What two fractions are equivalent to 12/27

Answer:

1. 192 books.  

2. 96 books.  

3. 24 books.

Step-by-step explanation:

1. Let's find the volume of each book and the volume of the box, this way:

Volume of a book = 4 * 6 * 1 = 24 inches ³  

Volume of the box = 24 * 24 * 8 = 4,608 inches ³

2. If Hardy fills the box completely, what is the greatest number of books that fit into the box?

Greatest number of books = Volume of the box/Volume of a book

Greatest number of books = 4,608/24

Greatest number of books = 192

3. If Hardy fills the box completely with the least number of layers, there will be (blank) books on the bottom layer.

The height of the box is 8 inches, so it can only can hold 2 or 8 layers of books, since the books are 4 * 6 * 1 inches.  

Greatest number of layers = Height of the box/Width of a book  

Greatest number of layers = 8/1 = 8  

Minimum number of layers = Height of the box/Height of a book  

Minimum number of layers = 8/4 = 2  

Upon saying that, we have:  

Number of books per layer = Greatest number of books/Minimum number of layers  

Number of books per layer = 192/2 = 96

4. To fill the box completely, Hardy places 8 layers of books in the box. There are (blank) books in each layer.

Number of books per layer = Greatest number of books/Number of layers

Number of books per layer = 192/8  

Number of books per layer = 24

Note: Same answer to question 14559894, answered by me today.

Final answer:

The greatest number of books Hardy can fit into the box is 192. With the least number of layers and the box completely filled, there would be 24 books on the bottom layer. And if there are 8 layers of books in the box, there would be 24 books in each layer.

Explanation:

Hardy is packing books into a box and wants to maximize the number of books while also considering different arrangements. The dimensions of each book are 4 inches by 6 inches by 1 inch, and the dimensions of the box are 24 inches by 24 inches by 8 inches. The volume of a book is 4in x 6in x 1in = 24in³, and the volume of the box is 24in x 24in x 8in = 4,608in³. Therefore, the greatest number of books that fit into the box is the volume of the box divided by the volume of one book, which gives us 4,608in³ / 24in³ = 192 books.

If Hardy fills the box completely with the least number of layers, he would place the books so that the largest book dimensions are aligned with the box's. This means laying the books down in layers where each layer measures 24in by 24in. Since each book has a 6-inch side, we can fit four books along the width of the box (24in / 6in = 4 books), and similarly, we can fit six books along the length of the box (24in / 4in = 6 books), resulting in 4 x 6 = 24 books on the bottom layer.

If Hardy fills the box completely with 8 layers of books, he is dividing the height of the box by the height of a book (8in / 1in = 8 layers). In this case, since there are 24 books per layer (as calculated previously), and there are 8 layers, it means there are still 24 books in each layer.

Answer:

D(-6,-4)

Step-by-step explanation:

-5x + y = 26

2x - 7y = 16

-5x/-5 = 26-y/-5

x = -26/5 + y/5

2(-26/5 + y/5) = 7y = 16

-52/5 + 2y/5 = 16 + 52/5

-33y/5 = 80/5 + 52/5

-33y/5 = 132/5

-33y = 132

y = -4

2x - 7(-4) = 16

2x + 28 = 16

2x = -12

x = -6

Answer:

Each friend gets 3 1/2 cookies each.

Answer:

D

Step-by-step explanation:

it is the only figure that looks like a transformation from P

Answer:

1-c

2-b

3-a

Step-by-step explanation:

1. 7y=14

y=2

-7y=-14

y=2

so the equation has one solution

2. 0=0

so the equation has infinite solution

3. 0=2 false

so the equation has no solution

1 solution

8x+7y=30

8x-7y=2

infinitely many solutions

-8x+7y=-2

8x-7y=2

no  solution

8x-7y=2

-8x+7y=2

Explanation

The number of solutions of a pair of linear equations are determined by the following criteria

1 solution

-[tex]a1/a2 \neq b1/b2[/tex]

in the first pair [tex]a1/a2=8/8=1[/tex]

[tex]b1/b2=7/-7=-1[/tex]

therefore [tex]a1/a2 \neq b1/b2[/tex]

infinitely many solution

[tex]a1/a2=b1/b2=c1/c2[/tex]

