Maya made fruit punch for a party. She mixed 2 gallons of orange juice, 5 quarts of pineapple juice, 4 pints of cranberry juice, and 6 cups of apple juice. How many quarts did she make in all?

The value of the missing part of triangle DFC which is FD would be = 12.

Triangle ACD is congruent to triangle DFC

ED/AD = BC/AC

where;

ED = 9

AD = 15

BC= 12

AC=?

Make AC the subject of formula;

AC= 12×15/9

AC= 180/9

AC = 20

Using the adjacent values of the new and original sides of the triangle to calculate the scale factor.

That is ;

AD is congruent to FC = 15 = 9

But Scale factor = Dimension of the new shape ÷ Dimension of the original shape

Scale factor = 15/9= 1.67

To calculate FD using the scale factor;

1.67= 20/FD

FD= 20/1.67

FD= 12 (approximately)

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By proportion formulas and Pythagorean theorem, the length of side FD is approximately equal to 26.571.

Herein we find a geometric system formed by two similar right triangles (ΔABE, ΔACD) and a third distinct right triangle (ΔCDF). Two triangles are similar when both have congruent interior angles and sides that are not congruent though proportional.

Then, the system of similar triangles can be defined by following proportion formula:

AB / AE = AC / AD

x / 6 = (x + 12) / 15

15 · x = 6 · (x + 12)

15 · x = 6 · x + 72

9 · x = 72

x = 8

AB = 8

Now we determine the length of side CD by Pythagorean theorem:

CD = √(AC² - AD²)

CD = √[(x + 12)² + 15²]

CD = √(20² + 15²)

CD = 25

And the side FD is finally found by Pythagorean theorem:

FD = √(CD² + CF²)

FD = √(25² + 9²)

FD = √706

FD ≈ 26.571

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Van 't Hoff's law, also known as the law of osmotic pressure, states that the magnitude of the osmotic pressure is directly proportional to the concentration of solute particles in a solution at a given temperature.

Van 't Hoff's law is an important concept in chemistry and thermodynamics. It explains the relationship between osmotic pressure and the concentration of solute particles in a solution. According to the law, the osmotic pressure of a solution is directly proportional to the number of solute particles in the solution, regardless of the type of solute. This means that if the concentration of solute particles in a solution increases, the osmotic pressure also increases, and vice versa. This law has numerous applications, particularly in the field of biology, where it is used to explain the movement of water and nutrients in and out of cells. For example, when a plant cell is placed in a hypertonic solution, water moves out of the cell, causing it to shrink. On the other hand, when a plant cell is placed in a hypotonic solution, water moves into the cell, causing it to expand. Understanding Van 't Hoff's law is therefore critical in many fields of science, particularly in biology, chemistry, and chemical engineering.

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The weight of the object is 79.461 newtons.

The standard value for the acceleration due to gravity is approximately 9.81 m/s^2 near the Earth's surface.

To find the weight of an object with a mass of 8.1 kg, we can use the formula:

Weight = mass x acceleration due to gravity

So, the weight of the object is:

Weight = 8.1 kg x 9.81 m/s^2

Weight = 79.461 N (newtons)

Hence, the weight is 79.461 newtons.

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The values of the given expressions are respectively,  -5.33, 5.33, -6,  -6,  6

An expression is a sentence with at least two numbers or variables having mathematical operation. Math operations can be addition, subtraction, multiplication, division.

For example, 2x+3

Here are the calculations for each expression:

1. (-8) x 2/3

  = (-8) x 2/3

  = -16/3

  = -5.33

2. (-8) x (-2/3)

   = (-8) x (-2/3)

   = 16/3

   = 5.33

3. -18/3 = -6

4. 18/(-3) = -6

5. (-18)/(-3) = 18/3

                 = 6

So, the values of each expression are -5.33..., 5.33..., -6, -6, and 6, respectively.

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There are 24 children in the group.

To divide something into equal groups or to determine how many equal groups there are, use the division procedure. When equal groups are combined to find a total in multiplication, division is the opposite process.

If 6 pizzas were shared among 8 groups of children, each group would receive 6/8 = 3/4 of a pizza.

If each child got 3/8 of a pizza, then in a group of children each group would have 8 * 3/8 = 3 children.

Therefore, in total, there were 8 * 3 = 24 children.

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The cost of each battery would be Battery 1 = $195, Battery 2 = $80 and Battery 3 = $65.

