Length: 2 and 1 over 4 feet
Width: 1 foot
Height: 1 and 1 over 4 feet
The lengths of the sides of a small cube are 1 over 4 foot each.

Part A: How many small cubes can be packed in the rectangular prism? Show your work. (5 points)

Part B: Use the answer obtained in part A to find the volume of the rectangular prism in terms of the small cube and a unit cube. (10 points)

Answers

Answer 1

Answer: 84 cubes

Step-by-step explanation: Given, The dimension of the rectangular prism are, 1 1/3 ft. * 1 * 2 1/3 = 4/3 * 7/3 = 28/9 cube ft.

Now, the volume of a cube = side³, if side = 1/3 ft., Then the volume of each cube, V = (1/3)³ = 1/27 cube ft.

Hence, the number of cubes that can be packet in the prism = V/V1 = 28/9 / 1/27 = 27*28/9 = 3 * 28 = 84

Answer 2

A) The number of small cubes which can be packed in the rectangular prism are 180.

B) The volume of the rectangular prism in terms of the small cube and a unit cube will be 180 units³

What is mean by Rectangle?

A rectangle is a two dimension figure with 4 sides, 4 corners and 4 right angles. The opposite sides of the rectangle are equal and parallel to each other.

Given that;

Length = 2 1/4 feet

Width = 1 feet

Height = 1 1/4 feet

And, The lengths of the sides of a small cube are 1 /4 foot each.

Now,

Since, The volume of rectangular prism = Length x width x height

Substitute all the values, we get;

⇒ The volume of rectangular prism = 2 1/4 × 1 × 1 1/4

                                                       = 9/4 × 1 × 5/4

                                                       = 45/16 ft³

                                                       = 2.81 ft³

And, The Volume of one cube = Side³

Here, The length of side of cube = 1/4 feet = 0.25 feet

Hence, The Volume of one cube = Side³

The Volume of one cube = 0.25³

The Volume of one cube = 0.015625 ft³

So, The number of small cubes that can be packed in the rectangular prism = Volume of rectangular prism / Volume of cube

         = 2.81 /0.015625

         = 180

B) The length, the width and the height of the rectangular prism in term of units cubes is:

Length = 2 1/4 feet / 0.25 feet = 2.25 / 0.25 = 9 units

Width = 1 feet / 0.25 feet = 4 units

Height = 1 1/4 feet / 0.25 feet = 1.25 / 0.25 = 5 units

So, The volume of the rectangular prism in terms of the small cube and a unit cube is,

Volume = 9 x 4 x 5

            = 180 units³

Learn more about the rectangle visit:

https://brainly.com/question/2607596

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Related Questions

Need Answered ASAP. As part of the training for the cross-country team, you must run a total of 20 miles per week. You ran 6.3 miles in the first two days of the week. If you run the same amount each day for the remaining five days, how many miles must you run per day to complete the 20 miles?

Write and solve an equation to determine the number of miles, m, you must run per day.

Answers

Answer: 1.48 miles

Step-by-step explanation:

6.3 x 2 = 12.6

20 - 12.6 = 7.4

7.4/5 = 1.48

You him to complete the 20 miles he needs to do this for 4 days

An equation is written in standard form, match each word with the expression that is used to find it.

Answers

Answer:

slope : opposite of a

y-intercet:b/c

x-intercet:a/b

Step-by-step explanation:

May some pls help my head hurts

Answers

Answer:

20 minutes

Step-by-step explanation:

we can solve with an equation

9 : 12 = 15 : x

x = 12 × 15 : 9

x = 180 : 9

x = 20

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

check

9 : 12 = 15 : 20

3 : 4 = 3 : 4

the answer is good

She will take 20 minutes to load 15 trucks

Need Answered ASAP. Rewrite 12x^4y^3 − 48x^3y^4 using a common factor.

