Question

time x 0 1 2 3 4
distances travel y 0 712 19 25
9.

Use your line of best fit from #8 above to predict, to the nearest tenth of a foot, how many feet the sloth will have

moved after 3 minutes.

(1 point)
The sloth will have moved
feet (rounded to the nearest foot) in 3 minutes.

Answer 1

Use your line of best fit from #8 to determine how many minutes (to the nearest tenth) it will take for the

sloth to travel 37 feet.

(1 point)
It will take the sloth
minutes (round to the nearest tenth) to travel 37 feet.

Answer 2

To determine how far the sloth has moved after 3 minutes using a line of best fit, we first need to establish a linear equation based on the distances given in the table:

- Time (x): 0, 1, 2, 3, 4
- Distances (y): 0, 712, 19, 25

To create a line of best fit from these points, we first need to identify the coordinates for the points:

1. (0, 0)
2. (1, 712)
3. (2, 19)
4. (3, 25)

Since the values of y seem inconsistent, a linear regression approach or a simpler approximation can give us a close enough line of best fit.

To create a simple linear function for estimation, let's assume we only consider the points at intervals (ignoring the extreme outlier at x=1). Therefore we can use the points (0, 0), (2, 19), and (3, 25) for our approximation.

1. Calculate the average slope between two points:
Slope between (2, 19) and (3, 25):
\[
\text{Slope} = \frac{25 - 19}{3 - 2} = 6
\]

The linear equation can be derived:
Starting from point (2, 19), the linear equation can be approximated with:
\[
y = 6x + b
\]

We know that y = 19 when x = 2. Plugging this in to solve for b:
\[
19 = 6(2) + b \implies 19 = 12 + b \implies b = 7 \implies y = 6x + 7
\]

Now we can use this equation to predict the distance traveled after 3 minutes:
\[
y = 6(3) + 7 = 18 + 7 = 25
\]

Since we have a conflicting value of 25 from the distance at x = 3, it seems our linear equation is confirmed accurate.

Thus, after figuring out and confirming with the neighboring points for consistency, the sloth will have moved **25 feet** after 3 minutes.

Answer 3

To determine how many minutes it will take for the sloth to travel 37 feet using the line of best fit we approximated earlier, we can use the equation:

\[
y = 6x + 7
\]

where \(y\) is the distance (in feet) traveled and \(x\) is the time (in minutes). To find out how long it takes the sloth to travel 37 feet, we will set \(y\) to 37 and solve for \(x\):

\[
37 = 6x + 7
\]

Now, we can isolate \(x\):

1. Subtract 7 from both sides:
\[
37 - 7 = 6x
\]
\[
30 = 6x
\]

2. Divide both sides by 6:
\[
x = \frac{30}{6} = 5
\]

Thus, the calculations indicate that it will take the sloth **5.0 minutes** to travel 37 feet.

So, rounding to the nearest tenth, it will take the sloth **5.0 minutes** to travel 37 feet.