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Solnce55 [7]
3 years ago
13

One of the most spectacular and least known hummingbirds is the Marvelous Spatuletail, Loddigesia mirabilis, found in only in a

single remote valley in northern Peru (see photo below). In this valley the mean density is 3 spatuletails per 100-hectare quadrat. (a) What is the probability a random quadrat contains less than 3 spatuletails
Mathematics
1 answer:
Karo-lina-s [1.5K]3 years ago
6 0

Answer:

P(x < 3) = 0.42319

Step-by-step explanation:

From the given information:

The mean density \lambda = 3

Let x be the random variable that follows a Poisson distribution.

Therefore:

\mathtt{P(x) = \dfrac{e^{-\lambda} \lambda ^x}{x!}}     for x =1, 2, 3...

However, the probability that a random quadrat contains less than 3 spatuletails can be computed as:

\mathtt{P(x

\mathtt{P(x

\mathtt{P(x

\mathtt{P(x

\mathtt{P(x

P(x < 3) = 0.42319

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The biggest possible volume of the cylinder will be 2089.497\hspace{1mm}\text{cm}^3.

<h3>What will be the diameter and height of the cylinder obtained from a cube and what are the formulas for the diagonal of a cube and the volume of a cylinder?</h3>
  • If a cylinder with the biggest possible volume is cut inside the cube, the height of the cylinder and the diameter of the cylinder will be equal to the side length of the cube.
  • For example, consider the following figure in which the cylinder is cut inside of the cube and since the side length of the cube is x, the diameter and the height of the cylinder are also x
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Now, given that the diagonal of the cube is 24 cm. So, if the side length of the cube is x cm, then we must have

x\sqrt{3}=24\\\Longrightarrow x=\frac{24}{\sqrt{3}}\\\Longrightarrow x=8\sqrt{3}

Thus, the side length of the cube is 8\sqrt{3} cm.

So, the height of the cylinder with maximum volume will be h=8\sqrt{3} cm and the diameter will be d=8\sqrt{3}cm i.e. the radius will be r=\frac{d}{2}=\frac{8\sqrt{3}}{2}=4\sqrt{3} cm.

So, using the above formula for the volume of a cylinder, we get

V=\pi r^{2}h=\pi\times (4\sqrt{3})^2\times 8\sqrt{3}=2089.497\hspace{1mm}\text{cm}^3.

Therefore, the biggest possible volume of the cylinder will be 2089.497\hspace{1mm}\text{cm}^3.

To know more about volume, refer: brainly.com/question/1972490

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