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3 years ago

Which equation best represents the line of best fit for the scatterplot?

Mathematics

1 answer:

Masja [62]3 years ago

8 0

Answer:

The line of best fit would be the line in between all the points in the scatter plot that is the closest to having an equal amount of dots on each side.

If there isn't one with the exact number, pick the one that is the very closest.

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Find the number b such that the line y = b divides the region bounded by the curves y = 36x2 and y = 25 into two regions with eq

Gemiola [76]

Answer:

b = 15.75

Step-by-step explanation:

Lets find the interception points of the curves

36 x² = 25

x² = 25/36 = 0.69444

|x| = √(25/36) = 5/6

thus the interception points are 5/6 and -5/6. By evaluating in 0, we can conclude that the curve y=25 is above the other curve and b should be between 0 and 25 (note that 0 is the smallest value of 36 x²).

The area of the bounded region is given by the integral

$\int\limits^{5/6}_{-5/6} {(25-36 \, x^2)} \, dx = (25x - 12 \, x^3)\, |_{x=-5/6}^{x=5/6} = 25*5/6 - 12*(5/6)^3 - (25*(-5/6) - 12*(-5/6)^3) = 250/9$

The whole region has an area of 250/9. We need b such as the area of the region below the curve y =b and above y=36x^2 is 125/9. The region would be bounded by the points z and -z, for certain z (this is for the symmetry). Also for the symmetry, this region can be splitted into 2 regions with equal area: between -z and 0, and between 0 and z. The area between 0 and z should be 125/18. Note that 36 z² = b, then z = √b/6.

$125/18 = \int\limits^{\sqrt{b}/6}_0 {(b - 36 \, x^2)} \, dx = (bx - 12 \, x^3)\, |_{x = 0}^{x=\sqrt{b}/6} = b^{1.5}/6 - b^{1.5}/18 = b^{1.5}/9$

125/18 = b^{1.5}/9

b = (62.5²)^{1/3} = 15.75

8 0

3 years ago

Plz help

inn [45]

We are given with
P(pop quiz) = 60%
P(not do homework) = 85%

And the condition that
P (pop quiz and do homework) > 5%

So,
P (pop quiz) x P (do homework)
P (pop quiz) x ( 1 - P (not do homework) )
60% x ( 1 - 85%)

The result is greater than five percent so he will not do his homework.

5 0

3 years ago

5-2(x+5)=3x-15 solve for X

Maslowich

Answer:

x= 2

Step-by-step explanation:

5 -2(x +5)= 3x -15

Expand:

5 -2x -2(5)= 3x -15

5 -2x -10= 3x -15

Simplify:

-2x -5= 3x -15

Bring x terms to 1 side, constant to the other:

3x +2x= 15 -5

5x= 10

Divide both sides by 5:

x= 10 ÷5

x= 2

8 0

3 years ago

Read 2 more answers

Homework due at 12:00 I Need Help

Leya [2.2K]

Answer:

k = - 7.5

Step-by-step explanation:

Slope "m" of a line through points

( $x_{1}$ , $y_{1}$ )

( $x_{2}$ , $y_{2}$ )

is m = $\frac{y_{2} -y_{1} }{x_{2} -x_{1} }$

Slopes of perpendicular lines are opposite reciprocal: $m_{1}$ $m_{2}$ = - 1

~~~~~~~~~~~~~~~

The slope of a line through points (0, 7) and (2, 10)

$m_{1}$ = $\frac{10-7}{2-0}$ = $\frac{3}{2}$

Slope of perpendicular line through points (3, 5) and (k, 12) is $m_{2}$ = $-\frac{2}{3}$

or $m_{2}$ = $\frac{12-5}{k-3}$

$\frac{7}{k-3}$ = $-\frac{2}{3}$

2(k - 3) = - 21

k - 3 = - 10.5

k = - 7.5

6 0

2 years ago

Plz help me with these math questions

Akimi4 [234]

For b on the first paper you will start with the distribution property and multiply both x and 2 by 3 because they are in the ()
now you have 3x+ 6=x-18
from here you can subtract x from both sides
2x+6=-18
next subtract 6 from both sides
2x=-24
divide both sides by 2...
x=-12
hope this helped

8 0

3 years ago