A cylindrical container of six rubber balls has a height of 18 centimeters and a diameter of 3 centimeters. Each ball in the container has a radius of 1.5 centimeters. Find the amount of space in the container that is not occupied by rubber balls. Round your answer to the nearest whole number. - Could you help me with this?

Answers

Answer 1

Answer:

170 cm²

Step-by-step explanation:

Height of Cylindrical container = 18 cm ; diameter of cylindrical container = 6 cm.

Hence, radius of cylindrical container = 6/2 = 3 cm

Rubber balls = 3 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

Volume of 3 rubber balls = 3 * 113.04 = 339.12³

Take the difference to obtain answer :

Volume of cylinder - Volume of rubber ball

508.68 cm³ - 339.12³

= 169.56 cm²

170 cm² (nearest whole number


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Step-by-step explanation:

1 microsecond is equal to 1000 nanoseconds.

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96,000+318=96,318 nanoseconds.

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So the x-intercept is 3. Also, the y-intercept can also be obtained by putting x=0 in the equation to get y=12/(-6)=-2

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Each of the green lines has 3 times the length of the corresponding blue line.  Thus the dilution factor is 3.

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Step-by-step explanation:

see attached. hope it's helps

Complete the recursive formula of the arithmetic sequence -3, -1, 1, 3,...

b(1)= "answer"
b(n)=b(n-1)+ "answer"

Answers

Given:

The given arithmetic sequence is:

[tex]-3,-1,1,3,...[/tex]

To find:

The recursive formula of the given arithmetic sequence.

Solution:

We have,

[tex]-3,-1,1,3,...[/tex]

Here, the first term is -3. So, [tex]b(1)=-3[/tex].

The common difference is:

[tex]d=-1-(-3)[/tex]

[tex]d=-1+3[/tex]

[tex]d=2[/tex]

The recursive formula of an arithmetic sequence is:

[tex]b(n)=b(n-1)+d[/tex]

Where, d is the common difference.

Putting [tex]d=2[/tex], we get

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67. There are 15 clarinet players, 12 flute
players, and 7 saxophone players in a
marching band. How many ways can the
band director create a trio consisting of
one clarinet player, one flute player, and
one saxophone player?
A. 34 ways
B. 187 ways
C. 1,260 ways
D. 1,500 ways

Answers

Answer:

A

Step-by-step explanation: add 15+12+7

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The band director can create a trio in 1,260 different ways.

Hence, option C is correct.

Use the concept of permutations,

The formula for permutations is,

⇒  [tex]^{n}P_{r}[/tex] = n! / (n - r)!

Where n is the total number of items and r is the number of items we are selecting.

So in this case, we have,

⇒  n = 15 clarinet players

⇒ n = 12 flute players

⇒ n = 7 saxophone players

⇒ r = 1 clarinet player,

1 flute player, and 1 saxophone player

To find the number of ways we can create a trio with one player from each instrument, we need to calculate,

⇒ ([tex]^{15}P_{1}[/tex]) x ([tex]^{12}P_{1}[/tex]) x ([tex]^{7}P_{1}[/tex])

⇒  ([tex]^{15}P_{1}[/tex])   = 15! / (15 - 1)!

                = 15! / 14!

                = 15  

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([tex]^{12}P_{1}[/tex]) ) = 12! / (12 - 1)!

           = 12! / 11!

           = 12  

This represents the number of ways we can choose one flute player out of 12.

[tex]^{7}P_{1}[/tex] = 7! / (7 - 1)!

     = 7! / 6!

     = 7

This represents the number of ways we can choose one saxophone player out of 7.

So the total number of ways we can create a trio consisting of one clarinet player, one flute player, and one saxophone player is,

⇒ 15 x 12 x 7 = 1,260

Therefore,

The band director can create a trio in 1,260 different ways.

To learn more about permutations visit:

https://brainly.com/question/14368656

#SPJ2

Find the perimeter of the
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D
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Answers

Answer:

100cm

Step-by-step explanation:

From the given diagram;

Perimeter of the polygon = AB + BC+ CD + DA

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Step-by-step explanation:

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Answer:

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Gavin is subdividing land into two plots, where one plot is in the shape of a square and the other plot is in the shape of a rectangle. The square plot of land has a side length of 6x³ feet, and the rectangular plot of land has a length of 3x⁵ feet and a width of 7x² feet. Use the properties of exponents to determine the expression that represents the area for each plot of land. Then analyze which plot of land has a larger area if x is 3.

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The square plot of land has a larger area when x is 3.

What is Algebraic expression ?

Algebraic expression can be defined as combination of variables and constants.

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