### Investigating Collisions in Amusement Park Bumper CarsA study was conducted to explore the number of possible collisions between bumper cars at an amusement park. It's assumed that no two bumper cars can collide more than once. The intention was to determine which mathematical curve best fits the data presented.#### Data TableA table was created to record the number of possible collisions based on the number of bumper cars:| # of Cars | Possible Collisions ||-----------|---------------------|| 1 | 0 || 2 | 1 || 3 | 3 || 4 | 6 || 5 | 10 || 6 | 15 || 7 | 21 |#### Curve Fit OptionsBased on the data gathered, the following are the provided curves to determine the best fit for the data:1. \( y = 0.5x^2 - 0.5x \)2. \( y = -0.5x^2 + 0.5x \)3. \( y = 3.5x - 6 \)4. \( y = 6x - 3.5 \)#### AnalysisTo determine which curve best represents the data, evaluate each curve's appropriateness based on how closely it aligns with the data from the table provided.**Graphical Representation Explanation:**If you were to plot the data points from the table on a graph, you would plot \( x \) representing the number of cars and \( y \) representing the possible collisions.To match the data with any of the equations given:1. For \( y = 0.5x^2 - 0.5x \), substitute each \( x \) value to see if the corresponding \( y \) value matches the data.2. Repeat this process for each equation until you find the one that aligns perfectly with the data.**Educational Insights:**Analyzing such data helps in understanding the practical application of quadratic functions in real-life scenarios such as amusement parks. This example also illustrates the importance of modeling and curve fitting in statistical analysis.

Answered: Image /qna-images/answer/e7e55f51-10f0-42f0-9db3-eaf1e8314ab6.jpg

A study was conducted to investigate the number of collisions possible between bumper cars at an amusement park. Assuming that no two bumper cars can collide more than once, which of the following curves of best fit most closely describes the data in the table? # of Cars Possible Collisions 2 1 3 3 4 6 5 10 6 15 21 O y = 0.5z² – 0.5z O y = -0.5z² + 0.5z O y = 3.5x – 6 О у3 6х — 3.5

A study was conducted to investigate the number of collisions possible between bumper cars at an amusement park. Assuming that no two bumper cars can collide more than once, which of the following curves of best fit most closely describes the data in the table? # of Cars Possible Collisions 2 1 3 3 4 6 5 10 6 15 21 O y = 0.5z² – 0.5z O y = -0.5z² + 0.5z O y = 3.5x – 6 О у3 6х — 3.5

Algebra and Trigonometry (6th Edition)

6th Edition

ISBN:9780134463216

Author:Robert F. Blitzer

Publisher:Robert F. Blitzer

ChapterP: Prerequisites: Fundamental Concepts Of Algebra

Section: Chapter Questions

Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...

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