In the second pair of equations -8x+7y+2=0 and 8x-7y-2=0

[tex]a1/a2=-8/8=-1\\b1/b2=7/-7=-1\\c1/c2=2/-2=-1[/tex]

since [tex]a1/a2=b1/b2=c1/c2[/tex], the pair of equations have infinitely many solutions

no solution

[tex]a1/a2=b1/b2\neq c1/c2[/tex]

in the third pair of equation

[tex]a1/a2=8/-8=-1\\b1/b2=-7/7=-1\\c1/c2=-2/-2=1[/tex]

Here [tex]a1/a2=b1/b2\neq c1/c2[/tex]

The equivalent expression is 12j + 21 and 3(4j + 7)

Solution:

Given that we have to write 2 equivalent expression

Given expression is:

3(3j + 7 + j)

Combine the like terms. Combine 3j and j we get 4j

Thus the expression becomes,

3(4j + 7)

Now let us use distributive property

The distributive property lets you multiply a sum by multiplying each addend separately and then add the products.

The distributive property is represented as:

a(b + c) = ab + ac

Apply distributive property in 3(4j + 7)

[tex]3(4j + 7) = 3 \times 4j + 3 \times 7\\\\3(4j + 7) = 12j + 21[/tex]

Thus one of the equivalent expression is 12j + 21

Second equivalent expression:

From first equivalent expression,

12j + 21

Factor out the greatest common factor

The factors of 12 are: 1, 2, 3, 4, 6, 12

The factors of 21 are: 1, 3, 7, 21  

Then the greatest common factor is 3

Thus factor out 3 from 12j + 21

[tex]12j + 21 = 3(4j + 7)[/tex]

Thus the another equivalent expression is 3(4j + 7)

Answer:

A full batch of cookies will require [tex]\hspace{0.15cm} \frac{8}{3} cup \hspace{0.15cm}of\hspace{0.15cm} \hspace{0.15cm} sugar,\hspace{0.15cm} or \hspace{0.15cm}2\hspace{0.15cm}whole\hspace{0.15cm} cups\hspace{0.15cm} and \hspace{0.15cm} \frac{2}{3} cup\hspace{0.15cm} of \hspace{0.15cm}sugar.[/tex]

Step-by-step explanation:

i) [tex]\hspace{0.15cm}\frac{1}{4} batch \hspace{0.15cm}of \hspace{0.15cm}cookies\hspace{0.15cm} requires\hspace{0.15cm} \frac{2}{3} cup \hspace{0.15cm}of\hspace{0.15cm} sugar[/tex]

ii) multiplying the above by 4 we get

[tex]\hspace{0.15cm}(4\times\frac{1}{4}) batch \hspace{0.15cm}of \hspace{0.15cm}cookies\hspace{0.15cm} requires\hspace{0.15cm}( 4 \times\frac{2}{3} )cup \hspace{0.15cm}of\hspace{0.15cm} sugar[/tex]

iii) Therefore [tex]\hspace{0.15cm}1 batch \hspace{0.15cm}of \hspace{0.15cm}cookies\hspace{0.15cm} requires\hspace{0.15cm} \frac{8}{3} cup \hspace{0.15cm}of\hspace{0.15cm} sugar[/tex]

iv) Therefore a full batch of cookies will require [tex]\hspace{0.15cm} \frac{8}{3} cup \hspace{0.15cm}of\hspace{0.15cm} \hspace{0.15cm} sugar,\hspace{0.15cm} or \hspace{0.15cm}2\hspace{0.15cm}whole\hspace{0.15cm} cups\hspace{0.15cm} and \hspace{0.15cm} \frac{2}{3} cup\hspace{0.15cm} of \hspace{0.15cm}sugar.[/tex]

Answer:

He sold a packet for RM4.1

Step-by-step explanation:

number of Oranges = 63

Bought Oranges for. = RM 34.65

Number of packets. = 63/3

= 21

profit. = RM 51.45

the value that he sold a packet =

[tex] \frac{34.65 + 51.45}{21} = \frac{86.1}{21} = rm4.1[/tex]

Answer:

x=-29

Step-by-step explanation:

Answer:

3x + 42 = 2x - 45           (subtract 2x by bringing it to the other side)

1x + 42 = -45

1x = -45-42             (remember to change the SIGN)

1x = -87

x = -87/1

x = -87

Answer:

Student 3

Step-by-step explanation:

Part of the 3-4-5 Pythagorean triples.