Answers

Answer:

Step-by-step explanation:

12x^2y^3-36x^5y^3-48x^4y4

factor out 12

12(x^2y^3-3x^5 y^3 - 4x^4 y^4

consider X^2 y^3 - 3x^5 y^3

4x^4 y^4 Factor out x^2y^3

x^2 y^3 (1-3x^3 -4x^2 y)

Rewrite the complete factored expression

12x^2 y^3 (1-3x^3-4x^2y)

Which expression is equivalent to 2E-3/2E-5

a. 2E2
b. 1/2E2
c. 2E8
d. 1/2E8
E=exponent

Answers

Answer:

a 2E2

Step-by-step explanation:

[tex]\frac{2^{-3} }{2^{-5} }[/tex]  When powers have the same bases and you are dividing, you subtract the exponents.

[tex]2^{-3 - -5}[/tex] = [tex]2^{-3+5}[/tex] = [tex]2^{2}[/tex]

when powers have the same bace but it is going to be a. 2e2

Write the mixed number 4 ⅜ as an improper fraction.
Thank u!

Answers

Answer:

[tex]\frac{35}{8}[/tex]

Step-by-step explanation:

Another name for 1 is [tex]\frac{8}{8}[/tex] so 4 can be [tex]\frac{8}{8}[/tex] + [tex]\frac{8}{8}[/tex] + [tex]\frac{8}{8}[/tex] + [tex]\frac{8}{8}[/tex] = [tex]\frac{32}{8}[/tex].  we can now add this to [tex]\frac{3}{8}[/tex]

[tex]\frac{32}{8}[/tex] + [tex]\frac{3}{8}[/tex] = [tex]\frac{35}{8}[/tex]


explanation: 8×3=24, SO, 24+3=27.
27/8 is the answer .

"Based on the table, which best predicts the end behavior of the graph of f(x)?"

How do I figure out the answer to this question? I need a step-by-step explanation to the answer of the question.

Answers

Answer: How you figure out the answer to this question is figure out if it's a line by a constant rate of change

Step-by-step explanation: Because you gotta make sure before you plug in an answer you need to make sure it's a line

You have 2 different savings accounts. For Account​ A, the simple interest earned after 21 months is ​$5.95. For Account​ B, the simple interest earned after 30 months is ​$36.00. If the interest rate is ​%3.4 for Account A and ​%2.4 for Account​ B, how much is the principal in each​ account? Which account earned you the most interest the first​ month? Explain your answer.

Answers

Answer: Principal amount is A = $250.09

Principal amount is B = $400.

Account B earned you the most interest the first​ month

The formula for simple interest is expressed as

I = PRT/100

Where

P = the principal or initial amount of money invested.

R = interest rate

T = time

On account A,

I = $6.94

R = 3.7%

T = 9 months = 9/12 = 0.75 years.

Using the formula:

On account B,

I = $13.80

R = 2.3%

T = 18 months = 18/12 = 1.5 years

Using the formula:

To determine the account that earned more interest in the first month we divide the interest by the number of months.

$6.94/9 = $0.7711

$13.80/18 = $0.7667

Account B earned you the most interest the first​ month because $0.7667 is higher than $0.7711.

Answer:

Principal amount is A = $250.09

Principal amount is B = $400.

Account B earned you the most interest the first​ month

The formula for simple interest is expressed as

I = PRT/100

Where

P = the principal or initial amount of money invested.

R = interest rate

T = time

On account A,

I = $6.94

R = 3.7%

T = 9 months = 9/12 = 0.75 years.

Using the formula:

On account B,

I = $13.80

R = 2.3%

T = 18 months = 18/12 = 1.5 years

Using the formula:

To determine the account that earned more interest in the first month we divide the interest by the number of months.

$6.94/9 = $0.7711

$13.80/18 = $0.7667

Account B earned you the most interest the first​ month because $0.7667 is higher than $0.7711.

Scroll down

Hope it helps.

If x and y vary directly and y is 40 when x is 10, find y when x is 15.

Answers

Answer:

y is 60 when x is 15

Step-by-step explanation:

the ratio of x to y is 1:4

answer : y is 60 when x is 15! good luck and have a great day!

A sporting goods store is having a sale in which all sleeping bags are discounted by 20%. Priya has a coupon for $5 off the regular price of a sleeping bag. The store first applies this coupon and then takes 20% off the reduced price. If Priya pays $34.40 for the sleeping bag, what was the original price, x, before the sale and without the coupon?

