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Anna [14]
2 years ago
11

The Ratio of boys to girls at Verrado Middle School is 4 to 5. If there are 300 boys at VMS, how many more girls are

Mathematics
1 answer:
lyudmila [28]2 years ago
4 0

Answer:

75 more girls.

Explanation:-

Given:- Ratio of girls to boys = 5:3

And, the number of boys= 300

Let boys be 4x and girls be 5x

So, 4x = 300 (Given)

x = 300/4 = 75

Thus number of girls:- 5x = 5×75= 375 girls

now you take the 375 girls minus the 300 boys.

375-300 = 75 Girls more

~~~~-Hope this helped-~~~~

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A rancher wants to fence in an area of 1000000 square feet in a rectangular field and then divide it in half with a fence down t
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The shortest length of the fence used by the rancher in a rectangular field of 1000000 square feet is 4899 ft.

<h3>What is the area of a rectangle?</h3>

The area of a rectangle is a region enclosed in four corners where two opposite sides are equal. The area of the rectangle is mathematically expressed as:

Area of a rectangle = length(x) × breath(y)

1000000 sq.ft = (x) × (y) ---- (1)

However, to determine the fencing, we have:

Length of fencing = 2x + 2y  

  • since the rectangle has four sides and opposite sides are equal

Suppose we use the x-direction to estimate the region where the fencing is located, we have:

Length of fencing = 2x + 2y + x

Length of fencing = 3x + 2y ---- (2)

From equation (1), make (y) the subject of the formula and replace the value of y with equation (2)

The Length of fencing is:

\mathbf{L = 3x - 2( \dfrac{1000000}{x})}

\mathbf{\dfrac{dL}{dx} = 3 - \dfrac{2000000}{x^2} = 0}

\mathbf{ x^2= \dfrac{2000000}{3} }

\mathbf{ x= \dfrac{1000\sqrt{2}}{\sqrt{3}} }

\mathbf{x = \dfrac{1000 \sqrt{6}}{3}}

Now, if we replace the value with equation (1), then y will be:

\mathbf{y = \dfrac{1000000}{\dfrac{1000 \sqrt{6}}{3}} }\\ \\  \\ \\ \mathbf{y = \dfrac{3000 }{\sqrt{6}}}

\mathbf{x =500\sqrt{6}}

Now, the shortest length of the fencing can be computed by using the equation (2):

L = 3x + 2y

\mathbf{L = 3( \dfrac{1000  \sqrt{6}}{3}) + 2(500 \sqrt{6})}

\mathbf{L =1000  \sqrt{6} + 1000 \sqrt{6}}

\mathbf{L =2000  \sqrt{6} }

\mathbf{L \simeq 4899 \ ft}

Learn more about the area of a rectangle here:

brainly.com/question/25292087

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