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USPshnik [31]
3 years ago
7

Solve for x. 2x^2+12x+11-(x+4)^2

Mathematics
1 answer:
Andru [333]3 years ago
5 0
2x² + 12x + 11 - (x - 4)²
2x² + 12x + 11 - 1(x - 4)²
2x² + 12x + 11 - 1(x - 4)(x - 4)
2x² + 12x + 11 - 1(x(x - 4) - 4(x - 4))
2x² + 12x + 11 - 1(x(x) - x(4) - 4(x) + 4(4))
2x² + 12x + 11 - 1(x² - 4x - 4x + 16)
2x² + 12x + 11 - 1(x² - 8x + 16)
2x² + 12x + 11 + 1(x²) + 1(8x) - 1(16)
2x² + 12x + 11 + x² + 8x - 16
2x² + x² + 12x + 8x + 11 - 16
3x² + 20x - 5
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Answer:

The confidence interval on this case is given by:

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

For this case the confidence interval is given by (62.532, 76.478)[/tex]

And we can calculate the mean with this:

\bar X = \frac{62.532+76.478}{2}= 69.505

So then the mean for this case is 69.505

Step-by-step explanation:

Previous concepts

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

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A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

\bar X represent the sample mean  

\mu population mean (variable of interest)  

\sigma represent the population standard deviation  

n represent the sample size  

Assuming the X follows a normal distribution  

X \sim N(\mu, \sigma)

The confidence interval on this case is given by:

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

For this case the confidence interval is given by (62.532, 76.478)[/tex]

And we can calculate the mean with this:

\bar X = \frac{62.532+76.478}{2}= 69.505

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