Answers

the original price was "x", which oddly enough is the 100%.

now, let's pluck out of "x" 5 bucks, so that makes it "x-5", that's our new adjusted 100%, from which the lady at the counter is happy to apply a 20% discount.  Now, if the lady discounts 20% off of that "x-5" amount, what Priya is really paying for the sleeping bag is just 100% - 20% = 80%, and we happen to know that that 80% was really $34.40.

now, if "x - 5" is the 100%, and we know that 34.40 is the 80%, what the heck is "x"?

[tex]\begin{array}{ccll} amount&\%\\ \cline{1-2} x-5 & 100\\ 34.40& 80 \end{array} \implies \cfrac{x-5}{34.40}~~=~~\cfrac{100}{80} \implies \cfrac{ x-5 }{ 34.40 } ~~=~~ \cfrac{ 5 }{ 4 } \\\\\\ 4x-20=172\implies 4x=192\implies x=\cfrac{192}{4}\implies x=48[/tex]

PLEASE HELP MY ASSIGNMENT IS OVERDUE

In the triangle ABC, AB = (x + 3)cm, BC = (x + 2)cm, AC = x cm and angle BAC = 60degrees

Find the value of x.

Answers

Answer:

x = 5

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

Side BC is opposite to ∠BAC and adjacent sides are AB and AC.

Use the law of cosines:

BC² = AB² + AC² - 2AB*AC*cos ∠BAC

Substitute and solve for x:

(x + 2)² = (x + 3)² + x² - 2x(x + 3) cos 60°x² + 4x + 4 = x² + 6x + 9 + x² - 2(x² + 3x)*1/2x² + 4x + 4 = 2x² + 6x + 9 - x² - 3xx² + 4x + 4 = x² + 3x + 94x - 3x = 9 - 4x = 5
x would equal 5 in the problem

Which expression has like terms?
Group of answer choices
8x - 4y
8x - 4x
13c + 13d
4 + 4y
thx!

Answers

8x - 4x because they both have an x and you can subtract


The answer is 8x -4x

When Jackson works more than 40 hours in a week, he earns 1.5 times his normal hourly rate for each of the extra hours. Jackson worked 43 hours one week. What was his total pay before deductions? Justify your answer.

Answers

Answer:

44.5 hr

Step-by-step explanation:

40x+(3*1.5x) = 40x+4.5x = 44.5x

PLEASEEEE HELPPPPPPPPP

Answers

Answer: The difference between the angle measure is 152 degrees

Step-by-step explanation: Supplementary angles are angles that add up to 180

So if one angle is x in this case, the other will be 14x

Adding both ;

x + 14x = 180

15x = 180

x = 180/15

x = 12

The other angle is 14 * 12 = 168

The difference between the two will be;

168-12 = 156

Answer:

168

Step-by-step explanation:

m<B + m<C = 180 since the angles are supplementary.

m<B = 14m<C since the measure of angle B is 14 times the measure of angle C.

m<B + m<C = 180

14m<C + m<C = 180

15m<C = 180

m<C = 180/15

m<C = 12

m<B = 14m<C = 14 × 12

m<B = 168

Answer: 168

20 points to whoever answers this asap <3

Joe and Andrew shot baskets in a school fair. Joe made 9 baskets, which is 2 baskets more than Andrew. Supply the correct numbers to complete the equation that can be used to determine the number of baskets, b, that Andrew made.

Answers

Answer:

The answer to the question is 7. This is the number of baskets that Andrew made, as calculated using the equation b = 9 - 2.

Step-by-step explanation:

the answer is 7 !!! have a great day

This Is a Math Test. Help please ASAP! 30 POINTS!

Use the following model to answer the question.

3 groups are shown. Each group shows 2 tens rods and 6 ones cubes.

Which division problem is shown by the model?

