(Help with this Please?)

The dimensions of a rectangular prism are shown below:

Length: 1 1/2
Width: 1 foot
Height: 2 1/2
The lengths of the sides of a small cube are 1/2 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. (5 points)

Answers

Answer 1

Answer:

A) 30 cubes.

B) 30 units³.


Step-by-step explanation:

A) 1. Calculate the volume of the rectangular prism, as following:

[tex]Vr=(lenght)(width)(height)[/tex]

2. You have that:

- The length is: [tex]1^{\frac{1}{2}}ft=1.5ft[/tex]

- The width is: [tex]1ft[/tex]

- The heigth is: [tex]2^{\frac{1}{2}}ft=2.5ft[/tex]

3. Substitute these values into the formula:

[tex]Vr=(1.5ft)(1ft)(2.5ft)=3.75ft^{3}[/tex]

4. The volume of one cube is:

[tex]Vc=side^{3}[/tex]

5. The length of one side is: [tex]\frac{1}{2}ft=0.5ft[/tex]

6. Substitute this value into the formula:

[tex]Vc=(0.5ft)^{3}=0.125ft^{3}[/tex]

7. The number of small cubes that can be packed in the rectangular prism is:

[tex]cubes=\frac{Vr}{Vc}\\cubes=\frac{3.75ft^{3}}{0.125ft^{3}}\\cubes=30[/tex]

B) 1. The length, the width and the height of the rectangular prism in term of units cubes is:

[tex]Length=\frac{1.5ft}{0.5ft}=3units[/tex]

[tex]Width=\frac{1ft}{0.5ft}=2units[/tex]

[tex]Heigth=\frac{2.5ft}{0.5ft}=5units[/tex]

2. Therefore, the volume of the rectagular prism in terms of the small cube and a unit cube is:

[tex]Vr=(3units)(2units)(5units)=30units^{3}[/tex]

Answer 2

Answer:

30 cubes.

Step-by-step explanation:


Related Questions

Which of the following is not a tool for monitoring your finances?
A. Personal balance sheet
B. Budget
C. Liability
D. Cash flow statement

Answers

You may want to take this question over to the business category though I believe the answer is C.

The others show how your money is moving, how it's being spent, where you plan on spending it, how much you save, etc. Wouldn't think liability is one of those.

HEEEEEEEEEEEEEEEEEEEELP

For which value of x is the equation 3(3 + x) = 15 + x true?
A) 1
B) 2
C) 3
D) 4

Answers

C) 3 is the correct anwser

If alice is $24 per hour painting houses if he works 263 hours how much money will alex earn

Answers

$24 per hour * 263 hours = $6,312

It is a rate per hour times hours worked.

What is the greatest common factor of the terms of the polynomial 6x4 + 24x3 − 72x2.

Answers

6x2 would be the greatest factor. This is because 2 is the greatest power for x shown and 6 is the greatest number that all three terms are divisible by.

What is the sum of 2 to the power of 4 and 7 to the power of 2 write the answer in standard form

Answers

            2⁴ + 7²

= 2x2x2x2 + 7x7

=        16     + 49

=             65

Answer: 65

The sum of [tex]2^4[/tex] and [tex]7^2[/tex] in standard form is [tex]6.5 \times 10^1[/tex].

To find the sum of [tex]2^4[/tex] and [tex]7^2[/tex] and write the answer in standard form, follow these steps:

Calculate [tex]2^4[/tex]:
[tex]2^4 = 2 \times 2 \times 2 \times 2 = 16[/tex]

Calculate [tex]7^2[/tex]:
[tex]7^2 = 7 \times 7 = 49[/tex]

Add the results from steps 1 and 2:
[tex]16 + 49 = 65[/tex]

Write the sum in standard form (also called scientific notation):
A number in standard form is written as [tex]a \times 10^n[/tex], where [tex]1 \leq a < 10[/tex] and [tex]n[/tex] is an integer.

For 65, we can write it as:
[tex]65 = 6.5 \times 10^1[/tex]

Jonas has 40 marbles. He gave 1/5 of the marbles to marvin and 3/8 of the marbles to leroy. How many marbles did each boy get?

Answers

1/5 x 40

= 8 marbles

3/8 x 40

= 15 marbles



just multiply all both fraction with 40, hence u will get

Marvin=1/5 x 40=8
Leroy=3/8 x 40=15
Jonah will have 17 marbles left.

The set of all points in a plane that are equidistant from two points is an (n):

Answers

ANSWER

Perpendicular bisector

EXPLANATION

The perpendicular bisector of a line divides the line into two equal parts.