Battery 1 (most expensive).= 3(X)

Battery 2 ( third battery) = 15+ X

Battery 3 (least expensive) = X

The total cost of the whole battery = $340

That is;

$340 = 3x + 15+ X + X

340 = 5x + 15

5x = 340 - 15

5x = 325

X = 325/5

X = $65

Therefore the cost of each battery;

Battery 1 = 3× 65 = $195

Battery 2 = 15 + 65 = $80

Battery 3 = $65

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The dimensions of the original mat are 27 inches by 21 inches.

A closed figure bounded by four sides in which opposite sides are equal is known as rectangle.

The area of rectangle is calculated by the given formula,

A = length x breadth

Length and width  of the rectangle can be found from the following expression after solving for x. The expression is given by :

outside area - inside area = 184 square inches

{(2·x - 3)·(x + 8)} - {(2·x - 7)·(x + 4)} = 184  (On substitute length and width expressions. Each area is the product of length and width.)

⇒{( 2·x² + 16·x - 3x - 24)} - {(2·x² +  8x  -7x -28) }= 184

⇒(2·x² + 13x - 24) - ( 2·x² + x -28) = 184

⇒ 12·x + 4 = 184 .................(On simplifying the expression)

⇒ 12·x = 180

⇒ x = 15

Then the original length of the mat is given by substituting value of x in outside length expression :

2·x - 3 = 2·15 - 3 = 30 - 3 = 27 inches

and the original width of the mat is given by :

x + 6 = 15 + 6 = 21 inches

Hence, the overall dimensions of the original mat are 27 inches by 21 inches.

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Answer:13

Step-by-step explanation:

y=2x+7
x=3

2*3+7=13?

The solution is, the value of w is 13.

Here, we have,

We are given that the point (3,w) lies on the line y = 2x + 7.

This means that if we substitute x = 3 into the equation y = 2x + 7,

we will get the value of y at x = 3, which is equal to w.

so, we get,

Substituting x = 3 into the equation y = 2x + 7, we have:

y = 2(3) + 7

y = 6 + 7

y = 13

So, after simplification we get, w = 13

Therefore, the value of w is 13.

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Arithmetic operations consists primarily of operations such as addition, subtraction, multiplication, and division. So the option A is correct.

The process of adding things together is known as addition. The '+' sign represents the addition process. It entails combining two or more numbers into a single expression.

The difference between two numbers is calculated using the subtraction operation. The '-' sign represents subtraction. It is nearly identical to addition, but it is the conjugate of the second term.

Multiplication is also referred to as repeated addition. It is indicated by " or '*'. It can also be combined with two or more values to produce a single value.

Division is the inverse of multiplication and is usually denoted by ". It is made up of two terms, dividend and divisor, and the dividend is divided by the divisor to yield a single term value.

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Answer:

8.1

Step-by-step explanation:

100%= 45

1%= 45÷100

= 0.45

18%= 0.45×18

= 8.1

Answer:

length = 21 in , width = 14 in

Step-by-step explanation:

the ratio of length : width = 3 : 2 = 3x : 2x ( x is a multiplier )

the area (A) of a rectangle is calculated as

A = length × width

given A = 194 , then

3x × 2x = 194

6x² = 194 ( divide both sides by 6 )

x² = 49 ( take square root of both sides )

x = [tex]\sqrt{49}[/tex] = 7

then

length = 3x = 3 × 7 = 21 in

width = 2x = 2 × 7 = 14 in

The area of the triangle is A = 10x¹⁰y³

A triangle is a plane figure or polygon with three sides and three angles.

A Triangle has three vertices and the sum of the interior angles add up to 180°

Let the Triangle be ΔABC , such that

∠A + ∠B + ∠C = 180°

The area of the triangle = ( 1/2 ) x Length x Base

For a right angle triangle

From the Pythagoras Theorem , The hypotenuse² = base² + height²

if a² + b² = c² , it is a right triangle

if a² + b² < c² , it is an obtuse triangle

if a² + b² > c² , it is an acute triangle

Given data ,

Let the triangle be represented as ΔABC

Let the area of the triangle be represented as A

Now , the base of the triangle is = 4x³y

Let the height of the triangle be = 5x⁷y²

And , The area of the triangle = ( 1/2 ) x Length x Base

Substituting the values in the equation , we get

Area of Triangle = ( 1/2 ) ( 4x³y ) ( 5x⁷y² )

On simplifying the equation , we get

Area of Triangle A = 10x¹⁰y³

Hence , the area of the triangle is A = 10x¹⁰y³

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The centroid of this triangle is located at the point (6, 3).

The centroid of a triangle is the point where the three medians of a triangle intersect. Medians are the line segments that connect each vertex of the triangle to the midpoint of the opposite side.