A. 0.66÷3=0.22
B. 0.66÷3=0.26
C. 0.78÷3=0.62
D. 0.78÷3=0.26

Answers

0.66/3=0.26

The blocks add up to 26

Answer:

D

Step-by-step explanation:

well, it all starts with a check, what calculations in the answer options are even correct.

A. is correct. 0.66/3 = 0.22

B. is incorrect

C. is incorrect

D. is correct. 0.78/3 = 0.26

so is it A or B ?

one group of 2 tens and 6 ones : how much is that ?

2×10 + 6×1 = 20 + 6 = 26

3 groups of 26 means

3×26 = 78

so, the combination of the 3 groups would either show that

3×26 = 78

or

78/3 = 26

and that is the same as showing

0.78/3 = 0.26

because

0.78 = 78/100

0.26 = 26/100

therefore

78/100 / 3 = 26/100

78/100 = 3×26/100 = 78/100

correct.

SOMEONE HELP ME PLEASE I DONT KNOW HOW TO DO THIS!!!

if you're a tad confused, o represents one of the options and you're supposed to fill it in. x represents number for bags

A coffee shop sells bags of coffee for a regular price of $8 per bag. Chang bought some bags and used a coupon for $10 off his entire purchase. After applying the coupon, he paid $30.

How many bags of coffee did he buy?

(a) Write an equation to help answer the question above.
Choose the correct form below and fill in the blanks using only 8, 10, and 30.
(The variable x is used to represent the number of bags.)
ox+o=o OR o×-o=o

(b) Write an expression to help answer the question above.
Choose the correct form below and fill in the blanks using only 8, 10, and 30.
o+o/o OR o-o/o

(c) How many bags of coffee did Chang buy? answer: _x_ bags ​

Answers

If the number of bags is x, the cost of them is 8x.

After applying a $10 coupon the total was $30.

Part (a)

Set equation:

8x - 10 = 30

Part (b)

Solve it for x:

8x = 30 + 108x = 40x = 40/8x = 5

Part (c) Answer: 5 bags
Pretty sure the answer is five bags

ok, my let’s try this again. can someone please help fill out the ? for this table.

Answers

Answer:

60 months

$9,000

4.6%

Step-by-step explanation:

[tex]\boxed{\begin{minipage}{6.5cm}\underline{Simple Interest Formula}\\\\$ A = P(1 + rt)$\\\\where:\\\\ \phantom{ww}$\bullet$ $A =$ final amount \\ \phantom{ww}$\bullet$ $P =$ principal amount \\ \phantom{ww}$\bullet$ $r =$ interest rate (in decimal form) \\ \phantom{ww}$\bullet$ $t =$ time (in years) \\ \end{minipage}}[/tex]

Given:

A = $5,000P = $4,000r = 5% = 0.05

Substitute the given values into the formula and solve for t:

[tex]\implies 5000=4000(1+0.05t)[/tex]

[tex]\implies \dfrac{5000}{4000}=1+0.05t[/tex]

[tex]\implies1.25=1+0.05t[/tex]

[tex]\implies 0.05t=1.25-1[/tex]

[tex]\implies 0.05t=0.25[/tex]

[tex]\implies t=\dfrac{0.25}{0.05}[/tex]

[tex]\implies t=5\; \rm years=60\; months[/tex]

Given:

A = $11,160r = 8% = 0.08t = 36 months = 3 years

Substitute the given values into the formula and solve for P:

[tex]\implies 11160=P(1+0.08 \cdot 3)[/tex]

[tex]\implies 11160=P(1.24)[/tex]

[tex]\implies P=\dfrac{11160}{1.24}[/tex]

[tex]\implies P=\$9000[/tex]

Given:

A = $3,207P = $3,000t = 18 months = 1.5 years

Substitute the given values into the formula and solve for r:

[tex]\implies 3207=3000(1+r \cdot 1.5)[/tex]

[tex]\implies \dfrac{3207}{3000}=1+1.5r[/tex]

[tex]\implies 1.069=1+1.5r[/tex]

[tex]\implies 1.5r=1.069-1[/tex]

[tex]\implies 1.5r=0.069[/tex]

[tex]\implies r=\dfrac{0.069}{1.5}[/tex]

