What is the GFC of 72 and 36

1 answer:

6 0

The GCF of 72 and 36 is: 36

List out the factors of each number (72 and 36), and find the common factors between the two numbers.

Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36
Factors of 72: 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72

Looking at the factors above, the common ones are 1, 2, 3, 4, 6, 9, 12, 18, and 36. But... considering we are looking for the "greatest" common factor, our highest number out of the listed ones is 36, making it the greatest common factor of 72 and 36.

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a) The 99% confidence interval would be given by (24.409;24.979)

b) n=464

Step-by-step explanation:

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".

Part a

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:

$df=n-1=47-1=46$

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(0.025,46)".And we see that $t_{\alpha/2}=2.01$