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The relation as a set of ordered pairs is expressed below.

The domain of the relation is {0, 1, 2, 3, 4, 5}.

The range of the relation is {8, 11, 12, 23, 28}.

In Mathematics, an ordered pair can be defined as a pair of two (2) elements that are commonly written in a fixed order within parentheses as (x, y), which represents the x-coordinate (abscissa) and the y-coordinate (ordinate) on the coordinate plane of any graph such as the following:

Mathematically, the set of ordered pairs which represents the relation include the following:

Based on the mapping diagram (see attachment), the domain and range of the relation is given by:

Domain = {0, 1, 2, 3, 4, 5}.

Range = {8, 11, 12, 23, 28}.

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By distributive property (5k + 2m)(3p + 4s) this we get   15kp + 20 ks + 6mp +8ms.

It is possible to multiply a single value by two or more values enclosed in a set of parenthesis using the distributive property, an algebraic property.

According to the distributive property, it is necessary to multiply each of the two terms by the factor when adding two terms to a factor. Only then may the addition operation be done. The following is a symbol for this property:

A (B+ C)=AB + AC

When there are three distinct values for A, B, and C.

Example : (5k + 2m)(3p + 4s)

Apply FOIL method:

(a + b) (c + d) = ac + ad + bc + bd

(5k + 2m)(3p + 4s) = 5k . 3p + 5k. 4s + 2m. 3p + 2m . 4s

5k . 3p + 5k. 4s + 2m. 3p + 2m . 4s

Simplify 5k . 3p + 5k . 4s + 2m .3p + 2m .4s : 15kp + 20 ks + 6mp +8ms

= 15kp + 20 ks + 6mp +8ms.

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     A variable whose value is decided by a random process or experiment is known as a random variable.

    Depending on how the experiment or random process turns out, it may have a range of distinct numerical values. Random variables come in two varieties: discrete and continuous. A continuous random variable can take on any value within a specific range, such as real numbers, but a discrete random variable can only take on a countable number of values, such as integers.

This random variable has the following distribution and is discrete in nature:

P(X=0) = probability of red or white = P(red) + P(white)

P(X=1) = probability of green or blue = P(green) + P(blue)

P(X=2) = probability of yellow or violet = P(yellow) + P(violet)

P(X=x) must have a sum of all possible values of 1, which indicates that

   P(red) + P(white) + P(green) + P(blue) + P(yellow) + P(violet) = 1

    Therefore ,with a probability  of 1/3 for each value, this random variable has a discontinuous uniform distribution over the set of values 0, 1, and 2.

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For x = 0, the sides of parallelogram are equal.

A parallelogram is a straightforward quadrilateral with two sets of parallel sides in Euclidean geometry. A parallelogram's facing or opposing sides are of equal length, and its opposing angles are of similar size.

There are six crucial parallelogram characteristics to be aware of:

Congruent sides are those when AB = DC.

Congruent opposite angels are D = B.

(A + D = 180°) Consecutive angles are supplementary.

All angles are correct if just one of them is.

A parallelogram's diagonals cut each other in half.

A parallelogram is a four-sided, two-dimensional form in geometry. This particular quadrilateral example has equal and parallel opposite sides.

As the sides of parallelogram are parallel and equal,

2x + 15 = x + 15

2x = x

x = 0

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The minimum amount of framing Lorraine needs for the square painting is 31 inches.

We can use the Pythagorean theorem to calculate the length of the side of the square given the length of its diagonal. The Pythagorean theorem states that in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.

We know that the diagonal of the square painting is 44 inches, and since the diagonal of a square bisects its angles, the square can be divided into two congruent right-angled triangles. Therefore, the length of one side of the square can be calculated using the Pythagorean theorem:

44 inches^2 = x^2 + x^2

x^2 = 11*11

x = 11 inches

Since the square painting has a side length of 11 inches, and the framing material is sold by the inch, Lorraine will need a minimum of 11 inches of framing on each side, for a total of 44 inches.

The equation for Tomas and Emilio birthday party's celebration is 200 = 45.99 + 17p

In math the term called equation is defined as a mathematical statement that shows that two mathematical expressions are equal.

