What is the sum of the distinct prime factors of the number 560?
A. 20
B. 14
C. 18
D. 16
E. 1488

The rate of change in the given graph is 21/4.

The rate of change defines the speed of a variable changes over another variable. On the given graph, we can calculate the rate of change using the formula:

Rate of change = Δy / Δx

To calculate the rate of change of the given graph, we need to identify 2 points first. We take:

(0, 0)

(4, 21)

Rate of change = Δy / Δx

Rate of change = y₂ - y₁

                             x₂ - x₁

Rate of change = 21 - 0

                               4 - 0

Rate of change = 21/4

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The probability that the number cube and the card have the same number is 2/39.

Probability refers to potential. A random event's occurrence is the subject of this area of mathematics.

The range of the value is 0 to 1. Mathematics has incorporated probability to forecast the likelihood of various events.

The degree to which something is likely to happen is basically what probability means.

Given:

Outcomes of cube = { 1, 2, 3, 4, 5, 6}

Outcome of Card = {1, 2, 3} from each group.

So, we have three number both in common as {1, 2, 3}

So, the probability that the number cube and the card have the same number is

= 1/6 x 16/52

= 8/156

= 2/39

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The amount earned is $88,709.68

It is a payroll tax that is paid on wages earned by employees.

We have,

We will assume the current Social Security tax rate for employees as 6.2%.

Now,

The amount earned.

= 5,500 / 6.2%

= 5500 / 0.062

= $88,709.68

Thus,

The amount earned is $88,709.68

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The measure of angles ∠DEM and ∠MEF will be the same which is 41.8 degrees.

The inclination is the separation seen between planes or vectors that meet. Degrees are another way to indicate the slope. For a full rotation, the angle is 360°.

Adjacent angle - In math, two points are nearby in the event that they have a typical side and a typical vertex.

EM bisects DEF and ∠DEF = 83.6°. Then the measure of the angle ∠DEM and ∠MEF will be the same. Then we have

∠DEM + ∠MEF = ∠DEF

∠DEM + ∠DEM  = 83.6°

2∠DEM = 83.6°

∠DEM = 41.8°

The measure of angles ∠DEM and ∠MEF will be the same which is 41.8 degrees.

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The volume of the cone is 64π

From the question, we have the following parameters that can be used in our computation:

Height, h = 12 m

Radius, r = 4 m

The volume is calculated s

V = 1/3πr²h

Substitute the known values in the above equation, so, we have the following representation

V = 1/3π * 4² * 12

Evaluate

V = 64π

Hence, the volume is 64π

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The total weight of the four heaviest eggs, in ounces, is 8 ³ / ₄ ounces .

Given the line plot, the weights of the heaviest eggs are :
2 ¹ / ₂ , 2 ¹ / ₄ , 2, 2

This is because these are the highest numbers on the line plot.

The total weight of these four heaviest eggs is :

= 2 ¹ / ₂ +  2 ¹ / ₄ +  2 + 2

= 4 ³ / ₄ + 4

= 8 ³ / ₄ ounces

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The measurement of angle FGH is 27.9° after transformation.

A transformation is a process that manipulates a polygon or other two-dimensional object on a plane or coordinate system.

Given that, a translation composed with a rotation maps quadrilateral ABCD to quadrilateral EFGH. and m ∠ BCD = 27.9°, we are asked to find measurement of angle FGH,

We know that, any transformation or set of transformation will make similar figures, and similar figures have congruent corresponding angles,

Therefore,

m ∠ BCD = m ∠ FGH

m ∠ BCD = m ∠ FGH = 27.9°

Hence, the measurement of angle FGH is 27.9° after transformation.

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The statement that describes the relationship is: option B.

The situation that can be represented by the equation y = 12x is: B. "Yvonne has y dollars. This is one half more dollars than her friend Marie who has x dollars."

In the equation y = 13x, y is equal to 13 times x. This means that y increases by a factor of 13 for every increase in x.

