Solve the formula 2x+3y=12 for y

Mathematics

1 answer:

rjkz [21]3 years ago

3 0

Answer:

y=4−2x/3

Step-by-step explanation:

Move all terms that don't contain y to the right side and solve.

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A survey organization has used the methods of our class to construct an approximate 95% confidence interval for the mean annual

lawyer [7]

Answer:

$\bar X = \frac{66000+70000}{2}= 68000$

We can estimate the margin of error with this formula:

$ME= \frac{Upper -Lower}{2}= \frac{70000-66000}{2}= 2000$

And the margin of error is given by:

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

And we can rewrite the margin of error like this:

$ME =z_{\alpha/2}*SE$

Where $SE= \frac{\sigma}{\sqrt{n}}$

For 95% of confidence the critical value is $z_{\alpha/2}= \pm 1.96$

The Standard error would be:

$SE= \frac{ME}{z_{\alpha/2}}= \frac{2000}{1.96}= 1020.408$

For 99% of confidence the critical value is $z_{\alpha/2}= \pm 2.58$

And the new margin of error would be:

$ME = 2.58* 1020.408 = 2632.653$

And then the interval would be given by:

$Lower = 68000- 2632.653 = 65367.347$

$Upper = 68000+ 2632.653 = 70632.653$

Step-by-step explanation:

Previous concepts

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".

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".

$\bar X$ represent the sample mean for the sample