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m_a_m_a [10]
3 years ago
14

X^2-11=53 in the simplest form

Mathematics
1 answer:
Vedmedyk [2.9K]3 years ago
3 0

Answer:

x=±8

Step-by-step explanation:

You add 11 on both sides

x^2=53+11

x^2 = 64 so

x=8 or x=-8

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Find the y-intercept and x-intercept of the line.<br> -x+4y = 8
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Answer:

x-intercept(s):  ( − 8 , 0 )

y-intercept(s):  ( 0 , 2 )

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To find the x-intercept, substitute in  0  for  y  and solve for  x . To find the y-intercept, substitute in  0 for  x  and solve for  y.

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2 years ago
A laptop producing company also produces laptop batteries, and claims that the batteries
gregori [183]

Answer:

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The null and alternative hypothesis are:

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<em>The question is incomplete: To test this claim a sample or population standard deviation is needed.</em>

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<em> NOTE (after solving): The difference between the sample mean and the mean of the null hypothesis is big enough to reject the null hypothesis, even when we have a sample standard deviation of 3.5 hours, which can be considered bigger than the maximum standard deviation for the sample.</em>

This is a hypothesis test for the population mean.

The claim is that the batteries power the laptops for significantly less than 4 hours.

Then, the null and alternative hypothesis are:

H_0: \mu=4\\\\H_a:\mu< 4

The significance level is 0.05.

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The sample mean is M=3.5.

As the standard deviation of the population is not known, we estimate it with the sample standard deviation, that has a value of s=2.

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s_M=\dfrac{s}{\sqrt{n}}=\dfrac{2}{\sqrt{500}}=0.0894

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t=\dfrac{M-\mu}{s/\sqrt{n}}=\dfrac{3.5-4}{0.0894}=\dfrac{-0.5}{0.0894}=-5.5902

The degrees of freedom for this sample size are:

df=n-1=500-1=499

This test is a left-tailed test, with 499 degrees of freedom and t=-5.5902, so the P-value for this test is calculated as (using a t-table):

P-value=P(t

As the P-value (0) is smaller than the significance level (0.05), the effect is  significant.

The null hypothesis is rejected.

There is enough evidence to support the claim that the batteries power the laptops for significantly less than 4 hours.

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