The table below shows the heights of 6 pairs of brothers and sisters, labeled A through F .
Heights are rounded to the nearest inch. (table is attached)
The line of best fit for this data is y=1.42105x−32.2632 .
For the brother and sister whose heights are both 71 inches, what is the difference between the sister’s actual height and
the height predicted by the line of best fit?

The difference is 2 inches

Step-by-step explanation:

Firstly, we identify the equation as given in the question;

y = 1.42105x - 32.2632

We need to know which of the two is the dependent variable i.e y-value and which is the independent variable x-value between the brothers' heights and the sisters' heights. To do this, we have to start with an assumption and check which of the two is for the brothers' or for the sisters,

Let's say the brothers' heights is x, we select any of the data points; (68,64)

we input this into the line of best fit equation; 64 =1.42105(68) - 32.2632 = 96.6314-32.2632=  64.3682

We can see the value on the left hand side of the equation correlates with that on the right hand side. This confirms our assumption that the brothers' heights refer to the independent variable x.

Now, let's plug the values for the 71 inches heights

y = 1.42105(71) - 32.2632 = 68.63 approximately 64

In the table, we can see that the predict sister height at that particular data point is 71 inches. The difference between the predicted height and the actual height is thus 71-69 = 2 inches  

37/3

step-by-step explanation:

step 1: simplify both sides of the equation.

7x+8(x+

1

4

)=3(6x−9)−8

7x+(8)(x)+(8)(

1

4

)=(3)(6x)+(3)(−9)+−8(distribute)

7x+8x+2=18x+−27+−8

(7x+8x)+(2)=(18x)+(−27+−8)(combine like terms)

15x+2=18x+−35

15x+2=18x−35

tep 2: subtract 18x from both sides.

15x+2−18x=18x−35−18x

−3x+2=−35

step 3: subtract 2 from both sides.

−3x+2−2=−35−2

−3x=−37

step 4: divide both sides by -3.

−3x

−3

=

−37

−3

x=

37

3