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

12. Fancy goldfish x cost $3 each and
common goldfish y cost $1 each. Graph
the function y
20
3x to determine
how many
of each type of goldfish Tasha
can buy for $20.

Answers

Answer:

x (Fancy Gold fish) = 3

y (Common goldfish) = 29

Step-by-step explanation:

Fancy goldfish x cost $3 each

common goldfish y cost $1 each

Graph: y  = 20 +  3x (I'm hoping this is the correct line equation, please do leave a comment below if it's not)

Thus, we graph it by subtitude either the x or y values. (Or you can use just X = 1,2,3).

Now, to find how many of each type of goldfish Tasha can buy. We subtitude the line equation by either using x = 3 or y = 1

Using either values to solve the equation, we get:

x = 3

y = 29

Hope this helps!

How many centimeters equal 128.9 meters?.

*Enter you answer in the box*

|___| cm

Answers

12890 centimeters

Hope this helped :)

Please help I don't understand i'm in the lowest class!

Answers

Answer:

Step-by-step explanation:

The equation y + 6 = one-third (X minus 9) is written in point-slope form. What is the equation written in slope-intercept form?

A: y = 1/3 x - 3
B: y = 1/3 x + 9
C: y = 1/3 x - 9
D: y = 1/3 x + 3

Answers

Pretty sure it’s D yeah okay yes I’m sure now

Gia started to solve the equation 3(x − 10) − 5x = 2x − 26 below. They want to move the variables to the left side of the equation for their next step.



Fill in Line 4 and give the property.


Line 1: 3(x − 10) − 5x = 2x − 26 Original Problem
Line 2: 3x − 30 − 5x = 2x − 26 Distributive Property
Line 3: -2x − 30 = 2x − 26 Collect Like Terms

Line 4:


please helpp

Answers

Answer:

Subtract 2x from each side, Subtraction Property

Step-by-step explanation:

Mr. Jackson likes to play a game in which rolling a 4 on a number cube doubles your score. He wants to know the probability that he will roll a 4 exactly 3 times out of 10 rolls. Define the variables for describing a binomial probability, and identify their values in this experiment.

Answers

Answer:

Step-by-step explanation:

Binomial Probability

P(x) =  n!/(n-x)!x! * p^x q^(n-x)

P(x) = probability there will be x required outcomes (here x is 3)

n = number of trials (here it is 10)

p = probability of 1 required outcome (getting a 4) on a single roll ( = 1/6).

q = probability of required outcome not occurring on a single roll.

p = 1/6

q = 1 -1/6 = 5/6

n = 10

x = 3

So the required probability

= 10!/ 7!3! (1/6)^3 (5/6)^7

= 0.155.

Graph the line with the equation
y = -1/3x + 4.

Answers

Answer:

Answer in the image

Step-by-step explanation:

If we express $3x^2 - 6x - 2$ in the form $a(x - h)^2 + k$, then what is $a + h + k$?

Answers

If we express  [tex]3x^2-6x-2[/tex] in the form  [tex]a(x-h)^2+k[/tex], then a + h + k = -1

The given quadratic expression is:

[tex]3x^2-6x-2[/tex]

To express [tex]3x^2-6x-2[/tex] in the form [tex]a(x-h)^2+k[/tex], follow the steps below

Rewrite [tex]3x^2-6x-2[/tex] as  [tex]3x^2-6x+3-5[/tex]

Factorize common terms

[tex]3(x^2-2x+1)-5[/tex]

This can be further simplified as:

[tex]3(x-1)^2-5[/tex]

Therefore, the vertex form of the equation  [tex]3x^2-6x-2[/tex] is [tex]3(x-1)^2-5[/tex]

Compare [tex]3(x-1)^2-5[/tex] with  [tex]a(x-h)^2+k[/tex]

a = 3, h = 1, k = -5

a  +  h  +  k  =  3  +  1 - 5

a  +  h  +  k  =  -1

Therefore if we express  [tex]3x^2-6x-2[/tex] in the form  [tex]a(x-h)^2+k[/tex], then a + h + k = -1

