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Aleksandr [31]
4 years ago
15

A sprinter started his race slowly and then increase his speed by 12.5 miles per hour to reach a top speed of 21 miles per hour

what was the sprinters speed before he increased his speed
Mathematics
1 answer:
IRINA_888 [86]3 years ago
8 0
21 mph - 12.5 mph = 8.5 mph
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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
The numbers Of students in the four sixth-grade classes at Northside School are 26,19,,34,and 21.Use the properties to find the
Dafna11 [192]
Basically there are 3 addition properties and they are associative property, identity property, and commutative property.

Commutative property is just changing the order of the addends. Example: 26+19+34+21= 21+34+19+26

Identity Property is just adding a 0 to the number that doesnt change anything. Example: 26+19+34+21 +0 = 100

Associative property is just changing the grouping of the addends. Example: (26+19) + (34+21)

I know these properties may be complicated i know inhate them too haha but i hope i helped :) if you want you can search up the distributive property too but its with multiplication and addition combined and its harder but i think these are the 3 main properties.
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3 years ago
HELLLLLLLLLLPPPPPPPPPPPPPPPP NO LINKS PLZZZZZZZZZZ
melisa1 [442]

Answer:

I cant see any pictures?

Step-by-step explanation:

7 0
3 years ago
Emily attends a Film Festival. The admission fee is $10. Each movie ticket cost $5 each. Emily wants to determine how many movie
Rashid [163]

Answer:

Emily can buy 6 movie tickets after paying the admission fee

Step-by-step explanation:

Let x be the number of movie tickets

If each movie ticket costs 5 dollars then the cost of x movies will be 5x

And the admission fee will be a constant.

She has $40 in total

So the equation can be written as

10+5x = 40\\5x = 40-10\\5x = 30\\\frac{5x}{5} = \frac{30}{5}\\x = 6

Hence,

Emily can buy 6 movie tickets after paying the admission fee

7 0
3 years ago
How is it possible for the whale watching adventure and volcano tour charge you for a zero hour tour?
yanalaym [24]
You could have stayed in one place

I think
5 0
3 years ago
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