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rosijanka [135]
3 years ago
15

A rational number can be written as the ratio of on BLANK to another.

Mathematics
1 answer:
swat323 years ago
4 0
"Integer" I think! As all rational numbers can be written as integer fractions.
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The prior probabilities for events A1 and A2 are P(A1) = 0.30 and P(A2) = 0.55. It is also known that P(A1 ∩ A2) = 0. Suppose P(
k0ka [10]

We're given the following probabilities:

P(A_1)=0.30

P(A_2)=0.55

P(A_1\cap A_2)=0

P(B\mid A_1)=0.20

P(B\mid A_2)=0.05

(a) Yes, A_1 and A_2 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:

P(A_1\cap B)=P(A_1)P(B\mid A_1)=0.30\cdot0.20=0.06

P(A_2\cap B)=P(A_2)P(B\mid A_2)=0.55\cdot0.05=0.0275

(c) By the law of total probability,

P(B)=P(A_1\cap B)+P(A_2\cap B)=0.06+0.0275=0.0875

(d) Bayes' theorem says

P(A_1\mid B)=\dfrac{P(A_1)P(B\mid A_1)}{P(B)}=\dfrac{0.30\cdot0.20}{0.0875}\approx0.686

P(A_2\mid B)=\dfrac{P(A_2)P(B\mid A_2)}{P(B)}=\dfrac{0.55\cdot0.05}{0.0875}\approx0.314

3 0
3 years ago
A factory makes car batteries. The probability that a battery is defective is 1/14. If 400 batteries are tested, about how many
Rufina [12.5K]

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:

E(X) = np

The probability that a battery is defective is 1/14.

This means that p = \frac{1}{14}

400 batteries.

This means that n = 400

How many are expected to be defective?

E(X) = np = 400*\frac{1}{14} = 28.6

28.6, that is, about 29 are expected to be defective

3 0
3 years ago
Describe two methods that can be used to find the area of the composite figure.
vekshin1

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!

4 0
2 years ago
Read 2 more answers
Pls help It’s due tomorrow question is in the picture
Slav-nsk [51]

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:

A=\pi r^2\\A=\pi (5)^2\\A=25\pi

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:

A=\pi r^2\\A=\pi (10)^2\\A=100\pi

Now, find the ratio between them by dividing:

\frac{\text{Smaller}}{\text{Larger}}=\frac{25\pi}{100\pi}

Simplify:

\frac{\text{Smaller}}{\text{Larger}}=\frac{1}{4}

1/4 is the same as 1:4

So, our answer is C      :)

5 0
3 years ago
Calculate the rate of change.
Tpy6a [65]

Answer:

2

Step-by-step explanation:

Rise is 10 run is 5 Rate of Change is rise over run.

7 0
2 years ago
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