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BartSMP [9]
3 years ago
7

If you were to use the substitution method to solve the following system, choose the new equation after the expression equivalen

t to x from the second equation is substituted into the first equation. 3x + 2y = −21 x − 3y = 4
Mathematics
1 answer:
Svetllana [295]3 years ago
3 0
Hello,

\left \{ {{3x+2y=-21} \atop {x-3y=4}} \right. \\\\
 \left \{ {{3x+2y=-21} \atop {x=4+3y}} \right. \\\\
 \left \{ {{3(4+3y)+2y=-21} \atop {x=4+3y}} \right. \\\\

 \left \{ {{12+9y+2y=-21} \atop {x=4+3y}} \right. \\\\
 \left \{ {{12+11y=-21} \atop {x=4+3y}} \right. \\\\
 \left \{ {{11y=-21-12} \atop {x=4+3y}} \right. \\\\
 \left \{ {{11y=-33} \atop {x=4+3y}} \right. \\\\
 \left \{ {{y=-3} \atop {x=4+3(-3)}} \right. \\\\
 \left \{ {{y=-3} \atop {x=5}} \right. \\\\
Sol=\{(5,-3)\}\\\\




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1. Calculate the variance of the set of data to two decimal places.
Komok [63]
<h3>Answer:  3.14 (choice C)</h3>

============================================================

Explanation:

First we need the arithmetic mean

Add up the values to get 1+2+4+4+5+6+6 = 28

Divide this over the number of values (n = 7) to get 28/n = 28/7 = 4

The mean is 4.

Next, we subtract the mean from each data value and square the difference

  • (1-4)^2 = 9
  • (2-4)^2 = 4
  • (4-4)^2 = 0
  • (4-4)^2 = 0
  • (5-4)^2 = 1
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  • (6-4)^2 = 4

Add up those results: 9+4+0+0+1+4+4 = 22

Lastly, we divide over the number of items (n = 7) to get the population variance: 22/n = 22/7 = 3.14 approximately

----------

Side note:

If you wanted the sample variance, then you divide over n-1 = 7-1 = 6

22/(n-1) = 22/6 = 3.67 is the approximate sample variance

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