Learn more on vertex form of a quadratic equation here: https://brainly.com/question/17987697

Is x+2y=6
2x-3y=26
have no solution,one solution, or infinity many solution

Answers

Answer:

1

Step-by-step explanation:

x + 2y = 6, multiply by 2 = 2x + 4y = 12

2nd equation:                    2x - 3y = 26

It has one solution

Answer: One solution

Step-by-step explanation:

Convert both equations into slope-intercept form:

x+2y=6

2y=6-x

[tex]y=\frac{6-x}{2}[/tex]

Slope = 6/2 = 3

2x-3y=26

y=2x-26/3

Slope = 2/3

Therefore, he system of equations have one solution because their slopes are not equal.  

(02.02 LC)
If g(x) = x2 + 2, find g(3).
O9
O8
O 11
O6

Answers

Answer:

8

Step-by-step explanation:

g(x) = 2x + 2

g(3) = 2*3 + 2             Substitute 3 for x.

g(3) = 6 + 2                 Multiply.

g(3) = 8                       Add.

Answer:

g(3) = 11

Step-by-step explanation:

Substitute x = 3 into g(x) , that is

g(3) = 3² + 2 = 9 + 2 = 11

write the inequality this number line represents "14-15-16-17-18-19-20-21-22-23-24"
PLEASE HELP!!

Answers

Answer:

x≤19

Step-by-step explanation:

because its everything to the left of 19 including 19

Answer:

Interval notation:  (- ∞, 19]

Inequality notation:  -∞ < x ≤ 19

Step-by-step explanation:

Given the inequality graphed on a number line, where there is a closed circle on 19:

A closed circle represents the endpoint as part of the solution.  Moreover, the direction of the arrow on the number line points toward the left, which implies that all of the values that are less than or equal to 19 are included on the solution.

Therefore, the inequality represented on the number line is:

Interval notation:  (- ∞, 19]

Inequality notation:  -∞ < x ≤ 19

find the domain of y= 2/3 square root of x+5-4

Answers

Set the radicand in

x

5
x
-
5
greater than or equal to
0
0
to find where the expression is defined.
x

5

0
x
-
5

0
Add
5
5
to both sides of the inequality.
x

5
x

5
The domain is all values of
x
x
that make the expression defined.
Interval Notation:
[
5
,

)
[
5
,

)
Set-Builder Notation:
{
x
|
x

5
}
{
x
|
x

5
}
The range of an even indexed radical starts at its starting point
(
5
,
0
)
(
5
,
0
)
and extends to infinity.
Interval Notation:
[
0
,

)
[
0
,

)
Set-Builder Notation:
{
y
|
y

0
}
{
y
|
y

0
}
Determine the domain and range.

Simplify 7 1/3t−(10 2/3t−6) pls

Answers

Answer:

[tex]-\frac{10t}{3}+6[/tex]

Step-by-step explanation:

[tex]7 \frac{1}{3}t-(10 \frac{2}{3} t-6)[/tex]

Convert [tex]7\frac{1}{3}[/tex] to a mixed number

[tex]7\frac{1}{3}=\frac{7\cdot 3+1}{3}[/tex]

[tex]=\frac{22}{3}[/tex]

[tex]\bold{\frac{22}{3}t-\left(10\frac{2}{3}t-6\right)}[/tex]

Convert [tex]10\frac{2}{3}[/tex] into a mixed number

[tex]10\frac{2}{3}=\frac{10\cdot 3+2}{3}[/tex]

[tex]=\frac{32}{3}[/tex]

[tex]\bold{\frac{22}{3}t-\left(\frac{32}{3}t-6\right)}[/tex]

[tex]=\frac{22t}{3}-\frac{32t}{3}+6[/tex]

[tex]\bold{=\frac{-10t}{3}+6}[/tex]

Terms

Follow the PEMDAS order of operation:

P = ParenthesisE = ExponentsM = MultiplicationD = DivisionA = AdditionS = Subtraction

You do these steps in the order for which the equation comes. For example, start with the exponents if there are not any parentheses.

