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3 years ago

What’s the probability of pulling a yellow marble bag from a bag with 4 yellow, 8 red, 6 green, and 2 blue

Mathematics

1 answer:

BabaBlast [244]3 years ago

4 0

Answer:

4 out of 20 if I'm not mistaken

Step-by-step explanation:

Add all the numbers and then you get 20 and there are 4 yellow marbles so 4 out of 20

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Observe that $(x^2+2x+2)'=2x+2$ .

You have that $\int \frac{2x}{x^2+2x+2}\; dx=\int \frac{2x+2-2}{x^2+2x+2}\; dx=\int \frac{2x+2}{x^2+2x+2}\; dx+\int \frac{1}{x^2+2x+2}\; dx=I_1+2I_2$ .

To compute $I_1$ you set $y=x^2+2x+2$ , so $dy=2x+2\; dx$ . Therefore, $I_1=\int \frac{1}{y}\; dy=\ln |y|=\ln |x^2+2x+2|=\ln (x^2+2x+2)$ .

For $I_2$ observe that $x^2+2x+2=(x+1)^2+1$ . Let $y=x+1$ . Then $dy=dx$ and $I_2=\int \frac{1}{y^2+1}=\arctan y=\arctan (x+1)$ .

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