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The domain of the modulus function is the set of all real numbers. The range of the modulus function is the set of non-negative real numbers.

The modulus function, also known as the absolute value function, is a function that takes any real number as input and returns its distance from zero on the number line.

In mathematical notation, the modulus function can be represented as |x|, where x is the input.

For example, if x = -3, then |x| = 3, and if x = 5, then |x| = 5.

In class 11, the domain of the modulus function is all real numbers, which is represented by (-∞, +∞) and the range is non-negative real numbers represented by [0, +∞)

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Answer:

In algebra, the 3x + 1 semigroup is a special subsemigroup of the multiplicative semigroup of all positive rational numbers. The elements of a generating set of this semigroup are related to the sequence of numbers involved in the still open Collatz conjecture or the "3x + 1 problem".

Step-by-step explanation:

The magic ratio for muffins in 2:2:1:1.

The magic muffin ratio is 2:2:1:1. This equates to 2 parts flour, 2 parts liquid, 1 part fat, and 1 part eggs. The most crucial aspect is to remember to utilize the same unit of weight for each component!

Rinse frozen blueberries many times in cold water until the water turns lighter in color to prevent your batter and baked items from developing a purple-blue tint. Then, blot them dry with a paper towel and gently fold them into the batter. The goal of this procedure is to maintain fast breads light and delicate by limiting the quantity of gluten produced during the mixing process. To do this, the dry components are mixed in a one bowl, the wet ingredients are combined in a separate bowl, and then the two mixtures are combined together.

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The average deviation of predicted DVD sales from the actual is 12.2279 million dollars. F-critical value is 4.0785>4.0785 we can reject the null hypothesis. The 95% confidence interval is (17.1536, 25.1554). The 95% prediction interval for the given value of x is (-3.8623, 46.1713).

Estimate the level of DVD sales for movies, by using the amount of annual revenue  generated by the box office gross

We randomly selected a sample of 43 movies for the same year.

Excel  α = 0.05,  r^2 = 0.5123

=51.23%

51.23% of the DVD sales variation is explained by annual revenue.

SY.X = 12.2279.

Therefore, the average deviation of predicted DVD sales from the actual is 12.2279 million dollars.

b. The hypothesis being tested is:

Null Hypothesis, H0: β1 = 0

Alternative Hypothesis, H1: β1 ≠ 0

The test statistic, F = (6439.6133/1)/((12570.025 - 6439.6133)/(42 - 1)) = 43.07

The F-critical value is 4.0785.

Since 43.07 > 4.0785, we can reject the null hypothesis.

Therefore, we can conclude that there is a linear relationship between the revenues of DVD sales and the box-office gross.

c. y = bo + b1*x

y = 4.8445 + 0.1631*x

Put x = 100

y = 4.8445 + 0.1631*100 = 21.1545

The 95% confidence interval for the given value of x is:

= y ± t*s*[tex]\sqrt{0.026249}[/tex]

= 21.1545 ± 2.020*12.2279*[tex]\sqrt{0.026249}[/tex]

= (17.1536, 25.1554)

d.  The 95% prediction interval for the given value of x is:

= y ± t×s×[tex]\sqrt{}[/tex]1 + hin [The t-value is calculated using =TINV(0.05,42-1) in Excel]

= 21.1545 ± 2.020*12.2279*[tex]\sqrt{1 + 0.026249}[/tex]

= (-3.8623, 46.1713)

Therefore, the value is (-3.8623, 46.1713).

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Answer:

all i could do was simplify it

Step-by-step explanation:

Answer: false

Step-by-step explanation:

False

The solution to the following linear equation problem can be seen in the graph showing how the width and diameter of one face are linearly related.

In a linear model, one level is the maximum amount of levels that may be used. Any equation that has a theoretical extension of at least two is said to be nonlinear. There is a straight line on a map with a simple equation. A nonlinear equation's curve is depicted on the graph.

Here,

one face's perimeter and side lengths are linearly related.

line-drawing formula.

The formula y = mx + b can be used to describe a regular model.

If m is the rising rate and b is in reality the y intercept, then x and y are variables.

The graph shows a linear relationship between the length and perimeter of one face.