It forms a locus of points that are equidistant from the two given points.

Therefore the set of all points that are equidistant from two given points in a plane is the perpendicular bisector of the line joining the two points.

Please help me!!! Will mark BRAINLIEST.

Answers

Answer:

It is rotated 180 degrees then reflected on the y-axis

Step-by-step explanation:


In a parallel circuit, ET = 240 V, R = 5.6 kΩ, and XL = 3.6 kΩ. What is P?

Answers

Answer:

Real power,P is 10.286 Watts

Step-by-step explanation:

We are given that in a parallel circuit, [tex]E_{T}=240V[/tex],R=5.6kΩ and [tex]X_{L}[/tex]=3.6kΩ

We are asked to find P which means real power, that is power due to resistance.

Let us find current through resistor first.

That is [tex]I_{R}=\frac{E_{T}}{R}=\frac{240}{5.6}=\frac{300}{7}=42.86[/tex]milli Amps=0.04286 A

Hence [tex]P=E_{T}I_{R}[/tex]

                    =240X0.04286=10.286 Watts

What is 1/4 x 5.6? / means fractions.thanks!

Answers

1 4/10 = 1/4 * 5.6 = 1.4 = 1 4/10

The product of the numbers (1/4) and 5.6 will be ( 7/ 5 ).

What is multiplication?

Multiplication is the process of determining the product of two or more numbers in mathematics. A product, or an expression that specifies factors to be multiplied, is what happens when you multiply two numbers in mathematics.

Given numbers are ( 1/4 ) and 5.6. The product will be calculated as:-

1/4 x 5.6 = 5.6 / 4

1/4 x 5.6 = 56 / 40

1/4 x 5.6 = 14 / 10

1/4 x 5.6 = 7 / 5

Therefore, the product of the numbers (1/4) and 5.6 will be ( 7/ 5 ).

To know more about multiplication follow

https://brainly.com/question/10873737

#SPJ2

What is the decimal that is 10 times as great as 0.009

Answers

Your answer is .09 .

PLEASE HELP ASAP!!! CORRECT ANSWER ONLY PLEASE!!

Multiply.

√2 ⋅ √5 ⋅ √11

Answers

So remember the product rule of radicals: √ab = √a × √b

In this case:

√2 × √5 × √11 = √(2 × 5 × 11) = √110

√110 is your final answer.

Please help me with 1a, thanks

Answers

The answer should be x+x+x+x=y or it can be 4x=y.

Since 1A claims that the diagram is of a square, you can easily find the perimeter by multiplying just one side by 4, because the definition of a square says that all of its four sides are equal in length.

Take the left side, x and 4, and add them together, because both of these lengths add up to form the side of the square. You have found one side of the square, x + 4. Now multiply this side by 4 for the perimeter.

Perimeter is the length all around the figure, and since a square has 4 sides you would multiply one side by 4 to find the perimeter.

4(x + 4) is your expression for the perimeter of the square. You could probably solve 1B and 1C by substituting in 3 and 5 for x in the equation I've given you :)

what is the median of :
100 100 99 98 98 90

Answers

i believe that the median would be 98.5, because you add the two middle numbers which in this case are 99 and 98 and divide by 2.

98 or 98 1/2! Hope this helps ya! <3

Compare and contrast these four functions using complete sentences. Focus on the slope and the y-intercept first, and then in any additional properties of each function.

Answers

Hello,

Please, see the attached files.

Thanks.

A dairy needs 392 gallons of milk containing 5% butterfat. How many gallons each of milk containing 6% butterfat and milk containing 2% butterfat must be used to obtain the desired 392 gallons?

Answers

                       Qty                    %                       Qty * %

Solution 1:        x                 6% = 0.06        =      0.06x

Solution 2:    392 - x         2% = 0.02        =      0.02(392 - x)  = 7.84 - 0.02x

Mixture:          392              5% = 0.05        =     0.06x + 7.84 - 0.02x

                                                 392(0.05)   =    0.08x + 7.84

                                                           19.6   =    0.08x + 7.84

                                                          11.76   =    0.08x

                                                            147    =      x

Solution 2:  392 - x    = 392 - (147)   = 245

Answer: 147 gallons 6% and 245 gallons of 2%

{x*0.02+0.06y=392*0.05

{x+y=392, x=392-y

0.04y=11.76, y=294; x=392-294=98

There is need 98 gallons of milk with 2% butterfat and 294 gallons of milk with 6% butterfat


help plz solve 2y-3=4y+6 y=

Answers

here is your answer.

