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2 years ago

13

In a probability experiment, Craig rolled a six-sided die 64 times. The die landed on a number greater than three 39 times. What

is the ratio of rolls greater than three to rolls less than or equal to three?
A.

B.

C.

D.

1 answer:

Charra [1.4K]2 years ago

7 0

Answer:

The ratio is 34/22, or in simplest form, 17/11.

Step-by-step explanation:

We write the ratio with the number of rolls greater than three on top and the number of rolls less than or equal to 3 on bottom:

34/(56-34)

We have to subtract 34 from 56 to find out how many rolls were less than or equal to 3.

34/22

Both are divisible by 2, so we have 17/11.

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What is the antiderivative of 3x/((x-1)^2)

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Answer:

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Step-by-step explanation:

Given

$\int \:\:3\cdot \frac{x}{\left(x-1\right)^2}dx$

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$\mathrm{Apply\:u-substitution:}\:u=x-1$

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as

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$\int \frac{1}{u^2}du=-\frac{1}{u}$ ∵ $\mathrm{Apply\:the\:Power\:Rule}:\quad \int x^adx=\frac{x^{a+1}}{a+1},\:\quad \:a\ne -1$

so

$=3\left(\ln \left|u\right|-\frac{1}{u}\right)$

$\mathrm{Substitute\:back}\:u=x-1$

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$=3\left(\ln \left|x-1\right|-\frac{1}{x-1}\right)+C$

Therefore,

$\int \:3\cdot \frac{x}{\left(x-1\right)^2}dx=3\left(\ln \left|x-1\right|-\frac{1}{x-1}\right)+C$

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