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3 years ago

∫eˣ²dx find integral show all steps

Mathematics

1 answer:

tino4ka555 [31]3 years ago

4 0

Answer:

$\int \: e {}^{x {}^{2} } dx \\ y = {e}^{ {x}^{2} } \\ ln(y) = {x}^{2} \\ \frac{dy}{y} = 2xdx \\ dy/2x = {e}^{ {x}^{2} } dx \\ \int \: d( {e}^{ {x}^{2} } ) = \int {e}^{ {x}^{2} } .2xdx \\ \frac{{e}^{ {x}^{2} } }{2x} = \int \: {e}^{ {x}^{2} } dx \\ \int \: {e}^{ {x}^{2} } dx \: = \frac{1}{2x} {e}^{ {x}^{2} } + c$

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maxonik [38]

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<u>Explanation:</u>

Complementary angles are those two angles whose sum is 90 degrees.

Supplementary angles are those two angles whose sum is 180 degrees.

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(a)

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(b)

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(c)

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3 years ago

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3 years ago

The scores on the GMAT entrance exam at an MBA program in the Central Valley of California are normally distributed with a mean

Kaylis [27]

Answer:

58.32% probability that a randomly selected application will report a GMAT score of less than 600

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Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal probability distribution

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean $\mu$ and standard deviation $\sigma$ , the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean $\mu$ and standard deviation $s = \frac{\sigma}{\sqrt{n}}$ .