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3 years ago

6х + 4ув 32-6х + 4 y = 8

Mathematics

1 answer:

AveGali [126]3 years ago

6 0

Answer:

The Solution set is (x,y){(2,5)}

Step-by-step explanation:

The given equation is:

6x+4y=32

-6x+4y=8

We will use the elimination method:

By this method we will eliminate the variable x.

6x+4y=32

-6x+4y=8

________

8y=40

Divide both the sides by 8

8y/8=40/8

y=5

Now substitute the value of y in equation 2:

-6x+4y=8

-6x+4(5)=8

-6x+20=8

Move the constant value to the R.H.S

-6x=8-20

-6x= -12

Divide both the terms by -6

-6x/-6 = -12/-6

x= 2

The Solution set is (x,y){(2,5)}....

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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".

$\bar X=39$ represent the sample mean for the sample

$\mu$ population mean (variable of interest)

$\sigma=1$ represent the population standard deviation

n=25 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)

The margin of error is given by:

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

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 tabel to find the critical value. The excel command would be: "=-NORM.INV(0.025,0,1)".And we see that $z_{\alpha/2}=1.96$