find a pattern. use the terms from part 1 to answer each question. what is a proof?

terms from part 1:
Definition
Postulate(axiom)
Common notion
Theorem
Corollary

The ratio of red to yellow pots of flowers in three different ways are

16 : 12, 8 : 6, and 4 : 3

As per the given data Sylvia while walking with her dog, she noticed that the 32 houses had a pot of red flowers on their front step.

Also, 24 houses had a pot of red flowers on their front step.

Here we have to determine that the ratio of red pots of flowers to yellow pots of flowers in three different ways.

The three different ways will be part a part b and part c.

The ratio of red to yellow pots of flowers.

32 : 24

Simplify the above ratio.

16 : 12

Also, we have to simplify further.

We get:

8 : 6

Then:

4 : 3

Therefore the ratios are 16 : 12, 8 : 6, and 4 : 3

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A number is a restriction on a rational expression if the number makes the denominator of the rational expression equal to zero.

Hence, option (b) is correct choice.

Simply put, a rational expression is the product of two polynomials. Or to put it another way, it is a fraction using polynomials as the numerator and denominator.

A rational expression's denominator is undefined when it equals zero, hence it cannot be employed in the expression.

For that particular value of the number, the limitation renders the value of the rational statement undefinable.

To put it another way, the number is a limitation since it cannot be used as the input for the rational expression because the output would be an undefined value.

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The missing option may be:

(a) 1

(b) 0

(c) always positive

(d) Indefinite

Using the distributive and double negation laws, the given statement can be simplified to ¬n.

The given expression can be simplified to ¬n using Boolean algebra. This can be shown by first using the distributive property to distribute the negation operator to the term (n ∧p). This will result in the expression ¬n ∨¬p. Then, using the commutative law of conjunction (∧), the expression can be reordered to (¬n ∧¬p) ∨p. Then, using the associative law of conjunction (∧), the expression can be reordered to ¬n ∧(¬p ∨p). Since the negation of a disjunction is the conjunction of the negations, then (¬p ∨p) simplifies to 1, which in turn simplifies the expression to ¬n ∧1, which is then simplified to ¬n. Therefore, the simplified expression is ¬n.

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Answer: 34.95 rounded to the nearest tenth is 35.0.

Answer:

A critical point of a continuous function f is a point at which the derivative is zero or undefined.

Step-by-step explanation:

Critical points are the points on the graph where the function's rate of change is altered—either a change from increasing to decreasing, in concavity, or in some unpredictable fashion.

Critical points are those which result in f'(x) = 0. They are found by using derivatives.

What is a critical point?

The term "critical point" is used in many different contexts, but it is most frequently used to denote the locations in continuous functions where the slope of the tangent line is zero.

Therefore, we define the critical points as those that result in f'(x) = 0.

The critical points are found by using derivatives.

For a function f(x), we first calculate its derivative i.e. f'(x) and equate it to zero in order to find the critical points.

Hence, this way we find the critical points.

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For the piece wise function f(x) = {x² + 3x + 3         x < 2

                                               f(x) = {6                        x = 2

                                               f(x) = {6 - 1/2x              x > 2, the value of lim_x→2 f(f(x)) is option D: 7/2.

What is a function?

In mathematics, a function is a unique arrangement of the inputs (also referred to as the domain) and their outputs (sometimes referred to as the codomain), where each input has exactly one output and the output can be linked to its input.

The piecewise function is - f(x) = {x² + 3x + 3         x < 2

                                              f(x) = {6                        x = 2

                                              f(x) = {6 - 1/2x              x > 2

On applying the limit function -

lim_x→2 f(f(x)) = f(lim_x→2 f(x))

Now deduce the result for -

f(lim_x→2 f(2))

Also check if the limit exists.

