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Inessa05 [86]
3 years ago
11

X+y+z=−4 2x+3y−2z=10 −x+2y−3z=−12 solve for x,y,z WILL MARK BRAINLIEST!!!

Mathematics
1 answer:
Norma-Jean [14]3 years ago
7 0

Answer:

x = 13

y = -10

z = -7

Step-by-step explanation:

x+y+z=−4

2x+3y−2z=10

−x+2y−3z=−12

Add the first and the third equations to eliminate x

x+y+z=−4

−x+2y−3z=−12

--------------------

  3y -2z = -16  Equation A

Add the second and twice the third equation to eliminate x

2x+3y−2z=10

−2x+4y−6z=−24

----------------------------

     7y -8z = -14  Equation B

Take Equation A and multiply by -4

-4*(  3y -2z) = (-16)*-4

-12y + 8z = 64

Add this to Equation B

-12y + 8z = 64

 7y -8z = -14

-----------------------

-5y = 50

Divide by -5

-5y/-5 = 50/-5

y = -10

Now using equation A

  3y -2z = -16  

3*-10 -2z = -16

-30 -2z = -16

Add 30 to each side

-2z = -16+30

-2z = 14

Divide by -2

-2z/-2 = 14/-2

z = -7

Now find x using the first equation

x+y+z = -4

x -7-10 = -4

x -17 = -4

Add 17 to each side

x-17+17 = -4+17

x = 13

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Answer:

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b) r^2 = 0.7503^2 = 0.563

c) r=\frac{7(30095)-(4210)(49)}{\sqrt{[7(2595100) -(4210)^2][7(354) -(49)^2]}}=0.7503  

Step-by-step explanation:

Data given

x: 500, 700, 750, 590 , 540, 650, 480

y: 7.00, 7.50 , 9.00, 6.5, 7.50 , 7.0, 4.50

Part a

We want to create a linear model like this :

y = mx +b

Wehre

m=\frac{S_{xy}}{S_{xx}}  

And:  

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:  

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S_{xy}=\sum_{i=1}^n x_i y_i -\frac{(\sum_{i=1}^n x_i)(\sum_{i=1}^n y_i){n}}=30095-\frac{4210*49}{7}=625  

And the slope would be:  

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

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And we can find the intercept using this:  

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And the line would be:

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Part b

The correlation coefficient is 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]}}  

For our case we have this:

n=7 \sum x = 4210, \sum y = 49, \sum xy = 30095, \sum x^2 =2595100, \sum y^2 =354  

r=\frac{7(30095)-(4210)(49)}{\sqrt{[7(2595100) -(4210)^2][7(354) -(49)^2]}}=0.7503  

The determination coefficient is given by:

r^2 = 0.7503^2 = 0.563

Part c

r=\frac{7(30095)-(4210)(49)}{\sqrt{[7(2595100) -(4210)^2][7(354) -(49)^2]}}=0.7503  

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