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Katena32 [7]
3 years ago
12

The graphs below have the same shape. What is the equation of the blue graph? A. g(x) = (x-4)2 - 2 B. g(x) = (x + 4)2 + 2 C. g(x

) = (x - 4)2 + 2 D. g(x) = (x + 4)2 - 2​

Mathematics
1 answer:
Doss [256]3 years ago
4 0

Answer:

The answer is D. g(x) = (x+4)^2 - 2

Step-by-step explanation:

This is because f(x) = (x-h)^2 + k

where h = horizontal translations and k = vertical translations

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Find the domain of the function.<br> f(x)= x+2/1-X
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all real numbers expect  1.

Step-by-step explanation: This is a rational function. when we  usually the find the domain of a rational function we would look at the bottom because you don't want the denomonatior to be zero because dividing by zero in math makes the range undefined. so we use the equation and set it up to zero to find the domain. 1-x=0 -x=-1, divide by -1 and we get  1.  So x can be any numbers expect 1. Interval notation: (-∞,1)∪(1,+∞)

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Suppose that the walking step lengths of adult males are normally distributed with a mean of 2.5 feet and a standard deviation o
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Answer:

0% probability that the mean of the sample taken is less than 2.2 feet.

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 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:

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 p-value, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem establishes 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 2.5 feet and a standard deviation of 0.2 feet.

This means that \mu = 2.5, \sigma = 0.2

Sample of 41

This means that n = 41, s = \frac{0.2}{\sqrt{41}}

Find the probability that the mean of the sample taken is less than 2.2 feet.

This is the p-value of Z when X = 2.2 So

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

By the Central Limit Theorem

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

Z = \frac{2.2 - 2.5}{\frac{0.2}{\sqrt{41}}}

Z = -9.6

Z = -9.6 has a p-value of 0.

0% probability that the mean of the sample taken is less than 2.2 feet.

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