A box measures 4 inches by 2 inches by 3 inches. Find the volume of the box
in cubic feet. Enter your answer as a fraction. Use the '/' as the fraction bar.
Do not include units in your answer.

Answer: y=3x+4.50

Step-by-step explanation:

Answer:

4.50- 10.50/ 3x

6/3x= 2

Answer:

Therefore,

The height is 23.3 ft.

Step-by-step explanation:

Given:

ΔABC ~ ΔXYZ

AC = 108.5 ft

BC = h

XZ = 14 ft

YZ = 3ft

To Find:

h = ?

Solution:

Δ ABC ~ Δ XYZ….Given  

If two triangles are similar then their sides are in proportion.  

[tex]\dfrac{AB}{XY} =\dfrac{BC}{YZ}=\dfrac{AC}{XZ} \textrm{corresponding sides of similar triangles are in proportion}\\[/tex]  

Substituting the values we get

[tex]\dfrac{BC}{YZ}=\dfrac{AC}{XZ}[/tex]

[tex]\dfrac{h}{3}=\dfrac{108.5}{14}\\\\h=\dfrac{325.5}{14}=23.25=23.3[/tex](nearest tenth)

Therefore,

The height is 23.3 ft.

The amount of tip is $6

Step-by-step explanation:

So let cost of meal be 20 x and the tip be 3 x.

⇒ 3x + 20x = 46

⇒ 23x = 46

⇒ x = 2

⇒ 3x = 3 × 2 = $6

Answer:

4 4/9

Step-by-step explanation:

2 1/5 X 2 2/9

= 11/5 * 20/9

= 11/1 * 4/9

= 44/9

= 4 4/9

Answer:

K=7

Step-by-step explanation:

Answer:

7

Step-by-step explanation:

k + 22 = 29

collect like terms

k = 29 - 22

k = 7

Answer:

2x

Step-by-step explanation:

x and 2 are common to both 10x and 22x, so 10x + 22x = 2x(5 + 11)

The GCF is 2x.

Answer:

Step-by-step explanation:

3x1=3

2x3=6

2+1=3

3+3=6

Two equations that have the solution (3,6) include y = 2x and x + y = 9, satisfying the point when their values are substituted.

To write two equations that would have the solution of (3,6), we need to construct linear equations where the point (3,6) satisfies both equations. Here are two examples that fit the criteria:

The first equation could be y = 2x, because when x=3, then y=2(3)=6.

The second equation could be x + y = 9, because when x=3 and y=6, then 3 + 6 = 9.

These two examples clearly have the solution (3,6) when the respective values for x and y are substituted.

Answer:

a) 31c + 19m ≤ 706

b) 7500c + 4300m > 84000

Step-by-step explanation:

hope it helps :p

Answer:

make sure variables are capital!

Step-by-step explanation:

Answer: Perimeter = 2(L + W) and

as a simplified expression is, 8x + 2

Step-by-step explanation: The length is represented by L and the width is represented by W in the expression above.

However, since we have been given the sides of the rectangle as x + 2 and 3x - 1, we shall substitute for the values of these in the expression representing the perimeter.

2(L + W) can now be written as

2( {x + 2} + {3x - 1} )

2(x + 2 + 3x - 1)

By collecting like terms, we now have

2(4x + 1)

8x + 2.

The expression can now be simplified as 8x + 2

Answer:

486

Step-by-step explanation:

Just multiply them by each other

Answer:

The answer is 486 in. squared! :)

Step-by-step explanation:

With PEMDAS, you multiply 9 x 3 which equals 27 x 3 = 81 x 3 = 243 x 2 = 486!

I hope this helped, sorry I answered so late.

Good Luck! :)

To find the area of the orange band, subtract the area of the yellow square from the area of the larger square.

To find the area of the orange band, we need to subtract the area of the yellow square from the area of the larger square. The side length of the larger square is 8 inches because it is twice the side length of the yellow square, which is x inches. So, the area of the larger square is 8 * 8 = 64 square inches. The area of the yellow square is x * x = x^2 square inches. Therefore, the area of the orange band is 64 - x^2 square inches.

