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2 years ago

A rainwater collection system uses a cylindrical storage tank with a diameter of

Mathematics

2 answers:

elixir [45]2 years ago

6 0

Answer:

157079.6

Step-by-step explanation the formula to find volume of a cylinder is pi radius squared(half of diameter) times height.

ozzi2 years ago

4 0

Answer:

157,080 cubic centimeters.

Step-by-step explanation:

We have been given that a rainwater collection system uses a cylindrical storage tank with a diameter of 50 centimeters and a height of 80 centimeters. We are asked to find the volume of water.

We know that volume of water will be equal to volume of tank. To find the volume of tank, we will use volume of cylinder formula.

$\text{Volume of cylinder}=\pi r^2h$ , where,

r = Radius of cylinder,

h = Height of cylinder.

We know that diameter is two times radius, so radius of cylinder would be half of 50 cm, that is 25 cm.

$\text{Volume of cylinder}=\pi (\text{25 cm})^2\times \text{80 cm}$

$\text{Volume of cylinder}=\pi \times 625\text{ cm}^2\times \text{80 cm}$

$\text{Volume of cylinder}=\pi \times 50,000\text{ cm}^3$

$\text{Volume of cylinder}=157,079.632679\text{ cm}^3$

$\text{Volume of cylinder}\approx 157,080\text{ cm}^3$

Therefore, the volume of water is 157,080 cubic centimeters.

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1 year ago

The number of messages arriving at a multiplexer is a Poisson random variable with mean 15 messages/second. Use the central limi

Mila [183]

Answer:

0.048 is the probability that more than 950 message arrive in one minute.

Step-by-step explanation:

We are given the following information in the question:

The number of messages arriving at a multiplexer is a Poisson random variable with mean 15 messages/second.

Let X be the number of messages arriving at a multiplexer.

Mean = 15

For poison distribution,

Mean = Variance = 15

$\text{Standard Deviation} = \sqrt{\text{Variance}} = \sqrt{15} = 3.872$

From central limit theorem, we have:

$z = \displaystyle\frac{x-n\mu}{\sigma\sqrt{n}}$

where n is the sample size.

Here, n = 1 minute = 60 seconds

P(x > 950)

$P( x > 950) = P( z > \displaystyle\frac{950 - (60)(15)}{\sqrt{(15)(60)}}) = P(z > 1.667)$

$= 1 - P(z \leq 1.667)$

Calculation the value from standard normal z table, we have,

$P(x > 950) = 1 - 0.952 = 0.048$

0.048 is the probability that more than 950 message arrive in one minute.

3 0

2 years ago

the performance score of 10 adults is recorded, and the results are 83 87 90 92 93 100 104 111 115 121 find the standard deviati

luda_lava [24]

Answer:

The standard deviation of the data set is $\sigma = 12.7906$ .

Step-by-step explanation:

The Standard Deviation is a measure of how spread out numbers are. Its symbol is σ (the greek letter sigma)

To find the standard deviation of the following data set

$\begin{array}{cccccccc}83&87&90&92&93&100&104&111\\115&121&&&&&&\end{array}$

we use the following formula

$\sigma = \sqrt{ \frac{ \sum{\left(x_i - \overline{X}\right)^2 }}{n-1} }$

Step 1: Find the mean $\left( \overline{X} \right)$ .

The mean of a data set is the sum of the terms divided by the total number of terms. Using math notation we have:

$Mean = \frac{Sum ~ of ~ terms}{Number ~ of ~ terms}$

$Mean = \frac{Sum ~ of ~ terms}{Number ~ of ~ terms}=\frac{83+87+90+92+93+100+104+111+115+121}{10} \\\\Mean = \frac{996}{10} =\frac{498}{5}=99.6$

Step 2: Create the below table.

Step 3: Find the sum of numbers in the last column to get.

$\sum{\left(x_i - \overline{X}\right)^2} = 1472.4$

Step 4: Calculate σ using the above formula.

$\sigma = \sqrt{ \frac{ \sum{\left(x_i - \overline{X}\right)^2 }}{n-1} } = \sqrt{ \frac{ 1472.4 }{ 10 - 1} } \approx 12.7906$

3 0

2 years ago

Write 12,430,090in expanded form

stira [4]

10,000,000+2,000,000+
400,000+30,000+90

7 0

2 years ago