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3 years ago

one number is equal to the square of another. find the numbers if both are positive and their sum is 1122

Mathematics

1 answer:

statuscvo [17]3 years ago

4 0

Answer:

One number is 561

The other number is 23.6854

Step-by-step explanation:

x = y^2 One number = the square of another

x + y^2 = 1122 The sum of the two numbers is 1122

Substitute y^2 in for x on the second equation.

y^2 + y^2 = 1122 Combine like terms on the left

2y^2 = 1122 Divide by 2

y^2 = 1122/2

y^2 = 561 Take the square root of both sides.

y = 23.6854

x = y^2

x = 561

y^2 = 561

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

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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".

$\bar X=8.2$ 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 $z_{\alpha/2}=2.58$