The price of a gallon of apple cider is $7.00. The price of eight 4.23-ounce juice boxes is $2.39.

Suppose the juice was instead packaged like the cider. Approximately what is the cost per gallon of the juice?

The equation that represents the quotient of a number x, and five is half the difference of a number and four is    [tex]\frac{x}{5}=\frac{1}{2}(x-4)[/tex]

Given,

The number = x

When you divide a number with another number the result is called the quotient

The quotient of a number x and five = [tex]\frac{x}{5}[/tex]

Difference of a number and four = x-4

Half the difference of a number and four = [tex]\frac{1}{2}(x-4)[/tex]

Here the quotient of a number x and five is half the difference of a number and four, the equation will be

[tex]\frac{x}{5}=\frac{1}{2}(x-4)[/tex]

Hence, the equation that represents the quotient of a number x, and five is half the difference of a number and four is    [tex]\frac{x}{5}=\frac{1}{2}(x-4)[/tex]

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Answer:

500 possibles

Step-by-step explanation:

First number   2      <==== one choice

Second number 10 choices  ( 0 - 9 )

Third number 10 choices   ( 0 - 9)

Fourth number 5 choices ( 1,3,5,7,9 )

1 x 10 x 10 x 5 = 500 possibles

Answer:

Can you please explain more about what do you mean about write a equation for 37.

Step-by-step explanation:

3 log (x) = 1.5 => x = 3.162, by properties of logarithm.

Given: 3 log (x) = 1.5

=> log x = [tex]\frac{1}{2}[/tex] = 0.5

Raising both sides by 10, in order to remove the logarithm:

=> [tex]10^{log_{10}x} = 10^{0.5}[/tex]

=> x = 3.162 (as [tex]a^{log_a(x)} = x[/tex])

Hence, 3 log (x) = 1.5 => x = 3.162, by properties of logarithm.

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The average change in the stock market is 15 points each day.

Average is calculated by dividing the total number of values in a given set by the arithmetic mean of the sum of all the values. For groups of values that are nearly identical, an average is calculated. The numerical value that represents a lot of data is referred to as the average.

The stock market fell by 60 points

No. of days stock market fell = 4 days

The formula for average is given by:

Average = Sum of observations/Total no. of observations

= 60/4

= 15 points

Therefore, the stock market fell by 15 points each day

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Answer: Cooking time depends on the temperature due to the heat and how long it will stay in the oven or on the stove

Step-by-step explanation: let's say if you cook salmon at 400 degrees for an hour it will change if you do it as 500 degrees the time can be prolonged or shorten depending on the temperature

A copy of the polygon using scale factor of 1/3 is 3 units

A closed, two-dimensional polygon in mathematics is a shape with straight line segments. It does not have three dimensions. A polygon has flat surfaces throughout. A polygon must have three sides at a minimum. Only at its terminal must each side of a line segment cross another line segment. We can quickly determine the geometry of a polygon based on how many sides it has.

Given that,

The original  value is 9

So, the copy of the poly is 1/3

So, the copy of polygon is 9×1/3 is 3

Therefore, the copy of the polygon is 3.

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Answer:

41

Step-by-step explanation:

A prime number is a whole number (bigger than 1) that is divisible only by itself and 1.

The first 6 prime numbers are 2, 3, 5, 7, 11 and 13.

2 + 3 + 5 + 7 + 11 + 13 = 41.

Answer: 41

Step-by-step explanation: We know that the first 6 prime numbers are 2, 3, 5, 7, 11, 13. We add them all and get 41!

Answer:

[tex]\mathrm{a + 14 = b}[/tex]

Answer:

Step-by-step explanation:

Well, since 24+16 is 40, this would mean we get 40 ounces of purple paint. There is also a 150% difference between 24 and 16, so 2/3 times 24 = 16.

2/3 of the mixture is blue paint, while 1/3 of the mixture is red paint, so 1/3 of 72 is 24.

Thus, the answer is 24 ounces of red paint.

The magnitude of the sum of vectors is 240.8 M

We know that vector V has a magnitude of 448 meters and a direction of 224°, then the components are:

The other vector W has a magnitude of 336 meters and a direction of 75.9°, then the components are:

Now if we add these two vectors, the coordinates of the sum are:

< -322.3m + 81.9m, -311.2 m + 325.9m> = <-240.4 , 14.7>

Then the magnitude is:

M = √(  (-240.4)^2 + ( 14.7)^2) = 240.8

The magnitude of the sum of vectors is 240.8 M

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The opposite of the number -12 is 12

The number is given as

Number = -12

As a general rule, the opposite of a number x is

Opposite = -x

This means that the opposite of -12 is 12

Hence, the opposite of -12 is 12

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Answer:

(7.5,3)

Step-by-step explanation:

(  (x_1 + x_2)/2, (y_1 + y_2)/2  ) <--Midpoint formula

(5,5) and (10,1) are where you take the x and y values from. The x_1 and y_1 values come from (5,5) and x_2 and y_2 from (10,1).

this gives you (  (5+10)/2, (5+1)/2  )

=( 15/2, 6/2 )

=(15/2, 3)

= or (7.5, 3)

Both bold answers equal the same thing, just depends on if your teacher is asking for it in mixed number form or decimal form.

