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bekas [8.4K]
3 years ago
5

Darla is training for a marathon. She starts out running 1.5 miles and plans to add additional miles each week. Below is a scree

n shot from her fitness tracker app on her phone.
Part a: assuming that this pattern of running continues for darla, write an equation that could be used to find the number of miles she runs for any number of weeks.

Part b: to complete a marathon, you must run 26.2 miles. Using the table and/or equation, will darla be able to complete a marathon after 14 weeks of training?

Mathematics
1 answer:
diamong [38]3 years ago
6 0
Part A:
As we can see on this table, Darla run 3 miles the first week. Then she began running 1.5 miles each week (4.5 - 3 = 1.5; 6 - 4.5 = 1.5; etc...). Let x be the number of weeks. But since the first week is different from the others, we need to remove 1 from x.
The equation is: 1.5(x-1) + 3

Part B:
To know how much she can run in 14 weeks, we replace x by 14 in the previous equation.
1.5x + 3 = 1.5 * 14-1 + 3 = 1.5*13 + 3 = 22.5

So no, she can't run 26.2 miles in 14 weeks.
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We are given with the following frequency distribution below;

 

     Age                      Frequency (f)               X                    X \times f

     0 - 9                            30                         4.5                   135

    10 - 19                           32                        14.5                  464

    20 - 29                         12                         24.5                 294

    30 - 39                         20                        34.5                 690

    40 - 49                         25                        44.5                1112.5

    50 - 59                         53                        54.5                2888.5

    60 - 69                         49                        64.5                3160.5

    70 - 79                          13                         74.5                968.5

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Now, the mean of the frequency distribution is given by the following formula;

                          Mean =  \frac{\sum X \times f}{\sum f}

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Hence, the mean age of the frequency distribution for the ages of the residents of a town is 43 years.

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