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10.4 Outdoor Sports

10.4 Outdoor Sports
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  • 15. Mountain Bike Trails with Downhill Sections

    The graph shows the data for eight mountain bike trails. Do any of the trails have downhill sections? Explain your reasoning. (See Example 5 and Example 6.)

    • Worked-Out Solution

      Yes, a line that decreases from left to right indicates a downhill section. For instance, Trail 5 has a downhill section between the 3-mile and 3.5-mile markers.

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    __    __    ______    _  __    _____     ______  
    \ \\ / //  /_   _//  | |/ //  |  ___||  /_   _// 
     \ \/ //    -| ||-   | ' //   | ||__      | ||   
      \  //     _| ||_   | . \\   | ||__     _| ||   
       \//     /_____//  |_|\_\\  |_____||  /__//    
        `      `-----`   `-` --`  `-----`   `--`     
                                                     
    
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  • 16. Mountain Bike Trails Longer than 6 Miles

    The graph shows the data for eight mountain bike trails. What percent of the trails are longer than 6 miles? (See Example 5 and Example 6.)

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                ______   __   __    _____    ______   
        ___    /_   _//  \ \\/ //  |  ___|| |      \\ 
       /   ||   -| ||-    \   //   | ||__   |  --  // 
      | [] ||   _| ||_    / . \\   | ||__   |  --  \\ 
       \__ ||  /_____//  /_//\_\\  |_____|| |______// 
        -|_||  `-----`   `-`  --`  `-----`  `------`  
         `-`                                          
    
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  • 17. Mountain Bike Trail that Requires the Most Energy

    The graph shows the data for eight mountain bike trails. Which trail requires the most energy to complete? Explain your reasoning. (See Example 5 and Example 6.)

    • Worked-Out Solution

      Trail 2 requires the most energy to complete because it is the longest trail and it has the steepest incline (after the 8-mile marker).

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     __   __    _____     ____      _____    _    _   
     \ \\/ //  |  ___||  |  _ \\   |  ___|| | \  / || 
      \   //   | ||__    | |_| ||  | ||__   |  \/  || 
      / . \\   | ||__    | .  //   | ||__   | .  . || 
     /_//\_\\  |_____||  |_|\_\\   |_____|| |_|\/|_|| 
     `-`  --`  `-----`   `-` --`   `-----`  `-`  `-`  
                                                      
    
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  • 18. Grade Reference Line

    The graph shows the data for eight mountain bike trails. What is the purpose of the 10% grade reference line? (See Example 5 and Example 6.)

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     __   _      ___                 ___     _____    
    | || | ||   / _ \\    ____      / _ \\  |  __ \\  
    | '--' ||  / //\ \\  |    \\   / //\ \\ | |  \ || 
    | .--. || |  ___  || | [] ||  |  ___  ||| |__/ || 
    |_|| |_|| |_||  |_|| |  __//  |_||  |_|||_____//  
    `-`  `-`  `-`   `-`  |_|`-`   `-`   `-`  -----`   
                         `-`                          
    
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  • 19. Mean and Median Vertical Rises of Mountain Bike Trails

    The graph shows the data for eight mountain bike trails. Estimate the mean and median vertical rises of the trails. Are any of the trails outliers? Explain your reasoning. (See Example 5 and Example 6.)

    • Worked-Out Solution

      Using the graph, you can estimate the vertical rise of the trails by estimating the value on the vertical axis that corresponds to the end of each trail's line. The estimated vertical rise for each trail is shown in the box.

      You can use your estimates to find the mean and the median. To find the mean, add the vertical rises and divide by the total number of vertical rises.

      The mean is 2437.5 feet.

      To find the median, order the data from least to greatest. Because there is an even number of vertical rises, you must add the two middle values and divide their sum by 2.

      So, the median is 1800 feet.

      Trail 1 and trail 2 are outliers. The vertical rise of both trails is a lot greater than the rest of the data.

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     _    _    __   __    _  _      ___       _____  
    | || | ||  \ \\/ //  | \| ||   / _ \\    / ___// 
    | || | ||   \ ` //   |  ' ||  / //\ \\   \___ \\ 
    | \\_/ ||    | ||    | .  || |  ___  ||  /    // 
     \____//     |_||    |_|\_|| |_||  |_|| /____//  
      `---`      `-`'    `-` -`  `-`   `-` `-----`   
                                                     
    
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  • 20. Mountain Biking

    The graph shows the data for eight mountain bike trails. Which trail would you prefer to ride? Explain your reasoning. (See Example 5 and Example 6.)

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      _  _     ______    _  __    ______   _    _   
     | \| ||  /_   _//  | |/ //  /_   _// | || | || 
     |  ' ||   -| ||-   | ' //    -| ||-  | || | || 
     | .  ||   _| ||_   | . \\    _| ||_  | \\_/ || 
     |_|\_||  /_____//  |_|\_\\  /_____//  \____//  
     `-` -`   `-----`   `-` --`  `-----`    `---`   
                                                    
    
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