What is the supplement of a 30° angle?

Answers

Answer:

150˚

Step-by-step explanation:

To find the supplement of a 30˚ angle, we need to know what an supplement in geometry is.

A supplement is when two angles add up that results in 180

So what value adds to 30˚ will get 180?

To find out that we just subtract 180 with 30

Which is 150

Thus the Supplement of a 30˚ angle is 150˚

Hope this helps!

answer: The supplement of 30° is the angle that when added to 30° forms a straight angle (180°.

Problem:

how to solve improper fractions to mixed numbers with example?

Answers

Answer: If it was the other way around I would have helped you  

Step-by-step explanation:

e.g.    

Graph the line y= 2/3x +1

Answers

Step-by-step explanation:

Given the linear equation, y = ⅔x + 1, where the slope, m = ⅔, and the y-intercept, (0, 1) where b = 1.

Start at the y-intercept:

In order to graph the given linear equation, start by plotting the coordinates of the y-intercept, (0, 1). As we know, the y-intercept is the point on the graph where it crosses the y-axis. It coordinates are (0, b), for which the value of b represents the value of the y-intercept in slope-intercept form, y = mx + b.

Plot other points using the slope:

From the y-intercept, (0, 1), we must use the slope, m =  ⅔ (rise 2, run 3) to plot the other points on the graph. Continue the process until you have sufficient amount of plotted points on the graph that you could connect a line with.

Attached is a screenshot of the graphed linear equestion, which demonstrates how I plotted the other points on the graph using the "rise/run" techniques" discussed in the previous section of this post.    

[tex]\huge\boxed{Hello,\:hope\:you\:are\:having\:a\:wonderful\:day.}[/tex]We are asked to graph the line y=2/3x+1.

2/3 is the slope of this line (Rise/Run)

The rise is how many units we move up; the run is how many units we move left or right.

For this line, 2 is the rise, and 3 is the run.

Now, 1 is the y-intercept. (where the graph touches the y-axis)

First, plot this point: (0,1)

Then, move 2 units up and 3 to the left (Up 2, over 3, up 2, over 3)

When you have a line, take a ruler and connect these points, and you will have the graph of y=2/3x+1.

[tex]\huge\bold{Hope\:it\:helps!}[/tex]

[tex]\huge\mathfrak{LoveLastsAllEternity}[/tex]

[tex]\huge\sf{Good\:luck}[/tex]

Evaluate the function.

f(x)=-3x^2-20

Find f(−7)

Answers

Answer:

Answer: f(-7) = -167

Step-by-step explanation:

[tex]{ \tt{f(x) = - {3x}^{2} - 20}}[/tex]

• When x is -7, f(x) is f(-7):

[tex]{ \tt{f( {}^{ - }7) = {}^{ - } 3( { {}^{ - }7) }^{2} - 20 }} \\ \\ { \tt{f( {}^{ - } 7) = ( {}^{ - } 3 \times 49) - 20}} \\ \\{ \tt{ f( {}^{ - }7) = {}^{ - } 147 - 20 }} \\ \\ { \boxed{ \tt{f( {}^{ - }7) = {}^{ - } 167 }}}[/tex]

Based on the calculations, the evaluation of this function is equal to -167.

Given the following data:

[tex]f(x)=-3x^2-20[/tex]

How to evaluate a function.

In this exercise, you're required to evaluate the given function. This ultimately implies that, we would substitute the vale of x into the function as follows.

Note: The value of x is equal to -7.

Substituting the given parameter into the function, we have;

[tex]f(-7)=-3(-7)^2-20\\\\f(-7)=-3(49)-20\\\\f(-7)=-147-20[/tex]

f(-7) = -167.

