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2 years ago

The sum of two numbers is 20. The difference

Mathematics

1 answer:

Leno4ka [110]2 years ago

7 0

Hence, the numbers are 16 and 4

Further Explanation:

First of all we have to make the equations from the word problem.

Let x be the first number and y be the second number.

Then,

The sum of two numbers is 20 => x + y = 20 => Eqn 1

The difference between three times the first number and twice the second is 40 => 3x-2y = 40 => Eqn 2

$From\ Eqn\ 1\\x+y=20\\y = 20-x\\Putting\ y=20-x\ into\ Eqn\ 2\\3x - 2(20-x) = 40\\3x-40+2x = 40\\5x-40 = 40\\5x = 40+40\\5x = 80\\\frac{5x}{5} = \frac{80}{5} \\x = 16\\y = 20-x\\y=20-16\\y = 4$

The numbers can be verified:

$x+y = 20\\16+4 =20\\20=20\\$

As the equation is verified by the values of x and y.

Hence, the numbers are 16 and 4

Keywords: Linear equations, Substitution method to solve equations

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Answer:

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Step-by-step explanation:

Assuming the following dataset:

Monthly Sales (Y) Interest Rate (X)

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Part a

And we want a linear model on this way y=mx+b, where m represent the slope and b the intercept. In order to find the slope we have this formula:

$m=\frac{S_{xy}}{S_{xx}}$

Where:

$S_{xy}=\sum_{i=1}^n x_i y_i -\frac{(\sum_{i=1}^n x_i)(\sum_{i=1}^n y_i)}{n}$

$S_{xx}=\sum_{i=1}^n x^2_i -\frac{(\sum_{i=1}^n x_i)^2}{n}$

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And the slope would be:

$m=\frac{-91.225}{14.5875}=-6.254$

Nowe we can find the means for x and y like this:

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$b=\bar y -m \bar x=24.25-(-6.254*8.125)=75.064$

So the line would be given by:

$y=-6.254 x +75.064$

Part b

For this case we need to calculate the correlation coefficient given by:

$r=\frac{n(\sum xy)-(\sum x)(\sum y)}{\sqrt{[n\sum x^2 -(\sum x)^2][n\sum y^2 -(\sum y)^2]}}$

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