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Vladimir [108]
3 years ago
8

When 36 is added to a certain two-digit number, the results is the number with the digits reversed. The units' digit is one more

than twice the tens' digit. Find the number​.
Mathematics
1 answer:
AnnZ [28]3 years ago
3 0

Answer:

37

Step-by-step explanation:

T = two digit number

X = first digit

Y = second digit

T = XY where XY are two numbers placed next to eachother rather than multiplied.

36 + XY = YX

The units' digit is one more than twice the tens' digit.

Y = 1 + 2X

Since Y is a 1 digit number it can't be greater than 9.

9 ≥ 1 + 2X

This means X can't be greater than 4.

9 - 1 ≥ 2X

8 ≥ 2X

8/2 ≥ X

4 ≥ X

If X = 1, Y = 3

36 + 13 = 48

If X = 2, Y = 5

36 + 25 = 58

If X = 3, Y = 7

36 + 37 = 73

If X = 4, Y = 9

36 + 49 = 88

37 is the reverse of 73

Therefore the number is 37

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Bottles of a popular cola drink are supposed to contain 300 ml of cola. There is some variation from bottle to bottle because th
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Answer:

We conclude that the mean contents of cola bottles is more than or equal to the advertised 300 ml.

Step-by-step explanation:

We are given that Bottles of a popular cola drink are supposed to contain 300 ml of cola. The distribution of the contents is normal with standard deviation of 3 ml.

A student who suspects that the bottler is under-filling measures the contents of six bottles. The results are: 299.4, 297.7, 301.0, 298.9, 300.2, 297.0

<u><em>Let </em></u>\mu<u><em> = mean contents of cola bottles.</em></u>

SO, Null Hypothesis, H_0 : \mu \geq  300 ml   {means that the mean contents of cola bottles is more than or equal to the advertised 300 ml}

Alternate Hypothesis, H_A : \mu < 300 ml   {means that the mean contents of cola bottles is less than the advertised 300 ml}

The test statistics that will be used here is <u>One-sample z test statistics</u> as we know about the population standard deviation;

                       T.S.  = \frac{\bar X -\mu}{\frac{\sigma}{\sqrt{n} } }  ~ N(0,1)

where, \bar X = sample mean contents of cola bottle = \frac{\sum X}{n} = 299.03 ml

            \sigma = population standard deviation = 3 ml

            n = sample of bottles = 6

So, <em><u>test statistics</u></em>  =  \frac{299.03-300}{\frac{3}{\sqrt{6} } }     

                               =  -0.792

<em>Now at 5% significance level, the z table gives critical value of -1.6449 for left-tailed test. Since our test statistics is more than the critical value of z as -0.792 > -1.6449, so we have insufficient evidence to reject our null hypothesis as it will not fall in the rejection region due to which we fail to reject our null hypothesis.</em>

Therefore, we conclude that the mean contents of cola bottles is more than or equal to the advertised 300 ml.

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