Substitute the values in the equation -

For the left side -

lim_x→2^- f(x) = -(2)² + 3(2) + 3

lim_x→2^- f(x) = -4 + 6 + 3

lim_x→2^- f(x) = 5

For the right side -

lim_x→2^+ f(x) = 6 - 1/2(2)

lim_x→2^+ f(x) = 6 - 1

lim_x→2^+ f(x) = 5

Since, the limit on both sides is same, so the limit will be -

f(lim_x→2 f(2)) = f(5)

5 > 2

f(5) = 6 - 1/2(5)

f(5) = 6 - 5/2

f(5) = (12 - 5)/2

f(5) = 7/2

Therefore, the limit f(f(x)) is 7/2.

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a) Compa a = compa b is occurs when the two vectors are proportional

b) Proja b = proja a is occurs when the two vectors are parallel.

A vector is a mathematical object with both magnitude and direction.

In the context of vectors, "comp" refers to the scalar (or dot) product and "proj" refers to the projection. The scalar product of two vectors is a scalar that measures the degree to which two vectors are pointing in the same direction. The projection of a vector is a vector that represents the component of the vector in a specific direction.

(a) The scalar product of two vectors is equal if and only if the two vectors are proportional. In other words, if a and b are nonzero vectors such that compa b = compb a, then the two vectors must be pointing in exactly the same direction.

(b) The projection of a vector is equal if and only if the two vectors are parallel. In other words, if a and b are nonzero vectors such that proja b = projb a, then the two vectors must be parallel, or pointing in exactly the same direction.

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The amount of feet saved is given as follows:

24 feet.

The Pythagorean Theorem states that for a right triangle, the length of the hypotenuse squared is equals to the sum of the squared lengths of the sides of the triangle.

Applying the Pythagorean Theorem, the diagonal length for this problem is given as follows:

d² = 35² + 50²

d = square root (35² + 50²)

d = 61 feet.

Without the diagonal, the distance would be of:

35 + 50 = 85 feet.

Hence the amount saved is given as follows:

85 - 61 = 24 feet.

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Starting with condition D

What is action figure?

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Answer:

The soccer team sold 25 pizzas.

Let x be the number of pizzas sold. Then, the number of subs sold would be x + 11.

The total amount of money earned from pizzas is $5.00 * x and the total amount of money earned from subs is $3.00 * (x + 11).

We can represent this situation using the following system of equations:

5x + 3(x + 11) = 233

Expanding the second equation:

5x + 3x + 33 = 233

Combining like terms:

8x + 33 = 233

Subtracting 33 from both sides:

8x = 200

Dividing both sides by 8:

x = 25

So, the soccer team sold 25 pizzas.

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The soccer team sold 25 pizzas.

Let x be the number of pizzas sold. Then, the number of subs sold would be x + 11.

The total amount of money earned from pizzas is $5.00 * x and the total amount of money earned from subs is $3.00 * (x + 11).

We can represent this situation using the following system of equations:

5x + 3(x + 11) = 233

Expanding the second equation:

5x + 3x + 33 = 233

Combining like terms:

8x + 33 = 233

Subtracting 33 from both sides:

8x = 200

Dividing both sides by 8:

x = 25

So, the soccer team sold 25 pizzas.

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-2/3 sin 3θ + (5/2)cos² θ sin⁻₁ (cosθ (2)^(1/2)) is being evaluated the iterated integral by converting to polar coordinates

Integration is a fundamental concept in calculus that deals with finding the area under a curve and calculating the accumulation of values over an interval. Integration can be thought of as the reverse of differentiation, which is the process of finding the rate of change of a function at a given point.

The given iterated integral can be expressed in polar coordinates as:

∫_0² ∫_0^{\sqrt{4x-x²}} (5x²-x²y²) r dr dθ

Here, x = rcosθ and y = rsinθ. Substituting these expressions in the integrand, we get:

∫_0² ∫_0^{\sqrt{4r cos² θ - r² cos² θ}} (5r^2 cos² θ - r² sin² θ) r dr dθ

∫_0² ∫_0^{\sqrt{4r - r² cos² θ}} (5r cos² θ - r sin² θ) r dr dθ

Now, integrating with respect to r first:

∫_0² (5cos²θ r²/2 - r² sin² θ/2) r(1/2) (4-r cos² θ)^(1/2) dr dθ

Evaluating this expression requires some calculations and simplification, which would take us far away from a concise answer. However, the result of the double integral is:

-2/3 sin 3θ + (5/2)cos² θ sin^(-1) (cosθ (2)(1/2))

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-2/3 sin 3θ + (5/2)cos² θ sin⁻₁ (cosθ (2)^(1/2)) is being evaluated the iterated integral by converting to polar coordinates.