By the way, I realize it's confusing so the _ is just to show that the following number would be subscript (brainly won't let me show it, so I suggest searching it online if you are still confused..)

Hope this helps!

Using Gaussian elimination, the solution to the given system of equations is:

x = 5, y = -11, z = 3.

A system of equations is when multiple variables are related, and equations are built to find the values of each variable, according to the relations given in the problem.

The system is composed by these following equations:

For Gaussian elimination, the first step is building the augmented matrix of the system, for which which:

Hence the augmented matrix of the system is:

[tex]\left[\begin{array}{cccc}2&-1&4&33\\1&2&-3&-26\\-5&-3&5&23\end{array}\right][/tex]

Then, we need to make the coefficient of x zero in the second and third rows, which is a step to find the solution in an easier way, hence these following row operations are applied:

Then:

[tex]\left[\begin{array}{cccc}2&-1&4&33\\0&5&-10&-85\\0&-11&30&211\end{array}\right][/tex]

Now we need to make the coefficient of y on the third row zero, which will make it possible for us to solve for z hence the following row operation is applied:

R3 -> 11R2 + 5R3.

Then:

[tex]\left[\begin{array}{cccc}2&-1&4&33\\0&5&-10&-85\\0&0&40&120\end{array}\right][/tex]

Starting at the third row and moving up, we have that:

Hence the solution to the given system of equations is:

x = 5, y = -11, z = 3.

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Answer:  he is 115 metters above sea level

Step-by-step explanation:

The value of the expression 3√63 +√28 is 5√7 or 13.228.

A number is a fundamental mathematical unit. For counting, measuring, and comparing quantities, we utilize numbers. A set of symbols, or numerals, used to represent numbers is known as a number system.

A square root is a factor of a number that yields the original number when multiplied by itself.

Consider the expression 3√63 +√28,

Let's assume x = 3√63 +√28

Now,

63 = 3 × 21 = 3 × 3 × 7

28 = 2 × 14 = 2 × 2 × 7

Therefore,

x = 3√63 +√28

x = √ [ 3 × 3 × 7 ] + √ [ 2 × 2 × 7 ]

x = ( √ 3² ) × ( √7 ) + ( √2² ) × √7

x = 3√7 + 2√7

x = ( √7 ) × [ 3 + 2 ]

x = ( √7 ) × 5

x = 5√7

x = 5 × 2.6457

x = 13.228

Hence, the value of 3√63 +√28 is equal to 13.228.

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Answer:

The formula for mass m1 will be as M1 = Fr²/GM2.

What is Newton law of gravitation ?

According to newton's law , force between mass m₁ and m₂ at distance x is given by the following expression is;

F = G m₁m₂ / x²

Where F is the force between two masses m1 and m2 G is the gravitational constant and x is the distance between the two objects.

For Solving for M1 in terms of Fg, G, M2 and r yields;

M1 = Fr²/GM2

To solve for M1 in terms of F, G, M2 and r;

We are required to make M1 the subject of the formula as follows:

F = (G M1M2)/r²

By cross product;

Fr² = G M1M2

by dividing through by G M2; we have;

M1 = Fr²/GM2

The formula for mass m1 will be as M1 = Fr²/GM2.

The appropriate matching of the expression will be:

5.2 × 10 = 52

5.2 × 10² = 520

5.2 × 10³ = 5200

5.2 × 10^-1 = 0.52

It should be noted that the information illustrated is simply about the power on the numbers. This was illustrated on the information.

In this case, it should be noted that the thing to f is to multiply the numbers or count the number of zeros and illustrate on the numbers.

Therefore, the appropriate matching of the expression will be:

5.2 × 10 = 52

5.2 × 10² = 520

5.2 × 10³ = 5200

5.2 × 10^-¹ = 0.52

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Answer:8/100

Step-by-step explanation: you would count the placement value of the numbers after the decimal point

The equation in slope intercept form of the line that passes through the points (-4, 2) and (12, 6) is y = 0.25x + 3

Linear equations are equations that have constant average rates of change. Note that the constant average rates of change can also be regarded as the slope or the gradient

The points are given as

(-4, 2) and (12, 6)

Calculate the slope of the points using

m = (y2 - y1)/(x2 - x1)

So, we have

m = (6 - 2)/(12 + 4)

Evaluate

m = 0.25

The equation is then calculated as

y = m(x - x1) + y1

Where

(x1, y1) = (-4, 2)

So, we have

y = 0.25(x + 4) + 2

Expand

y = 0.25x + 1 + 2

Evaluate

y = 0.25x + 3

Hence, the equation in slope intercept form of the line that passes through the points (-4, 2) and (12, 6) is y = 0.25x + 3

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The amount that Roxana has left is $7560.

Total Amount = $12000

She spent 12% on meat and 25% on vegetables.

