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Oksi-84 [34.3K]
3 years ago
11

A number consists of two digits whose sum is 12. If 16 is added to the number, then one of the digits is four times the value of

the other. What is the number?
Mathematics
1 answer:
NeX [460]3 years ago
7 0

Answer: The number is 12.

Step-by-step explanation:

Since we have given that

Sum of two digits = 12

Let the one's digit be 'x'

Let the ten's digit be '12-x'

So, Original number would be

x+10(12-x)\\\\=x+120-10x\\\\=-9x+120

If 16 is added to the number, then one of the digit is four times the value of the other.

According to question, we get that

-9x+120+16\\\\=-9x+136

so, the one's digit be 'x'.

Let the ten's digit be '4x'.

so, New number would be

10x+4x=14x

According to question, it becomes,

14x=-9x+136\\\\14x+9x=136\\\\23x=136\\\\x=\dfrac{136}{23}=12

So, the number would be

-9x+120=-9\times 12+120=-108+120=12

Hence, the number is 12.

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Answer:

ME= \frac{Width}{2}=\frac{0.078}{2}=0.039

\hat p =0.688+0.039=0.727

\hat p =0.766-0.039=0.727

Step-by-step explanation:

Assuming that the confidence interval is (0.688; 0.766)

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.  

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The population proportion have the following distribution  

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The confidence interval would be given by this formula  

\hat p \pm z_{\alpha/2} \sqrt{\frac{\hat p(1-\hat p)}{n}}  

For the 95% confidence interval the value of \alpha=1-0.95=0.05 and \alpha/2=0.025, with that value we can find the quantile required for the interval in the normal standard distribution.  

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Use the confidence interval to find the point estimate and margin of error for the proportion

The margin of error is given by :

Me=z_{\alpha/2} \sqrt{\frac{\hat p(1-\hat p)}{n}}

And for our case we can find the width of the confidence interval like this:

Width =0.766-0.688=0.078

And the estimation for the margin of error would be given by:

ME= \frac{Width}{2}=\frac{0.078}{2}=0.039

Now we can find th point of estimate adding the margin of error to the lower limit of the interval or subtracting the margin of error to the upper limit, like this:

\hat p =0.688+0.039=0.727

\hat p =0.766-0.039=0.727

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<u>Given</u>:

Given that the measure of arc DF is 162°

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