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Svetlanka [38]
2 years ago
6

You are the administrator of an annual essay contest scholarship fund. This year a $90,000 college scholarship is being divided

between the top two contestants so that the winner receives five times as much as the runner-up. How much will each contestant receive (in dollars)?
runner-up amount :

winner amount:
Mathematics
1 answer:
Vinil7 [7]2 years ago
3 0

Answer:

Runner-up: $15,000

Winner: $75,000

Step-by-step explanation:

Let's create an equation for this problem.

Let x=the amount the runner-up receives

Let 5x=the amount the winner receives

Then,

x+5x=90,000

6x=90,000

x=15,000

5x=75,000

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Answer: graph E.


A geometric sequence can be written as:

a_{n} = a_{1} \cdot r^{(n - 1)}

where:

a₁ = first term = 4

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Substituting the numbers, we have:

a_{n} = 4 \cdot (\frac{1}{2})^{n-1}

or else

f(x) = 4 \cdot (\frac{1}{2})^{x - 1}


This is an exponential function with base less than 1. Therefore, we can exclude graph C (which depicts a linear function), and graphs A and D (which depict an exponential function with base greater than 1).


In order to choose between graph B and E, let's evaluate the function in two different points:

f(1) = 4 \cdot (\frac{1}{2})^{1 - 1} = 4

f(2) = 4 \cdot (\frac{1}{2})^{2 - 1} = 4 \cdot \frac{1}{2} = 2


Therefore, we need to look for the graph passing through the points (1, 4) and (2, 2). That is graph E.




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3 years ago
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Step-by-step explanation:

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