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4 years ago

Work out the circumference of a circle with radius 7.5 cm take pi to be 3.142

Mathematics

2 answers:

Elanso [62]4 years ago

5 0

Answer:

47.13

Step-by-step explanation:

Circumfrence= 2 x pi x Radius

2 x 3.142 x 7.5 =47.13

lord [1]4 years ago

4 0

Answer:

47.13

Step-by-step explanation:

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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 ≈<u> -0.969</u>

<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<em> i</em>th observation

b₀ = Estimated regression equation intercept

b₁ = The estimate of the slope regression equation

$X_i$ = The <em>i</em>th 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;

<u>Correlation coefficient, r ≈ -0.969</u>

Learn more about regression analysis here:

brainly.com/question/14279500

7 0

3 years ago

which fractions are equivalent to the value of 2/10 + 20/100? drag and drop the fractions into the box.

NISA [10]

Lets see

2/10+20/100
2/10+2/10
2+2/10
4/10
2/5

6 0

2 years ago

Simplify the following expression (30/45g+20)-(8/9g+7)

amid [387]

The answer is: $13-\frac{2}{9}g$

The explanation is shown below:

1- You have the following expression given in the exercise:

$(\frac{30}{45}g+20)-(\frac{8}{9}g+7)$

2- When you multiply signs, you obtain:

$\frac{30}{45}g+20-\frac{8}{9}g-7$

3. Now, you must add like terms, as following:

$-\frac{2}{9}g+13$

4. Therefore, you have that the expression simplified is:

$13-\frac{2}{9}g$

8 0

3 years ago

Please help!! I will make you brainlest.

Law Incorporation [45]

Answer:

5) x = 12 6) y = 3.5

Step-by-step explanation:

For number 6 that one may be right I tried several ways and kept getting that answer

5. is completely write though

Hope that helps

3 0

3 years ago

Read 2 more answers

A bicycle was originally sold for $400 was on sale for $320. what percent was the bike marked down?

Eva8 [605]

100% of the price = $400
x % of the price = $320
we need to find x

using a proportion
100 : 400 = x : 320
100 * 320 = 400 * x
32000 = 400x
x = 32000 / 400
x = 80

That means the new price is 80% of the previous price.
100% - 80% = 20%
and based on this we can make a conclusion that the discount was 20%

I hope it is clear to you, feel free to ask anything about it :)

6 0

3 years ago

Read 2 more answers