We're given the following probabilities:





(a) Yes,
and
are mutually exclusive. This is exactly what zero probability of their intersection means. The two events cannot occur simultaneously.
(b) Use the definition of conditional probability to expand:


(c) By the law of total probability,

(d) Bayes' theorem says


Answer:
28.6, that is, about 29 are expected to be defective
Step-by-step explanation:
For each battery, there are only two possible outcomes. Either it is defective, or it is not. The probability of a battery being defective is independent of other betteries. So the binomial probability distribution is used to solve this question.
Binomial probability distribution
Probability of exactly x sucesses on n repeated trials, with p probability.
The expected value of the binomial distribution is:

The probability that a battery is defective is 1/14.
This means that 
400 batteries.
This means that 
How many are expected to be defective?

28.6, that is, about 29 are expected to be defective
You can draw a line to make a square and a rectangle to help find the area. The other method would be to form 2 squares and 1 rectangle.
This is probably wrong but I hope it helps!
Answer:
C
Step-by-step explanation:
Let's find the area of each of the two circles.
First Circle:
The first circle has a diameter of 10 inches. That means the radius is 5 inches. So, its area is:

Second Circle:
The second circle has a diameter twice that of the first. So, the diameter is 20 inches. This means that the radius is 10 inches. Find the area:

Now, find the ratio between them by dividing:

Simplify:

1/4 is the same as 1:4
So, our answer is C :)
Answer:
2
Step-by-step explanation:
Rise is 10 run is 5 Rate of Change is rise over run.