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Jet001 [13]
3 years ago
9

Find the volume of the triangular prism ​

Mathematics
1 answer:
RoseWind [281]3 years ago
7 0

Answer:

<h3>168cm3</h3>

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
2 years ago
Total revenue is 3,000 cost of goods 1,500 total selling expence is 500 what is profit
12345 [234]
Cost of goods = 1,500
Selling expense = 500

Total cost in selling = 1500 + 500 = 2000

Profit = Total Revenue - Total cost in selling = 3000 - 2000 = 1000

Profit = 1000

Hope this explains it.
8 0
3 years ago
Read 2 more answers
What proof do you see that contaminated water seeped into the well? How could scientists use a similar approach to understand wa
Veseljchak [2.6K]

Answer:

because of the fungus that may have growne is the asnwer

Step-by-step explanation:

6 0
2 years ago
-9n&gt;-36? Solve and graph
wlad13 [49]
-9n>-36
divide both sides by -9
n<4 

6 0
3 years ago
What is the value of y in the equation 6.4x + 2.8y = 44.4, when x = 3
Georgia [21]

Answer:

9

Step-by-step explanation:

6.4(x)+2.8y=44.4

6.4(3)+2.8y=44.4

19.2+2.8y=44.4

2.8y=25.2

y=9

7 0
2 years ago
Read 2 more answers
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