Therefore, the graph showing how the perimeter or edge length of one face are linearly connected is the solution to the provided linear equation problem.

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Answer:

x = 16

Step-by-step explanation:

[tex]\frac{8+x}{24+x}=\frac{3}{5}\\ \\ 5(8+x)=3(24+x)\\\\40+5x=72+3x\\\\5x=32+3x\\\\2x=32\\\\x=16[/tex]

Answer:

3 seconds?

Step-by-step explanation:

I mean he throws it up at x= 0 and it drops at x=3 So technically it must be 3?

This seems too simple, but see if it is correct.

The partial fraction expansion for the rational function

S/ (s - 7) (s^2 - 49) = -25-56/ (5+3) (s^2+ 16) - 2s - 56 / (s +3) (s^2 + 16)

can be found by decomposing it into the sum of simpler fractions.

One way to do this is to use the method of long division and then match the coefficients of the resulting polynomials. The process is as follows:

Divide S by (s - 7) to get a quotient of S1 and a remainder of R1.

Divide R1 by (s^2 - 49) to get a quotient of S2 and a remainder of R2.

Write the expansion as S1 + S2 + R2/(s - 7)(s^2 - 49)

Alternatively, we can use the method of partial fraction decomposition by inspection.

To do this, you will write the rational function as the sum of simpler fractions with the same denominator.

S/ (s - 7) (s^2 - 49) = A/(s-7) + B/ (s^2 - 49) + (C*s + D)/(s^2 - 49)

where A, B, C, and D are unknowns that you will find by matching coefficients.

S = (A(s^2-49) + B(s-7) + C*s + D) / (s-7) (s^2-49)

You can use this equation to solve for A, B, C, and D by matching coefficients.

-25-56/ (5+3) (s^2+ 16) - 2s - 56 / (s +3) (s^2 + 16) = A/(s-7) + B/(s^2 - 49) + (C*s + D)/ (s^2 - 49)

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Answer:

39°

Step-by-step explanation:

[tex]angle \: 1 + 2 = 180(co \: interior \: angles \: \:in \: parallel \: lies \: are \: add \: up \: t \: equal \: 180) \\ [/tex]

13x + 24 + 5x -6 = 180

18x+ 18 =180

18x +18 -18 =180-18

18x = 162

18 18

x = 9

Therefore,

m<2 = 5x- 6

= 5(9) -6

= 45-6

= 39°

The y-intercept of the graph of f(x) = x^2 - 3x + 5 is (0, 5).

The equation of the axis of symmetry is x = (3/2).

The x-coordinate of the vertex is (3/2), and the y-coordinate of the vertex is (5 - (9/4)) = (-1/4).

So the vertex of the graph of f(x) = x^2 - 3x + 5 is (-1/4, (3/2)).

To graph the function, you can start by plotting the vertex, then use the axis of symmetry to reflect the parabola across the line x = (3/2). The y-intercept is the highest point of the parabola if it opens upwards, and the lowest if opens downwards. This can be used to confirm the direction of the parabola.

A quadratic function's U-shaped curve is seen on a parabola graph. A right circular cone and a plane surface intersect to generate one of the conic sections known as a parabola in mathematics. It has a U-shaped symmetry in the plane. The conventional form of a parabola is a graph whose equation takes the form f(x) = ax2+bx+c. A parabola's vertex is its most extreme point, and the vertical line that runs through it forms its axis of symmetry.

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The price of a new video game, before tax in the shop that London visited is $10.00

The question is a percentage problem, percent is a fraction of hundred and the calculations will be using 100

In the store that London visited, they were offering a 20% discount

= 20 percent

= 20 / 100

= 0.2

discount factor = 1 - 0.2 = 0.8

the discount factor will be used to multiply by the price of the video game to get a new price

selling price of the new video game before tax = $50 * 0.2 = $10

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The image of (12,-12) after a dilation by a scale factor of 1/3 centered at the origin is (4, -4).

What is dilation at origin?

On the coordinate plane, figures can be magnified. The centre of dilation is frequently the origin. The coordinates of the points in the preimage can be multiplied by the scale factor to get the points in the image if you are distorting a figure that is centered at the origin.