[tex]\implies r=0.046[/tex]

[tex]\implies r=4.6\%[/tex]

Therefore, the completed table is:

[tex]\begin{array}{|c|c|c|c|}\cline{1-4} \vphantom{\dfrac12} \rm BALANCE & \rm PRINCIPAL & \rm INTEREST \; RATE & \rm TIME \\\cline{1-4} \vphantom{\dfrac12} \$5,000 & \$4,000 & 5\% & \rm 60 \; months\\\cline{1-4} \vphantom{\dfrac12} \$ 11,\!160 & \$9,000 & 8\% & \rm 36 \; months \\\cline{1-4} \vphantom{\dfrac12} \$3,207 & \$3,000 & 4.6\% & \rm 18 \; months\\\cline{1-4} \end{array}[/tex]

The zoom feature on a copier sets the percent size of a copy. Lebron wants to make a 200% copy of a photograph. The original photo has a width of 5 in. What width will the copy be?
a) 2.5in
b) 10in
c) 25in
d) 100in

Answers

the answer is b, i believe :)
The answer was is b) ten

A tree that is 14 feet tall casts a shadow that is 7 feet long. What is the distance from the top of the tree to the tip of the shadow? Round to the nearest tenth.
15.7 feet
12.1 feet
4.6 feet
2.6 feet

Answers

Answer:

2.7

Step-by-step explanation:

Enter the expression −3−8 as an equivalent addition expression.

Answers

Answer:

8 + 3

Step-by-step explanation:

Your answer would be 8+3







Which frequency table matches the data?

Answers

Answer: A

Step-by-step explanation: hope it helps

Which story problem can be solved using the expression 5 divided by ¼?
Group of answer choices
-Alex cuts ¼ of a pizza into 5 slices. What part of the pizza is one of the slices he cuts?
-Nicole cuts 5 feet of string into ¼ - foot pieces. How many pieces does she cut?
-Suzy needs 5 pieces of ribbon that are each ¼ yard long. What is the total length of the ribbon?
-Sammy pours ¼ cup of honey equally into 5 teacups. How much honey does he pour into each teacup?
Thank u! <3

Answers

Answer: Nicole cuts 5 feet of string into ¼ - foot pieces. How many pieces does she cut?

Step-by-step explanation:

Nicole cuts 5 feet of string into ¼ - foot pieces. How many pieces does she cut?

When you cut one piece of string into smaller pieces, that is the same as dividing.

5/1/4 is the same as 5*4/1

=20

Which table shows a function that is decreasing only over the interval (–1, ∞)?


What answer is it and why? To me it seems it can either be C or D (One all the way to the right on the top row and one all the way to the bottom right), but I'm not sure why it would be either one over the other and would need an explanation. If it is neither C nor D I need an explanation on how to solve this question correctly.

Answers

Answer: The table to the farthest right the last one.

Explanation:

The interval (-1, ∞) represents x-values anywhere from -1 and higher.  

As such, you are looking for a table with y-values that decrease as the x-values increase.

Starting from -1 -

The first option: -5, -2, -1, 2. This is increasing.

The second option: -7, -6, 1, -1. This increases from -7 to -6 to 1.

The third option: -1, 2, 1, -6. This increases from -1 to 2.

The fourth option: 1, 0, -4, -8. This decreases across all coordinates in the range specified.

Answer:

The last graph (d) represents it

If xx and yy vary directly and yy is 40 when xx is 5, find yy when xx is 6.

Answers

Answer:

41

Step-by-step explanation:

41
step by step equation

z/2>2


hey help me please

Answers

Answer:

Z > 4

Step-by-step explanation:

Multiply to remove the fraction, then set equal to 0 and solve.
Z>4
Hope this helps have a good day!

A circle’s circumference is 600 m.
What is a good approximation of the circle’s area? 1. 300\ m^{2} 2. 3,000\ m^{2} 3. 30,000\ m^{2} 4. 300,000\ m^{2}

Answers

The area of the circle is approximately 30,000 [tex]m^{2}[/tex]

The circumference of the circle is given as 600m.

