
Answer:
x = -4
Step-by-step explanation:
-2(3x - 4) - x - 3 = 33
~Simplify
-6x + 8 - x - 3
-7x + 5 = 33
~Subtract 3 to both sides
-7x = 28
~Divide -7 to both sides
x = -4
Best of Luck!
P = 2w + 2L
Flip
2w + 2L = P
Subtract both sides by 2L
2w = P - 2L
Divide both sides by 2
w = (P - 2L) / 2
You chose the right answer choice!
Have an awesome day! :)
Answer:
B
Step-by-step explanation:Jk I sont know