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Gwar [14]
3 years ago
13

Is (0, 3) a solution to the following system?

Mathematics
1 answer:
daser333 [38]3 years ago
6 0

Solve each equation with (0, 3)

y = -x + 3

3 = -0 + 3

y = 3 (correct since y = 3 in (0, 3))

y = 2x - 3

3 = 2(0) - 3

3 = 0 - 3

3 = -3 (incorrect since it isn't equal)

So... No, because it does not check in the second equation.

Best of Luck!

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8.2-2.58\frac{2.2}{\sqrt{18}}=6.86    

8.2+2.58\frac{2.2}{\sqrt{18}}=9.54    

So on this case the 90% confidence interval would be given by (6.86;9.54)    And the error is given by:

ME= 2.58\frac{2.2}{\sqrt{18}} =1.338

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=8.2 represent the sample mean for the sample  

\mu population mean (variable of interest)

\sigma=2.2 represent the population standard deviation

n represent the sample size  

Solution to the problem

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

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

Since the Confidence is 0.90 or 90%, the value of \alpha=0.1 and \alpha/2 =0.005, and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-NORM.INV(0.005,0,1)".And we see that z_{\alpha/2}=2.58

Now we have everything in order to replace into formula (1):

8.2-2.58\frac{2.2}{\sqrt{18}}=6.86    

8.2+2.58\frac{2.2}{\sqrt{18}}=9.54    

So on this case the 90% confidence interval would be given by (6.86;9.54)    And the error is given by:

ME= 2.58\frac{2.2}{\sqrt{18}} =1.338

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