Final answer:

To calculate the area of the orange band, find the area of the larger square using the side length of x + 22 inches and subtract the area of the smaller yellow square with side length x. The expression for the area of the orange band is [tex](x + 22)^2 - x^2[/tex], which simplifies to 44x + 484 square inches.

Explanation:

To calculate the area of the orange band, you need to determine the area of the outer (larger) square and subtract the area of the inner (smaller) yellow square. First, find the side length of the larger square, which is the side length of the yellow square plus twice the width of the orange band, so it's x + 2(11) inches. Thus, the side length of the larger square is x + 22 inches.

Now, calculate the area of both squares. The area of the larger square is [tex](x + 22)^2[/tex] square inches, and the area of the yellow square is [tex]x^2[/tex] square inches. The area of the orange band is the difference between these two areas:

Area of the larger square:[tex](x + 22)^2[/tex]

Area of the yellow square: [tex]x^2[/tex]

Area of the orange band: [tex](x + 22)^2 - x^2[/tex]

To find the area of the orange band, you expand the expression [tex](x + 22)^2[/tex], which gives you [tex]x^2 + 44x + 484[/tex], then subtract the area of the yellow square [tex]x^2[/tex], resulting in 44x + 484 square inches, which is the area of the orange band.

3/5x

= 60%

Step-by-step explanation:

Assume that Parcel 2 is assigned x acres; Parcel 1 will be 2x (because its twice as large as parcel 2).

Therefore if the farmer has planted on 30% on parcel 2;

30/100 * 2x area

60/100x

=3/5x

Parcel 1 ;

60/100 * x area

60/100x

3/5x

The total area planted =

(3/5x + 3/5x ) /2

= 3/5x

3/5 * 100

= 60%

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Answer:

-5.65

Step-by-step explanation:

Answer:

3

Step-by-step explanation:

First find the given number(x)

40% : 40/100 × x = 8

the value of x is 20.

Next find 15% of 20

15/100 × 20 = 3

The 15% of 20 is 3.

Percentage, a relative value indicating hundredth parts of any quantity. One percent (symbolized 1%) is a hundredth part; thus, 100 percent represents the entirety and 200 percent specifies twice the given quantity.

Given:

40% of a given number is 8

let the number be x

So, 40% of x = 8

40/100*x= 8

x= 8*100/40

x= 800/40

x= 20

and 15 % of 20

=0.15*20

= 3

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The unknown number is -8.

To find the unknown number, we can set up an equation based on the given information.

We are told that -6 is 2 more than the unknown number, so we can represent this as:

Unknown number + 2 = -6

To isolate the unknown number, we need to subtract 2 from both sides of the equation:

Unknown number = -6 - 2

Unknown number = -8

So, the unknown number is -8. This means that when you add 2 to -8, you get -6, which satisfies the condition given in the problem.

In summary, by setting up and solving the equation Unknown number + 2 = -6, we determined that the unknown number is -8.

This equation represents the relationship between the unknown number and the given value of -6, where -6 is 2 more than the unknown number, as specified in the problem statement.

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Answer:

161 to the nearest 10 = 160

161 to the nearest 100 = 200

Step-by-step explanation:

161 to the nearest 10:

Since you know that 60 is the tenth unit in this number, and 1 is the one unit, the one unit will indicate if it should be rounded up or down. If the one unit it 4 and below, the number will be rounded down. If the one unit is 5 and above, the number will be rounded up.

With this information, we know that he one unit in this number is "1", which will make the 61, be rounded down to 60, resulting in 160.

Using the same information with rounding to the nearest 100, since the tenth unit is above 5, the number will be rounded to the nearest 100, which is 200.

You use the number before the number you are trying to round, to find the nearest "_th".