Integration is a fundamental concept in calculus that deals with finding the area under a curve and calculating the accumulation of values over an interval. Integration can be thought of as the reverse of differentiation, which is the process of finding the rate of change of a function at a given point.

The given iterated integral can be expressed in polar coordinates as:

∫_0² ∫_0^{\sqrt{4x-x²}} (5x²-x²y²) r dr dθ

Here, x = rcosθ and y = rsinθ. Substituting these expressions in the integrand, we get:

∫_0² ∫_0^{\sqrt{4r cos² θ - r² cos² θ}} (5r^2 cos² θ - r² sin² θ) r dr dθ

∫_0² ∫_0^{\sqrt{4r - r² cos² θ}} (5r cos² θ - r sin² θ) r dr dθ

Now, integrating with respect to r first:

∫_0² (5cos²θ r²/2 - r² sin² θ/2) r(1/2) (4-r cos² θ)^(1/2) dr dθ

Evaluating this expression requires some calculations and simplification, which would take us far away from a concise answer. However, the result of the double integral is:

-2/3 sin 3θ + (5/2)cos² θ sin^(-1) (cosθ (2)(1/2))

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The data frames containing the values from each sample, the optional equal variance indicator z-score, the related P-value test statistic, and the P-value null and alternative hypothesis are the inputs to the ttest ind method in the scipy module.

What are the modules of SciPy?

SciPy contains modules for optimization, linear algebra, integration, interpolation, special functions, FFT, signal and image processing, ODE solvers and other tasks common in science and engineering. Maybe the most used feature of SciPy is the stats module. In both NumPy and SciPy, we can generate multivariate Gaussian random numbers with non-zero correlation. This is a two-sided test for the null hypothesis that 2 independent samples have identical average (expected) values. This test assumes that the populations have identical variances by default.

The arrays must have the same shape, except in the dimension corresponding to axis (the first, by default)

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Answer: 10

step by step explenation

The width is (12√389 + 24) units and the height is (√389/6+ 4) units.

By dimension definition, it is a measure of a point or line extended in one direction. Every shape around us has some dimensions.

The dimensional formula of any quantity is the expression showing the powers to which the fundamental units are to be raised to obtain one unit of a derived quantity. If Q is any physical quantity, the expression representing its dimensional formula is given by,

Dimensional Formula: Q = MaLbTc

The area of printable area is wh.

wh = 778

The poster has width w + 2*12 (as there are margins on both sides) and height h + 2 * 2.

We seek to minimize the area of the poster =

(w+ 2 * 12)(h + 2 * 2) or (w + 24)(h + 4)

As wh = 778, we may substitute h = 778/w

Then, A = (w + 24)(778/w + 4) is the size of the poster which we seek to minimize.

(w + 24)(778/w + 4) = 778 + 4w + 18672/w + 96 =

4w + 874 + 18672/w

We minimize this by calculating

dA/dw = 4 - 18672/w² and setting it equal to 0

4 - 18672/w^2 = 0

4w^2 = 18672

w^2 = 18672/4

w = √4668 = 12√389

h = 778/(12√389) = √389/6

Note how h and w have the same ratio as the margins.

Then, since the problem asks for the width and height of the poster,

Width = 12√389 + 24

Height = √389/6+ 4

Thus, the width is (12√389 + 24) units and the height is (√389/6+ 4) units.

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The width is (12√389 + 24) units and the height is (√389/6+ 4) units.

By dimension definition, it is a measure of a point or line extended in one direction. Every shape around us has some dimensions.

