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3 years ago

Solve the system of equations: x+y=6 3x−5y=2

Mathematics

1 answer:

Crank3 years ago

7 0

Answer:

x=4, y=2

Step-by-step explanation:

x+y=6

3x−5y=2

Multiply the first equation by 5

5(x+y)=6*5

5x+5y = 30

Add this to the second equation

5x+5y = 30

3x -5y = 2

---------------------

8x = 32

Divide each side by 8

8x/8 = 32/8

x = 4

Now we need to find y

x+y =6

4+y =6

Subtract 4 from each side

4+y-4 =6-4

y = 2

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3 years ago

Read 2 more answers

The temperature in Scottsdale increased by 2 degrees in 2 days. If the temperature changed by the same

Vsevolod [243]

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yniar hcum oot sti ereh pleh esaelp retaw eht rednu ma i uoy era woh olleh

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2 years ago

A doctor wants to estimate the mean HDL cholesterol of all 20- to 29-year-old females. The number of subjects needed to estima

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Answer:

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And the sample size would decrease by 160-65=95 subjects

Step-by-step explanation:

1) 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

$\mu$ population mean (variable of interest)

s represent the sample standard deviation

n represent the sample size

ME represent the margin of error

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

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

2) Solution to the problem

Since the new Confidence is 0.90 or 90%, the value of $\alpha=0.1$ and $\alpha/2 =0.05$ , and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-NORM.INV(0.05,0,1)".And we see that $z_{\alpha/2}=1.64$