Which coordinate is a solution for the system containing the equations y=x+3 and y=4x?

Mathematics

1 answer:

ohaa [14]3 years ago

4 0

Answer:

(1, 4 )

Step-by-step explanation:

Given the 2 equations

y = x + 3 → (1)

y = 4x → (2)

Substitute y = 4x into (1)

4x = x + 3 ( subtract x from both sides )

3x = 3 ( divide both sides by 3 )

x = 1

Substitute x = 1 into either of the 2 equations and evaluate for y

Substituting into (2)

y = 4x = 4 × 1 = 4

Solution is (1, 4 )

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A survey of 35 individuals who passed the seven exams and obtained the rank of Fellow in the actuarial field finds the average s

arsen [322]

Answer:

$150000-2.032\frac{15000}{\sqrt{35}}=144847.94$

$150000+2.032\frac{15000}{\sqrt{35}}=155152.06$

So on this case the 95% confidence interval would be given by (144847.94;155152.06)

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".

$\bar X=150000$ represent the sample mean

$\mu$ population mean (variable of interest)

s=15000 represent the sample standard deviation

n=35 represent the sample size

Solution to the problem

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:

$df=n-1=35-1=34$

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(0.025,34)".And we see that $t_{\alpha/2}=2.032$