Read more on function here: https://brainly.com/question/10439235

I need help please!!!!

Answers

Answer:

MOREEE

Step-by-step explanation:

Derek and Jeannine buy a car for a total price, including tax, of $19,795. The price of the car was $18,500. What is the tax rate.

Answers

Answer:1.07

Step-by-step explanation:

13. A new bank customer with $5,000 wants to open a money market account. The bank is
offering a simple interest rate of 1.3%.
a. How much interest will the customer earn in 10 years?
b. What will the account balance be after 10 years?
2 POINTS

Answers

Answer:

a) 900 dollars

b) 5900 dollars

Step-by-step explanation:

The complete question is

A new bank customer with $5,000 wants to open a money market account. The bank is offering a simple interest rate of 1.8%. a. How much interest will the customer earn in 10 years? b. What will the account balance be after 10 years?

Paula caught a tarpon with a weight that was 10 times as great as the weight of a permit fish she caught. The total weight of the two fish was 154 pounds.

How much did each fish weigh?

The permit fish weighed _____ pounds.

The tarpon weighed ______ pounds.

Answers

Answer:

The weight of permit fish 140 pounds

The weight of Tarpon fish 14 pounds

Step-by-step explanation:

Let the weight of Tarpon fish ve 'x' Then by question weight of permit fish be '10x'

Now by question

x+10x=154 pounds

or,11x=154 pound

or,x=154pound/11

Therefore, x = 14 pounds

Again by question weight of permit fish

for 10x

by substituting value of x we have,

=10×14 pounds

=140 pounds

Two squares are congruent if and only if:
A. any two corresponding angles are
congruent
B. two pairs of corresponding angles are
congruent
C. all four pairs of corresponding angles are
congruent
D. a side of one is congruent to a side of the
other

Answers

D) a side of one is congruent to side of the other

Coz in the question it specified that both the shapes are square so obviously all angles are equal (90°)

Now we only need one side of it congruent .

what is 2/3 x 9/8 as a fraction in simplest form

Answers

Answer: [tex]\frac{3}{4}[/tex]

Have attached the picture for explanation...

The product of the fraction in the simplest form is 3/4

What is a fraction?

A fraction is a figure that is not a whole number. A fraction usually has a numerator and a denominator. The numerator is the number above. While the denominator is the number below.

What is the product of the fraction?

2/3 x 9/8 = 18/24 = 3/4

To learn more about multiplication of fractions, please check: https://brainly.com/question/1114498

A supervisor finds the mean number of miles that the employees in a department live from work. He finds x Overbar = 29 and s = 3. 6. Which mileage is within a z-score of 1. 5? 21 miles 24 miles 36 miles 41 miles.

Answers

The correct option is (B).24 miles.

Z-score is basically another term for the specific number of standard deviations. I suppose we can assume normality here, even though it isn't given, so I'd make a rough sketch.

Otherwise, just use the basic formula:

[tex]z_{score} =\dfrac{x-\mu}{\sigma}[/tex]

 Given that,

[tex]\bar{x}=29[/tex] (statistic for a mean) and [tex]s=3.6[/tex] (statistic for a standard deviation).

Since z-score must be Less than 1.5, So

[tex]1.5> \dfrac{x-29}{3.6}\\[/tex]

[tex]1.5 \times3.6 > x-29\\5.4+29> x\\34.4> x[/tex]

I just used normal cdf and got [tex]23.6<x<34.4[/tex].

Hence the correct option is (B).24 miles.

For more details on z score follow the link:

https://brainly.com/question/13299273

 

Answer:

B

Step-by-step explanation:

Correcct on edge22

Kitty Foods sells their cat food in 3 3/4 lb bags, while Cat Caterers sells 2 1/8 lb bags. How much bigger are the bags Kitty Food sells than those sold by Cat Caterers? Reduce your answer to lowest terms.

