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Inessa [10]
3 years ago
11

Which equation has solution x = -3?

Mathematics
1 answer:
____ [38]3 years ago
4 0
A) 2x - 7 = -1

Add 7 to both sides of the equation.

2x = 6

x = 3

Choice A is not the answer.


B) 3x + 8 = 1

Subtract 8 from both sides.

3x = -7

Divide both sides by 3.

x = -2.3 repeating

Choice B is not the answer.

C) 1/2x + 8 = 10

1/2x = 2

Divide both sides by 1/2.

x = 4

Choice C is not the answer.

By process of elimination, choice D is the answer.

D) 1/2(2x - 6) = -6

x - 3 = -6

Add 3 to both sides.

x = -3
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Confidence =1-\alpha=1-0.01=0.99

And then the confidence level would be given by 99%

Step-by-step explanation:

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

Assuming the X follows a normal distribution

X \sim N(\mu, \sigma)

The distribution for the sample mean is given by:

\bar X \sim N(\mu, \frac{\sigma}{\sqrt{n}})

\bar x =512 represent the sample mean

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n= 100 sample size selected.

The confidence interval is given by this formula:

\bar X \pm z_{\alpha/2} \frac{\sigma}{\sqrt{n}}   (1)

The marginof error for this case is given by Me=25.76. And we know that the formula for the margin of error is given by:

Me=z_{\alpha/2} \frac{\sigma}{\sqrt{n}}

25.76=z_{\alpha/2} \frac{100}{\sqrt{100}}

And we can find the critical value z_{\alpha/2} like this:

z_{\alpha/2}=\frac{25.76(\sqrt{100})}{100}=2.576

And we know that on the right tail of the z score =2.576 we have \alpha/2 of the total area. We can find the area on the right of the z score using this excel code:

"=1-NORM.DIST(2.576,0,1,TRUE)" or using a table of the normal standard distribution, and we got 0.004998=\alpha/2, so then \alpha=0.00498*2=0.009995 \approx 0.01, and then we can find the confidence like this:

Confidence =1-\alpha=1-0.01=0.99

And then the confidence level would be given by 99%

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