I'm having trouble solving this:
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 3inches 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.

Answers

Answer 1

Corry's conjecture is right, and the volume follows a pattern

The volume of a cube of side length l is:

[tex]V = l^3[/tex]

For the first cube of length 1 in, the volume is:

[tex]V = 1^3[/tex]

[tex]V = 1[/tex]

For the second cube of length 2 in, the volume is:

[tex]V = 2^3[/tex]

[tex]V = 8[/tex]

For the third cube of length 1 in, the volume is:

[tex]V = 3^3[/tex]

[tex]V = 27[/tex]

So, the total volume is:

[tex]Total =1 + 8 + 27[/tex]

[tex]Total =36[/tex]

The volume of a rectangular prism of base lengths 6 in and height 1 in is:

[tex]Volume = 6^2 \times 1[/tex]

[tex]Volume = 36[/tex]

Assume, he adds a cube of side length 4 in, the volume is:

[tex]V = 4^3[/tex]

[tex]V = 64[/tex]

The total volume would be:

[tex]V =36 + 64[/tex]

[tex]V =100[/tex]

The base length of the rectangular prism would be:

[tex]Length =1+2+3+4[/tex]

[tex]Length =10[/tex]

The volume of the rectangular prism would be:

[tex]Volume = 10^2 \times 1[/tex]

[tex]Volume = 100[/tex]

So, the pattern is:

Cubes                Volumes

1, 2, 3                    36

1, 2, 3,4                  100

Corry's conjecture is right, and the volume follows a pattern

Read more about conjectures at:

https://brainly.com/question/4125198


Related Questions

Is 30 squared, 10 squared, 50 squared, 30 squared, or 60squared closest to 5?

Answers

Answer:

if you are dividing by 2 then 10 is closer but if you multiplying .. 10 is still closer

Robert and Tony love to read. Robert reads 30 pages the first day and 20 pages each day after that. Tony reads 40 pages the first day and 15 pages each day after that. Will the boys ever read the same amount of pages? If so, how many days will it take them to read the same number of pages? A. Yes. They will read the same amount of pages in 3 days. B. Yes. They will read the same amount of pages in 5 days. C. Yes. They will read the same amount of pages in 6 days. D. No. They will never read the same amount of pages.

Answers

Answer:

Yes they will read the same amount of pages in 3 days

Step-by-step explanation:

Because when you do the math they add up to the same amount of pages.

The correct statement is;

''Yes. They will read the same amount of pages in 2 days.''

What is an expression?

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

Robert reads 30 pages the first day and 20 pages each day after that.

And, Tony reads 40 pages the first day and 15 pages each day after that.

Now,

Let the number of days for same pages read = x

So, We can formulate;

For Robert;

Number of pages = 30 + 20x

For Tony;

Number of pages = 40 + 15x

For equal days, we get;

⇒ 30 + 20x = 40 + 15x

Solve for x as;

⇒ 20x - 15x = 40 - 30

⇒ 5x = 10

⇒ x = 2

Thus, The correct statement is;

''Yes. They will read the same amount of pages in 2 days.''

Learn more about the mathematical expression visit:

brainly.com/question/1859113

#SPJ2

I need helppp pleaseee

Answers

Answer:

One solution

Step-by-step explanation:

Start by simplifying the equation.

Distribute 3 to 4 and 2 to get 12x + 6Combine 8x and -2x to get 6x

Then you have 12x + 6 = 6x + 24,

Continue to solve

Subtract 6 from the left and right to get 12x = 6x + 18Subtract 6x from both sides to get 6x = 18Divide both sides by 6 to get x = 18

Because x is equal to one digit and not x = x or 3 = 5, you have one solution

                                                            (Infinite) or (none)

Hope this helps!

f the family decides to fly, they know that they will need a rental car for at least part of their trip. Gabriela and Luis estimate a budget of $315
$
315
for rental car expenses. One rental car company charges $55
$
55
per day and $35
$
35
in taxes and fees. They also estimate that they will spend $15
$
15
per day on gas. Gabriela wrote the equation (55d+35)+15d=315
(
55
d
+
35
)
+
15
d
=
315
to determine the number of days the family can rent a car from this company.