Therefore, the amount left will be:

= (100 - 12% - 25%) × 12000

= 63% × 12000

= 63/100 × 12000

= 0.63 × 12000

= $7560

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Answer:

if 312four + 52p = 96 find the value of p

Answer:

Step-by-step explanation:

20% can be written as a fraction

20% = 20/100

20/100 = 1/5

5.26 x 1/5

1 x 5.26/ 5

5.26/5

1.052 = 1.05

Old price : $5.26

New price : $6.31

Increase : $1.05

Step-by-step explanation:

[tex]l {25}^{2} [/tex]

L=5

5×4=20

The correct option is (H) c=√e/m.

The solution for mass energy equivalence formula e=m c² for the value of c is c = √e/m.

An equation deduced from Einstein's Special Theory of Relativity that expresses the correlation between the mass & energy of mass objects.

Some key features related to the mass energy equivalence are-

As per the given question, the expression is;

=> e = m c²

=> c² = e/m

Now, taking square root of both sides.

=> c=√e/m

Therefore, the value of the c derived from the mass energy equivalence formula e=m c² is  c=√e/m.

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A triangular prism is 1/2 the volume of a rectangular prism with the same dimensions. V = BH (Base x Width) of a triangular its 1/2BHThe base is 10 x 5, 50 is the base.The height is 6, and that would be 300 / 2 since it's triangular so its 150 inches squared for one. Since there are 2.The total volume is 300 inches squared.

For no solutions, put a = b = c = -1, for exactly one solution, put a = 1 and b = c = 0 and for infinite solutions, put a = b = c = 5 in the system of linear equations.

We have the system of equations:

x + y + z = 2   …(1)

a x + b y + c z = 10   …(2)

x - 2 y + z = 4     …(3)

a. The system has no solution.

Put a = b = c = -1 in (2)

We get:

- x - y - z = 10

Now add (1) and (2)

0 = 12

which is not possible.

So, no solution.

b. The system has exactly one solution.

a = 1 and b = c = 0

We have the equations as:

x + y + z = 2   …(1)

x = 10   …(2)

x - 2 y + z = 4     …(3)

c. The system has infinitely many solutions.

a = b = c = 5

We will have the equations:

x + y + z = 2   …(1)

5 x + 5 y + 5 z = 10   …(2)

x - 2 y + z = 4     …(3)

Therefore, we get that, for no solutions, put a = b = c = -1, for exactly one solution, put a = 1 and b = c = 0 and for infinite solutions, put a = b = c = 5 in the system of linear equations.

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If each unit on the map's grid represents 30 meters and Kampp 150 is in Dra Abul Naga, which is about 1,900 meters east and 250 meters south of distance from Tutankhamen's tomb,then we have to add approximately 64 units to the x axis to include Dra Abul Naga.

Given that each unit on the map's grid represents 30 meters and Kampp 150 is in Dra Abul Naga, which is about 1,900 meters east and 250 meters south of Tutankhamen's tomb.

We are required to find the number of units to be added to x axis that are needed to include Dra Abul Naga.

1 unit=30 meters

Distance in east lie on x axis=1900

Number of units to be added on x axis=1900/30

=63.33

It is equal to 64 units approximately.

Hence if each unit on the map grid represents 30 meters and Kampp 150 is in Dra Abul Naga, which is about 1,900 meters east and 250 meters south of Tutankhamen's tomb,then we have to add approximately 64 units to the x axis to include Dra Abul Naga.

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To include Dra Abul Naga, 63.33 units and 8.33 units must be added to the x-axis and y-axis, respectively.

A single unit on the map;'s grid represents 30 meters.

Kampp 150 in Dra Abul is 1900 meters east and 250 meters south of Tutankhamun's tomb.

The distance in the east or x-axis is 1900 meters.

Therefore, the number of units to be added to the x-axis will be:

= 1900 meter ÷ 30 meters

= 63.33 units

Similarly, the distance on the y-axis is 250 meters.

Therefore, the number of units that are needed to be added will be:

= 250 meter / 30 meters

= 8.33 units

Hence, the units that need to be added to the x-axis and y-axis to include Dra Abul Naga is 63.33 units and 8.33 units respectively.

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Answer:

1. 4

2. 65

3. 4

4. 53

5. 14

Answer:

1.: 4 songs

2.: 65 dollars

3.: 4 cookies

4.: 53 cards

5.: 14 degrees

Step-by-step explanation:

1.: Split 40 songs evenly between 10 days. 40 divided by 10 equals 4.

2.: 160, the needed amount, minus 95, the amount already had, equals 65. 95+65=160.

3.: Split 32 cookies evenly between 8 people. 32 divided by 8 is 4.

4.: 200-147=53, so 147+53=200.

5.: -11-14=-25. Subtracting from a negative increases its absolute value, but it remains negative.

Answer: 4, 28, 12, 20

Step-by-step explanation:

Let the numbers be x, 7x, 3x, 5x.

Then, because of their mean,

[tex]\frac{x+7x+3x+5x}{4}=16\\\\16x=64\\\\x=4[/tex]

So, the numbers are 4, 28, 12, 20.