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3 years ago

Find the percentage increase from 360km to 540km

Mathematics

1 answer:

vodomira [7]3 years ago

6 0

Answer: 66 2/3

Step-by-step explanation:

360 x

—— = ——

540 100

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#10 i The table shows the admission costs (in dollars) and the average number of daily visitors at an amusement park each the pa

lions [1.4K]

The line of best fit is a straight line that can be used to predict the

average daily attendance for a given admission cost.

Correct responses:

The equation of best fit is; $\underline{ \hat Y = 1,042 - 4.9 \cdot X_i}$

The correlation coefficient is; r ≈ -0.969

<h3>Methods by which the line of best fit is found</h3>

The given data is presented in the following tabular format;

$\begin{tabular}{|c|c|c|c|c|c|c|c|c|}Cost, (dollars), x&20&21&22&24&25&27&28&30\\Daily attendance, y&940&935&940&925&920&905&910&890\end{array}\right]$

The equation of the line of best fit is given by the regression line

equation as follows;

$\hat Y = \mathbf{b_0 + b_1 \cdot X_i}$

Where;

$\hat Y$ = Predicted value of the ith observation

b₀ = Estimated regression equation intercept

b₁ = The estimate of the slope regression equation

$X_i$ = The ith observed value

$b_1 = \mathbf{\dfrac{\sum (X - \overline X) \cdot (Y - \overline Y) }{\sum \left(X - \overline X \right)^2}}$

$\overline X$ = 24.625

$\overline Y$ = 960.625

$\mathbf{\sum(X - \overline X) \cdot (Y - \overline Y)} = -433.125$

$\mathbf{\sum(X - \overline X)^2} = 87.875$

Therefore;

$b_1 = \mathbf{\dfrac{-433.125}{87.875}} \approx -4.9289$

Therefore;

The slope given to the nearest tenth is b₁ ≈ -4.9

$b_0 = \mathbf{\dfrac{\left(\sum Y \right) \cdot \left(\sum X^2 \right) - \left(\sum X \right) \cdot \left(\sum X \cdot Y\right)} {n \cdot \left(\sum X^2\right) - \left(\sum X \right)^2}}$

By using MS Excel, we have;

n = 8

∑X = 197

∑Y = 7365

∑X² = 4939

∑Y² = 6782675

∑X·Y = 180930

(∑X)² = 38809

Therefore;

$b_0 = \dfrac{7365 \times 4939-197 \times 180930}{8 \times 4939 - 38809} \approx \mathbf{1041.9986}$

The y-intercept given to the nearest tenth is b₀ ≈ 1,042

The equation of the line of best fit is therefore;

$\underline{\hat Y = 1042 - 4.9 \cdot X_i}$

The correlation coefficient is given by the formula;

$\displaystyle r = \mathbf{\dfrac{\sum \left(X_i - \overline X) \cdot \left(Y - \overline Y \right)}{ \sqrt{\sum \left(X_i - \overline X \right)^2 \cdot \sum \left(Y_i - \overline Y \right)^2} }}$

Where;

$\sqrt{\sum \left(X - \overline X \right)^2 \times \sum \left(Y - \overline Y \right)^2} = \mathbf{446.8121}$

$\sum \left(X_i - \overline X \right) \times \left(Y - \overline Y\right) = \mathbf{-433.125}$

Which gives;

$r = \dfrac{-433.125}{446.8121} \approx \mathbf{-0.969367213}$

The correlation coefficient given to the nearest thousandth is therefore;

Correlation coefficient, r ≈ -0.969

Learn more about regression analysis here:

brainly.com/question/14279500

7 0

2 years ago

What is one fourth of one ton HELP

Alekssandra [29.7K]

1/4 is the same thing as 25%. So we know that we have to find 25% of 2000 pounds, which is 1 ton. Convert 25% into a decimal and then multiply.

2000 times .25 is 500.
One fourth of one ton is 500 pounds.

7 0

3 years ago

Read 2 more answers

What is the volume of this rectangular prism? 10/3 4/5 1/5

Lunna [17]

Answer:

.53

Step-by-step explanation:

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3 years ago

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After simplifying, which expressions are equivalent? Select three options. (3.42 – 1.75) + (235a – 3.95) (2.5a + 1.65) + (3.4a +

poizon [28]

9514 1404 393

Answer:

C, D, E

Step-by-step explanation:

Collect terms. The last three options are all equivalent to ...

5.9a - 5.6b

3 0

3 years ago

A square rug covers 79 square feet of floor. What is the approximate length of one side of the rug? (Approximate to the nearest

Mice21 [21]

A = a^2.....where " a " is the length of one side
A = 79

79 = a^2...take sqrt of both sides, eliminating the ^2
sqrt 79 = a
8.89 = a

so the length of one side is approximately 8.89 ft <==

8 0

3 years ago