Cost To Play At Mini-golf Course A${ \begin{tabular}{|l|l|} \hline \text{Games Played } (x) & \text{Cost In Dollars } (y) \ \hline 3 & 16.50 \ \hline 6 & 27 \ \hline 8 & 34 \ \hline 11 & 44.50 \ \hline \end{tabular} }$The Table Shows

Mar 9, 2025 by ADMIN 235 views

Cost to Play at Mini-golf Course: A Mathematical Analysis

Mini-golf courses are a popular recreational activity for people of all ages. They offer a fun and challenging experience, with obstacles and challenges that test one's skills and strategy. However, before heading out to play, it's essential to know the cost involved. In this article, we'll analyze the cost to play at a mini-golf course using a mathematical approach.

The table below shows the cost to play at a mini-golf course for different numbers of games played.

Games Played (x)	Cost in Dollars (y)
3	16.50
6	27
8	34
11	44.50

We can see that the cost increases as the number of games played increases. However, the relationship between the number of games played and the cost is not immediately apparent. To understand this relationship, we need to analyze the data mathematically.

One way to analyze the data is to use linear regression analysis. This involves finding the best-fitting line that describes the relationship between the number of games played (x) and the cost (y). The equation of the line is given by:

y = mx + b

where m is the slope of the line and b is the y-intercept.

To find the values of m and b, we can use the following formulas:

m = (n * Σxy - Σx * Σy) / (n * Σx^2 - (Σx)^2) b = (Σy - m * Σx) / n

where n is the number of data points, Σx is the sum of the x-values, Σy is the sum of the y-values, and Σxy is the sum of the products of the x and y values.

Plugging in the values from the table, we get:

m = (4 * 216.5 - 22 * 27) / (4 * 169 - 22^2) = 2.5 b = (27 + 2.5 * 22) / 4 = 6.875

So, the equation of the line is:

y = 2.5x + 6.875

This equation describes the relationship between the number of games played and the cost. We can use this equation to predict the cost for any number of games played.

The results of the linear regression analysis show that the cost to play at the mini-golf course increases by $2.50 for every additional game played. This means that if you play 3 games, the cost will be $16.50, but if you play 4 games, the cost will be $19.00, and so on.

The y-intercept of the line is $6.875, which means that if you play 0 games, the cost will be $6.875. However, this is not a realistic scenario, as you cannot play 0 games and still incur a cost.

In conclusion, the cost to play at the mini-golf course can be analyzed using linear regression analysis. The results show that the cost increases by $2.50 for every additional game played, and the equation of the line can be used to predict the cost for any number of games played.

**Cost to Play at Mini-golf Course: A Mathematical Analysis** ===========================================================

Q: What is the cost to play at the mini-golf course?

A: The cost to play at the mini-golf course is not fixed and depends on the number of games played. However, based on the data provided, we can see that the cost increases by $2.50 for every additional game played.

Q: How can I calculate the cost to play at the mini-golf course?

A: You can use the equation of the line y = 2.5x + 6.875 to calculate the cost to play at the mini-golf course. Simply plug in the number of games played (x) and solve for y.

Q: What is the y-intercept of the line?

A: The y-intercept of the line is $6.875. This means that if you play 0 games, the cost will be $6.875. However, this is not a realistic scenario, as you cannot play 0 games and still incur a cost.

Q: How can I use the equation of the line to predict the cost to play at the mini-golf course?

A: You can use the equation of the line to predict the cost to play at the mini-golf course by plugging in the number of games played (x) and solving for y. For example, if you want to play 5 games, you would plug in x = 5 and solve for y:

y = 2.5(5) + 6.875 y = 12.50 + 6.875 y = 19.375

So, the cost to play 5 games would be $19.375.

Q: What is the slope of the line?

A: The slope of the line is 2.5. This means that for every additional game played, the cost increases by $2.50.

Q: How can I use the slope to calculate the cost to play at the mini-golf course?

A: You can use the slope to calculate the cost to play at the mini-golf course by multiplying the number of games played (x) by the slope (2.5) and adding the y-intercept (6.875). For example, if you want to play 5 games, you would multiply 5 by 2.5 and add 6.875:

5(2.5) + 6.875 = 12.50 + 6.875 = 19.375

So, the cost to play 5 games would be $19.375.

Q: What is the relationship between the number of games played and the cost to play at the mini-golf course?

A: The relationship between the number of games played and the cost to play at the mini-golf course is linear. This means that for every additional game played, the cost increases by a fixed amount ($2.50).

Q: How can I use the linear relationship to predict the cost to play at the mini-golf course?

A: You can use the linear relationship to predict the cost to play at the mini-golf course by plugging in the number of games played (x) into the equation of the line (y = 2.5x + 6.875) and solving for y.