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3 years ago

Based on the scatter plot, which equation represents the line best fit for the data about cups of beads?

Mathematics

1 answer:

e-lub [12.9K]3 years ago

5 0

Answer:

Option B. y = 1.81x + 44.36

Step-by-step explanation:

The graph represents a scatter plot with a positive correlations and has a positive y-intercept.

By drawing the best line to fit the data the y-intercept will be approximately at the midpoint of 45 and 50

We will check which option is true:

A. y = 4.25 x

The equation of option A represents a line pass through the point (0,0)

Which mean y-intercept is 0 and this is wrong.

B. y = 1.81x + 44.36

According to the best line to fit the data option B is true.

Also by substitution with x = 2

y = 1.81 * 2 +44.36 = 47.98

which is near to the actual point on the graph (50)

C. y = 1.81 x ⇒ Wrong ⇒ same explanation of option A

D. y = 4.25 x + 50 ⇒ Wrong

Because the y-intercept will be approximately at the midpoint of 45 and 50

So, The answer is option B. y = 1.81x + 44.36

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3 years ago

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The population of two different cities are modeled by the equations shown below. The population (in thousands) is represented by

lesya [120]

Answer: years of equal population are 1995 and 2022.

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3 years ago

A candle has been burning for 20 min and is now 25 cm tall. In an hour it will be 10 cm tall. Which equation models the height y

stiv31 [10]

Answer:

(y - 25) = - 0.25(x - 20)

Step-by-step explanation:

Given that :

Height of candle after burning for 20 minutes = 25 cm

Height after burning for 1 hr (60 minutes) = 10 cm

Height (y) in cm of candle x minutes after being lit:

Using the equation :

(y - y1) = m(x - x1)

m = (change in y / change in x)

Change in height within 60 minutes :

Height at 20 minutes = 25cm

Height after an hour = 10

Change in height per hour = (25 - 10) = 15cm

Hence, m = change in height per minute

15cm / 60 = 0.25cm ( - 0.25) (decrease in height)

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3 years ago

Consider the function f ( x ) = − 2 x 3 + 27 x 2 − 108 x + 9 . For this function there are three important open intervals: ( − [

Darya [45]

Answer:

A=3 and B=6

Step-by-step explanation:

Increasing and Decreasing Intervals of Functions

Given f(x) as a real function and f'(x) its first derivative.

If f'(a)>0 the function is increasing in x=a

If f'(a)<0 the function is decreasing in x=a

If f'(a)=0 the function has a critical point in x=a

As we can see, the critical points may define open intervals where the function has different behaviors.

We have

$f ( x ) = - 2 x^3 + 27 x^2 - 108 x + 9$

Computing the first derivative:

$f' ( x ) = - 6 x^3 + 54 x - 108$

We find the critical points equating f'(x) to zero

$- 6 x^3 + 54 x - 108=0$

Simplifying by -6

$x^2 -9 x +18=0$

We get the critical points

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3 0

3 years ago

Can you guys help me with this one please

PilotLPTM [1.2K]

Answer:

1 to 100,000

Step-by-step explanation:

1 km is equivalent to 100,000 cm.

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3 years ago