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4 years ago

The ratio of boys to girls in the 9th grade is approximately 7 to 9. There are 228 girls. How many boys are there?

Mathematics

1 answer:

Keith_Richards [23]4 years ago

7 0

Answer:

Approximately 177 boys

Step-by-step explanation:

Let

x ----> the number of boys

y ----> the number of girls

we know that

$\frac{x}{y}=\frac{7}{9}$

isolate the variable x

$x=\frac{7}{9}y$ ----> equation A

$y=228$ ----> equation B

substitute equation B in equation A

$x=\frac{7}{9}(228)$

$x=177.33$

therefore

Approximately 177 boys

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Answer:

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Step-by-step explanation:

If variables x and y vary directly, this is expressed as;

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Let's assume the value of x and y since we are not given;

x = 20

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A cylinder has a 12-inch diameter and is 15 inches tall. It is filled to the top with water. A 6-inch-diameter ball is placed wi

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The volume of the cylinder is the space occupied by the cylinder. The volume of the water in the cylinder is 1583.36266 in³.

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The volume of the cylinder is the space occupied by the cylinder. It is calculated with the help of the formula,

$\text{Volume of the cyllinder}= \pi r^2h$

As it is given that the diameter of the cylinder is 12 inches while the height of the cylinder is 15 inches, also, it has a ball of the diameter of 6 inches placed inside the cylinder, therefore, the volume of the water that is inside the cylinder is the difference in the volume of the cylinder and the volume of the spherical ball.

$\text{Volume of the cyllinder}= \pi r^2h = \dfrac{\pi}{4}d^2 h$

Substitute the values,

$\begin{aligned}\text{Volume of the cyllinder}&= \dfrac{\pi}{4}d^2 h\\& = \dfrac{\pi}{4} \times (12^2) \times 15\\ &=1696.46\rm\ in^3\end{aligned}$

Now, the volume of the ball is equal to the volume of the sphere therefore, the volume of the ball can be written as,

$\text{Volume of the sphere} = \dfrac{4}{3}\pi r^3$

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Further, the volume of the water that is inside the cylinder can be written as,

The volume of water = Volume of the cylinder - Volume of the sphere

= 1696.46 - 113.097

= 1583.36266 in³

Hence, the volume of the water in the cylinder is 1583.36266 in³.

Learn more about Volume of the Cylinder:

brainly.com/question/1780981

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