We have to find the image of (12,-12) after a dilation by a scale factor of 1/3 centered at the origin.

To find the image after dilation multiply both coordinates (12, -12) by 1/3 which is the same as dividing by 3.

⇒  (12, -12)*1/3 = (4, -4)

Hence, the image of (12,-12) after a dilation by a scale factor of 1/3 centered at the origin is (4, -4).

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Answer:

  ∠MAR = 28

Step-by-step explanation:

Given angle MAR bisected by ray AT to form angle MAT = (6x-4) and RAT = (2x+8), you want to know the measure of MAR.

An angle bisector divides an angle into two congruent parts:

  ∠MAT = ∠RAT

  6x -4 = 2x +8

  4x = 12 . . . . . . . . add 4-2x

  x = 3 . . . . . . . divide by 4

Then the measure of one of the halves is ...

  ∠RAT = 2x +8 = 2·3 +8 = 14

So, the measure of the whole is ...

  ∠MAR = 2·14

  ∠MAR = 28

The factoring of the polynomial x^4+4x^3+7x^2+16x+12 = 0, considering it's linear factors, is given as follows:

(x² + 5.4x + 11.29)(x + 1)(x + 3).

The polynomial for this problem is defined as follows:

x^4+4x^3+7x^2+16x+12 = 0.

We want to factor the polynomial according to it's linear factors, hence the Factor Theorem is used.

The Factor Theorem states that a polynomial function with roots(also called zeros) [tex]x_1, x_2, \codts, x_n[/tex], is represented by the product of it's linear factors [tex]x - x_1, x - x_2, \cdots x - x_n[/tex], according to the rule the rule presented as follows:

[tex]f(x) = a(x - x_1)(x - x_2) \cdots (x - x_n)[/tex]

The coefficients of the polynomial in this problem are given as follows:

a = 1, b = 4, c = 7, d = 16, e = 12.

Inserting these coefficients into a 4th degree equation solver, the roots are given as follows:

Hence the polynomial is factored as follows:

(x + 2.7 - 2i)(x + 2.7 + 2i)(x + 1)(x + 3).

Applying the subtraction of perfect squares for the first two linear factors, considering that i² = -1, we have that:

(x + 2.7 - 2i)(x + 2.7 + 2i) = (x + 2.7)² - (2i)²

(x + 2.7 - 2i)(x + 2.7 + 2i) = (x² + 5.4x + 11.29).

Hence the factored polynomial is of:

(x² + 5.4x + 11.29)(x + 1)(x + 3).

The problems asks to factor the polynomial according to it's linear factors.

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The expression 70x-40x^4 if  factor is:-10x (4x^3-7).

Expressions  can be defined as equation that has both number that are known as well as numbers that are not known .

Example of expression is the sum of 9 and 1  will gives us 10  which is calculated as (9+1 =10).

Given data:

Expression: 70x-40x^4

Now let factor the expression using the given expression

70x-40x^4

Rearrange the expression

-40x^4 +70x

Common factor

-10(4x^4 -7x)

So the expression is:

-10x (4x^3-7)

Therefore we can conclude that the expression is -10x (4x^3-7).

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The correct choice is:

y= x^2 and y= 2x+3

Given equation,

x^2=2x+3

this can be used for factorization by taking all the factors in one side of the equation

x^2-2x-3=0

or, x^2-3x+x-3=0

or, x(x-3)+x(x-1)=0

or, (x-3)(x-1)=0

Therefore,

x=-1 or x= 3

The result indicates,

when we plot the equation x^2=2x+3 in graph, as a function of y=x^2-3x+x-3, the x axis will be intersected on x=-1 and x=3

Now, if we consider

y=2x+3 and y=x^2

it gives  x^2-2x-3=0 all over again, when combined.

The solution to,

x^2=2x+3 is the intersection point of the graph of straight line alongside the graph for the quadratic equation curve.

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The correct answer is y= [tex]x^{2}[/tex] and y= 2x+3 that can be graphed to find the solution(s) to [tex]x^{2}[/tex]= 2x + 3 .

