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Umnica [9.8K]
3 years ago
11

A rectangular box has interior dimensions 6-inches by 5-inches by 10-inches. The box is filled with as many solid 3-inch cubes a

s possible, with all of the cubes entirely inside the rectangular box. What percent of the volume of the box is taken up by the cubes?
Mathematics
1 answer:
Arte-miy333 [17]3 years ago
8 0

Answer: The box would have 99% of its volume taken up.

Step-by-step explanation: The box has dimensions as follows;

Length = 6 inches

Width = 5 inches

Height = 10 inches

Therefore the volume of the box shall become

Volume = L x W x H

Volume = 6 x 5 x 10

Volume = 300 cubic inches

Also a 3 inch cube would have its volume given as follows (

Volume = 3 x 3 x 3 (All sides of a cube has equal lengths)

Volume = 27 cubic inches

To find out how many of 3-inch cubes can fit in, divide 300 by 27 and that equals 11.11.

Hence you can have at most 11 cubes in the box. The total volume of 11 cubes is given as 11 x 27 which equals 297. Therefore, the percentage of the box taken up completely by the cubes is given as;

Percentage = (Volume of cubes/Volume of box) x 100

Percentage = (297/300) x 100

Percentage = 99

Therefore the box would have 99% of its volume taken up by the cubes.

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Please help it would be much appreciated!
sergiy2304 [10]

Answer:

Part a) Option d

Part b) Option a

Step-by-step explanation:

Part a

if we look at the options given and the data available

Option a) x^4+9

Putting x= 2 we get (2^4) + 9 =25

Putting x= 3 we get (3^4) + 9 =90 but f(x) =125 so not correct option

Option b) (4^x)+9

Putting x= 2 we get (4^2) + 9 =25

Putting x= 3 we get (4^3) + 9 =73 but f(x) =125 so not correct option

Option c) x^5

Putting x= 2 we get (2^5)  =32 but f(x) =25 so not correct option

Option d) 5^x

Putting x= 2 we get (5^2)  =25

Putting x= 3 we get (5^3)  =125

Putting x= 4 we get (5^4)  =625

So Option d is correct.

Part (b)

3(2)^3x

can be solved as:

=3(2^3)^x

=3(8)^x

So, correct option is a

8 0
3 years ago
Please help I will mark Brainly
Illusion [34]

Answer:

its C


Step-by-step explanation:

if x- small  and y = large and there's 180 small 370 large then its 180x and 370 small and if the maximum is 2000 he needs to get less than or equal to and that's the symbol. how that helps

3 0
3 years ago
The equation A = x(x - 7) describes the area, A, of a rectangular flower garden, where x is the width in feet.
mamaluj [8]

x(x-7)=8

x^2-7x-8=0

(x-8)(x+1)=0

so x=8 (and -1 but width can’t be negative)

So your answer is C. 8

8 0
3 years ago
Step by step plz <br> 2x^2 + x - 3
Aleks04 [339]

Answer:

x = 1 or x = -3/2

Step-by-step explanation:

Solve for x over the real numbers:

2 x^2 + x - 3 = 0

The left hand side factors into a product with two terms:

(x - 1) (2 x + 3) = 0

Split into two equations:

x - 1 = 0 or 2 x + 3 = 0

Add 1 to both sides:

x = 1 or 2 x + 3 = 0

Subtract 3 from both sides:

x = 1 or 2 x = -3

Divide both sides by 2:

Answer: x = 1 or x = -3/2

7 0
3 years ago
Bruno claims that the solution to the linear equation −3(2x+6)+25=1 is x=1. He shows the steps below to justify his solution.
jonny [76]

Answer:

Bruno is correct x=1

Step-by-step explanation:

-3(2x+6)+25=1

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1=x

6 0
3 years ago
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