how many learners how many learners can a school enrol if there are 12 teachers and the ratio of learners to teachers is 30:1 ​

In total, there are 252 ways to choose five members without assigning positions, 5 ways to choose five members with assigned positions, and 56 ways to choose five members with two members assigned to a particular position.

a.) The number of ways that the five team members can be chosen without assigning them positions is 10C5 = 252. This is calculated using the formula for combinations, which is n!/(r!(n-r)!), where n is the total number of members and r is the number to choose. In this case, n=10 and r=5, so 10!/(5!(10-5)!) = 252.

b.) The number of ways that the five team members can be chosen with assigned positions is 5!. This is because there are five positions, and each team member must occupy one of the positions. The order of the positions is irrelevant, so there is only one possible combination.

c.) The number of ways that the five team members can be chosen with the two members assigned to position five is 8C5 = 56. This is calculated using the same formula as in part a, but with n=8 since two members are already assigned to position five. 8!/(5!(8-5)!) = 56.

In total, there are 252 ways to choose five members without assigning positions, 5 ways to choose five members with assigned positions, and 56 ways to choose five members with two members assigned to a particular position.

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For a 35 number of pages, the price would be equal. & it would cost $82.

An equation is a  mathematical statement that is made up of two expressions connected by an equal sign.  In its simplest form in algebra, the definition of an equation is a mathematical statement that shows that two mathematical expressions are equal. For instance, 3x + 5 = 14 is an equation, in which 3x + 5 and 14 are two expressions separated by an 'equal' sign.

here, we have,

An online scrapbooking company charges $12 for a basic book and $2 per page.

Meanwhile, a family friend is willing to make a scrapbook for $47 plus $1 per page.

let, the number of page = x, the price would be equal.

so, we get,

12 + 2x = 47+x

i.e. x = 35

Hence, For a 35 number of pages, the price would be equal. & it would cost $82.

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The probability of drawing a heart as the first card is 1/52.

The probability of drawing a jack as the second card given that the first card is a heart is 4/51 (since there are 4 jacks and 51 remaining cards after one heart is drawn). The probability of rolling the same number twice with a fair six-sided die is 1/6. The total probability is (1/52) * (4/51) * (1/6) = 1/1098.

Assume that there are a finite number of elementary events that are all equally likely to occur in the sample space of the experiment under consideration.

Where total cases equal the extent of the sample space, and favorable instances are those elementary occurrences that belong to E.

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The statement which best describes the function is The function is negative when x < 0, the correct option is B.

All the points (and only those points) which lie on the graph of the function satisfy its equation.

Thus, if a point lies on the graph of a function, then it must also satisfy the function.

Given;

The graph of the function

Now

We can say that the graph is negative when x<0

The function is never negative is false

The function is negative when x > 0 false

The function is negative when x < 0 and when x > 0 false

Therefore, the function will be negative when x<0.

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A moving average is used to smooth the option  2) seasonal variation .

Therefore, a moving average which is used to smooth the seasonal variation.

The above question is incomplete , the complete question is:

A moving average can be used to smooth which of the following options?

1) cyclical variation                  2) seasonal variation

3) irregular variation               4) all responses are correct

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Complementary Angles :  ( ∠1 , ∠5 )  , ( ∠2 , ∠6 ) , ( ∠3 , ∠7 ) , ( ∠4 , ∠8 )

Supplementary Angles : ( ∠1 , ∠2 ) , ( ∠2 , ∠4 ) , ( ∠3 , ∠4 ) , ( ∠1 , ∠3 )

Congruent Angles : ( ∠1 , ∠5 )  , ( ∠2 , ∠6 ) , ( ∠3 , ∠7 ) , ( ∠4 , ∠8 )

Straight, equally spaced lines that never cross each other and are on the same plane are called parallel lines. The angles that are created when any two parallel lines are intersected by a line (referred to as the transversal) have a relationship. Corresponding angles, Alternate Interior Angles, Alternate Exterior Angles, and Consecutive Interior Angles are some of the several pairs of angles that are created at this intersection.

Corresponding angles

When two parallel lines are intersected by a transversal, the corresponding angles have the same relative position

Alternate Interior Angles

Alternate interior angles are formed on the inside of two parallel lines which are intersected by a transversal.

Alternate Exterior Angles

The pairs of angles formed on either side of a transversal that divides two parallel lines are known as alternate exterior angles.

Consecutive Interior Angles

When two parallel lines are cut by a transversal, the pairs of angles formed on the inside of one side of the transversal are called consecutive interior angles or co-interior angles.

Given data ,

Let the parallel lines be represented as m and n

Now , the lines m and n are cut by the transversal line t

So , the angles are

The corresponding angles are ( ∠1 , ∠5 )  , ( ∠2 , ∠6 ) , ( ∠3 , ∠7 ) , ( ∠4 , ∠8 )

The supplementary angles are having a sum = 180°

The supplementary angles are angles in a straight line

So , ( ∠1 , ∠2 ) , ( ∠2 , ∠4 ) , ( ∠3 , ∠4 ) , ( ∠1 , ∠3 ) are supplementary angles

And , ( ∠5 , ∠6 ) , ( ∠6 , ∠8 ) , ( ∠7 , ∠8 ) , ( ∠5 , ∠7 ) are supplementary angles

The congruent angles are having the same measure

So , corresponding angles and alternate interior angles are also congruent angles

Hence , the angles are solved

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When using the elimination method to solve, what would be a possible first step in the process is to write the equations in standard forms.