Steps:

2y-3=4y+6

2y-3+3=4y+6+3

2y=4y+9

2y-4y=4y+9-4y

-2y=9

-2y/-2=9/-2

y=-9/2

The correct answer is y=-9/2

Which of the numbers below correctly describes 63.45 Mhz? Select one: a. 0.06345 Ghz b. 63,450 khz c. Both a and b d. None of the above

Answers

To solve this question, let us take one part at a time.

Part 1 (MHz to GHz)

We know that 1 MHz=0.01 GHz

Therefore, [tex]63.45 MHz=63.45\times 0.001 GHz=0.06345 GHz[/tex]

Thus, for the time being we know that Option A is correct.

Part 2 (MHz to KHz)

We know that 1 MHz=1000 KHz

Therefore, [tex]63.45 MHz=63.45\times 1000 KHz=63450 KHz[/tex]

Thus, Option B too is correct.

Therefore, Both A and B are correct. Thus, out of the given options, Option C is correct.

The cost of a phone is reduced by 20%. The new cost is $70.40 . What was the original price?1. $88.002.$84.003.$58.404.$56.00

Answers

to get this answer you got to multiply each answer by .20% and then subtract the answer from what you divided .20% by and you should get the answer which is 88.002

Answer:

In this case, the answer is $88.00. Have a nice day! <3

Step-by-step explanation:

Mr. Brown has 35 students in his class and wants to make teams of 5 students.

Answers

Divide total students by the size of the group:

35 / 5 = 7 groups.

Do 35 divided by 5 and it will give you 7. So Mr. Brown will have 7 teams of 5.

PLEASE HELP QUICK 

Which graph represents a function?

Answers

The correct answer is the third graph, C!

I hope this helped you!

There were 262 hamburgers cooked for the school fair . What is 262 rounder to the nearest hundred

Answers

For this you look one place to the left of the hundred at the tenths. Since it is a 6 and 6 is greater than 5, the two in the hundredths place is rounded up to a three. This means the final answer would be 300!

Mr. Moore has 21 feet of wallpaper he cuts it into sections that are each 3 feet long how many

Answers

Total = 21 feet

if each is 3 feet

21/3 = 7

Therefore, there are 7 sections

Mathematics defines division as breaking into parts a larger unit to make several smaller units.

Division of 21 feet wallpaper into 3 feet section will give 7 small parts of the wallpaper.

To reach above answer, following calculation was made:

[tex]\begin{aligned} \rm Total\: length\:of \: the \:wallpaper &= 21\rm \:centimetres\\Length \:of\:each\:section &= 3\: \rm centimetres\end[/tex]

Therefore, number of sections will be the division of total length to length of each section.

[tex]\rm \begin{aligned} Number \:of \:sections &= \dfrac{\rmTotal\: length}{\rmLength\:of\:each\:section}\\ \\&= \dfrac{\rm 21\:centimetres}{\rm 3\:centimetres}\\\\&= \rm 7 \:sections \end[/tex]

Hence, 21 centimetres long wallpaper can be divided into 7 sections that are 3 centimetres long.

Learn more about division here:

https://brainly.com/question/243497

find the quanity 103% of 19

Answers

Answer:

19.57

Step-by-step explanation:

100% of 19 is 19.

In order to find out what 1% of 19, move the decimal point two place to the left. 1% of 19= 0.19. To find 3% of 19, multiply .19 x 3. add 0.19 x 3 to 19, aka add 0.57 to 19 to get 19.57= 103% of 19

Answer:

19.57 is the answer

Step-by-step explanation:


James is solving the equation x^2+10x=50 by completing the square. What number must be added to both sides of the equation to complete the square?

Answers

Let f (x) be a quadratic equation of the form:

[tex]x^2+bx+c\\[/tex]

Where b and c are real numbers.

So a generic procedure for completing squares is:

1) identify b

In this case b = 10

2) divide b between 2 and then square it

[tex](\frac{b}{2})^ 2\\[/tex]

[tex](\frac{10}{2})^ 2=25\\[/tex]

3) Add and subtract [tex]b ^ 2[/tex] in the equation

[tex]x ^2+10x + 25 - 25 = 50\\[/tex]

[tex]x ^ 2 + 10x +25 = 75\\[/tex]

4) Rewrite the equation as follows

[tex](x+\frac{b}{2})^2=c\\[/tex]

[tex](x + 5) ^ 2 = 75\\[/tex]

The number that you must add to both sides of the equation is number [tex]25 = (\frac{b}{2})^2[/tex]

The completed form of the equation is (x + 5)² = 75.

