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2 years ago

What is the approximate line of best fit for the scatter plot

Mathematics

1 answer:

ch4aika [34]2 years ago

3 0

Answer:

The first one, or y= -x + 8

Step-by-step explanation:

You can rule out the last one, because there is no y intercept. If there was no y intercept, the dots would be passing through the origin (0).

The one with -8 is not right because the y intercept is positive 8. If you count on the y axis (up 8), it matches with the overall direction of the line.

The line/ slope of this scatter plot is negative, so the only one that makes sense would be the first one. Going up and from right to left is a positive slope. Going down from left to right is a negative slope.

You might be interested in

Find the critical numbers of the function f(x) = x6(x − 1)5 what does the first derivative test tell you that the second derivat

patriot [66]

The given function is f(x) = x⁶(x-1)⁵

The first derivative is
f'(x) = 6x⁵(x-1)⁵ + 5x⁶(x-1)⁴
= x⁵(x-1)⁴(6x - 6 + 5x)
= x⁵(x-1)⁴(11x - 6)
The critical values are the zeros of f'(x). They are
x = 0, 6/11, and 1.
The critical values indicate that turning points exist for f(x) at the critical points. However, we do not know the nature of the turning points.

Write the first derivative in the form f'(x) = (x-1)⁴(11x⁶ - 6x⁵).
The second derivative is
f''(x) = 4(x-1)³(11x⁶ - 6x⁵) + (x-1)⁴(66x⁵ - 30x⁴)
= (x-1)³(44x⁶ - 24x⁵ + 66x⁶ - 30x⁵ - 66x⁵ + 30x⁴)
= (x-1)³(110x⁶ - 120x⁵ + 30x⁴)
= 10x⁴(x-1)³(11x² - 12x + 3)
The sign of f''(x) at the critical values tell us the nature of the turning point.

f''(0) = 0, therefore a point of inflection exists at x = 0.
f''(6/11) > 0, therefore a local minumum exists at x = 6/11.
f''(1) = 0, therefore a point of inflection exists at x=1.

The graphs shown below confirm these results.

8 0

2 years ago

Use the drop-down menus to choose steps in order to correctly solve 5m – 8 = 3m + 8 for m.

olga nikolaevna [1]

5m - 3m = 8 + 8
2m = 16
m = 8

3 0

2 years ago

Read 2 more answers

1.5(x−2)−3(2−x)

adell [148]

Answer:

1. x = 2

2. x = 61/25

Step-by-step explanation:

Solve for x:

5 (x - 2) - 3 (2 - x) = 0

-3 (2 - x) = 3 x - 6:

3 x - 6 + 5 (x - 2) = 0

5 (x - 2) = 5 x - 10:

5 x - 10 + 3 x - 6 = 0

Grouping like terms, 5 x + 3 x - 10 - 6 = (3 x + 5 x) + (-6 - 10):

(3 x + 5 x) + (-6 - 10) = 0

3 x + 5 x = 8 x:

8 x + (-6 - 10) = 0

-6 - 10 = -16:

8 x + -16 = 0

Add 16 to both sides:

8 x + (16 - 16) = 16

16 - 16 = 0:

8 x = 16

Divide both sides of 8 x = 16 by 8:

(8 x)/8 = 16/8

8/8 = 1:

x = 16/8

The gcd of 16 and 8 is 8, so 16/8 = (8×2)/(8×1) = 8/8×2 = 2:

Answer: x = 2

_____________________________

Solve for x:

3 (2 x - 7) + (7 x + 2)/3 = 0

Put each term in 3 (2 x - 7) + (7 x + 2)/3 over the common denominator 3: 3 (2 x - 7) + (7 x + 2)/3 = (9 (2 x - 7))/3 + (7 x + 2)/3:

(9 (2 x - 7))/3 + (7 x + 2)/3 = 0

(9 (2 x - 7))/3 + (7 x + 2)/3 = (9 (2 x - 7) + (7 x + 2))/3:

(9 (2 x - 7) + 2 + 7 x)/3 = 0

9 (2 x - 7) = 18 x - 63:

(18 x - 63 + 7 x + 2)/3 = 0

Grouping like terms, 18 x + 7 x - 63 + 2 = (18 x + 7 x) + (2 - 63):

((18 x + 7 x) + (2 - 63))/3 = 0

18 x + 7 x = 25 x:

(25 x + (2 - 63))/3 = 0

2 - 63 = -61:

(25 x + -61)/3 = 0

Multiply both sides of (25 x - 61)/3 = 0 by 3:

(3 (25 x - 61))/3 = 3×0

(3 (25 x - 61))/3 = 3/3×(25 x - 61) = 25 x - 61:

25 x - 61 = 3×0

0×3 = 0:

25 x - 61 = 0

Add 61 to both sides:

25 x + (61 - 61) = 61

61 - 61 = 0:

25 x = 61

Divide both sides of 25 x = 61 by 25:

(25 x)/25 = 61/25

25/25 = 1:

Answer: x = 61/25

7 0

3 years ago

Solve 7/8c-3(1/8c-7)=-6

Sergeu [11.5K]

Answer:

c = -54

Step-by-step explanation:

Solve for c:

(7 c)/8 - 3 (c/8 - 7) = -6

Put each term in c/8 - 7 over the common denominator 8: c/8 - 7 = c/8 - 56/8:

(7 c)/8 - 3 c/8 - 56/8 = -6

c/8 - 56/8 = (c - 56)/8:

(7 c)/8 - 3(c - 56)/8 = -6

(7 c)/8 - (3 (c - 56))/8 = (7 c - 3 (c - 56))/8:

(7 c - 3 (c - 56))/8 = -6

-3 (c - 56) = 168 - 3 c:

(7 c + 168 - 3 c)/8 = -6

7 c - 3 c = 4 c:

(4 c + 168)/8 = -6

Multiply both sides of (4 c + 168)/8 = -6 by 8:

(8 (4 c + 168))/8 = -6×8

(8 (4 c + 168))/8 = 8/8×(4 c + 168) = 4 c + 168:

4 c + 168 = -6×8

8 (-6) = -48:

4 c + 168 = -48

Subtract 168 from both sides:

4 c + (168 - 168) = -168 - 48

168 - 168 = 0:

4 c = -168 - 48

-168 - 48 = -216:

4 c = -216

Divide both sides of 4 c = -216 by 4:

(4 c)/4 = (-216)/4

4/4 = 1:

c = (-216)/4

The gcd of -216 and 4 is 4, so (-216)/4 = (4 (-54))/(4×1) = 4/4×-54 = -54:

Answer: c = -54

4 0

3 years ago

Rachel has 20 nickels, dimes, and quarters worth $3.70. if she has twice as many quarters as dimes, how many nickels does she ha

marta [7]

Answer: 2 nickels

Rachel has 20 coins composed of nickles, dimes and quarters amounting to $3.70. Her quarters are twice the number of her dimes, the number of nickels can be computed as follows:

If X= the number of dimes at .10 each

Then 2x= the number of quarters at .25 each and

20-(X-2X)= the number of nickels at .05 each

The equation will be: X(.1)+2(X).25+(20-X-2X).10=3.70 .1X+2X(.25)+(20-X-2X).05=3.70 .1X+.5X+(20-3X).05=3.70 .6X+(1-.15X)=3.70 .6X+1-.15X=3.70 .45X=3.70-1 .45X=2.70 X=2.70/.45 X=6 number of dimes 2X=12 number of quarters 20-6-12=2 number of nickels

5 0

3 years ago