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Olenka [21]
3 years ago
5

A cylindrical container of five rubber balls has a height of 30 centimeters and a diameter of 6 centimeters. Each ball in the co

ntainer has a radius of 3 centimeters. Find the amount of space in the container that is not occupied by rubber balls. Round your answer to the nearest whole number.
Mathematics
1 answer:
Artyom0805 [142]3 years ago
3 0

Answer:

There is 170 cm³ free space in the container.

Step-by-step explanation:

Cylindrical container: height = 18 cm ; diameter = 6 cm.

3 balls each have a radius of 3 cm.

Volume of a cylinder = π r² h

V = 3.14 * (3cm)² * 18 cm

V = 508.68 cm³

Volume of rubber ball = 4/3  π r³

V = 4/3 * 3.14 * (3cm)³

V = 113.04 cm³

113.04 cm³  * 3 balls = 339.12 cm³

508.68 cm³ - 339.12 cm³ = 169.56 cm³ or 170 cm³

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The price of a European tour includes stopovers at five cities to be selected from 15 cities. In how many ways can a traveler pl
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The correct answer is D. 360,360.

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Number of cities as stopovers available for selection for an European tour = 15

A traveler has to select a total of five cities from these the given 15 cities for his tour and order is determined by the travel company.

Therefore the number of ways the traveler plan such a tour is given by \left[\begin{array}{ccc}15\\5\end{array}\right] = 3003.

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Simplify fully: √18 / √8
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3 0
3 years ago
A. The average yearly salary of a lawyer is $24 thousand less than twice that of an architect.
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Answer:

The average yearly salary of  the architect is <u>$62,000</u> and the lawyer is <u>$100,000</u>.

Step-by-step explanation:

Given:

The average yearly salary of a lawyer is $24 thousand less than twice that of an architect.

Combined, an architect and a lawyer earn $ 210 thousand.

Now, to find the average yearly salary of  an architect and a lawyer.

Let the average yearly salary of  an architect be x.

So, the average yearly salary of  the lawyer = 2x-24,000.

Combined, architect and lawyer earn = \$210,000.

Now, to get the average salary of the architect and lawyer:

x+(2x-24000)=210000

x+2x-24000=210000\\\\3x-24000=210000

<em>Adding both sides 24000 we get:</em>

3x=186,000\\\\Dividing\ both\ sides\ by\ 3\ we\ get:\\\\x=62000.

<u>The average salary of architect = $62,000.</u>

Now, to get the average salary of lawyer by substituting the value of x:

2x-24000\\\\=2(62000)-24000\\\\=124000-24000\\\\=\$100,000.

<u>The average salary of lawyer = $100,000.</u>

Therefore, the average yearly salary of  the architect is $62,000 and the lawyer is $100,000.

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3 years ago
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