The centroid is the "center of mass" or the "balance point" of the triangle. In other words, if the triangle were made of a solid material and suspended by a string attached to the centroid, it would balance.

To find the coordinates of the centroid of a triangle, we will use the following formula:

G = (x1 + x2 + x3)/3, (y1 + y2 + y3)/3

Where G is the centroid, and (x1, y1), (x2, y2), and (x3, y3) are the coordinates of the triangle's vertices.

So for the triangle with the vertices s(2, 5), t(6, 5), and r(10, 0), we have:

G = (2 + 6 + 10)/3, (5 + 5 + 0)/3

G = (18/3, 10/3)

G = (6, 3.333...), which we can round to (6, 3)

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Answer:

a= 77, b= 77, c= 103.

Step-by-step explanation:

a= 77 (vertically opposite)

b= a= 77 (corresponding angles)

c= 180-77

 = 103 (angles on a straight line)

Using mathematical operators, the value of the expression is 23

Simplification of an expression is the process of reducing a mathematical expression to its simplest form while retaining the same value. This is done by using various rules and techniques, such as combining like terms, using the distributive property, and applying the order of operations.

The goal of simplification is to make the expression easier to work with and understand. It also helps to avoid errors when solving problems or simplifying more complex expressions.

In this expression given;

3(x + 2y) - 2x + 10 = ?

x = 1, y = 2

3(1 + 2(2)) - 2(1) + 10 = 23

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Answer:

Step-by-step explanation:

its 3.02

The probability that the country is in the south Asia region is 7/87

The probability is a mathematical concept that tells us how likely an event is to occur.

The probability that a country is in South Asia given that it has high business startup costs is represented as P(A|B). This is calculated as follows:

P(A|B) = P(A and B) / P(B)

Where P(B) is the probability that a country has high business startup costs and can be calculated as:

P(B) = B / Total number of countries

And P(A and B) is the probability that a country is in South Asia and has high business startup costs, which can be calculated as:

P(A and B) = A / Total number of countries

So, substituting the values, total high startup cost is 87 and and, South Asia start up cost is 7, Then, the probability that the country is in the south Asia region is

=> 7/87

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Answer:

3v + 14w + 13

Step-by-step explanation:

The expression can be simplified as follows:

(3v + 8w + 19) + (6w - 6)

Combining like terms, we have:

(8w + 6w) and (19 - 6)

3v + 14w + 13

So the simplified expression is equal to 3v + 14w + 13.

The simplified form of a rational equation [x + 1 / (x - 2)] / [x² / (x - 2) + 1] is equivalent to (x - 1) / (x + 2).

In this problem we need to determine the simplified form of a rational equation, whose form is:

R(x) = P(x) / Q(x)

Where:

The simplification process can be done by means of algebra properties. First, write the rational equation:

[x + 1 / (x - 2)] / [x² / (x - 2) + 1]

Second, expand the numerator and the denominator:

[(x² - 2 · x + 1) / (x - 2)] / [(x² + x - 2) / (x - 2)]

Third, simplify the fraction by algebra properties:

[(x² - 2 · x + 1) · (x - 2)] / [(x² + x - 2) · (x - 2)]

(x - 1)² / [(x + 2) · (x - 1)]

(x - 1) / (x + 2)

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Answer:

Step-by-step explanation:

A refrigerator is a cuboid, so W=3ft, L= 2.5ft, and H=6ft,

the volume of the refrigerator =W x L x H=3x2.5x6=45ft^3

The walls and other parts have 20ft^3 volume, so we have to minus them, so

volume left for food =45-20=25ft^3

Answer:

Step-by-step explanation:

Volume of the fridge = 3 × 2.5 × 6 = 45 ft³

then subtract the 20 ft³

45 - 20 = 25 ft³

Answer:

1. b = [tex]\sqrt{20}[/tex]

2. c = [tex]\sqrt{2[/tex]

3. b = [tex]\sqrt{105}[/tex]

4. c = [tex]\sqrt{113}[/tex]

5. c = [tex]\sqrt{52}[/tex]

6. b = [tex]\sqrt{80}[/tex]

7. b = [tex]\sqrt{130}[/tex]

8. a = [tex]\sqrt{48}[/tex]

9. c = [tex]\sqrt{149[/tex]

10. c = [tex]\sqrt{5}[/tex]

Example:

[tex]a^{2}[/tex] + [tex]b^{2}[/tex] = [tex]c^{2}[/tex]

[tex]8^{2}[/tex] + [tex]b^{2}[/tex] = [tex]12^{2}[/tex]

64 + [tex]b^{2}[/tex] = 144

64 + [tex]b^{2}[/tex] = 144 - 64

[tex]b^{2}[/tex] = 80

[tex]\sqrt{b}[/tex] = [tex]\sqrt{80}[/tex]

The statement "a line segment is a part of a line that is bounded by two distinct end points and contains every point on the line between its endpoints." is True because a line segment is defined as a part of a line that is bounded by two distinct end points and contains all the points on the line between those endpoints.