Answer:

if its rounded to the nearest 10 it would be = 160

if its rounded to the nearest 100 it would be = 200

Step-by-step explanation:

The proportion that could be used to solve for the variable is:

[tex]\frac{7}{1.68}=\frac{p}{2.88}[/tex] ; p = 12 ⇒ b

Step-by-step explanation:

Direct proportion means that two (or more) quantities increase or decrease in the same ratio

The number of pencils and the cost of them is increased together or decreased together

∴ The number of the pencils and their costs are in direct proportion

- By using the 2nd rule above

∵ The cost of the 7 pencils is $1.68

∵ The cost of p pencils is $2.88

∴ [tex]\frac{7}{1.68}=\frac{p}{2.88}[/tex]

The proportion that could be used to solve for the variable is: [tex]\frac{7}{1.68}=\frac{p}{2.88}[/tex]

∵ [tex]\frac{7}{1.68}=\frac{p}{2.88}[/tex]

- By using cross multiplication

∴ p × 1.68 = 7 × 2.88

∴ 1.68 p = 20.16

- Divide both sides by 1.68

∴ p = 12

The value of variable p is 12

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Answer:

19.99 + 0.99x ; 21.97

Step-by-step explanation:

19.99 + 0.99x

19.99 + 0.99(2)

19.99 + 1.98

21.97

Answer:

The price of a drink = $4

The price of a bag of popcorn = $5.5

Step-by-step explanation:

Let p represent popcorn and d represent drink

Harper bought 10 bags of popcorn and 6 drinks and paid $79 ➡ 10p + 6d = $79

Damian bought 3 bags of popcorn and 5 drinks and paid $36.50 ➡ 3p + 5d = $36.50

Now multiply first equation by -3 and second equation by 10

-3 × (10p + 6d) = $79 ➡ -30p - 18d = -$237

10 × (3p + 5d) = $36.50 ➡ 30p + 50d = $365

Now add the new equationd

30p + 50d -30p - 18d = $365 - $237 (-30p will eliminate 30p)

32d = $128 divide both sides of the equation by 32

32 ÷ 32d = 32 ÷ $128 ➡ d = 4

If d = 4 that means a drink costs $4 we can use this information to find the price of a bag of popcorn

3p + 5d = $36.50 (replace d with 4)

3p + 4×5 = $36.50

3p + 20 = $36.50

3p = $36.50 - 20

3p = 16.50 divide both sides by 3

p = $5.5

The question asked to set up a system of equations to determine the price of each bag of popcorn and each drink. Using the variables x and y to represent the price of popcorn and drinks respectively, the system of equations based on the information given is 10x + 6y = $79 and 3x + 5y = $36.50.

To solve this problem, we need to setup a series of equations based on the information given. Let's say:

According to the first scenario with Harper, we get:

10x + 6y = $79

From Damian's shopping, we have:

3x + 5y = $36.50

This gives us the system of equations which can be used to find individual prices of a bag of popcorn and a drink.

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Answer: 25 by 50 ft

Hope this helps

The dimensions of the rectangle will allow for the most economical fence to be built are 30 feet by 15 feet

Given that, rectangular area=450 square feet.

The formula to find the area of a rectangle is Area=Length×Breadth.

Let the length of the rectangle be x and the breadth of the rectangle be y.

Now, 450=xy.

x=450/y

The cost of three sides is $3 per foot.

That is, 3x+3x+3y

The cost on the fourth side is $9 per foot.

That is, 9y

Total cost=6x+12y

Now, Total cost=6×450/y+18y

Let the minimum cost be 0.

2700/y+12y=0

⇒2700/y²-12=0

⇒12y²=2700

⇒y=15 feet

So, 450/15=x=30 feet.

Therefore, the dimensions of the rectangle are 30 feet by 15 feet.

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Answer:74

Step-by-step explanation:

Answer:

no

...

...

...

....

shajajs

Answer:

NO

A= 1/2 x B x H

P= A+B+C

Step-by-step explanation:

ex: triangle side 13, 6,8.5

high: 8

A= 52

P= 27.5

Answer:

450

Step-by-step explanation:

If 81 is 18% of a number then we can say that:

x × 0.18 = 81

We multiply by 0.18 because 18% is 0.18 as a decimal. So to work out the real number we divide 81 by 0.18:

81 ÷ 0.18 = 450

It would take 6.99 kilometers of thread to make 9 boxes of shirts.

