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Morgarella [4.7K]
3 years ago
7

Mai biked 5 1/4 miles today, and Noah biked 2 1/2 miles. How many times the length of Noah’s bike ride was Mai’s bike ride?

Mathematics
1 answer:
OlgaM077 [116]3 years ago
5 0

Answer:

The length of Mai's bike ride was 2.1 times the length of Noah's ride.

Step-by-step explanation:

Mai biked 5 1/4 miles today

So he biked, in miles:

5 + \frac{1}{4} = \frac{5*4 + 1}{4} = \frac{20+1}{4} = \frac{21}{4}

Noah biked 2 1/2 miles.

So, in miles, he biked:

2 + \frac{1}{2} = \frac{2*2 + 1}{2} = \frac{4+1}{2} = \frac{5}{2}

How many times the length of Noah’s bike ride was Mai’s bike ride?

We divide the Mai distance by Noah's distance. In a division of fractions, we multiply the numerator by the inverse of the denominator. So

\frac{\frac{21}{4}}{\frac{5}{2}} = \frac{21}{4} \times {2}{5} = \frac{21*1}{2*5} = \frac{21}{10} = 2.1

The length of Mai's bike ride was 2.1 times the length of Noah's ride.

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This problem involves several steps. The first step is to realize that the given figure does not show the required number of vertical stringers. It shows 5, but there will be 7 of them. The given diagram is helpful in that it shows a vertical stringer on the centerline of the arches.

The second step is to write a function that will tell you how long the stringer will be. I find it convenient to write the equation for an arch shape such as this using the parent function h(x) = 1-x^2. This parent function gives an arch of height 1 and width 1 from center (a total width of 2). You want an arch that is 16 ft high and 40 ft wide (one side from center), so you must scale this parent function both horizontally (by 40) and vertically (by 16). It becomes ...

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