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3 years ago

If P(A)=0.43 and P(B)=0.09, find P(A and B). Round your answer to the nearest hundredth.

Mathematics

1 answer:

AleksAgata [21]3 years ago

5 0

Answer:

0.04 to the nearest hundredth.

Step-by-step explanation:

P(A and B)

= P(A ∩ B

= P(A) * P(B)

= 0.43 * 0.09

= 0.0387.

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3 years ago

Evaluate the definite integral. <br> 1 x4(1 + 2x5)5 dx.

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Answer:

Step-by-step explanation:

Given the definite integral $\int\limits {\dfrac{x^4}{(1-2x^5)^5} } \, dx$ , we to evaluate it. Using integration by substitution method.

Let u = 1-2x⁵ ...1

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$= \int\limits {\dfrac{x^4}{u^5} } \, \dfrac{du}{-10x^4}$

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$= \dfrac{u^{-4}}{40} \\\\\\= \dfrac{1}{40u^4} +C$

substitute u = 1-2x⁵ into the result

$= \dfrac{1}{40(1-2x^5)^4} +C$

Hence $\int\limits {\dfrac{x^4}{(1-2x^5)^5} } \, dx$ $= \dfrac{1}{40(1-2x^5)^4} +C$

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