Step-by-step explanation:

Step 1; First we convert the mixed fractions into improper fractions. So

2[tex]\frac{1}{5}[/tex] becomes [tex]\frac{11}{5}[/tex] after multiplying 2 with 5 and adding 1 while 5 remains.

2[tex]\frac{5}{6}[/tex] becomes [tex]\frac{17}{6}[/tex] after multiplying the 2 with 6 and adding 5 while 6 remains.

Step 2; Next we equate the given data; [tex]\frac{11}{5}[/tex] kilometers of thread = [tex]\frac{17}{6}[/tex] boxes of thread. We must make the RHS equal to 1 to find out the kilometers of thread needed to make 1 box of shirts. So we multiply [tex]\frac{6}{17}[/tex] on both sides to make the RHS equal to 1.

[tex]\frac{11}{5}[/tex] × [tex]\frac{6}{17}[/tex] = [tex]\frac{17}{6}[/tex]× [tex]\frac{6}{17}[/tex]= 1, So [tex]\frac{11}{5}[/tex] × [tex]\frac{6}{17}[/tex] = [tex]\frac{66}{85}[/tex] km of thread. So [tex]\frac{66}{85}[/tex] kilometers of the thread is required to make 1 box of shirts so we multiply this with 9 to see thread required to make 9 boxes of shirts.

Thread required for 9 boxes of shirts = [tex]\frac{66}{85}[/tex] × 9= [tex]\frac{594}{85}[/tex] = 6.9882 kilometers of thread. This is rounded off to 6.99 kilometers of thread.

Answer:

Option D.

Step-by-step explanation:

        A = 1/2 (base × perpendicular height)

       A = 1/2 (x.x)

           =1/2 (x²)

      32 = 1/2 (x²)

     Multiplying both sides by 2 gives:

     32×2 = x²

     64  = x²

       8   = x

To find the third side, we use the Pythagoras theorem:

    C² = A² + B²

         = 8² + 8²

         = 128

   C = √128

       = 8√2

However, the answer will not be exact, so we  multiply the length of the base and height by 2. This gives x = 16 (Length of base = length of height)

Repeating the steps above gives C = √ (16)² + (16)²

                                                           = √256

This corresponds to option D.

Answer:

Mean=23

Median =23.5

Range=22

Interquartile range = 14

Step-by-step explanation:

Given set of data

11,13,17,20,22,25,27,31,31,33

Mean [tex]=\frac{11+13+17+20+22+25+27+31+31+33}{10}[/tex]

          [tex]=\frac{230}{10}[/tex]

          =23

The[tex](\frac{n}{2})[/tex] th term= the 5th term

                        =22

The  [tex](\frac{n}{2}+1)^{th}[/tex] term = The [tex]6^{th[/tex] term

                               = 25

The median = [tex]\frac{22+25}{2}[/tex]

                   =23.5

Range = Highest term - lowest term

           =33- 11

            =22

Here lower half {11,13,17,20,22}

The middle number of lower half is first quartile.

Q₁ = 17

And lower half is{25,27,31,31,33}

The middle number of upper half is third quartile.

Q₃=31

Interquartile Range =Q₃-Q₁

                                =31-17

                                 =14

Answer:

Mean = 23

Median = 23.5

Range = 22

Interquartile range = 14

Answer:

10%

Step-by-step explanation:

1200-1080= 120 , 1200/10 is 120 which means 10% is 120 students , so if you subtract 120 from 1200 you get 1080.

The percentage decrease in the number of students​ is -10%.

Given that,

Based on the above information, the calculation is as follows:

[tex]= \frac{1080 - 1200}{1200} \\\\= -10\%[/tex]

Therefore we can conclude that the percentage decrease in the number of students​ is -10%.

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