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lorasvet [3.4K]
3 years ago
10

The internal dimension of a cylindrical container has a base area of 20 cm^2 and a height of 10 cm. What is the internal volume

of the container?
A) 2 cm^3

B) 30 cm^3

C) 200 cm^3

D) 2,000 cm^3
Mathematics
1 answer:
yawa3891 [41]3 years ago
5 0

Answer:

<u><em>C) 200 cm^3 </em></u>

<u><em></em></u>

Step-by-step explanation:

we observe that

Area=20 cm² and   Height=10 cm

The  formula to find volume is :

Volume= Area×Height

putting the values of area and height in above formula,we get

Volume= 20 cm²×10 cm

Volume= 200 cm³

The internal volume of the container is 200 cm³.

hope this helps

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A playground is being designed where children can interact with their friends in certain combinations. If there is 1 child, ther
mariarad [96]
<h2>Answer:</h2>

<em><u>Recursive equation for the pattern followed is given by,</u></em>

a_{n}=a_{n-1}+(n-1)^{2}

<h2>Step-by-step explanation:</h2>

In the question,

The number of interaction for 1 child = 0

Number of interactions for 2 children = 1

Number of interactions for 3 children = 5

Number of interaction for 4 children = 14

So,

We need to find out the pattern for the recursive equation for the given conditions.

So,

We see that,

a_{1}=0\\a_{2}=1\\a_{3}=5\\a_{4}=14\\

Therefore, on checking, we observe that,

a_{n}=a_{n-1}+(n-1)^{2}

On checking the equation at the given values of 'n' of, 1, 2, 3 and 4.

<u>At, </u>

<u>n = 1</u>

a_{n}=a_{n-1}+(n-1)^{2}\\a_{1}=a_{1-1}+(1-1)^{2}\\a_{1}=0+0=0\\a_{1}=0

which is true.

<u>At, </u>

<u>n = 2</u>

a_{n}=a_{n-1}+(n-1)^{2}\\a_{2}=a_{2-1}+(2-1)^{2}\\a_{2}=a_{1}+1\\a_{2}=1

Which is also true.

<u>At, </u>

<u>n = 3</u>

a_{n}=a_{n-1}+(n-1)^{2}\\a_{3}=a_{3-1}+(3-1)^{2}\\a_{3}=a_{2}+4\\a_{3}=5

Which is true.

<u>At, </u>

<u>n = 4</u>

a_{n}=a_{n-1}+(n-1)^{2}\\a_{4}=a_{4-1}+(4-1)^{2}\\a_{4}=a_{3}+9\\a_{4}=14

This is also true at the given value of 'n'.

<em><u>Therefore, the recursive equation for the pattern followed is given by,</u></em>

a_{n}=a_{n-1}+(n-1)^{2}

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3 years ago
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Step-by-step explanation:

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A ramp has a height of 7 feet and
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Grading managers. Some companies "grade on a bell curve" to compare the performance of their managers and professional workers.
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Answer:

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Previous concepts

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".  

Solution to the problem

Let X the random variable that represent the grades of a population, and for this case we know the distribution for X is given by:

X \sim N(\mu,\sigma)  

For this case we have two conditions given:

P(X

P(X>475) = 0.1 or equivalently P(X

And the best way to solve this problem is using the normal standard distribution and the z score given by:

z=\frac{x-\mu}{\sigma}

So we can find a value from the normal standard distribution that accumulates 0.1 and 0.9 of the area in the left, for this case the two values are:

z= -1.28, z=-1.28

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And then using the z score we have the following formulas:

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1.28 = \frac{475 -\mu}{\sigma}   (2)

If we add equations (1) and (2) we got:

\frac{25 -\mu}{\sigma} + \frac{475 -\mu}{\sigma} =0

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\sigma = \frac{25-250}{-1.28}=175.781

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3 years ago
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