While reviewing detailed statistics from an entire tournament, Tara and Emek noticed that one team's success was not explained by average scores alone. They compared different ratio models connecting successful plays, total possessions, and scoring efficiency. Each model was represented as a function and tested against performance data from different stages of the tournament. By examining how well each model matched the changing conditions, they identified the function that consistently explained the team's results. Their analysis gave the coaching staff a reliable mathematical model for planning future strategies.
Challenges
Challenge 1 of 5
Challenges
Challenge 1 of 4
Hint
Substitute x = 50 into the function and multiply by the fraction.
Tara and Emek test a ratio model for scoring efficiency. The function is f(x) = 3/5*x, where x is the number of successful play opportunities. What is the predicted efficiency value when x = 50?
30253550Correct! The function gives 3/5*50 = 30.
Check that you multiply the input value by the ratio 3/5.
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Hint
Multiply the total possessions by the success ratio.
A tournament model shows that successful plays are 4/7 of total possessions. If the team has 140 total possessions, how many successful plays does the model predict?
Correct! The model predicts 80 successful plays.
Use 4/7 as the fraction of the total possessions.
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Hint
Convert the fraction to a decimal before comparing the two models.
Tara and Emek compare two ratio models for predicting scoring efficiency. Model A is represented by 0.72, and Model B is represented by 7/10. Which conclusion is correct?
Model A is stronger because 0.72 is greater than 0.7Model B is stronger because fractions are always larger than decimalsBoth models are equal because 0.72 and 7/10 represent the same valueModel B is stronger because 7/10 equals 0.75Correct! 7/10 equals 0.7, so 0.72 is the larger value.
Compare both models using the same form before deciding.
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