Answer:

Domain: {-2, 0, -1,  4}

 Range: { 4, 2,  3, -2}

Step-by-step explanation:

In a set of ordered pairs, the domain is the set of the first number in every pair, and the range is the set of the second number in every pair.

If the set of ordered pairs is { (-2, 4), (0, 2), (-1, 3), (4, -2)},

                       the domain is {  -2,       0,       -1,       4      }

                   and the range is {       4,       2,        3,       -2}

Answer:

Domain: {-2, -1, 0, 4}

Range: { -2, 2, 3, 4}

^in order^

Step-by-step explanation:

Answer:

Step-by-step explanation:

[tex]\frac{6*10^{2}}{3*10^{-5}}=2*10^{2}*10^{5}\\\\=2*10^{(2+5)}=2*10^{7}[/tex]

Final answer:

The volume of a beach ball with a diameter of 24 inches is approximately 4.19 cubic feet, which is rounded to 4 cubic feet.

Explanation:

To find the volume of a beach ball with a diameter of 24 inches, we first need to find the radius by dividing the diameter by 2, giving us a radius of 12 inches. The formula for the volume of a sphere is V = (4/3) * π * r^3, where V is the volume and r is the radius of the sphere.

Using the formula:

V = (4/3) * π * (12 inches)^3

V = (4/3) * π * 1,728 cubic inches

V ≈ 7,238 cubic inches (rounded to the nearest whole number)

Now, we need to convert cubic inches to cubic feet since 1 cubic foot equals 1,728 cubic inches.

V = 7,238 cubic inches / 1,728 cubic inches per cubic foot

V ≈ 4.19 cubic feet

Rounded to the nearest cubic foot, the volume of air in the beach ball is approximately 4 cubic feet.

Answer:

16.75

Step-by-step explanation:

7.5+9.25=16.75

Line up the digits and use traditional algorithm.

Answer:

Step-by-step explanation:

Subtract 2x

from both sides of the equation.

y=8−2x

x−y=2

Replace all occurrences of y

in x−y=2 with 8−2x

.

y=8−2x

x−(8−2x)=2

Simplify the left side.

Tap for more steps...

y=8−2x

3x−8=2

Solve for x

in the second equation.

Tap for more steps...

y=8−2x

x=103

Replace all occurrences of x

in y=8−2x with 103

.

y=8−2(103)

x=103

Simplify 8−2(103)

.

Tap for more steps...

y=43

x=103

The solution to the system of equations can be represented as a point.

(103,43)

If you read the question you can find that the question is incomplete. By googling it you can find the complete question here: https://brainly.com/question/11917098.

The area of the window is 182 square inches.

Option: B.

Step-by-step explanation:

From the given data, we are given with the length of the upper side of the trapezoid, the right side's bottom excluded the length upper side's length and height of the trapezoid.

Area of an isosceles trapezoid = [tex]\frac{1}{2}[/tex]( a+b) h.

where a is the length of upper side of the trapezoid, b is the length of lower side of the trapezoid and h is the height of the trapezoid.

a= 12 inches.

h= 13 inches.

We are given only with the right side's length of base excluding the length of upper side.

So we have to calculate b= left side + upper side+ right side.

                                        b= 2+12+2.

                                        b= 16 inches.

Area of an isosceles trapezoid = [tex]\frac{1}{2}[/tex] (12+16)(13).

                                                   = [tex]\frac{1}{2}[/tex] (28)(13).

                                                   = 14(13).

                                                   = 182 square inches.

∴ Area of the window= 182 square inches.

Answer:

332324

Step-by-step explanation:

b4hbf3hkrbf;h3bfh3bfc;khjbr3fkhbn;vb 4;khvcj3nc

Answer:

X = -3/7

Step-by-step explanation:

Answer:

(-2,5) and (7,23)

Step-by-step explanation:

we have

[tex]y=x^{2} -3x-5[/tex] ---> equation A

[tex]y=2x+9[/tex] ---> equation B

Solve the system by graphing

Remember that the solution of the system is the intersection point both graphs

Using a graphing tool

The intersection points are (-2,5) and (7,23)

see the attached figure

therefore

The solutions are (-2,5) and (7,23)

The solution points are [tex](-2,5)[/tex] and [tex](7,23)[/tex].

