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3 years ago

-4x + y = -9 - 5x + 2y = 3 : Solve the Linear equation

1 answer:

6 0

-4x+y= -9 can be turned into
y= -9 + 4x

5x+2y=3 (plug y in)
5x+2(-9+4x)=3
5x-18+8x=3
5x+8x=3+18
13x=21
divide 13 on both sides
x=1.6

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Simplify the expression. 6c − 8d + 3c + 4d

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Answer:

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Step-by-step explanation:

6c − 8d + 3c + 4d

Combine like terms

6c + 3c − 8d +4d

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3 years ago

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Find the percentage area of moss in a lawn if 3 out of 24 squares contained moss

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4 years ago

An economist is studying the job market in Denver area neighborhoods. Let x represent the total number of jobs in a given neighb

lbvjy [14]

Answer:

a) $\sum X = 13+34+52+28+50+25 =202$

$\sum Y = 1+4+5+5+9+3= 27$

$\sum X^2 = 13^2+34^2+52^2+28^2+50^2+25^2 = 1074$

And in order to calculate the correlation coefficient we can use this formula:

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

$r=\frac{6(1074)-(202)(27)}{\sqrt{[6(7938) -(202)^2][6(157) -(202)^2]}}=0.821$

b) $m=\frac{165}{1137.33}=0.145$

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

$\bar x= \frac{\sum x_i}{n}=\frac{202}{6}=33.67$

$\bar y= \frac{\sum y_i}{n}=\frac{27}{6}=4.5$

And we can find the intercept using this:

$b=\bar y -m \bar x=4.5-(0.145*33.67)=-0.384$

So the line would be given by:

$y=0.145 x -0.384$

c) The coefficient of variation is given by:

$r^2 = 0.821^2 = 0.674$

And we can conclude that 67.4% of the variation in y can be explainedby the corresponding variation in x and the least-squares line

d) For this case we just need to replade x = 34 into our model and we got:

$y=0.145*34 -0.384= 3.097$

Step-by-step explanation:

For this case we have the following data:

x 13 34 52 28 50 25

y 1 4 5 5 9 3

Part a

$\sum X = 13+34+52+28+50+25 =202$

$\sum Y = 1+4+5+5+9+3= 27$

$\sum X^2 = 13^2+34^2+52^2+28^2+50^2+25^2 = 1074$

And in order to calculate the correlation coefficient we can use this formula:

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

$r=\frac{6(1074)-(202)(27)}{\sqrt{[6(7938) -(202)^2][6(157) -(202)^2]}}=0.821$

Part b

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

Where:

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

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

With these we can find the sums:

$S_{xx}=\sum_{i=1}^n x^2_i -\frac{(\sum_{i=1}^n x_i)^2}{n}=7938-\frac{202^2}{6}=1137.33$

$S_{xy}=\sum_{i=1}^n x_i y_i -\frac{(\sum_{i=1}^n x_i)(\sum_{i=1}^n y_i){n}}=1074-\frac{202*27}{6}=165$

And the slope would be:

$m=\frac{165}{1137.33}=0.145$

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

$\bar x= \frac{\sum x_i}{n}=\frac{202}{6}=33.67$

$\bar y= \frac{\sum y_i}{n}=\frac{27}{6}=4.5$

And we can find the intercept using this:

$b=\bar y -m \bar x=4.5-(0.145*33.67)=-0.384$

So the line would be given by:

$y=0.145 x -0.384$

Part c

The coefficient of variation is given by:

$r^2 = 0.821^2 = 0.674$

And we can conclude that 67.4% of the variation in y can be explainedby the corresponding variation in x and the least-squares line

Part d

For this case we just need to replade x = 34 into our model and we got:

$y=0.145*34 -0.384= 3.097$

3 0

4 years ago