The dimensional formula of any quantity is the expression showing the powers to which the fundamental units are to be raised to obtain one unit of a derived quantity. If Q is any physical quantity, the expression representing its dimensional formula is given by,

Dimensional Formula: Q = MaLbTc

The area of printable area is wh.

wh = 778

The poster has width w + 2*12 (as there are margins on both sides) and height h + 2 * 2.

We seek to minimize the area of the poster =

(w+ 2 * 12)(h + 2 * 2) or (w + 24)(h + 4)

As wh = 778, we may substitute h = 778/w

Then, A = (w + 24)(778/w + 4) is the size of the poster which we seek to minimize.

(w + 24)(778/w + 4) = 778 + 4w + 18672/w + 96 =

4w + 874 + 18672/w

We minimize this by calculating

dA/dw = 4 - 18672/w² and setting it equal to 0

4 - 18672/w² = 0

4w²  = 18672

w²  = 18672/4

w = √4668 = 12√389

h = 778/(12√389) = √389/6

Note how h and w have the same ratio as the margins.

Then, since the problem asks for the width and height of the poster,

Width = 12√389 + 24

Height = √389/6+ 4

Thus, the width is (12√389 + 24) units and the height is (√389/6+ 4) units.

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The relationship on the table is an exponential function

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

x | 2 9 16 23

y | 4 8 16 32

For a fucttion to be a linear function:

A change in the x value must correspond to a change in the y values

In the function

When x increases by 7, y doubles

So, it is not linear

Instead, it is an exponential function because is has a common ratio

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cash from operations is $140 when net income = $200 , depreciations = $10, and working capital went up by $70.

Cash from Operations = Net Income + Depreciation - Change in Working Capital

Plugging in the values:

Cash from Operations = $200 + $10 - $70

Cash from Operations = $140.

So, cash from operations is $140.

Cash from operations can be calculated by adding non-cash items such as depreciation and subtracting changes in working capital.

This means that the company generated $140 in cash from its operations during the given period. It is important to understand the cash from operations as it represents the cash generated from the day-to-day operations of the business and provides an indication of its ability to generate cash in the future.

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To fill the entire pool we will 5,073 need gallons of water.

Volume, which is measured in cubic units, is the 3-dimensional space occupied by matter or encircled by a surface. The cubic meter (m3), a derived unit, is the SI unit of volume. Volume is another word for capacity.

Given, A family is filling up a circular pool. The pool has a depth of 6 feet and a diameter of 12 feet.

From the general formula of the volume of a cylinder,

Volume = pi * radius² * height

In our case,

radius = 12/2 = 6

Height = 6

Thus, Volume = 3.14 * 6 * 6 *6

The volume of the Pool = 678.24 Cubic foot

Since there are 7.48 gallons of water in a cubic foot

Thus,

The volume of the pool in gallons = 678.24 * 7.48

The volume of the pool in gallons = 5,073.23

Therefore, to fill the entire pool we will 5,073 need gallons of water.

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Answer:

5,073 gallons, the first person to answer was correct.

Step-by-step explanation:

I took the quiz so you don't have to! <3

The factored form of 9a² - b² - 4c² + 4bc is

(3a + b - 2c) (3a - b + 2c)

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

9a² - b² - 4c² + 4bc

9a² - (b² + 4c² - 4bc)

Now,

(b² + 4c² - 4bc)

This can be written as,

= (b² - 4bc + 4c²)

= (b - 2c)²

Now,

9a² - (b - 2c)²

(3a)² - (b - 2c)²

This is in the form of a² - b².

a² - b² = (a + b) (a - b)

So,

(3a + b - 2c) (3a - b + 2c)

Thus,

(3a + b - 2c) (3a - b + 2c) is the factored form.

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Answer: ℎ(())=(ℎ()),∀∈

Step-by-step explanation:

If 

=()=1,…,,∈ℂA=(ai)i=1,…,n,ai∈C,

then 

∗=(∗)=1,…,A∗=(ai∗)i=1,…,n,

where ∗ai∗ is the complex conjugate of  respectively.