Here we have know that seven friends accept the invitation to the twins' birthday party.

Where the possible equation that can be set up will have the total budget equal to total expenses.

So it can be written as the Total Cost of party is 200,

Then the amount can be divided as

=> Cost of Party Room + Cost of Movie Tickets + Cost of popcorns

Let us consider that if p people attend the party, then the cost of movie tickets will be $12.50p and cost of popcorns will be $4.50p, assuming that each person get a small popcorn bag.

Hence the equation will be written as

=> 200 = 45.99 + 12.50p + 4.50p

=> 200 = 45.99 + 17p

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25 percent of $120 is $30 and yes, he has enough money to buy the music player.

A) Find 25% of $120:

To find 25% of $120, we divide $120 by 100 and then multiply by 25:

$120 / 100 * 25 = $30

So, 25% of $120 is $30.

B) Does Wyatt have enough:

To find the sale price of the music player, we need to apply the 24% discount:

$120 - $120 * 24% = $120 - $120 * 0.24 = $120 - $28.80 = $91.20

So, the music player will be sold for $91.20.

Wyatt has $95, so he has enough money to buy the music player.

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The particle is at the point (-1.112,3.909) after traveling for 20 microseconds.

We have been given a circle,

(x-3)²+(y-4)²=25

whose center is (3,4)

and with a radius of 5 units.

The particle starts at (3,-1) which is the 6 o'clock position in the circle, and ends at (8,4) after 7 microseconds which are at the 3 o'clock position in the circle.

So, the particle traveled 1/4 of the circumference of the circle in 7 microseconds

therefore according to the unitary method it will travel 5/7 of the circumference of the given circle.

so it will subtend 2π×5/7 of the circle from (3,-1)

from the polar form of the circle and the shifting of center of the circle we can conclude

that it's location will be

(5 × cos (10π/7) - 3 , 5 × sin (10π/7) - 4)

= (-1.112,3.909)

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The solution of (n⁴ - 14n³ + 51n² - 19n - 30) / (n - 8) using synthetic division is n³ - 6n² + 3n + 5 + 10/n - 8.

The solution of (n⁴ - 14n³ + 51n² - 19n - 30) / (n - 8) using synthetic division is given below:

(n⁴ - 14n³ + 51n² - 19n - 30) / (n - 8)

The divisor is 8

The coefficients are:

 1   -14   51   -19   -30

Using synthetic division:

the first coefficient is 1

the second coefficient = 1 * (8) + (-14)

the second coefficient = -6

the third coefficient = -6 * (8) + (51)

the third coefficient = 3

the fourth coefficient = 3 * (8) + (-19)

the third coefficient = 5

the remainder = 5 * (8) + (-30)

the remainder = 10

Therefore, the solution =  1(n⁴/n) -6(n³/n) + 3(n²/n) + 5(n/n) + 10/n - 8

The solution = n³ - 6n² + 3n + 5 + 10/n - 8

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Answer:

A. C(x) = 495,000 (1.0325)^ x

Step-by-step explanation:

c(x) = 495,000 x (1+3.25%)^x

= 495,000(1.0325)

The reflected function is the one below:

g(x) = -√x

This function is represented by the last table.

For a general function y = f(x), we define a reflection over the x-axis as:

g(x) = -f(x)

In this case f(x)=  √x, then the reflected function will be:

g(x) = -f(x) = -√x

Now we can evaluate this function to get some pairs of values.

Then when x = 1

g(1) = -√1 = -1

g(2) = -√2 = -1.41

And so on.

Then the correct option is the last table.

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The equation of the trend line, can be found to be y = - 25 + 250

To find the equation of the trend line, you first need to find the slope. To do this, pick two points on the trend line. ( 4, 150) and ( 8, 50 ).

The slope is:

= ( Y2 - Y1 )/ ( X 2 - X 1 )

= ( 50 - 150 ) / ( 8 - 4 )

= - 100 / 4

= - 25

The equation of the trend line takes the form:

y = mx + b

m = slope

b = y - intercept

The slope allows you to find the y - intercept :

y = mx + b

50 = - 25 ( 8 ) + b

b = 250

The equation is:

y = - 25 + 250

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Answer:

because they are not equal in size

Two variables are primarily linked when there is a proportionate relationship, which means that as 1 variable rises or falls, the other rises or falls at the same rate.

