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Neporo4naja [7]
2 years ago
11

You own a Roulette Wheel, which has 37 (European Version) equally distributed parts, each has a number number associated. 0 is g

reen, the rest 36 includes 18 red and 18 black. The money you have to pay to the gambler for hitting green, red and black are 10, 1 and 2 dollars respectively. How much you have to charge per play in order to make sure you will make money?
Mathematics
1 answer:
Anika [276]2 years ago
4 0

Answer:

To expect a profit in the long run, we have to charge more than $1.73 per play.

Step-by-step explanation:

We hace a roulette wit 37 slots.

One is green, eighteen are red and eighteen are black.

The expected pay for the gambler can be calculated as the sum of the probability of getting green, red or black multiplied by the respective pay.

E(g)=\sum p_iG_i=p_gG_g+p_rG_r+p_bG_b\\\\\\E(g)=\dfrac{1}{37}(10)+\dfrac{18}{37}(1)+\dfrac{18}{37}(2)\\\\\\E(g)=\dfrac{10+18+36}{37}=\dfrac{64}{37}\approx1.73

If $1.73 per play is the expected pay that will receive the gambler, we have to charge at least this amount to make sure we will make a profit in the long run.

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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
Q = m-a/x (solve for m)​
DaniilM [7]

Answer:

m=a/x+Q

Step-by-step explanation:

Q=m-a/x

To solve this we need to isolate m so we will bring -a/x to the other side of the equal sign so it will become positive i.e. ax now will be  written as a/x+Q=m

in other wards m=a/x+Q

7 0
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Which equation has the same solution as 10x-x+5=4110 x − x + 5 = 41?
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D or the last dot how ever you wanna describe it
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Write mixed number for p so that 3 1/4 × p is more than 3 1/4
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Answer:

1 3/5

Step-by-step explanation:

Anything larger than 1 multiplied by 3 1/4 would result in a number more than 3 1/4.

8 0
3 years ago
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horrorfan [7]
I think it represents the height hope that helps:)
8 0
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