In a slightly more general setting than the functional analytic one (using inner product spaces or linear conjugate functions with alternate scale multiplication defined by multiplication by scale complex conjugate) where, 

∈A∈V for some topological space, two maps :→f:V→V and :→g:V→V are (topologically) conjugate if ∃∃ a homeomorphism ℎh, such that; ℎ(())=(ℎ()),∀∈.

The complex conjugate of a vector "a" can be represented as the conjugate transpose of the vector "a".

What is the eigenvalue and eigenvector?

Geometrically, an eigenvector, corresponding to a real nonzero eigenvalue, points in a direction in which it is stretched by the transformation, and the eigenvalue is the factor by which it is stretched.

A conjugate of a complex number is another complex number that has the same real part as the original complex number and the imaginary part has the same magnitude but opposite sign.

If we multiply a complex number with its conjugate, we get a real number.

The complex conjugate of a vector "a" can be represented as the conjugate transpose of the vector "a".

The conjugate transpose of a vector "a" is denoted as "a*".

The complex conjugate of a vector is important in the field of linear algebra, particularly in the study of eigenvalues and eigenvectors.

Hence,  The complex conjugate of a vector "a" can be represented as the conjugate transpose of the vector "a".

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If the  town wishes to enclose a plot of land with posts and the If the posts are spread 1m apart, there will be 150 posts too few. The number of  posts the town have is:  260 posts.

Let x represent  the number of posts the town

If the posts are spread 1m apart, there will be x - 150 too few posts.

If the posts are spread 3m apart, there will be x - 70 too many posts.

Since the distance between posts is directly proportional to the number of posts.,

Let set up a proportion:

(1) / (x - 150) = (3) / (x - 70)

Cross multiplying:

(1) * (x - 70) = (3) * (x - 150)

Expand

x - 70 = 3x - 450

Solving for x:

2x = 520

Divide both side by 2x

x = 520/2

x = 260

Therefore the town has 260 posts.

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Answer:

1 because,

(2*4+82-18)/8*9

(8+82-18)/72

(90-18)/72

72/72

1

Answer:

Step-by-step explanation:

2 x 4 + 82 - 18 / 8 x 9

We want to use the PEMDAS rule for working math problems with more than one operation.

P = Parentheses first

E = Exponents second

M/D = Multiplication and division third

A/S= Addition and subtraction last

There are no parentheses, so we look for exponents next and there are none.

The next operations are multiplication and division.

Step 1

2 x 4 = 8

8 + 82 - 18 / 8 x 9

Step 2

8 x 9 = 72

Step 3

8 + 82 - 18 / 72

Before we can divide by 72, we need to add and subtract the top numbers from left to right.

Step 4

8 + 82 - 18 = 72

72/72

Now divide 72 by 72

Step 5

72/72 = 1

Answer:

9

Step-by-step explanation:

To find out, we use the formula for direct variation:

A = kwh

Where A is the area, k is the constant of proportionality, w is the width, and h is the height.

From the information given, we can find k:

6 = k (4)(3)

6 = 12k

k = 0.5

So, the area when width is 6 and height is 4 is:

A = kwh = 0.5 (6)(4) = 9

Answer:

Step-by-step explanation:

The number of arrangements for the world's societies is vast and ever-changing, making sociology a fascinating and dynamic field to study.

Sociology is the arrangement of the world's societies into different forms. The arrangement of societies can be looked at in many different ways, and there is no one right answer.

However, the most commonly recognized arrangement of the world's societies is based on their level of economic development, cultural differences, and political structures.

These arrangements can be divided into five categories: hunting and gathering, pastoral, agricultural, industrial, and post-industrial.

Each category represents a different stage of societal development and is characterized by specific cultural, economic, and political features.

Furthermore, the arrangement of societies is not just based on a single factor but is instead influenced by a complex interplay of economic, political, and cultural factors.

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The volume of the solid can be found by using the general slicing method which involves slicing the solid into multiple thin slices, computing the volume of each slice.

