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Reptile [31]
3 years ago
15

F(x) = 9 - x, g(x) = x2 + x, h(x) = x - 2 Compute the following: f(g(x)

Mathematics
1 answer:
Sonbull [250]3 years ago
4 0

Answer:

f(g(x))=9-x-x^{2}

Step-by-step explanation:

Given ,

f(x)=9-x

g(x)=x^{2} +x

here,.

fog

=f(g(x))

=f(x^{2} +x)

=9-(x^{2} +x)

=9-x^{2} -x

=9-x-x^{2}

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Step-by-step explanation:

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The weight of an adult swan is normally distributed with a mean of 26 pounds and a standard deviation of 7.2 pounds. A farmer ra
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Let X denote the random variable for the weight of a swan. Then each swan in the sample of 36 selected by the farmer can be assigned a weight denoted by X_1,\ldots,X_{36}, each independently and identically distributed with distribution X_i\sim\mathcal N(26,7.2).

You want to find

\mathbb P(X_1+\cdots+X_{36}>1000)=\mathbb P\left(\displaystyle\sum_{i=1}^{36}X_i>1000\right)

Note that the left side is 36 times the average of the weights of the swans in the sample, i.e. the probability above is equivalent to

\mathbb P\left(36\displaystyle\sum_{i=1}^{36}\frac{X_i}{36}>1000\right)=\mathbb P\left(\overline X>\dfrac{1000}{36}\right)

Recall that if X\sim\mathcal N(\mu,\sigma), then the sampling distribution \overline X=\displaystyle\sum_{i=1}^n\frac{X_i}n\sim\mathcal N\left(\mu,\dfrac\sigma{\sqrt n}\right) with n being the size of the sample.

Transforming to the standard normal distribution, you have

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and the probability is equivalent to

\mathbb P\left(\overline X>\dfrac{1000}{36}\right)=\mathbb P\left(6\dfrac{\overline X-26}{7.2}>6\dfrac{\frac{1000}{36}-26}{7.2}\right)
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3 years ago
An oven heating element turns on when the internal temperature falls to 20 degrees below the set temperature and turns off when
son4ous [18]

Answer:

The range of the oven is 385\leq T\leq 410

Step-by-step explanation:

Consider the provided information.

The internal temperature falls to 20 degrees below the set temperature and turns off when the temperature reaches 5 degrees above the set temperature.

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The internal temperature falls to 20 degrees, therefore the lowest set can be:

405-20=385 degree.

The temperature reaches 5 degrees above the set temperature 405, therefore the upper set is: 405+5=410 degree.

Hence, the temperature will be lying between 385 degree and 410 degree.

This can be written as: 385\leq T\leq 410

Hence, the range of the oven is 385\leq T\leq 410

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