Solve each equation. 6x2 + 1 = 13

2 answers:

7 0

Hello!

Do you mean only this one(?), or are there more? If only this, it'll be like this. (it could be 1 of 2 ways the way I see it.)

6x² + 1 = 13 or 6 * x * 2 + 1 = 13

If the first one, it'll be x = √2 or ≈1.41
If the second one, it'll be x = 1

Hope this helps! ☺♥

pashok25 [27]4 years ago

4 0

6x^2 + 1 = 13
subtract 1 from both sides
6x^2 = 12 take the square root of both sides
6x = sqr rt 12 divide by 6
x = plus or minus sqr rt 12 divided by 2

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From 19 measurements of a pressure controller, the mean operating pressure is 4.97 kPa with a standard deviation of 0.0461 kPa.

Semenov [28]

Answer:

$4.97-2.10\frac{0.0461}{\sqrt{19}}=4.95$

$4.97+2.10\frac{0.0461}{\sqrt{19}}=4.99$

So on this case the 95% confidence interval would be given by (4.95;4.99)

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".

$\bar X =4.97$ represent the sample mean

$\mu$ population mean (variable of interest)

s=0.0461 represent the sample standard deviation

n=19 represent the sample size

Confidence interval

The confidence interval for the mean is given by the following formula:

$\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}$ (1)

In order to calculate the critical value $t_{\alpha/2}$ we need to find first the degrees of freedom, given by:

$df=n-1=19-1=18$

Since the Confidence is 0.95 or 95%, the value of $\alpha=0.05$ and $\alpha/2 =0.025$ , and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-T.INV(0.025,18)".And we see that $t_{\alpha/2}=2.10$