The Given equation was ,

[tex]x^{2}[/tex]= 2x + 3 .

this can be used for factorization by taking all the factors in one side of the equation

[tex]x^{2}[/tex] - 2x - 3 =0

or, [tex]x^{2}[/tex]-3x+x-3=0

x(x-3)+x(x-1)=0

(x-3)(x-1)=0

∴x=-1 or x= 3

The result indicates,

when we plot the equation [tex]x^{2}[/tex]=2x+3 in graph, as a function of y=[tex]x^{2}[/tex]-3x+x-3, the x axis will be intersected on x=-1 and x=3

Now, if we consider

y=2x+3 and y=x^2

it gives  [tex]x^{2}[/tex]-2x-3=0 all over again, when combined.

The solution to,

[tex]x^{2}[/tex]=2x+3 is the intersection point of the graph of straight line alongside the graph for the quadratic equation curve.

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The number of aerobics classes that will cost the same for members and non-members is 5 classes.

The linear equation that represents the amount paid by members is:

membership fee + (amount per class x number of classes)

= $10 + ($3 x m)

= $10 + $3m

The linear equation that represents the amount paid by no-members is: (amount per class x number of classes)

$5 x m

= $5m

When the two costs are the same, the two equations would be equal:

$5m = $10 + $3m

$5 - $3m = $10

$2m = $10

m = $10 / $2

m = 5

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The area of the triangle is 42 cm².

To calculate the area of a triangle, we need to use the formula:

Area = (base x height) ÷ 2

Therefore, the area of a triangle with a base of 7 cm and a height of 12 cm is:

Area = (7 cm x 12 cm) ÷ 2

Area = 42 cm²

The area of a triangle with a base of 7 cm and a height of 12 cm is 42 cm². This can be calculated by using the formula: Area = (base x height) ÷ 2. The base and the height of the triangle are multiplied together and then divided by two to get the area. Therefore, the area of the triangle is 42 cm².

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It is not possible to construct a triangle whose sides are 2 cm 3 cm and 7 cm because the sum of two sides(2 cm and 3 cm) are smaller than third sides(7 cm).

In the given question, we have to check that it is possible to construct a triangle whose sides are 2 cm 3 cm and 7 cm.

To check whether the given sides can make a triangle or not, we have to check that the sum of two sides always grater than the third side.

To check this we firstly add the 2 and 3

2 + 3 < 7

5 > 7

Now we add 2 and 7

2 + 7 > 3

9 > 3

Now we add 3 and 7

7 + 3 > 2

10 > 2

It is not possible to construct a triangle whose sides are 2 cm 3 cm and 7 cm because the sum of two sides(2 cm and 3 cm) are smaller than third sides(7 cm).

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Answer:

cubic polynomial

Answer：[tex]2\sqrt34+12[/tex]

Step-by-step explanation:Draw a planar Cartesian coordinate system and that's it

The 3 cans of peas cost 39 = $27

The 5 bags of flour cost 515 = $75

The 7 packs of milk cost 7*12.50 = $87.50

The total cost of all the items is 27+75+87.50 = $189.50

To calculate the change she received, you subtract the total cost from the amount she had:

change = 200 - 189.50 = $10.50

So Alicia received $10.50 change.

Due to the lack of spatial thinking instruction in most math classes, geometry is hard. They should acquire geometrical ideas easily instead.

The father of geometry, Euclid was a brilliant mathematician. The terms "ge" and "metria," which both imply "measuring," are the origins of geometry. For more than 2000 years, the Greeks' method of approaching geometry has served as the foundation for geometry.

The study of various mathematical or actual-world forms, figures, and sizes is known as Geometry. We learn about various angles, transformations, and similarities between the forms in geometry. The point, line, and plane are the main building blocks of geometry.

Everyone finds it difficult to dive into the issue of proofs. Children must realize that this issue affects everyone, even the mathematically skilled. Because they have trouble seeing how 3D, and 2D, forms, angles, and lines connect from various viewpoints, most youngsters struggle with geometry issues. Even kids who are really good at solving sum problems in math might be utterly stumped by this.

