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Maurinko [17]
2 years ago
14

How many marbles, each with a volume of 36 cubic centimeters, are needed to fill in a cylindrical vase with a radius of 6 centim

eters and a height of 28 centimeters?
6 marbles
9 marbles
14 marbles
28 marbles
Mathematics
2 answers:
ANEK [815]2 years ago
7 0
The volume of a cylinder can be found using the formula:

π r² h, 

where r is the radius of the circular base and h is the height of the cylinder.

If we plug in the measurements of the cylinder, we get:

π (6²) (28)

When this is simplified, we get that the volume of the cylinder is:

1008π cubic cm

Thus, if each marble has a volume of 36π cubic cm, then to find how many marbles will fit into the vase we must divide the vases total volume by the volume of each marble.

1008π / 36π = 28

Therefore, the answer is D. 28 marbles
Karolina [17]2 years ago
4 0
The correct answer is 28 marbles
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Which equations represent a line that passes through the points given in the table? Check all that apply.
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Answer:

I believe the answer is the 2nd box{y-2=1/6 (x+10)}, 3rd box{y-1=1/6(x+4)}, and the 5th box{y=1 x/6 +1/3}.

Step-by-step explanation:

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1 year ago
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Vanna is saving for a trip. The hotel room will be $298.17 for 3 nights, and there will be additional fees. What is her daily co
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Answer:

Step-by-step explanation:

Total cost for the three nights

Total_3 = $298.17 + 3*u

Where <em>u </em>represents the unknown fees for a single day

To find the daily cost, we divide the previous equation by three

Daily cost = ($298.17 + 3*u)/3

Daily cost = ($99.39 + u)

So, if we create an inequality for the daily cost

Let x = Daily cost

x > $99.39

She will pay more than $99.39 per night

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2 years ago
Joseph received a $20 gift card for downloading music. Each downloaded song costs $1.29. Explain how to write and solve an inequ
poizon [28]
<span>Let x be the number of songs downloaded.
Each song is $1.29; the total cost would be found by multiplying the cost by the number of songs, or 1.29x.
This cannot be more than 20, so we set this less than or equal to 20:
1.29x ≤ 20.

<u>To solve this, we divide both sides by 1.29: </u>
</span>\frac{1.29x}{1.29}<span> ≤ </span>\frac{20}{1.29}<span>;
x ≤15.5.

We <u>cannot download half of a song</u>, so we round this down to 15 (although the number rounds up mathematically, he would not have enough money to download 16 songs). This means he can download at most 15 songs.</span>
8 0
2 years ago
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A rectangular tank measuring 35 cm by 28 cm by 16 cm is 2/5 filled with
Alina [70]

Answer:

Amount of water left in tank = 440 cm³

Step-by-step explanation:

Given:

Sides of tank respectively = 35 cm , 28 cm , 16 cm  

Water level in tank = 2/5

Side of a cubic tank = 18 cm

Find:

Amount of water left in tank

Computation:

Volume level in rectangular tank = [2/5][35 x 28 x 16]

Volume level in rectangular tank = [2/5][15,680]

Volume level in rectangular tank = [31,360/5]

Volume level in rectangular tank = 6,272 cm³

Volume of cube = side³

Volume of cube = 18³

Volume of cube = 5,832 cm³

Amount of water left in tank = Volume level in rectangular tank - Volume of cube

Amount of water left in tank = 6,272 - 5,832

Amount of water left in tank = 440 cm³

7 0
1 year ago
According to the Fundamental Theorem of Algebra, which polynomial function has exactly 8 roots?f(X) 3x4 +2xfox)- (6x -4x5-10 3x2
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<u><em>Answer:</em></u>
A. (3x²-4x-5)(2x⁶-5)

<u><em>Explanation:</em></u>
<u>The fundamental theorem of Algebra states that:</u>
"A polynomial of degree 'n' will have exactly 'n' number of roots"

We know that the degree of the polynomial is given by the highest power of the polynomial.
Applying the above theorem on the given question, we can deduce that the polynomial that has exactly 8 roots is the polynomial of the 8th degree

<u>Now, let's check the choices:</u>
<u>A. (3x²-4x-5)(2x⁶-5)</u>
The term with the highest power will be (3x²)(2x⁶) = 6x⁸
Therefore, the polynomial is of 8th degree which means it has exactly 8 roots. This option is correct.

<u>B. (3x⁴+2x)⁴</u>
The term with the highest power will be (3x⁴)⁴ = 81x¹⁶
Therefore, the polynomial is of 16th degree which means it has exactly 16 roots. This option is incorrect.

<u>C. (4x²-7)³</u>
The term with the highest power will be (4x²)³ = 64x⁶
Therefore, the polynomial is of 6th degree which means that it has exactly 6 roots. This option is incorrect

<u>D. (6x⁸-4x⁵-1)(3x²-4)</u>
The term with the highest power will be (6x⁸)(3x²) = 18x¹⁰
Therefore, the polynomial is of 10th degree which means that it has exactly 10 roots. This option is incorrect

Hope this helps :)
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1 year ago
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