How many days could the Morales family rent a car if they choose this rental car company with their estimated budget?

Answers

Answer:

4 days

Step-by-step explanation:

55d+35+15d=315

70d=315-35

70d=280

d=280/70

d=4

8,17,26 find the 31st term

Answers

Answer:

T31= 278

Step-by-step explanation:

formula is Tn=a +(n-1)d

T31= 8+(31-1)9

T31=8+(30)9

T31=8+270

T31=278

x+y=15
- 2x+5y=-2

solve the system of equations

please answer i’ll name you brainliest

Answers

Answer:

x= 11 and y = 4

Step-by-step explanation:

(solving by elimination)

Multiply the first equation by 2 and multiply the second one by 1.

2(x+y= 15)

1(-2x+5y=-2)

is now

2x+2y=30

-2x+5y-2

add them together to eliminate x

7y=28

then solve for y

7y=28

[tex]\frac{7y}{7}[/tex]=[tex]\frac{28}{7}[/tex]

y=4

---

Now you have y. put that back into the original equation for X

---

x+y=15

y= 4 so

x+4=15

x= 15-4

x=11

x=11, y=4

HELP ASAP will give brainliest for answer

Answers

Answer:

This is the answer

x=π/10

-88-3x=-35x-29(x-18)

Answers

Answer:

-88-3x=-35x-29(x-18)

-88-3x=-35x-29x-522

-88-3x=-6x-522

-88=-3x-522

424=-3x

x=10

Hope This Helps!!!

What is the measure of Zx?
Angles are not necessarily drawn to scale.

Answers

Answer:

This question is straightforward if you find different triangles in the figure itself.

Property of a triangle: All internal angles of a triangle must add up to 180°

Take a look at Triangle DBH.

Method A

Angle BHD = 180°-33°-46° (sum of angles in a triangle)

                   = 101°

Property of angles on a straight line: All angles on a straight line must add up to 180°

Angle x = 180°-101° (supplementary angles)

             = 79°

Method B

Take a look at Triangle DBH.

Property of exterior angle (in this case, angle x): An exterior angle of a triangle is equal to the sum of its two opposite non-adjacent interior angles.

Angle x = 33°+46°

             = 79°

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Answers

hello there! you did not put any question so i would not be able to answer your question :(

A backyard measures 30 feet by 40 feet. If the owner builds a fence around, about how many feet of fencing will be needed?

Answers

Answer:

140 feet

Step-by-step explanation:

You will need to find the perimeter of the backyard to find how many feet of fencing will be needed

the formula for perimeter is: 2l+2w

So 2 times 30 is 60

with 2 times 40 80

60+80 is 140

Thus you will need 140 feet to cover the backyard

Hope this helps!

Answer:

140 ft

Step-by-step explanation:

Perimeter = 2(l+w)

Perimeter = 2(30+40)

Perimeter = 2(70)

Perimeter = 140

A rectangle has a width of 9 units and a length of 40 units. What is the length of a diagonal? 0 34 units 0 39 units 0 41 units o 49 units Mark ihis and return Save and Exit​

Answers

Answer:

41

Step-by-step explanation:

a² + b² = c²

9² + 40² = c²

81 + 1,600 = c²

√1681 = √c²

41 = c

when x varies directly as 2y and x=6 when y=20 find y when x=9

Answers

Answer:

x=k×2y

substitute x for 6 and y for 20

6=2(20)×k

6=40k

Divide both sides by the coefficient of k

6/40=40k/40

3/20=k

To find y, when x=9

9=3/20×2y

9=6y/20

cross multiply

9×20=6y×1

180=6y

Divide both sides by the coefficient

y=30

2+5+8+….+3n-1=n(3n+1)/2

Answers

Answer:

all you do is() first divide then go from left to right answers 4

i really dont know this

Answers

Answer:

your answer is b 8/10 - 5/10

Step-by-step explanation:

Which function is represented by the graph?
O f(x) = (x – 11 + 3
O f(x) = 5x + 11 – 3
O f(x) = |x – 11 – 3
Of(x) = x + 1] + 3

Answers

Answer:

b

Step-by-step explanation:i took the quiz

Solve each system of linear equations by elimination.