It is given equations are,

Explanation:

From the given graph it is clear that the curve and line intersect each other at two points. These points are the solutions for the given system of equations.

The graph of line and curve intersect each other at [tex](-2,5)[/tex] and [tex](7,23)[/tex].

Thus, the solution points are [tex](-2,5)[/tex] and [tex](7,23)[/tex].

Learn more:

https://brainly.com/question/14300335

Answer:

2.41

Step-by-step explanation:

First you make 7 a decimal that matches 4.59. if you understand decimals then you know its 7.00. after that you just subtract. borrow is necessary in this problem.

To solve 7-4.59, subtract 4.59 from 7 to get 2.41.

To solve 7-4.59, we need to subtract 4.59 from 7.

Step 1: Write down the subtraction problem: 7-4.59

Step 2: Subtract the ones place value: 7 - 4 = 3

Step 3: Subtract the tenths place value: 0 - 5 = -5

Step 4: Combine the values: 3 - 0.59 = 2.41

Therefore, 7 - 4.59 equals 2.41.

To find the length of segment EF, first equate ED and DF as D is the midpoint, solve for x, and then calculate EF as 2 times either ED or DF.

To find the length of segment EF, we need to use the given information: since D is the midpoint of EF, ED is equal to DF. The expressions given for ED (4x + 6) and DF (7x - 9) can therefore be set equal to each other to solve for x:

4x + 6 = 7x - 9

After solving for x, we can find the lengths of ED and DF, which are equal. Finally, we get the total length of EF by adding ED plus DF (or simply 2 times one of them since they're equal).

Here's how you solve for x:
3x = 15
x = 5

Now, substitute x back into one of the original equations to find one of the segment lengths:
ED = 4(5) + 6 = 20 + 6 = 26

Therefore, EF, which is made up of two segments of length 26, is 26 + 26 = 52 units long.

To find the length of EF, use the fact that D is the midpoint of EF. Set ED and DF equal to each other, solve for x, and substitute the value of x back into either ED or DF to find the length of EF.

To find the length of EF, we can use the fact that D is the midpoint of EF. This means that ED is equal to DF.

Given that ED = 4x + 6 and DF = 7x - 9, we can set these two expressions equal to each other:

4x + 6 = 7x - 9

Simplifying the equation:

6 + 9 = 7x - 4x

15 = 3x

Dividing both sides by 3:

x = 5

Now, we can substitute this value of x back into either ED or DF to find the length of EF. Let's use ED:

EF = 4x + 6 = 4(5) + 6 = 20 + 6 = 26

Therefore, EF = 26.

Answer:

8.71 x 10^3N - C

Step-by-step explanation:

Force = mass x acceleration

mass = 1.7 x 10^3 and acceleration = 4.75m/s^2

Force = 1.7 x 10^3 x 4.75 = 8075N = 8.71 x 10^3N

Answer:

8,075N

Step-by-step explanation:

The information we have is:

Mass:

[tex]m=1.7x10^3kg[/tex]

Acceleration:

[tex]a=4.75m/s^2[/tex]

We are asked to find the force that is necessary to create that acceleration in the given mass.

For this we use the equation of Newton's second law:

[tex]F=ma[/tex]

and now we susbtitute all the values into the equation to find the force [tex]F[/tex]:

[tex]F=(1.7x10^3kg)(4.75m/s^2)\\F=8,075N[/tex]

The magnitude of the force required is 8,075N

Each guest will get [tex]\frac{1}{2}\ pound[/tex] of meat on their sandwich.

Step-by-step explanation:

Given,

Number of guests = 15

Meat bought by Susie = [tex]7\frac{1}{2}=\frac{15}{2}[/tex] pounds

Therefore;

[tex]15\ guests = \frac{15}{2}\ pounds[/tex]

For 1 guest, we will divide the pounds by number of guest

Quantity of meat 1 guest gets= [tex]\frac{15}{2}\ divide \frac{15}{1}[/tex]

The fraction is reciprocated when division sign is changed into multiplication.

Quantity of meat 1 guest gets = [tex]\frac{15}{2}*\frac{1}{15}[/tex]

Quantity of meat 1 guest gets = [tex]\frac{1}{2}\ pound[/tex]

Each guest will get [tex]\frac{1}{2}\ pound[/tex] of meat on their sandwich.

