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Mariana [72]
2 years ago
12

Corry collects cube containers. She fills them with water and pours them into a rectangular prism. She was playing with them and

discovered something interesting. She had three cube containers. One cube was 1 inch by 1 inch by 1 inch. A second cube was 2 inches by 2 inches by 2 inches and a third cube was 3 inches by 3 inches by 3 inches.She filled all three with water. Then Corry poured all three cubes into a rectangular prism filling it exactly! The rectangular prism has a square base with a side length (1+2+3 = 6) inches and the height is 1 inch.Corry wonders whether she has found a pattern. Investigate using more cube containers to fill square base prisms with heights of 1 in. Describe any conjectures you discover.
Mathematics
1 answer:
Alinara [238K]2 years ago
3 0

Answer:

  \displaystyle\sum_{i=1}^n{i^3}=\left(\sum_{i=1}^n{i}\right)^2

Step-by-step explanation:

The only sum of three cubes that has a total equal to the square of the sum of their dimensions is the one Corry found.

However, we notice that ...

  1³ +2³ +3³ +4³ = (1 +2 +3 +4)² = 100

If we add the next number in sequence, we get ...

  100 +5³ = 225 = (10 +5)²

  225 +6³ = 441 = (15 +6)²

So, it seems that the sum of the first n cubes is equal to the square of the sum of the first n natural numbers.

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0,2,4,0,2,3,2,8,6
zubka84 [21]

Answer:

LOOK BELOW

Step-by-step explanation:

Mean= add all of the numbers together and divide by total amount of

            numbers

            aka=3

Median= put all the numbers in order and find the number in the middle

               aka=2.5

Minimum=0

Maximum=8

This data can only be found using a Box and Whisker Plot....

I can't really explain a box and whisker plot so you have to look that up to understand that..  SRY!!!

------------------------------------

First Quartile=1

Third Quartile=5

Interquartile Range=4

8 0
3 years ago
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In a fruit cocktail, for every 30 ml of orange juice you need 45 ml of apple juice and 25 ml of coconut milk. What proportion of
sveta [45]

Answer: \frac{1}{4}

Step-by-step explanation:

Given

For 30 ml of orange Juice

45 ml of apple Juice is needed and

25 ml of coconut milk is required

The proportion of coconut milk in the cocktail is

\Rightarrow \dfrac{\text{amount of coconut milk}}{\text{total volume of mixture}}\\\\\Rightarrow \dfrac{25}{30+45+25}=\dfrac{25}{100}\\\\\Rightarrow \dfrac{1}{4}

5 0
3 years ago
What is the percentage of 7 out of 12 show work
Nata [24]

Convert the fraction to a decimal, then multiply by 100.

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Answer:

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4 0
2 years ago
Now that you have the height of the cone how can you solve for the slant height ?
avanturin [10]

Answer:

what is the height of the cone

Step-by-step explanation:

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