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3 years ago

If P(A)=2/3, P(B)=4/5, and P(A U B) =11/15, what is P(A ∩ B)?

Mathematics

2 answers:

Evgen [1.6K]3 years ago

7 0

Answer:

P(A ∩ B) = $\frac{11}{15}$

Step-by-step explanation:

If P(A)=2/3, P(B)=4/5, and P(A U B) =11/15

we need to find out P(A ∩ B)

P(A U B) = P(A) + P(B) - P(A ∩ B)

Now we add P(A ∩ B) on both sides and subtract P(A U B) from both sides

P(A ∩ B) = P(A) + P(B)- P(A U B)

now we plug in the values

P(A ∩ B) = $\frac{2}{3} + \frac{4}{5} - \frac{11}{15}$

Make the denominators same . LCD is 15

P(A ∩ B) = $\frac{10}{15} + \frac{12}{15} - \frac{11}{15}$

P(A ∩ B) = $\frac{22}{15}-\frac{11}{15}$

P(A ∩ B) = $\frac{11}{15}$

Juliette [100K]3 years ago

3 0

The answer is A on apex

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Answer:

The rule of 72 is used to determine how long it will take an investment to Double

For an Investment of $5,000 earning 7% annually, this will take about ten years

Step-by-step explanation:

The rule of 72 says that to find the number of years required to double your money at a given interest rate, you just divide 72 by the interest rate

Example:

If you want to know how long it will take to double your money at 9% interest, divide 72 by 9 you will get 8 years

The formula of the rule of 72 is Y = $\frac{72}{r}$

Let us complete the missing

The rule of 72 is used to determine how long it will take an investment to Double

The missing word is "Double"

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∵ The annual interest is 7%

- By using the rule of 72

∵ Y = $\frac{72}{r}$

∵ r = 7

∴ Y = $\frac{72}{7}$

∴ Y = 10.29

- Round it to the nearest year

∴ Y ≅ 10 years

For an Investment of $5,000 earning 7% annually, this will take about ten years

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3 years ago

A shelf is designed so it will fit in a 90º corner between two walls. The shelf has dimensions, rounded to the nearest tenth, as

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Answer:

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Step-by-step explanation:

To do this, we simply need to check if the given sides of the shelf is right-angled.

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To check for right-angle triangle, we make use of:

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This gives:

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