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avanturin [10]
3 years ago
7

You might need:

Mathematics
1 answer:
Oduvanchick [21]3 years ago
5 0

Answer:

The maximum possible number of mosquitoes is 25 millions

Step-by-step explanation:

Let

m(x) -----> the number of mosquitoes in Minneapolis, Minnesota (in millions of mosquitoes)

x ----> the rainfall in centimeters

we have

m(x)=-(x-5)^{2} +25

This is a quadratic equation (vertical parabola) open downward

The vertex is the maximum

we know that

The maximum possible number of mosquitoes is equal to the y-coordinate of the vertex

Find out the coordinate of the vertex

The general equation of a vertical parabola in vertex form is equal to

y=a(x-h)^{2} +k

where

a is a coefficient

(h,k) is the vertex

so

In this problem

a=-1 (open downward)

(h,k)=(5,25)

The y-coordinate is 25

therefore

The maximum possible number of mosquitoes is 25 millions

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An athlete plains to run 3 miles. Each lap around th school yard is 3/7 miles how many laps will the athlete run
kati45 [8]

Answer: 7 laps

Step-by-step explanation:

The athlete planned to run 3 miles

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by proportion :

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Therefore: the athlete will run 7 laps

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\bf \cfrac{A}{B}=\cfrac{3}{6}\implies \cfrac{A}{B}=\cfrac{1}{2}\implies 2A=\boxed{B}&#10;\\\\[-0.35em]&#10;~\dotfill\\\\&#10;A+B=90\implies A+\boxed{2A}=90\implies 3A=90\\\\\\ A=\cfrac{90}{3}\implies \blacktriangleright A=30 \blacktriangleleft&#10;\\\\[-0.35em]&#10;\rule{34em}{0.25pt}\\\\&#10;2(30)=B\implies \blacktriangleright 60=B \blacktriangleleft

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