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3 years ago

PLEASE HELP ME PLEASE PLEASE

Mathematics

1 answer:

Nastasia [14]3 years ago

5 0

Of the two rows you ought to choose the top one
48 - 3x > 10
The second row makes the bottles grow. I wish this were true, but it is not.
After x gets to 13, she has dropped down below where she does not need to shop for more bottles.

48 - 3x > 10 Add 3x to both sides.
48 > 10 + 3x Subtract 10
38 > 3x Divide by 3
12 . 66666 So she can finish the 13th bottle but when she does, she has to go out and get more.

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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:

$y=0.145*34 -0.384= 3.097$

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Answer:

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The common difference is 52 - 22 = 30

a_1 = -38

a_2 = -38 + 30

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a_n = -38 + (n - 1)30 (since the term number is n, we multiply the common difference by n - 1)

a_n = -38 + 30(n - 1)

a_37 = -38 + 30(37 - 1)

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