The ratios between both the two variables should be considered in order to determine whether a relationship is proportional. The relation is proportional if the ratio remains constant. The relationship is indeed not proportional if the ratio shifts.

When two or more items are directly proportionate or change in size according to equivalent ratios, the relationship is said to be proportional. This proportional relationship can be expressed using the formula y = kx.

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Answer:

Two variables are primarily linked when there is a proportionate relationship, which means that as 1 variable rises or falls, the other rises or falls at the same rate.

What factors determine if one relationship is proportional?

The ratios between both the two variables should be considered in order to determine whether a relationship is proportional. The relation is proportional if the ratio remains constant. The relationship is indeed not proportional if the ratio shifts.

What are the two proportional relationships principles?

When two or more items are directly proportionate or change in size according to equivalent ratios, the relationship is said to be proportional. This proportional relationship can be expressed using the formula y = kx.

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Step-by-step explanation:

The solution of a system of equations for a graph that intersects at (0, 6) is given by the ordered pair (0, 6).

In Mathematics, a point of intersection can be defined as the location on a graph where two (2) lines representing a system of linear equations cross each other (intersect), which is depicted by an ordered pair containing the point that corresponds to the x-axis and y-axis on a cartesian coordinate.

By critically observing the graph of the lines representing the system of linear equations, you would notice that the correct solution set lies on Quadrant I and it represents the y-intercept of the graph.

In conclusion, the ordered pair (0, 6) represents the point of intersection and solution set to the system of linear equations represented by the graph.

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Answer: False because 20 doesn't equal to 9. Have a nice day ;)

Answer: the answer is false

Step-by-step explanation:

Each person buys a number of cakes

The term "operation" in mathematics refers to the process of computing a value utilizing operands and a math operator. For the specified operands or integers, the math operator's symbol has predetermined rules that must be followed. In mathematics, there are five basic operations: addition, subtraction, multiplication, division, and modular forms.

Given, Andy buys x cakes, Betty buys 4 times as many cakes as andy, and colin buys 3 more cakes than andy

So,

Andy has = x Cakes

Betty have = 4x Cakes

Clin has = x +3 Cakes

Since each cake costs 65p and the total cost of the cakes is £52.65

thus,

0.65( x + 4x + x +3) = 52.62

x + 4x + x +3 = 81

6x = 78

x = 13

Therefore,

Andy has = 13 cakes

Betty has = 4x = 4*13 = 52 cakes

Colin has = x + 3 = 16 cakes

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The responses to the survey question are quantitative, as the respondents were asked to provide a numerical answer.

Out of the 79,659 respondents, 79,659 said that they expect driverless cars to be common in the next years.

Out of the 79,659 respondents, 15,030 answered in the range of years. This means that 15,030 respondents provided a numerical answer that was within the range of years.

It is important to note that the survey question was quantitative, so the responses provided by the respondents were numerical. This means that the responses were not categorical, as categorical responses would have been in the form of words or phrases.

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Answer:

30

Step-by-step explanation:

Because it is an isosceles triangle, then only two sides of the triangle are of the same length and since it said one angle of the triangle is 120° there are still 60° left, so split that into two, and it equals 30° for both equal sides

In the given parallelogram, the value of g is 116 degrees and that of h is 64 degrees.

A parallelogram is a simple quadrilateral with two pairs of parallel sides in Euclidean geometry. A parallelogram's opposite or facing sides are of equal length, and its opposite angles are of equal measure. A parallelogram is a type of quadrilateral with opposite pairs of sides that are parallel and equal. The diagram depicts a parallelogram ABCD with AB II CD and AD II BC. In addition, AD = BC and AB = CD. Non-Example: A trapezium is a parallelogram's non-example.

Here,

Since the given figure is parallelogram. Opposite angles are equal.

g=116 degree

h=64 degree

The value of g is 116 degrees and that of h is 64 degrees in the given parallelogram.

