All categories

2 years ago

Does the MVT apply? Explain why or why not. y=-x^2/x-1 ; [-1,1]

Mathematics

1 answer:

frez [133]2 years ago

8 0

Hi there!

$\large\boxed{\text{No, it does not.}}$

$y = \frac{x^{2} }{x-1}$

Looking at the equation, we can see that there is a discontinuity at x = 1 (Vertical Asymptote).

The interval given also includes x = 1 as an enclosed value.

Therefore, the MVT does not apply because the equation is not continuous on the interval [-1, 1].

You might be interested in

What is <br><img src="https://tex.z-dn.net/?f=f%284%29%20%3D%20%20%5Csqrt%7Bx%20%7B%7D%5E%7B2%7D%20%7D%20%20-%205" id="TexFormul

dexar [7]

<h3>Solution:</h3>

$f(x) = \sqrt{ {x}^{2} } - 5 \\ = > f(4) = \sqrt{ {(4)}^{2} } - 5 \\ \: \: \: \: \: \: \: \: \: \: = \sqrt{16 } - 5 \\ = 4 - 5 \\ = - 1 \\ or \\ = - 4 - 5 \\ = - 9$

<h3>Answer:</h3>

-1 or -9

<h3>Hope it helps</h3>

ray4918 here to help

3 0

2 years ago

Write an equation of the line that passes through (0, 6) and is parallel to y=5x-3<br><br> Y=

lina2011 [118]

Answer:The answer should be y = 5x + 6

Step-by-step explanation:

5 0

2 years ago

A. 1/3=0.33<br>B. 1/6=0.17<br>C. 1/10=0.10<br>D. 1/4=0.25

statuscvo [17]

B

lmk if this helped

4 0

2 years ago

Explain which event is more likely: rolling two dice and getting a total of 11, or, tossing a coin and getting three Heads in a

amm1812

Answer:

The gambler's fallacy, also known as the Monte Carlo fallacy or the fallacy of the maturity of chances, is the erroneous belief that if a particular event occurs more frequently than normal during the past it is less likely to happen in the future (or vice versa), when it has otherwise been established that the probability of such events does not depend on what has happened in the past. Such events, having the quality of historical independence, are referred to as statistically independent. The fallacy is commonly associated with gambling, where it may be believed, for example, that the next dice roll is more than usually likely to be six because there have recently been fewer than the usual number of sixes.

The term "Monte Carlo fallacy" originates from the best known example of the phenomenon, which occurred in the Monte Carlo Casino in 1913.[1]

8 0

3 years ago

An automobile manufacturer has given its van a 59.5 miles/gallon (MPG) rating. An independent testing firm has been contracted t

LekaFEV [45]

Answer:

The pvalue of the test is 0.0124 < 0.1, which means that there is sufficient evidence at the 0.1 level to support the testing firm's claim.

Step-by-step explanation:

An automobile manufacturer has given its van a 59.5 miles/gallon (MPG) rating. An independent testing firm has been contracted to test the actual MPG for this van since it is believed that the van has an incorrect manufacturer's MPG rating:

At the null hypothesis, we test if the mean is the same, that is:

$H_0: \mu = 59.5$

At the alternate hypothesis, we test that it is different, that is:

$H_a: \mu \neq 59.5$

The test statistic is:

$z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}$

In which X is the sample mean, $\mu$ is the value tested at the null hypothesis, $\sigma$ is the standard deviation and n is the size of the sample.

59.5 is tested at the null hypothesis:

This means that $\mu = 59.5$

After testing 250 vans, they found a mean MPG of 59.2. Assume the population standard deviation is known to be 1.9.

This means that $n = 250, X = 59.2, \sigma = 1.9$

Value of the test statistic:

$z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}$

$z = \frac{59.2 - 59.5}{\frac{1.9}{\sqrt{250}}}$

$z = -2.5$

Pvalue of the test and decision:

The pvalue of the test is the probability of finding a mean that differs from 59.5 by at least 0.3, which is P(|Z|>-2.5), which is 2 multiplied by the pvalue of Z = -2.5.

Looking at the z-table, Z = -2.5 has a pvalue of 0.0062

2*0.0062 = 0.0124

The pvalue of the test is 0.0124 < 0.1, which means that there is sufficient evidence at the 0.1 level to support the testing firm's claim.

5 0

2 years ago