A line segment is a part of a line that has two endpoints and connects them. It is the shortest distance between two points and has a definite length, but no width or height. A line segment can be part of a straight line or a curved line.

A line segment is a section of a line that is defined by two distinct end points and includes every point on the line between them. It is the basic building block of geometry and can be used to measure distances, angles, and shapes.

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Answer:B.Sample space

Step-by-step explanation:

Answer:

here are a total of 14 + 15 + 9 + 11 = 49 donuts.

The probability of selecting a maple donut is the number of maple donuts divided by the total number of donuts:

P(maple donut) = 14/49

So the probability of selecting a maple donut is 14/49, which can also be written as a fraction in simplest form: 2/7.

10 ml is equal to 2 teaspoons. This is because 1 teaspoon is equal to 5 ml. To calculate the number of teaspoons in 10 ml, you must divide 10 ml by 5 ml. 10 ml divided by 5 ml equals 2 teaspoons.

To convert milliliters to teaspoons, you must use the conversion factor of 1 teaspoon = 5 ml. This means that for every 1 teaspoon, there are 5 milliliters. To figure out the number of teaspoons in 10 ml, you must take 10 ml and divide it by 5 ml. This will give you the number of teaspoons in 10 ml.When converting from milliliters to teaspoons, it is important to use the correct conversion factor. If you use the wrong conversion factor, you will end up with incorrect results. For example, if you use 1 teaspoon = 4 ml instead of 1 teaspoon = 5 ml, you will end up with an incorrect result.In addition to using the conversion factor, it is also important to keep in mind that a teaspoon is a measure of volume, not weight. This means that the amount of liquid in a teaspoon may vary depending on the density of the liquid. For example, a teaspoon of water will contain more liquid than a teaspoon of honey.

In conclusion, 10 ml is equal to 2 teaspoons. To convert milliliters to teaspoons, you must use the conversion factor of 1 teaspoon = 5 ml. It is important to remember that a teaspoon is a measure of volume, not weight, and the amount of liquid in a teaspoon may vary depending on the density of the liquid.

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The equations are solved using graphing, elimination, substitution methods.

A system of equations are the set of equations where the solution for these equations are the intersecting point between the equations.

The systems of equations are given below are given below,

(a) -2x + 3y = 1(using elimination method)

     2x+6y= 2

     eliminating x term we get,

     9y = 3

     ⇒y=3.

(b)  y = x + 4 ---(1)(using substitution method)

     x = -3y---(2)

     Substitute (2) in (1) we get,

     y = -3y+4

     ⇒4y=4 ⇒y=1

(c)   3x - y = 7 (using graphing method)

      y = 3x - 2

     This system has no intersection point

     So this system has no solution.

    ( The graph is attached below.)

(d)   x + 2y = 1-----(1) (using elimination method)

      3x + 5y = 8-----(2)

     For eliminating x we have to the multiply equation(1) by 3,

      we get 3x+6y=3

      eliminating 3x we get, y=-5/3 substitute y in (1) we get x=49 /3

Hence, the equations are solved using graphing, elimination, substitution methods.

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71 degrees Fahrenheit is equal to approximately 21.7 degrees Celsius using the conversion method formula.

To convert Fahrenheit to Celsius, you can use the following formula:

Celsius = (Fahrenheit - 32) x 5/9

Plugging in 71 degrees Fahrenheit, we get:

Celsius = (71 - 32) x 5/9

Celsius = 39 x 5/9

Celsius = 195/9

Celsius ≈ 21.7

Therefore, 71 degrees Fahrenheit is approximately 21.7 degrees Celsius.

The Celsius scale is also known as the centigrade scale, because it is divided into 100 degrees between the freezing and boiling points of water at standard atmospheric pressure.

On the Fahrenheit scale, there are 180 degrees between the freezing and boiling points of water. Therefore, each degree on the Fahrenheit scale is equivalent to 5/9 of a degree on the Celsius scale.

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Answer: $20.10

Step-by-step explanation: If you multiply 3.90 by 4 and add 4.50 you get 20.10

Answer:

!20.1

Step-by-step explanation:

I got here by multiplying $3.90 by four and adding $4.50. This equals $20.1

Hence the answer is: She will earn $20.1

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