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3 years ago

A and B are independent events. P(A) = 0.80 and P(B) = 0.10. What is P(A and B)?

Mathematics

2 answers:

Mandarinka [93]3 years ago

7 0

Answer:

C 0.90

Step-by-step explanation:

Add 0.10 and 0.80=0.90

Anuta_ua [19.1K]3 years ago

4 0

Answer:

Step-by-step explanation:

P(A and B)=P(A)×P(B)=0.80×0.10=0.08

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The first equation is linear:

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Divide through by $x^2$ to get

$\dfrac1x\dfrac{\mathrm dy}{\mathrm dx}-\dfrac1{x^2}y=\sin x$

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$\dfrac{\mathrm d}{\mathrm dx}\left[\dfrac1xy\right]=\sin x$
$\implies\dfrac1xy=\displaystyle\int\sin x\,\mathrm dx=-\cos x+C$
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The second equation is also linear:

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Multiply both sides by $e^x$ to get

$x^2e^xy'+x(x+2)e^xy=e^{2x}$

and recall that $(x^2e^x)'=2xe^x+x^2e^x=x(x+2)e^x$ , so we can write

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- - -

Yet another linear ODE:

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$\dfrac1{\cos x}\dfrac{\mathrm dy}{\mathrm dx}+\dfrac{\sin x}{\cos^2x}y=\dfrac1{\cos^2x}$
$\sec x\dfrac{\mathrm dy}{\mathrm dx}+\sec x\tan x\,y=\sec^2x$
$\dfrac{\mathrm d}{\mathrm dx}[\sec x\,y]=\sec^2x$
$\implies\sec x\,y=\displaystyle\int\sec^2x\,\mathrm dx=\tan x+C$
$\implies y=\cos x\tan x+C\cos x$
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- - -

In case the steps where we multiply or divide through by a certain factor weren't clear enough, those steps follow from the procedure for finding an integrating factor. We start with the linear equation

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The integrating factor is a function $\mu(x)$ such that

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which requires that

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