To solve the equation x² + 10x = 50 by completing the square, you need to add a specific number to both sides to create a perfect square trinomial on the left side. Here’s how you do it step-by-step:

Start with the equation: x² + 10x = 50.Take the coefficient of the x term (which is 10), divide it by 2, and then square the result: (10/2)² = 25.Add 25 to both sides of the equation: x²+ 10x + 25 = 50 + 25.Now the left-hand side of the equation can be factored as a perfect square trinomial: (x + 5)² = 75.

Therefore, the number that must be added to both sides to complete the square is 25.

The triangular region shows the number of possible carnations, x, and the number of possible daisies, y, that can be used in a floral arrangement. The ordered pairs represent combinations of carnations and daisies that can be used in the floral arrangement.

Which ordered pairs make sense in the context of the situation?

Select each correct answer.


A) (6,8.5)

B) (7,5)

C) (13.5,6)

D) (12,5)

E) (14,7)

Answers

(7, 5) and (14, 7)  are inside the shaded region. I would rule out  those which are not whole numbers ( 1/2 a daisy would look silly!)

Answer (7, 5) and (14, 7)

we know that

If a ordered pair is a solution of the combination of carnations and daisies that can be used in the floral arrangement

then

the ordered pair must be in the triangular region graphed and make sense in the context of the situation

using a graphing tool

we're going to proceed to graph and analyze each of the cases

see the attached figure to better understand the problem

Step 1

point [tex]A(6,8.5)[/tex]

The point A is on the triangular region, but the number of daisies is not a whole number

therefore

The ordered pair A  does not make sense in the context of the situation

Step 2

point [tex]B(7,5)[/tex]

The point B is on the triangular region, and the number of carnations and daisies are a whole number

therefore

The ordered pair B  makes sense in the context of the situation

Step 3

point [tex]C(13,5.6)[/tex]

The point C is on the triangular region, but the number of daisies is not a whole number

therefore

The ordered pair C  does not make sense in the context of the situation

Step 4

point [tex]D(12,5)[/tex]

The point D is not on the triangular region

therefore

The ordered pair D  does not make sense in the context of the situation

Step 5

point [tex]E(14,7)[/tex]

The point E is on the triangular region, and the number of carnations and daisies are a whole number

therefore

The ordered pair E  makes sense in the context of the situation

The answer is

[tex]B(7,5)[/tex]

[tex]E(14,7)[/tex]

PLEASE HELP QUICK!! !!20 POINTS!!
1. Refer to the equation y = 1/3 x + 2

(a)Create a table of x, y values for 4 ordered pairs. Tip: choose an x, then find y four times. Use “easy numbers”, like x = 0, 3 (gets rid of fraction), or -3

Answers

The final table is in the attached picture.

Before beginning, you should note that:

To get rid of a fraction, this fraction should be multiplied that is equal to or is a multiple of its denominator.

This means that:

[tex]\frac{1}{y} * ay = a[/tex]

Now, for the given:

We have the equation: [tex]y = \frac{1}{3} x + 2[/tex]

The denominator of the fraction is 3, therefore to get rid of it we will need x to be a 3 or a multiple of 3.

Let's consider the x values to be -3, 0, 3 and 6.

For x = -3: [tex]y = \frac{1}{3} (-3) + 2[/tex] = -3 + 2 = -1 .....>First order pair is (-3,-1)

For x = 0: [tex]y = \frac{1}{3} (0) + 2[/tex] = 0 + 2 = 2 .....> Second order pair is (0,2)

For x = 3: [tex]y = \frac{1}{3} (3) + 2[/tex] = 1 + 2 = 3 .....> Third order pair is (3,3)

For x = 6: [tex]y = \frac{1}{3} (6) + 2[/tex] = 2 + 2 = 4 .....> Fourth order pair is (6,4)

Hope this helps :)

what is the answer for this? 72+10d>/= to 9:/

Answers

it is 8 or  10. multiply the 10d by 11 0r 12. 13 or 14



Help! What is the reciprocal of 5 3/5 ?

Answers

the reciprocal of 5 3/5 is 5/28

What are the two shortest measurements below?

300 millimeters

40 centimeters

0.002 kilometers

0.2 meters

Answers

answer:
300 millimeters (mm) then 40 centimeters (cm)


orders of magnitude from largest to smallest:

kilo, hecto, deca, meter, deci, centi, mili

or

King Henry Died Monday Drinking Chocolate Milk

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