Keywords: fraction, division

Learn more about fractions at:

#LearnwithBrainly

Answer:

The answer to the given equation is x=3

Step-by-step explanation:

Given equation is 2(4x-3)-8=4+2x

To find the answer for the given equation :

2(4x-3)-8=4+2x

Using the distributive property a(x+y)=ax+ay

2(4x)+2(-3)-8=4+2x

8x-6-8=4+2x

8x-14=4+2x

Subtracting (4+2x) on both sides we get

8x-14-(4+2x)=4+2x-(4+2x)

8x-14-4-2x=4+2x-4-2x ( by distributive property )

8x-2x-14-4=4-4-2x+2x ( combinig like terms on both sides)

6x-18=0

6x=8

[tex]x=\frac{18}{6}[/tex]

Therefore x=3

Therefore the answer to the given equation is x=3

Answer:

d) 1998 to 2000

Step-by-step explanation:

Consumer price index (CPI) is an economic indicator that shows the average change in prices of items, goods and services. Basically, if CPI is increasing over a period of time that means that there is inflation, and if it decreases that means that there is deflation (lowering of prices).

Now, looking at our table, we see that:

- 1992-1994: CPI increased from 44.3 to 58.2 -> inflation

- 1994-1996: CPI increased from 58.2 to 65.9 -> inflation

- 1996-1998: CPI increased from 65.9 to 70.4 -> inflation

- 1998-2000: CPI decreased from 70.4 to 69.1 -> deflation

Answer:

The correct answer is D. 1998 to 2000

Step-by-step explanation:

Answer:

1. sometimes true

A rhombus is a quadrilateral with all equal size and length. A square is a quadrilateral with all equal size and length, and all right angles around bus, however, can be a square if it has right angles.

2. always true

A square has to have all equal sides and all right angles, however, a rectangle has to have right angles and opposite sides are equal to each other. So if a square has equal sides, it can be considered a rectangle since both opposite sides are equal

3. sometimes true

A parallelogram is a quad roulette or with parallel and equal opposite sides, and a rectangle has right angles and equal opposite sides, therefore, if the parallelogram has right angles, then it is considered a rectangle

4. always true

A quadrilateral has to have 4 sides and the rectangle has 4 sides there, for it is considered a quadrilateral

5. never true

A parallelogram is a quadrilateral, therefore, it has to have 4 sides, but a hexagon has to have 6 sides, therefore, it is never a hexagon

Answer:

48.5 gal/min

Step-by-step explanation:

I used a ratio to solve this problem.

If 97 gallons flow in 2 minutes, the ratio is 97/2

To find the flow per one minute, the ratio is x/1

You can then cross multiply to get 97=2x

When solved, this gives you 48.5 gal/min.

To check, you can multiply x2.

Allow me to review before I start.  Inconsistent means there's no solution to the system of simultaneous equations, i.e. parallel lines.  Consistent means there's at least one solution.  Independent and dependent apply to consistent systems.  The former means exactly one solution (two lines in different directions which meet).  Dependent means an infinite number of solution; the two lines are really the same line.

1. We have two different slopes, lines in two different directions, so they'll meet in exactly one place.  That system is consistent and independent, the usual case.

2. We can write the first one y-3x= -2 and the second y-3x=+2.  These are parallel lines that are different, so no solution: inconsistent.

3.  The first equation is x+2y=4, same as the second. An infinite number of solutions.  Consistent and dependent.

By rewriting the 3 given systems, we will see that:

Let's analyze each system.

Let's look at the first one, we can rewrite it as:

y = 2x + 3

y = -x - 3

So, the slopes are different, meaning that we have one solution, so this system is consistent and independent.

Now let's look at the second system, we can rewrite it as:

y = 3x - 2

y = 3x + 2

Here both lines have the same slope, so the lines never do intersect, meaning that the system is inconsistent and independent.

For the final system we have:

y = (-1/2)*x + 2

y = (-1/2)*x + 2

So, we have two equal lines, so this system is dependent.

If you want to learn more about systems of equations:

https://brainly.com/question/13729904

#SPJ2

Answer:

A) (3, 11)

Step-by-step explanation:

Because 11=2(3)+5.