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Due to the lack of spatial thinking instruction in most math classes, geometry is hard. They should acquire geometrical ideas easily instead.

Visual Ability: While some kids think in terms of forms and proportions, others think visually. Children must comprehend geometry in order to visualize, or else they may not be able to see things in a larger context.

Numbers & Measurements: Children will learn about the link between shapes and sizes as numbers and measures come to life in shapes and sizes. Children will be able to comprehend the measurements and connections of lines, angles, surfaces, and solids using numbers and measures.

3D Thinking: Since these ideas originated in geometry, children cannot possibly comprehend 2 and 3 dimensions without having a working knowledge of geometry! The only way to visualize X, Y, and Z axis, triangles, and pyramids are with the aid of geometry.

Spatial Understanding: If it weren't for geometry, kids could have trouble comprehending the notion of spatial comprehension. Children will learn to appreciate the wonders of the world by studying concepts relating to space, location, size, and shape of objects.

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'Therefore , the solution of the given problem of function comes out to be  f⁻¹(x) =  1 + x / 5x+2 .

Mathematics is the study of number, their variations, the geographical tissue, architecture, and both both actual and fictitious locations. A equation  is a depiction of the relationship here between number of inputs and the corresponding outputs for each one. A function is just a collection of input that, when put together, provide one variable distinct output with each input. Every function is assigned a city, county, or scope, sometimes known as a realm.

Here,

Given:

=> f(x) = (1 -2x)/(5x-1)

To find f⁻¹(x)

So,

=> y = (1 -2x)/(5x-1)

=>  x =  (1 -2y)/(5y-1)

=> y = 1 + x / 5x+2

=> f⁻¹(x) =  1 + x / 5x+2

Therefore , the solution of the given problem of function comes out to be  f⁻¹(x) =  1 + x / 5x+2 .

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On solving the provided question, we can say that by trigonometry so sin 90 = p/h => y = 19

The area of mathematics known as trigonometry examines the correlation between triangle side lengths and angles. The area first appeared in the Hellenistic era, around the third century BC. from the use of geometry in astronomical study. The area of mathematics known as exact methods deals with specific trigonometric functions and how they might be used in calculations. There are six popular trigonometric functions in trigonometry. Sine, cosine, tangent, cotangent, secant, and cosecant are their respective names and acronyms (csc). Studying the characteristics of triangles, particularly right triangles, is called trigonometry. The study of geometry, however, is the characteristics of all geometric figures

here,

it is a right angled triangle

by trigonometry

so sin 90 = p/h

1 = 19/y

y = 19

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The substitution property states that if two expressions are equal, then they remain equal when the same values are substituted into them.

This is usually expressed as:

The substitution property states that if two expressions are equal, then they remain equal when the same values are substituted into them. This means that if one expression is equal to another, then the same value can be swapped in for any of the variables within them and the equality will still hold.

For example, if we have the equation 4x + 7 = 11, then we can swap in any value for x and the equation will still be true. This is because the substitution property allows us to make a substitution for any of the variables and the equation will remain true.

This property is useful in solving equations and is a key part of algebra.

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For the shape to be a quadrilateral, then the measure of angle k must 128 degrees

For quadrilateral PQRS to be an actual quadrilateral, then:

J+M=180 implies that:

2x+9+6x-1=180

Collect like terms:

2x+6x=180-9+1

8x=172

Divide both sides by 8

x=21.5

We have:

K=M

This becomes

K=6x-1

Substitute 21.5 for x

K=6*21.5-1

K=129-1

Subtract 1 from 129

K=128

Hence, the measure of angle K must be 128 degrees

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Answer: Mei had $21.25

Step-by-step explanation: if you add $12 to $9.25 you get $21.25

Answer:

The money she had in the beginning was $21.25

Step-by-step explanation:

Given ,

The cost of the ticket Mei spent = $12.00

Money remaining = $9.25

To Find : The Money she had in the beginning

When we add the given values we get the money she had in the beginning

which is,

Amount = Amount Spent on a Ticket + Money Remaining

Amount = [tex]$12.00 + 9.25[/tex]

Amount = [tex]21.25[/tex]

Hence ,  the amount she had in the beginning was $21.25