A. 1/2 lb
B. 5/8 lb
C. 1 5/8 lbs
D. 1 1/2 lbs

Answers

Answer: The answer for the question is: 1 5/8

Step-by-step explanation:

A music store is having a clearance sale. All items are discounted by 15%. What is the sale price of a radio that regularly costs $20?

Answers

Answer:

17$

Step-by-step explanation:

Answer:

$17

Step-by-step explanation:

Since the discount is 15%, and 100% would be the full price, 100 - 15 = 85. You are paying 85% of the price. 20 * .85 = 17.

This is for the real ones- find the missing side x. Giving brainliest.

Answers

Answer: The answer is X equals 10 2/3.

Explanation: This is a proportion. We see that the right rectangle when turned to the right is proportional to the left rectangle. On the left rectangle, the smaller side is 6 ft, and the larger side is 16 ft. On the right rectangle, the smaller side is 4 ft. 6 ÷ 1.5 = 4, therefore 16 ÷ 1.5 = 10 2/3.

Resultado de la operación -2-(5-3)+4

Answers

Answer:

0

Step-by-step explanation:

-2-(5-3)+4

-2-2+4

-4+4

0

Tommy is reading at a rate of 4 pages every 16 minutes. Write an equation that shows Tommy’s reading rate in pages per minute.

Answers

Answer:

0.25 pages per minute

Step-by-step explanation:

4 pages per 16 mins.

4/16 = 0.25

0.25 pages per minute

its a word equation, hopefully this helped!

Please help I’ll give brainliest ASAP

Answers

Answer:

1 I don't know if those are questions but try if they are try the first one a

Other Questions
the sum of three numbers is 182, the second is 6 times bigger than the first and the third is 14 times bigger than the second number, what are those numbers? GIVING BRAINLIEST PLSSSSSSS HELPBoth Jada and Jordan's eyes were saucers as their grandad carefully unlocked the chest and lifted the lid. "It's your lunch!" he said with a hearty laugh. "I bet all that treasure hunting has made you hungry." What is the meaning of the bolded phrase? Their eyes are hurting. Their eyes are wide open. Their eyes are different colors. Their eyes are tired. Determine the period of the function g(x) = (cos ;) URGENT WILL MARK BRAINLIEST 1. Suppose Q is the midpoint of PR. Use the information to find themissing value.PQ = 32 + 10 and QR = 2 + 14Find PR.A. 32B. 16C. 4D. 2 2(t+1)=10t= ? ............................................ 26.Which of the following food chainsshows one way that energy movesthrough an ocean ecosystem?A fish plankton + whale squidB squid whale fish planktonC plankton squid fish whaleD whale fish plankton squid WILL MARK BRAINLIEST PLEASE HELP x + 1 x 2 = 2 ( 2 x 2 1 )= Calculate the volume of cylinders with the following dimensions ( 22/7). (b) Diameter of the base = 84 cm, height = 1.5 m When you multiply a number by 25, subtract the result from 2000, and divide everything by 5, you will get 150. What is the initial number? Bread Line in New York City, 19326. Lines like the one shown here were partiallythe result of -A. growing demand for payment of militarypensions.B. a sudden increase in agricultural exports.C. the passage of the Selective Service Act.D. widespread business failures.LIKLIORRESTAUWILL ITED 0Source: Franklin D. Roosevelt Presidential Library An angle of 90 measures (___) Pi radians.An angle of -pi/5 radians measures ____?. What right was roes argument based on? the right to maternity leave the right to privacy the right to regulate medical standards the right to gender equality. 2b-3(1+b)=-3(b+7) help What is an equivalent expression to 7x - 3y + 8x ?Pls look at the image that I uploaded 1.Our school ........................................... by green fields.A. is surrounded B. is surround C. surrounds D. surround What is the central idea of this passage sundays are days of rest and ceremony on the farm. Andrew spent $80 on travel last month.Work out the amount Andrew spent on household bills last month.Will give brainliest Should student loan debt be terminated? What is the value of z?