50 POINTS .....................
1 answer:
The option (C) Mus. Apt. = -22.26 + 0.4925(IQ score) is correct because the value of slope is 0.4925 and y-intercept is -22.26.
<h3>What is the line of best fit?</h3>A mathematical notion called the line of the best fit connects points spread throughout a graph. It's a type of linear regression that uses scatter data to figure out the best way to define the dots' relationship.
We have data shown in the picture.
Let's suppose the regression line is:
y = mx + c
Where m is the slope of the regression line and c is the y-intercept of the line.
We can calculate the value of m and c by using the formula.
After calculating, we get:
m = 0.4925
c = -22.26
Mus. Apt. = 0.49253(IQ score) - 22.26
or
Mus. Apt. = -22.26 + 0.4925(IQ score)
Thus, the option (C) Mus. Apt. = -22.26 + 0.4925(IQ score) is correct because the value of slope is 0.4925 and y-intercept is -22.26.
Learn more about the line of best fit here:
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OK to solve this, we have to solve each system presented through elimination or substitution and find which one is equivalent to that of the teacher's!
First let's solve for the teacher's:
-2x+5y=10
-3x+9y=6
Solve by substitution (I think elimination might be easier to do for this one, but I don't really remember 100% sorry!)
Isolate the x (or y) variable in the first equation
-2x+5y=10
-2x=10-5y
Substitute x into the next equation and solve for y
-3(10-5y/2)+9y=6
3*10-5y/2+9y=6
(multiply both sides by 2)
3(10-5y)+18y=12
30-15y+18y=12
30+3y=12
3y=-18
y=-6
Substitute in x
x= -10-5(-6)/2
x=-20
TEACHER'S ANSWER (-20,-6)
GOKU
x-3y=-2
-2x+5y=-7
Do the same as above
Solve for x
x-3y=-2
x=3y-2
Plug in
-2(3y-2)+5y=-7
4-6y+5y=-7
4-y=-7
-y=-11
y=11
x=(3(11)-2)
x=31
GOKU'S ANSWER (31, 11)
SELINA:
-5x+14y=16
-3x+9y=12
One last time!! :)
-5x+14y=16
-5x=16-14y
x=(16-14y)/-5
-3(-(16-14y/5)+9y=12
3*16-14y/5+9y=12
3*16-14y+45y=60
48-42y+45y=60
48+3y=60
3y=12
y=4
x=-(16-14(4))/5
x=8
SELINA'S ANSWER
(8,4)
So neither Goku or Selina got the same answer as the teacher
First let's solve for the teacher's:
-2x+5y=10
-3x+9y=6
Solve by substitution (I think elimination might be easier to do for this one, but I don't really remember 100% sorry!)
Isolate the x (or y) variable in the first equation
-2x+5y=10
-2x=10-5y
Substitute x into the next equation and solve for y
-3(10-5y/2)+9y=6
3*10-5y/2+9y=6
(multiply both sides by 2)
3(10-5y)+18y=12
30-15y+18y=12
30+3y=12
3y=-18
y=-6
Substitute in x
x= -10-5(-6)/2
x=-20
TEACHER'S ANSWER (-20,-6)
GOKU
x-3y=-2
-2x+5y=-7
Do the same as above
Solve for x
x-3y=-2
x=3y-2
Plug in
-2(3y-2)+5y=-7
4-6y+5y=-7
4-y=-7
-y=-11
y=11
x=(3(11)-2)
x=31
GOKU'S ANSWER (31, 11)
SELINA:
-5x+14y=16
-3x+9y=12
One last time!! :)
-5x+14y=16
-5x=16-14y
x=(16-14y)/-5
-3(-(16-14y/5)+9y=12
3*16-14y/5+9y=12
3*16-14y+45y=60
48-42y+45y=60
48+3y=60
3y=12
y=4
x=-(16-14(4))/5
x=8
SELINA'S ANSWER
(8,4)
So neither Goku or Selina got the same answer as the teacher