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xenn [34]
2 years ago
6

The graph of F(x) can be stretched vertically and flipped over the x-axis to produce the graph of G(x). If F(x) = x^2, which of

the following could be the equation of G(x)?
Mathematics
1 answer:
katrin [286]2 years ago
6 0

The transformed function is G(x) = -4x² after applying the transformation stretched vertically and flipped over the x-axis option (C) G(x) = -4x² is correct.

<h3>What is a function?</h3>

It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.

The options are missing.

The options are:

A. G(x) = 4x²

B. G(x) = -(1/4)x²

C. G(x) = -4x²

D. G(x) = (1/4)x²

We have an equation of a function F(x)  

F(x) = x²

The transformation F(x) can be stretched vertically and flipped over the x-axis to produce the graph of G(x)

To stretch vertically if the function is multiplied by a constant value

f(x) = ax²

To flip over the x-axis if multiply by negative value.

g(x) = -ax²

From the options

G(x) = -4x²

Thus, the transformed function is G(x) = -4x² after applying the transformation stretched vertically and flipped over the x-axis option (C) G(x) = -4x² is correct.

Learn more about the function here:

brainly.com/question/5245372

#SPJ1

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Answer:

a) By the Central Limit Theorem, it is approximately normal.

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

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

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

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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 p-value, 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}}.

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

Mean of 36 hours and a standard deviation of 5.5 hours.

This means that \mu = 36, \sigma = 5.5

a. What can you say about the shape of the distribution of the sample mean?

By the Central Limit Theorem, it is approximately normal.

b. What is the standard error of the distribution of the sample mean? (Round your answer to 4 decimal places.)

Sample of 9 means that n = 9. So

s = \frac{\sigma}{\sqrt{n}} = \frac{5.5}{\sqrt{9}} = 1.8333

The standard error of the distribution of the sample mean is 1.8333.

c. What proportion of the samples will have a mean useful life of more than 38 hours?

This is 1 subtracted by the pvalue of Z when X = 38. So

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

By the Central Limit Theorem

Z = \frac{X - \mu}{s}

Z = \frac{38 - 36}{1.8333}

Z = 1.09

Z = 1.09 has a pvalue of 0.8621

1 - 0.8621 = 0.1379

0.1379 = 13.79% of the samples will have a mean useful life of more than 38 hours.

d. What proportion of the sample will have a mean useful life greater than 34.5 hours?

This is 1 subtracted by the pvalue of Z when X = 34.5. So

Z = \frac{X - \mu}{s}

Z = \frac{34.5 - 36}{1.8333}

Z = -0.82

Z = -0.82 has a pvalue of 0.2061.

1 - 0.2061 = 0.7939

0.7939 = 79.39% of the samples will have a mean useful life greater than 34.5 hours.

e. What proportion of the sample will have a mean useful life between 34.5 and 38 hours?

pvalue of Z when X = 38 subtracted by the pvalue of Z when X = 34.5. So

0.8621 - 0.2061 = 0.656

0.656 = 65.6% of the samples will have a mean useful life between 34.5 and 38 hours

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