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Dmitrij [34]
2 years ago
12

What are the vertical and horizontal asymptotes for the function f (x) = StartFraction 3 x squared Over x squared minus 4 EndFra

ction?

Mathematics
2 answers:
NISA [10]2 years ago
7 0

Answer:

The vertical asymptotes are x = 2 and x =  -2.

The horizontal asymptote is y = 3.

Step-by-step explanation:

Given the function

f(x)=\dfrac{3x^2}{x^2-4}

Rewrite it as follows:

f(x)\\ \\=\dfrac{3x^2}{x^2-4}\\ \\=3\dfrac{x^2-4+4}{x^2-4}\\ \\=3\left(1+\dfrac{4}{x^2-4}\right)\\ \\=3+\dfrac{12}{(x-2)(x+2)}

This function is undefined when the denominator is equal to 0. The denominator is equal to 0 when x = 2 or x = -2, so two vertical asymptotes are x = 2 and x =  -2.

The horizontal asymptote is y = 3.

Marrrta [24]2 years ago
6 0

Answer:

A

Step-by-step explanation:

Its the first one on edgeniuty (trash website)

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The fracture strength of tempered glass averages 14 (measured in thousands of pounds per square inch) and has standard deviation
Wewaii [24]

Answer:

0.1587 = 15.87% probability that the average fracture strength of 100 randomly selected pieces of this glass exceeds 14.2.

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.

The fracture strength of tempered glass averages 14 (measured in thousands of pounds per square inch) and has standard deviation 2.

This means that \mu = 14, \sigma = 2

Sample of 100:

This means that n = 100, s = \frac{2}{\sqrt{100}} = 0.2

What is the probability that the average fracture strength of 100 randomly selected pieces of this glass exceeds 14.2?

This is 1 subtracted by the p-value of Z when X = 14.2. So

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

By the Central Limit Theorem

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

Z = \frac{14.2 - 14}{0.2}

Z = 1

Z = 1 has a p-value of 0.8413.

1 - 0.8413 = 0.1587

0.1587 = 15.87% probability that the average fracture strength of 100 randomly selected pieces of this glass exceeds 14.2.

6 0
3 years ago
State the domain and range of the following relation.
olga nikolaevna [1]

Answer:

Step-by-step explanation:

domain (ur x values) = -3,-1,1,2

range (ur y values) = -3,1,2,4

do not have to write them more then once

answer is C

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3 years ago
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aleksklad [387]
The answer should be x=-2
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HURRY PLEASE! Which expression is equivalent to ^4sqrt6/^3sqrt2?<br><br> (options in the image)
melamori03 [73]

Answer:

According to the given problems the one that gets closer is the first option. ^12sqrt27/2

Step-by-step explanation:

<em>Simplify the radical by breaking the radicand up into a product of known factors.</em>

The answer for the first question is 12 √ 27 / 2


6 0
3 years ago
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