Slope = -3; y-intercept = 2

This week, we are covering relationships that can be approximated by linear equations. For instance, y = 453x + 3768 represents

lana [24]

Answer:

See explanation below.

Step-by-step explanation:

We assume that the data is given by :

x: 30, 30, 30, 50, 50, 50, 70,70, 70,90,90,90

y: 38, 43, 29, 32, 26, 33, 19, 27, 23, 14, 19, 21.

Where X represent the cost for scholarships in thousands of dollars and y represent the cost of life for an academic semester (The data comes from the web)

We can find the least-squares line appropriate for this data.

For this case we need to calculate the slope with the following formula:

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

Where:

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

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

So we can find the sums like this:

$\sum_{i=1}^n x_i = 30+30+30+50+50+50+70+70+70+90+90+90=720$

$\sum_{i=1}^n y_i =38+43+29+32+26+33+19+27+23+14+19+21=324$

$\sum_{i=1}^n x^2_i =30^2+30^2+30^2+50^2+50^2+50^2+70^2+70^2+70^2+90^2+90^2+90^2=49200$

$\sum_{i=1}^n y^2_i =38^2+43^2+29^2+32^2+26^2+33^2+19^2+27^2+23^2+14^2+19^2+21^2=9540$

$\sum_{i=1}^n x_i y_i =30*38+30*43+30*29+50*32+50*26+50*33+70*19+70*27+70*23+90*14+90*19+90*21=17540$

With these we can find the sums:

$S_{xx}=\sum_{i=1}^n x^2_i -\frac{(\sum_{i=1}^n x_i)^2}{n}=49200-\frac{720^2}{12}=6000$

$S_{xy}=\sum_{i=1}^n x_i y_i -\frac{(\sum_{i=1}^n x_i)(\sum_{i=1}^n y_i)}=17540-\frac{720*324}{12}{12}=-1900$

And the slope would be:

$m=-\frac{1900}{6000}=-0.317$

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

$\bar x= \frac{\sum x_i}{n}=\frac{720}{12}=60$

$\bar y= \frac{\sum y_i}{n}=\frac{324}{12}=27$

And we can find the intercept using this:

$b=\bar y -m \bar x=27-(-0.317*60)=46.02$

So the line would be given by:

$y=-0.317 x +46.02$

We have an inverse linear relationship since the slope is negative between the variables of interest.

8 0

3 years ago

What is the following product?

KiRa [710]

ANSWER

$2 \sqrt{42} +7 \sqrt{2}- 6- \sqrt{21}$

EXPLANATION

The given product is:

$( \sqrt{14} - \sqrt{3} )( \sqrt{12} + \sqrt{7} )$

We expand using the distributive property to obtain:

$\sqrt{14}( \sqrt{12} + \sqrt{7}) -\sqrt{3}( \sqrt{12} + \sqrt{7} )$

Extract the perfect squares to get:

$\sqrt{14}(2 \sqrt{3} + \sqrt{7}) -\sqrt{3}( 2\sqrt{3} + \sqrt{7} )$

Expand further to get;

$2 \sqrt{42} +7 \sqrt{2}- 2(3) - \sqrt{21}$

This simplifies to,

$2 \sqrt{42} +7 \sqrt{2}- 6- \sqrt{21}$

5 0

3 years ago

Examine the graphs and match each one with the correct coordinate rotation. You should match one graph with one rule.

irinina [24]

A is with b d with a c with e

8 0

2 years ago

A pet store has 9dog leashes. It has 8 Fewer dog leashes than the dog collars. How many dog collars does the store have?

Katen [24]

Answer:

Since you know that the pet store has 9 dog leashed, and we know that they have 8 fewer dog leashes than dog collars we can just add 8 to 9 to get 17 dog collars

4 0

2 years ago

Read 2 more answers

Now it is time to create your own graph. Listed below are the weights of 10 of your classmates. Remember, this is science so we

kakasveta [241]

No one answered my question how should I do

3 0

3 years ago