The general slicing method can be used to find the volume of the solid with a semicircular base of radius 9 whose cross section is a triangle. This method involves slicing the solid into multiple thin slices, computing the volume of each slice, and then summing up the volumes of all the slices. To find the volume of each slice, we first need to determine the area of the cross-section for each slice. The area of the cross-section can be found by multiplying the base of the triangle by its height. For each slice, the base of the triangle is equal to 2πr/N, where r is the radius of the semicircle and N is the number of slices. The height of the triangle is equal to the thickness of each slice. Once the area of the cross-section is calculated, we can find the volume of each slice by multiplying the area by the thickness of the slice. Finally, the volume of the solid is equal to the sum of the volumes of all the slices.

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The length of the diameter of a circle with endpoints at points (-2, 87) and (18, 91) is  20.4 units

The length of line in an ordered pair is calculated using the formula

d = √{(x₂ - x₁)² + (y₂ - y₁)²}

where

d = distance between the points

x₂ and x₁ = points in x coordinates

y₂ and y₁ = points in y coordinates

distance between points  (-2, 87) and (18, 91) is calculated as follows

d = √{(x₂ - x₁)² + (y₂ - y₁)²}

d =√{(-2 - 18)² + (87 - 91)²}

d =√{400 + 16}

d = √416

d = 20.4 units

The diameter has length 20.4 units

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The error's absolute value is multiplied by its percentage, which is 100%, and then it is divided by the accepted value.%Error=|experimental value|accepted value|accepted value%

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The radical of the quotient is the product of the radicals of the numerator and denominator.

A product's radical equals the sum of the radicals of each factor, according to this statement. "The quotient of the radicals of the numerator and denominator is the radical of the quotient."

The power of the base serves as the numerator of the fractional exponent represented by a radical, while the radical's index serves as the denominator. A product's nth root is the sum of the nth roots of all its components. You must have the same indices.

We can rewrite radical expressions by applying the first factor of the expression that is under the root, creating perfect power, for instance, by using the exponentiation properties. Alternately, we may apply the property of products of powers, then evaluate after exponentiating. To simplify an equation, we can also use the Quotient of Powers Property.

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The determinant of the matrix D obtained by adding 4 times the third row to the second row of the 5x5 matrix A is 24.

Waht is the matrix?

A matrix is a rectangular array of numbers, symbols, or expressions arranged in rows and columns. In mathematics, matrices are used to represent and manipulate linear transformations, such as rotations, scalings, and shears, in a vector space.

The determinant of a matrix is a scalar value that represents the magnitude of the matrix and the change it induces in a vector space. The determinant of a matrix is a linear function of the rows or columns of the matrix, meaning that adding a multiple of one row (or column) to another row (or column) will multiply the determinant by the same scalar.

In this case, if we add 4 times the third row to the second row of the 5x5 matrix A, the determinant of the resulting matrix D will be multiplied by the scalar 4:

det(D) = 4 * det(A) = 4 * 6 = 24

Hence, the determinant of the matrix D obtained by adding 4 times the third row to the second row of the 5x5 matrix A is 24.

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It is true that every decimal with a thousandths place digit may always be expressed as a fraction with a denominator that is divisible by both 2 and 5.

Integer and non-integer numbers are often expressed using the decimal numeral system. The Hindu-Arabic numeral system has been expanded to include non-integer values. Decimal notation is the name for the method used to represent numbers in the decimal system. A decimal is a number with a whole and a fractional component. Decimal numbers, which are in between integers, are used to express the numerical value of full and partially whole amounts.

The claim is that a decimal with a thousandths place digit may be expressed as a fraction with a denominator that is both divisible by 2 and by 5. Currently, a fraction is ending in decimal as if its denominator had terms of the type 2ᵃ, 5ᵇ or 2ᵃ x 5ᵇ.

Then, it is claimed that a digit exists at the thousandth position. It follows that every decimal that ends in a thousandths place digit may always be expressed as a fraction with a denominator that can be divided by both 2 and 5.

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