In the equation y = x + 13, y is equal to x plus 13. This means that y is always 13 more than x.

Therefore, the answer is:

B. "In y = 13x, the value of y is 13 times the value of x, and in y = x + 13, the value of y is 13 more than the value of x."

The equation y = 12x means that y is equal to 12 times x. In the given situation, Yvonne has y dollars and Marie has x dollars. Yvonne has 12 times more dollars than Marie, and one half more than Marie. Therefore, the situation can be represented by y = 12x.

The correct answer is:

B. "Yvonne has y dollars. This is one half more dollars than her friend Marie who has x dollars."

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Answer:

see image,

Area = 5 units^2

Step-by-step explanation:

Graph three points to make a triangle.

Use

Area = 1/2•b•h

to find the area.

Fortunately, the base is horizontal and the height is vertical, so we can just count the squares to find those lengths. (If they aren't horizontal and vertical, then you need distance formulas)

see image.

The quantity of liters of both 30% and 10% acid that will make up the 20liters would be= 15 liters and 5 liters respectively.

The quantity of liters of 30% acids ;

= 30+10 = 40

= 30/40×20/1

= 600/40

= 15 liters of 30 % acid will make up 20 liters of 20% acid.

The quantity of liters of 10% acids:

= 10/40× 20/1

= 200/40

= 5 liters of 10% acid will make up 20 liters of 20% acid.

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Answer:

We can solve for y in the equation y = 2y - 2 by substituting y = 2x - 5.

Starting with y = 2y - 2, we substitute y = 2x - 5:

2x - 5 = 2(2x - 5) - 2

Expanding the right side:

2x - 5 = 4x - 12

Next, we isolate y by subtracting 2x from both sides:

-2x - 5 = 4x - 12

Adding 2x to both sides:

-5 = 6x - 12

Adding 12 to both sides:

7 = 6x

Finally, we divide both sides by 6 to solve for x:

x = 7/6

So, y = 2x - 5 = 2(7/6) - 5 = 7/3 - 5 = -14/3.

Therefore, y = -14/3 is the solution to the system of equations y = 2y - 2 and y = 2x - 5.

Step-by-step explanation:

The type of sampling method used by Mrs. Trahan is clustering method. The correct option is 4.

A population is divided into many clusters that are representative of homogenous traits and have an equal probability of being included in the sample using the sampling technique known as cluster sampling.

Using this sampling approach, researchers examine a sample that includes a variety of sample criteria, including demographics, lifestyle, background, or any other population characteristic that may be the subject of the research being done. This approach is typically used when a statistical population is made up of comparable but internally heterogeneous groupings. Cluster sampling divides the population into smaller, more productive groups, allowing the researchers to obtain data without picking the full population.

Types of Cluster Samplings:

Hence this is all about clustering method in sampling technique.

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Check the picture below.

The length of KJ is 9 unit.

The  length of CB is 10 unit.

The section connecting a triangle's two sides at their midpoints is parallel to and only half as long as the third side.

Given:

12. Using Mid segment theorem

Mid segment= 1/2 of Triangle base

Mid segment= 1/2 x 18

Mid segment (KJ) = 9

13. Using Mid segment theorem

Mid segment= 1/2 of Triangle base

x+ 19 = 1/2(x+ 29)

2x + 38 = x+ 29

x = -9

So, length of CB = x + 19 = 10 unit

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Answer:

she can only invite 20 people max

Step-by-step explanation:

2.50x20= 50 + fee =100

Step-by-step explanation:

You can make a ratio. Put the first part of the question together and put the second part together.

