### 10.3 Professional Sports

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• Math Help

Here are some observations about the U.S. Open and the graph on page 478 (also shown below).

• Here is the order of the rounds: first round, second round, third round, fourth round, quarterfinals, semifinals, and final. The only time the top four seeds would play each other would be in the semifinals or the finals.
• At least two of the top four seeds reached the fourth round in every year except 1973.
• For any year, the sum of the percents adds up to 100%. This is because the outcomes are win in straight sets, win by dropping one or two sets, or lose.
• Notice that from 1977 to 1988 none of the top four seeds lost in the first three rounds.

• Consumer Suggestion

Wimbledon is one of the four Grand Slam tournaments in tennis. It is the only Grand Slam still played on grass. It has been held in London, England since 1877. To learn more about Wimbledon, visit the official website.

• Checkpoint Solution
1. The three line graphs always total 100% for a given year. A player can either win the first three sets and win the match, lose one or two of the sets and win the match, or lose the match. Those are the only three possibilities. If you add up the number of straight set wins, wins with one or two dropped sets, and losses and then divide that number by the total number of matches, you must get 1.
2. In the years in which there were no losses, the green value and the red value must add to 100. The green and red lines are mirror images of each other reflected over the 50% line because the following is true for any number X.

If the green graph is a certain distance above the 50% line, the red graph will be the exact same distance below the 50% line and vice versa.

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