1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
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.

You might be interested in
Jason claims that the absolute value of a nonzero number is always equal to the opposite of the number.
Ilya [14]

Answer:

See below

Step-by-step explanation:

| -5| = 5  

| 5 | does not equal - 5

7 0
2 years ago
3 of 10<br>What is the 5th equivalent fraction to 2/7?​
postnew [5]

Answer:

2 × 7 =14

Step-by-step explanation:

step by step that is the answer

6 0
2 years ago
The table shows the amount of red paint that can be added to different amounts of white paint while making a custom paint color:
KIM [24]

you are looking for a unit rate (for 1 quart of red, how much white is used).

notice all red amounts are less than white, so b and c make no sense.

I look at the 4:20 and think, half of the paint would be 2:10, half of that is 1:5

(you could also start with 4:20 and divide each by 4 to get this answer)

4 0
3 years ago
Write an equation for each description. a number increased by 10 is 114
laila [671]

x+10=114

114-10=x

x=104

3 0
3 years ago
Read 2 more answers
The CEO of a local tech company wants to estimate the proportion of employees that are pleased with the cleanliness of the break
Zigmanuir [339]

Answer:

Methods of obtaining a sample of 600 employees from the 4,700 workforce:

Part A:  The type of sampling method proposed by the CEO is Convenience Sampling.

Part B: When there are equal number of participants in both campuses, stratification by campus would give a more precise approximation of the proportion of employees who are satisfied with the cleanliness of the breakrooms than stratification by gender.  Another method to ensure that stratification by campus gives a more precise approximation of the proportion of employees who are satisfied with the cleanliness of the breakrooms than stratification by gender is to ensure that the sample is proportional to the proportion of each campus to the whole population or workforce.

Step-by-step explanation:

A Convenience Sampling technique is a non-probability (non-random) sampling method and the participants are selected based on availability (early attendees).  The early attendees might be different from the late attendees in characteristics such as age, sex, etc.  Therefore, sampling biases are present.  All non-probability sampling methods are prone to volunteer bias.

Stratified sampling  is more accurate and representative of the population.  It reduces sampling bias.  The difficulty arises in choosing the characteristic to stratify by.

3 0
3 years ago
Other questions:
  • Find the percent change from 2.15 to 1.99
    7·1 answer
  • the temperature at 4am was -13 f the temperature was rising at a steady rate of 5 f an hour at what time will the temperature be
    15·1 answer
  • What is the measure of angle AED A)46 B)134 C)136 D)146
    6·1 answer
  • There are 8 math classes in 7th grade.
    5·1 answer
  • Please help me with questions 5, 6, and 7
    7·1 answer
  • Use a 10x10 grid to express the fraction 11\20 as a percent. How many squares would I shade in?
    8·1 answer
  • Consider the equation.
    12·1 answer
  • Can someone help me? Right answer gets brainliest!!
    6·2 answers
  • If y = x^3 + x<br> please help! :)
    14·1 answer
  • Erica makes necklaces from beads. Each necklace consists of blue, white and green beads in the ratio of 6 : 4: 1 One necklace ne
    15·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!