[tex] \frac{75}{90} = \frac{x}{30} [/tex]

Next we cross multiply

[tex](75)(30) = 90x[/tex]

[tex]2250 = 90x[/tex]

Lastly we divide by 90

[tex]x = 25[/tex]

The length and width of the rectangular board is 27 inches and 23 inches respectively

The area of the rectangle is given by the product of the length of the rectangle and the width of the rectangle

Area of Rectangle = Length x Width

Given data ,

Let the area of the mat be = 184 inches²

Area of Rectangle = Length x Width

Substituting the values in the equation , we get

Let the area of the larger rectangle be = ( 2x - 3 ) ( x + 8 )

Let the area of the smaller rectangle be = ( 2x - 7 ) ( x + 4 )

Now , the area of mat = area of the larger rectangle - area of the smaller rectangle

So , 184 = ( 2x - 3 ) ( x + 8 ) - ( 2x - 7 ) ( x + 4 )

On simplifying the equation , we get

2x² - 3x + 16x - 24 - [ 2x² + x - 28 ] = 184

On further simplification , we get

12x + 4 = 184

Subtracting 4 on both sides of the equation , we get

12x = 180

Divide by 12 on both sides of the equation , we get

x = 15

So , the length of the board = ( 2x - 3 ) = 27 inches

And , width of the board = ( x + 8 ) = 23 inches

Hence , the dimensions of the rectangular board is 27 x 23 inches²

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Answer:

543 fee

Step-by-step explanation:

The difference between 535 and -8 is the distance between them, but it is not specified in what unit this distance should be measured. If you meant to find the difference in feet, then:

535 - (-8) = 535 + 8 = 543

So the distance between 535 and -8 in feet is 543 feet.

Answer:

    [tex]x - y = 14[/tex]

    [tex]x + y = 58[/tex]

Step-by-step explanation:

x = Number of tickets

y = Number of tickets your friend sells

Together, you and your friend sell 58 tickets: [tex]x + y = 58[/tex]

You sell 14 more tickets than your friend:        [tex]x = y + 14[/tex]
                                                                           = [tex]x -y = 14[/tex]

∴System of linear equations:

                     [tex]x - y = 14[/tex]….(equation i)

                     [tex]x + y = 58[/tex]….(equation ii)

The professions such as doctors, engineers (particularly in fields such as petroleum, software, or aerospace), and certain types of business executives tend to have some of the highest earning potentials.

The income of a job or profession can vary widely based on a variety of factors, such as location, experience, education, and demand.

According to the Bureau of Labor Statistics (BLS) in the United States, the highest-paying occupations as of 2021 are typically in the medical, dental, and managerial fields, with physicians and surgeons ranking as the highest-earning profession. However, it's important to note that there are many other factors that can impact earnings, such as the specific field of medicine, the size and type of organization or company, and geographic location.

Ultimately, the earning potential of a job or profession can depend on a wide range of factors, and it's important to research and consider all of them when deciding on a career path.

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The equations are two parallel lines, then the system of equations has no solutions.

Here we have a system of equations:

-7x + 7y = 1

2x - 2y = -18

Now, if we multiply the second equation by (7/2) we will get:

(7/2)*(2x - 2y) = -18*7/2

7x - 7y = -63

If we multiply this by -1 we will get:

-1*(7x - 7y) = -1*-63

-7x + 7y = 63

Then the system of equations becomes:

-7x + 7y = 1

-7x + 7y = 63

Notice that the left side is equal in both equations but the right side is different, then the system has no solutions.

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The probability that the bag is not orange is given as follows:

p = 5/12.

A probability is calculated as the division of the desired number of outcomes by the total number of outcomes.

In this problem, the parameters are given as follows:

Hence the probability that the bag is not orange is given as follows:

p = 5/12.

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Answer:

  105°

Step-by-step explanation:

You want the measure of the remaining angles of a pentagon if one of the angles is 120° and the remaining angles are congruent to each other.

The sum of the interior angles of a pentagon is 180* × (5 -2) = 540°. If one of the angles is 120°, the sum of the other four is ...

  540° -120° = 420°

Then each of those four congruent angles has a measure of ...

