Which of the following samples would meet the "random" condition?

Mathematics

1 answer:

Troyanec [42]3 years ago

7 0

Answer:

Brother there's nothing there

Step-by-step explanation:

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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

Tems11 [23]

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

<h3>What is the volume of a cylinder?</h3>

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,

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

$= \dfrac{4}{3}\pi r^3\\\\= \dfrac{4}{3}\times \pi \times (3^3)\\\\= 113.097\rm\ in^3$

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:

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5 0

2 years ago

What constant term is necessary to complete the perfect square trinomial pictured in the algebra tiles?

gayaneshka [121]

The algebra tiles show two equal factors. They are (x + 4).

Then, the perfect square is the product of the two equal factors, (x + 4) * (x +4).

That is (x + 4)^2.

Then develop that perfect square to find the constant term.

(x + 4)^2 = x^2 + 8x + 16.

That means that the constant term needed to complete the trinomial is 16.

Answer: 16

3 0

3 years ago

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murzikaleks [220]

The arc length, radius and the included angle are related as

$r\theta=\widehat {XYZ}$ where $\theta$ is in radians.