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4 years ago

Rafael must choose a number between 67 and 113 that is a multiple of, 2,4, and 5 . Write all the numbers that he could choose.

1 answer:

5 0

First, find out what the greatest common factor is between 2, 4, and 5.

This is 20. So any number divisible by 20 is also divisible by 2, 4, and 5. 

Now we find the list of numbers that are multiples of 20 between 67 and 113. 

The solutions are: 

80 and 100.

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In a data distribution, the first quartile, the median and the means are 30.8, 48.5 and 42.0 respectively. If the coefficient sk

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Answer:

a) The third quartile Q₃ = 56.45

b) Variance $\mathbf{ \sigma^2 =2633.31}$

Step-by-step explanation:

Given that :

$Q_1$ = 30.8

Median $Q_2$ = 48.5

Mean = 42

a) The mean is less than median; thus the expression showing the coefficient of skewness is given by the formula :

$SK = \dfrac{Q_3+Q_1-2Q_2}{Q_3-Q_1}$

$-0.38 = \dfrac{Q_3+30.8-2(48.5)}{Q_3-30.8}$

$-0.38Q_3 + 11.704 = Q_3 +30.8 - 97$

$1.38Q_3 = 77.904$

Divide both sides by 1.38

$Q_3 = 56.45$

b) The objective here is to determine the approximate value of the variance;

Using the relation

$SK_p = \dfrac{Mean- (3*Median-2 *Mean) }{\sigma}$

$-0.38= \dfrac{42- (3 *48.5-2*42) }{\sigma}$

$-0.38= \dfrac{(-19.5) }{\sigma}$

$-0.38* \sigma = {(-19.5) }{}$

$\sigma =\dfrac {(-19.5) }{-0.38 }$

$\sigma =51.32$

Variance = $\sigma^2 =51.32^2$

$\mathbf{ \sigma^2 =2633.31}$

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Step-by-step explanation:

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