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9 days ago

7

The scatterplot represents the total fee for hours renting a bike. The line of best fit for the data is y = 6.855x + 10.215. Whi

ch table shows the correct residual values for the data set?

2 answers:

Leona [4.1K]9 days ago

7 0

Conclusion:

Yes, it is. This is quite clear since x 1 should be negative, which negates the middle, leading us to options A or D. x 3 is positive, and it also appears positive on the first chart, confirming that the correct answer is the initial option.

Step-by-step reasoning:

Inessa [3.9K]9 days ago

5 0

Solution: A- represents the first chart

You might be interested in

Find the point on the circle x^2+y^2 = 16900 which is closest to the interior point (30,40)

Leona [4166]

Response-

(78,104) represents the point closest to the interior.

Explanation-

The equation defining the circle,

$\Rightarrow x^2+y^2 = 16900$

$\Rightarrow y^2 = 16900-x^2$

$\Rightarrow y = \sqrt{16900-x^2}$

Since the point lies on the circle, its coordinates must be,

$(x,\sqrt{16900-x^2})$

The distance "d" from the point to (30,40) can be calculated as,

$=\sqrt{(x_1-x_2)^2+(y_1-y_2)^2}$

$=\sqrt{(x-30)^2+(\sqrt{16900-x^2}-40)^2}$

$=\sqrt{x^2+900-60x+16900-x^2+1600-80\sqrt{16900-x^2}}$

$=\sqrt{9400-60x-80\sqrt{16900-x^2}}$

Next, we need to determine the value of x for which d is minimized. The minimum distance occurs when $9400-60x-80\sqrt{16900-x^2}$ is at its lowest value.

Let’s set up the equation,

$\Rightarrow f(x)=9400-60x-80\sqrt{16900-x^2}$

$\Rightarrow f'(x)=-60+80\dfrac{x}{\sqrt{16900-x^2}}$

$\Rightarrow f''(x)=\dfrac{1352000}{\left(16900-x^2\right)\sqrt{16900-x^2}}$

We find the critical points,

$\Rightarrow f'(x)=0$

$\Rightarrow-60+80\dfrac{x}{\sqrt{16900-x^2}}=0$

$\Rightarrow 80\dfrac{x}{\sqrt{16900-x^2}}=60$

$\Rightarrow 80x=60\sqrt{16900-x^2}$

$\Rightarrow 80^2x^2=60^2(16900-x^2)$

$\Rightarrow 6400x^2=3600(16900-x^2)$

$\Rightarrow \dfrac{16}{9}x^2=16900-x^2$

$\Rightarrow \dfrac{25}{9}x^2=16900$

$\Rightarrow x=\sqrt{\dfrac{16900\times 9}{25}}=78$

$\Rightarrow x=78$

Then,

$\Rightarrow f''(78)=\dfrac{1352000}{\left(16900-78^2\right)\sqrt{16900-78^2}}=\dfrac{125}{104}=1.2$

Since f''(x) is positive, the function f(x) achieves its minimum at x=78

When x is set to 78, the corresponding y value will be

$\Rightarrow y = \sqrt{16900-x^2}=\sqrt{16900-78^2}=104$

This leads us to conclude that the closest point is (78,104)

5 0

8 days ago

Jason solved the following equation to find the value for x. –8.5x – 3.5x = –78 x = 6.5 Describe how Jason can check his answer.

Inessa [3907]

Jason can confirm the accuracy of his solution by substituting the calculated x value back into the original equation to check if it holds true. If the equality fails, it indicates that his calculated x is incorrect.

5 0

4 days ago

Read 3 more answers

For a data set of weights (pounds) and highway fuel consumption amounts (mpg) of seven types of automobile, the linear correl

zzz [4022]

Answer:

The P-value signifies that the likelihood of obtaining a linear correlation coefficient that is as extreme or more extreme is 3.5%, which is considered significant at α=0.05. Thus, we have sufficient evidence to assert that there exists a linear correlation between the weight of automobiles and their highway fuel consumption.

Step-by-step explanation:

The correlation coefficient demonstrates the relationship between the weights and highway fuel consumption values across seven distinct types of automobiles.

The P-value expresses the significance of this connection. If the p-value is beneath a significance level (e.g., 0.05), it indicates that the relationship is indeed significant.

5 0

13 hours ago

Each August a restaurant rent is adjusted to the cost of living index. The rent has $1,550 a month, the cost-of-living index for

Inessa [3907]

Answer:
new rent = $1,607.35

Explanation:
Let's consider the original rent as x

Given that the increase in rent is 3.7%.
Thus:
new rent = x + 3.7% of x
new rent = x + 0.037 x

With x = 1550, we find:
new rent = 1550 + 0.037(1550)
new rent = 1550 + 57.35
new rent = $1,607.35

I hope this clarifies!:)

5 0

13 days ago

Read 2 more answers

If hair grows at a rate of approximately 0.44 mm per day, how many

lawyer [4008]

Answer:

91

Step-by-step explanation:

40/.44

8 0

5 days ago

Read 2 more answers