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The expected value for each set of 50 items that Sammi sells is $1.82.

The expected value can be calculated by multiplying the profit from each successful sale by the probability of making that sale, and then subtracting the expected cost of each defective item.

Expected value = (Profit from each successful sale * Probability of making that sale) - (Expected cost of each defective item)

Let's assume that Sammi plans to sell 50 items. So, the probability of a successful sale is 49/50 = 0.98. The expected cost of each defective item is $7.

Expected value = ($2 * 0.98) - ($7 * 1/50) = $1.96 - $0.14 = $1.82

So, the expected value for each set of 50 items that Sammi sells is $1.82.

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The proof that shows that triangles ABC and EDC are similar is explained in the table below.

A proof is a logical argument that demonstrates the truth of a statement. So, each step must be justified and flow logically from the previous step.

The proof that shows that the triangles are similar is explained as shown below.

Statement Reason

1. AB || DE 1. Given

2. <A ≅ <E 2. Alternate interior <s theorem

3. <B ≅ <D 3. Alternate interior <s theorem

4. ∆ABC ~ ∆EDC 4. AA Similarity theorem

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Answer:d

Step-by-step explanation:

The energy in the pendulum as it swings from point A to point B

Potential energy is converted to kinetic energy.

Now, According to the question:

Energy is defined as the ability of an object to do work. Energy can be classified in two different types of energy, Kinetic and potential energy. This two may be the principal ones, but we can see how energy manifests in different ways in nature, like heat, chemical potential energy, solar energy, electric potential energy, and so on.

Energy is constantly changing from kinetic to potential energy, and vice-versa in a pendulum. At the lowest point of the pendulum swing, the pendulum will have reach a state of maximum kinetic energy. This due to it attaining the maximum speed the pendulum can reach due to it's movement. As the pendulum start to rise again, it will start to lose kinetic energy and will gain potential energy. This loss in kinetic energy will cause the pendulum to slow down until it reaches it's max height. At this point the pendulum will have converted all of it's kinetic energy to potential energy.

Hence, Potential energy is converted to kinetic energy.

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The coordinates of B, C, and D are (3,-5), (3,5), and (-7,5) respectively.

Given point A (-2,-5) and the lengths of the sides AB = 5 and BC = 10, we can use this information to determine the coordinates of B, C, and D.

Using the information provided, we know that B is 5 units away from A in the positive x-direction. Therefore, the x-coordinate of B is (-2) + 5 = 3 and the y-coordinate of B is the same as that of A, which is -5. So point B is (3,-5).

Next, we know that C is 10 units away from B in the positive y-direction. Therefore, the x-coordinate of C is the same as that of B, which is 3, and the y-coordinate of C is (-5) + 10 = 5. So point C is (3,5).

Finally, we know that D is 10 units away from C in the negative x-direction. Therefore, the x-coordinate of D is 3 - 10 = -7 and the y-coordinate of D is the same as that of C, which is 5. So point D is (-7,5).

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The question is -

Find the coordinates of B, C, and D given that AB = 5 and BC = 10 where A = (-2,-5).

Answer:

29/4 or as a mixed fraction 7 1/4

Step-by-step explanation:

Answer:

125,664 mm³/s

Step-by-step explanation:

V = (4/3)πr³

dV/dt = (4π/3) × 3r² × dr/dt

dV/dt = 4πr² × dr/dt

dr/dt = 4 mm/s

d = 100 mm; r = 50 mm

dV/dt = 4π(50 mm)² × 4 mm/s

dV/dt = 125,664 mm³/s

Answer:

Step-by-step explanation:

I think it's 6 but I am not positive. I would double check it

Marvin should put at least $45 more cash in his wallet in order to have at least $60.

Let x be the amount of cash that Marvin needs to put in his wallet. We know that he wants to have at least $60, and he currently has $15, so we can write the inequality as:

x + 15 ≥ 60

To solve for x, we need to subtract 15 from both sides of the inequality:

x ≥ 60 - 15

x ≥ 45

Marvin should put at least $45 more cash in his wallet in order to have at least $60.

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