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Ainat [17]
3 years ago
9

Two ways you could evaluate 37% of the sum of 27 3/5 and 15.9 plz answer as soon as you can

Mathematics
1 answer:
zhannawk [14.2K]3 years ago
4 0

Answer:

16.095.  

Step-by-step explanation:

We can either find 37% of both the numbers and add the results, or we can add the numbers and then find the 37% of the sum.  

1. Let us find 37% of both numbers separately.

First of all we will convert our mixed fraction into improper fraction.

27\frac{3}{5}=\frac{138}{5}

37% of 27\frac{3}{5} will be,

\frac{138}{5}\times \frac{37}{100}=\frac{138}{5}\times 0.37

27.6\times 0.37=10.212

Now let us find 37% of 15.9.

15.9\times \frac{37}{100}=15.9\times 0.37=5.883

Now let us add 37% of both numbers.

10.212+5.883=16.095  

Therefore, 37% of our given numbers will be 16.095.

2. Now we will add both numbers and then find 37% of their sum.

27\frac{3}{5} +15.9=\frac{138}{5}+15.9

27.6 +15.9=43.5

Now let us find 37% of 43.5.  

43.5\times\frac{37}{100}=43.5\times 0.37=16.095

Therefore, 37% of 43.5 is 16.095. We have seen that using either way we got the same answer.


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Researchers are interested if a school breakfast program leads to taller children. Assume that the population of all 5 year-old
DedPeter [7]

Answer:

39-1.96\frac{1}{\sqrt{25}}=38.608    

39+1.96\frac{1}{\sqrt{25}}=39.392    

So on this case the 95% confidence interval would be given by (38.608;39.392)    

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

And replacing we got:

ME= 1.96 *\frac{1}{\sqrt{25}}= 0.392

Now we have everything in order to replace into formula (1):

39-1.96\frac{1}{\sqrt{25}}=38.608    

39+1.96\frac{1}{\sqrt{25}}=39.392    

So on this case the 95% confidence interval would be given by (38.608;39.392)    

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