  420°/4 = 105°

The size of the other angles is 105°.

The algebraic fraction which is an equivalent fraction with the denominator 24a^3b^2 is 15b/24a^3.

To find an equivalent fraction with the denominator 24a^3b^2, we need to find a common denominator for the two fractions 5b and 8a^3. This common denominator is 24a^3b^2.

To find an equivalent fraction for 5b, we can multiply both the numerator and denominator by the same factor to obtain the desired denominator. To do this, we need to find a factor that would give us a denominator of 24a^3b^2 when multiplied with 8a^3.

The factor that would give us a denominator of 24a^3b^2 is 3.

So, the equivalent fraction for 5b with the denominator 24a^3b^2 is (5b * 3)/(8a^3 * 3) = 15b/24a^3.

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According to the unit conversion table, there are 21.3 dL in 9 cups.

The unit conversion is the term used when we convert a unit of a quantity into another unit but the quantity remains the same.

Given that,

A table showing conversions for common units of capacity

                                      Units of capacity  

  Customary System Units                             Metric System Units

        1 gallon                                                           3.79 liters

        1 quart                                                            0.95 liters

         1 pint                                                              0.473 liters

         1 cup                                                              0.237 liters

We are asked to find there are how many deciliters which is equivalent to 9 cups,

Since,

1 cup = 0.237 liters

1 liter = 10 dL

Therefore,

1 cup = 0.237 x 10 = 2.4 dL

9 cups = 2.4 x 9

= 21.3

Hence, according to the unit conversion table, there are 21.3 dL in 9 cups.

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The given coordinates are all used (0, 6), (0, 4/3), (1, 0), (1, 4/3), (6, 0), (4/3, 0), (9/2, 0), (9/2, 6)

Coordinating refers to the process of organizing or synchronizing different elements or parts to work together in a harmonious and efficient manner towards a common goal or objective. In other words, coordinating involves bringing together various people, resources, activities, or tasks in a way that maximizes their effectiveness and minimizes any conflicts or inefficiencies.

given to the question.

Scale factor 1/3:

The new coordinates after dilation with a center at the origin by a scale factor of 1/3 are obtained by multiplying the original coordinates by 1/3. Hence, we have:

(0, 6) --> (0, 2)

(0, 4/3) --> (0, 4/9)

(1, 0) --> (1/3, 0)

(1, 4/3) --> (1/3, 4/9)

(6, 0) --> (2, 0)

(4/3, 0) --> (4/9, 0)

(9/2, 0) --> (3/2, 0)

(9/2, 6) --> (3/2, 2)

Scale Factor 3/2:

The new coordinates after dilation with a center at the origin by a scale factor of 3/2 are obtained by multiplying the original coordinates by 3/2. Hence, we have:

(0, 6) --> (0, 9)

(0, 4/3) --> (0, 2)

(1, 0) --> (3/2, 0)

(1, 4/3) --> (3/2, 2)

(6, 0) --> (9, 0)

(4/3, 0) --> (2, 0)

(9/2, 0) --> (27/4, 0)

(9/2, 6) --> (27/4, 9)

Point NOT USED:

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The required table

Cups of Flour               Number of Eggs

    10                                     2

    25                                     5

    30                                      6

The ratio can be defined as the number that can be used to represent one quantity as a percentage of another. Only when the two numbers in a ratio have the same unit can they be compared. Ratios are used to compare two objects.

Given, The ratio of flour to eggs in a pancake recipe is constant.

The pancake recipe uses 5 cups of flour for each egg.

Since,

With one egg we need a total number of cups of flour = 5

Thus,

For 2 eggs, we need a total number of cups of flour = 5*2

For 2 eggs, we need a total number of cups of flour = 10

For 5 eggs, we need a total number of cups of flour = 5*5

For 5 eggs, we need a total number of cups of flour = 25

Thus, the required table

Cups of Flour               Number of Eggs

    10                                     2

    25                                     5

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