And we know that circumference = [tex]2\pi r[/tex] where r is the radius of the circle.

Therefore,

[tex]2\pi r = 600[/tex]

[tex]r = \frac{600}{2\pi }[/tex]

[tex]r = \frac{300}{\pi }[/tex]

Now, we know that area of the circle = [tex]\pi r^{2}[/tex]

Putting the value of r in this, we get

area = [tex]\pi (\frac{300}{\pi } )^{2}[/tex]

area = [tex]\pi.\frac{300}{\pi } .\frac{300}{\pi }[/tex]

Therefore, area of the circle = 28,647.889 [tex]m^{2}[/tex]

Therefore, the correct answer is 30,000 [tex]m^{2}[/tex]

To learn more about circle and it's area, refer to:

https://brainly.com/question/16125353

Area is approximately 30,000m^2

Help, i have to do this in the next like 30 seconds -_-

Answers

I think your answer is 2/3

I am not sure

I believe your answer is 2/3

Evaluate the expression: 2 × 14 ÷ (3² − 2)
Group of answer choices
3
8
4
6

Answers

Answer: 4

Step-by-step explanation:

2 × 14 ÷ (3² − 2)

28 / (9-2)

28/7

4

[tex]2\times14\div(3^2-2)[/tex]

[tex]14\times2=28[/tex]

[tex](3^2-2)=7[/tex]

[tex]28\div7[/tex]

[tex]=\fbox{4}[/tex]

Distribute the negative sign to each term inside the parenthesis. - (9k-5p+7e-2)

Answers

Step-by-step explanation:

Distribute the negative sign to each term inside the parenthesis.

- (9k-5p+7e-2)

To distribute the negative sign to each term inside the parenthesis:

a negative and positive = -

a positive and positive = +

a negative and negative = +

- (9k-5p+7e-2)

- 9k + 5p - 7e + 2

Step-by-step explanation:

(-9k+5p-7e+2)

-×-=+

-×+=-

+×+=+

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This dividend should be distributed as follows:$24,500 preferred; $24,500 common.$26,000 preferred; $23,000 common.$17,400 preferred; $31,600 common.$0 preferred; $49,000 common.$12,250 preferred; $36,750 common. Show hintTS.4 = 64Review of logarithms (logs)Solve the equation and show all your work. Inaddition, label the base, argument, and exponent.Enter your answer below.Pro Tip: Use a calculator to evaluate your logarithm.Unfortunately the in-screen Desmos calculator can onlyevaluate logs with base 10.SubmitM A floating exchange rate:??is determined by the national governments involved.?remains extremely stable over long periods of time.?is determined by the actions of central banks.?is allowed to vary only within a narrow range.?adjusts in response to market forces.The Bretton Woods system:??established a worldwide gold standard.?established a worldwide system of fixed exchange rates.?established a worldwide system of flexible exchange rates.?harmonized tariff systems. Will a piece of paper produce the same kind of reflection as the mirror? Explain your answer. Help guys my computer is abt to die its due today Please awnswer the question below 27. evaluate yyye xex 21y21z2 dv, where e is the portion of the unit ball x 2 1 y 2 1 z 2 < 1 that lies in the first octant. an element e has the electron configuration [ar]3d104s24p2. what is the formula for the fluoride of e most likely to be? A student wants to increase the temperature of an ideal gas in a cylinder that is initially at room temperature. The cylinder has a movable piston with negligible friction. Which of the following correctly indicates an action the student could take to increase the temperature of the gas and why the temperature increases? Pull the poston out and Then wit expand violently and increase in temperature Pull the piston out slowly. The as will have time to absorb encesy from the surroundings by heatinst as it expands. Push the piston in rapidly. The temperature of the gas will increase because no enery will be transferred to the surroundinis bw coolinu Push the piston in slowtv: The gas will have time to absorb energy from the surroundings by heating as it is compressed At an instant in time, the electric and magnetic fields of an electromagnetic wave are given by E = -9.13 times 10^3k V/m and B = -3.04 times 10^-11i T. Find the Poynting vector for this wave. (Express your answer in vector form.) S = W/m^2