X-6y=7
-x+6y= -7 -​

Answers

Answer:

Infinitely many solutions.

Step-by-step explanation:

x-6y=7

-x+6y=-7

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

0=0

infinitely many solutions.

The graphs below have the same shape. What is the equation of the graph of gx)?
A. g(x) = (x+4)2
B. g(x) = x2 - 4
C. g(x) = x2 + 4
D. g(x) = (x - 4)
NO LINKS YOU BOTS

Answers

Answer:

the answer should be A Hope this helps!

Solve this system of equations using the Substitution method. Don't forget to write your final answer as a coordinate point.

3x + y = -2

y = 2x + 3

Answers

Answer:

(x, y) = (-1, 1)

Step-by-step explanation:

HELP ME PLEASE I NEED HELP WITH THIS

Answers

Answer:

V = 82,406.16 cm³

Step-by-step explanation:

Volume of a sphere

V = 4πr³/3

V = 4•3.14•27³/3

V = 247,218.48/3

V = 82,406.16 cm³

The digits from the serial number of a dollar bill are listed below.

6,8,5,8,2,8,5,8

Answers

Answer:

8 occurs most often so the number is 8.

Answer:

The mode is 8.

Step-by-step explanation:

mode means the number that occurs the most in a list.

1. Which value is the closest to 0.9.997?
a.
1,000
b.
81
C.
10,000
d.
10

Answers

I think the answer would be D. 10 is closest to 0.9997

PLEASE ANSWER ASAP!!!!

Answers

Answer:

68

Step-by-step explanation:

Determine whether it is possible to form a triangle
with side lengths 3, 6, and 10.
O yes
O no

Answers

Yes this is correct using equaivslent angles formula in order to do

Marvin has read 8% of the novel he started reading last Saturday. Which decimal is equivalent to the percentage of the novel Marvin has read?

Answers

Answer:

0.8 or 0.08 i believe

Step-by-step explanation:

hope this helps!

The graph shows a nonstandard normal distribution curve with
a mean of 59.0 and a standard deviation of 6.7.
Find the area of the shaded region.
.7761
.2177
.3650
.7823

Answers

Using the normal distribution, it is found that the area of the shaded region is of 0.7823.

In a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

It measures how many standard deviations the measure is from the mean.  After finding the z-score, we look at the z-score table and find the p-value associated with this z-score, which is the percentile of X.

In this problem:

The mean is of 59, hence [tex]\mu = 59[/tex].The standard deviation is of 7, hence [tex]\sigma = 7[/tex].

The shaded region is the region to the left of 64.2, hence it's area is the p-value of Z when X = 64.2.

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{64.2 - 59}{6.7}[/tex]

[tex]Z = 0.7761[/tex]

[tex]Z = 0.7761[/tex] has a p-value of 0.7823.

The area of the shaded region is of 0.7823.

To learn more about the normal distribution, you can take a look at https://brainly.com/question/24663213

Write the equation of the line that passes through the given points.
​(0​,−5​) and ​(9​,−1​)

Answers

Answer:

y=4/9x-5

Step-by-step explanation:

m=(y2-y1)/(x2-x1)

m=(-1-(-5))/(9-0)

m=(-1+5)/9

m=4/9

y-y1=m(x-x1)

y-(-5)=4/9(x-0)

y+5=4/9(x)

y+5=4/9x

y=4/9x-5

Question 2 of 5
-64
O A. - 16
O B. -4
O C. 4 or -4
OD. -8

Answers

Answer:

B.-4

Step-by-step explanation:

Hope it help!!!!!!

Find the solution(s) for x in the equation below.
x2 – 25 = 0

Answers

Answer:

x=5,-5

Step-by-step explanation:

How i can answer this question

Answers

Answer:

4k+11

Step-by-step explanation:

There you go. Happy to help.

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