The elimination method is a method used in  solving a pair of simultaneous linear equations  by reducing one equation to one that has only a single variable.

This method is called the Gaussian elimination method.

The steps in the Gaussian elimination method are;

Hence, the step is writing the equations in standard forms.

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The first step in solving this equation by using elimination is to multiply

(4x – 2y = -4) *2

(2x + y = 4)*4

8x – 4y = -8

8x + 4y = 16

The solution to the system of equation is (4, 1).

System of equation can be solved using different method such as elimination method, substitution method and graphical method. Therefore, the system of equations have been solved using graphical method.

Therefore, the point where the lines or graph intersect is the solution of the system of equation.

Hence, let's find the coordinates where the lines intersect as follows:

The lines intersect at (4, 1)

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From 1976 until 1987, red M&Ms were removed from packets owing to a research associating the food dye used to color them to cancer.

Arithmetic is defined as working with numbers through addition, subtraction, multiplication, and division. Adding two and two to produce four is an example of arithmetic. Arithmetic is a fundamental branch of mathematics that studies the characteristics of classical operations on numbers such as addition, subtraction, multiplication, division, exponentiation, and root extraction. Arithmetic (derived from the Greek word arithmos, "number") relates to the fundamental components of number theory, arts of mensuration (measuring), and numerical computing (that is, the processes of addition, subtraction, multiplication, division, raising to powers, and extraction of roots).

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The multiplication and division of the numbers 2 and 2 will be 4 and 1, respectively.

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.

The numbers are given below.

6/3 and 2

2 and 2

Then the multiplication of the numbers 2 and 2 is given as,

⇒ 2 x 2

⇒ 4

Then the division of the numbers 2 and 2 is given as,

⇒ 2 / 2

⇒ 1

The multiplication and division of the numbers 2 and 2 will be 4 and 1, respectively.

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The largest possible number of red socks in the drawer that is consistent with this data is 990.

Let r be the number of socks that are red, and t be the total number of socks. We get:

2(r(r-1)+(t − r)(t − r − 1)) = t(t − 1)

Expanding the left hand side and the right hand side,

we get: 4r²-4rt+2t²- 2t = t²- t

And, moving terms, we will get that:

47r²-4rt + t² = t

We notice that the left side is a perfect square.

(2r-t)² = t

Thus t is a perfect square. And, the higher t is, the higher r will be. So, we should set t =44²= 1936

And, we see, 2r- 1936 (+-)44

We will use the positive root, to get that 2r -1936 = 44, 2r =1980, and r = 990

Thoughts about probability began with a question from a French nobleman named Chevalier de Mere to Pascal (1623-1662). He wants to know how the pattern of distributing betting money in a gambling game is if the game has to be stopped before it is finished. This question then became the subject of discussion between Pascal and Fermat (1601-1665), based on this discussion came the theory of probability.

Although the basics of probability initially appeared to explain problems in gambling, in its development, the concept of probability can be applied to various problems such as social problems, engineering, health, biology, industry, transportation, management, accounting, education etc.

Probability is the amount of chance (likely) that an event will occur. The amount of opportunity can be written in the form of a decimal number, fraction or percent.

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A polynomial that represents the area of the soccer field is 40x² + 240x + 200

What is polynomial?

A polynomial is an expression consisting of variables (also called indeterminates) and coefficients, that involves only the operations of addition, subtraction, multiplication, and non-negative integer exponentiation of variables.

The area (A) of the rectangular pitch is calculated as

A = lb ( l is the length and b the breadth )

  = (10x + 10)(4x + 20)

Each term in the second factor is multiplied by each term in the first factor, that is

10x(4x + 20) + 10(4x + 20) ← distribute both parenthesis

= 40x² + 200x + 40x + 200 ← collect like terms, thus

A = 40x² + 240x + 200 ← in standard form

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True, If the zero vector is a solution of the system , then the system is homogeneous.

A system of linear equations is considered homogeneous if the zero vector (i.e., the vector with all components equal to 0) is a solution. This means that the system of equations only has the trivial solution of all variables equal to zero, but no non-trivial solutions.

A homogeneous system of linear equations is a system where all the equations have the same form and all the coefficients are proportional to each other. This means that if one equation is multiplied by a constant, the same constant must be multiplied by all the other equations in the system to maintain the homogeneous property.

The zero vector is a solution of a homogeneous system because if all the variables are equal to zero, all the coefficients in the equations are also equal to zero and the equations are satisfied. This is why the presence of the zero vector as a solution is a defining characteristic of homogeneous systems.

In contrast, a non-homogeneous system is a system where the zero vector is not a solution and there are both trivial (zero) and non-trivial (non-zero) solutions. Non-homogeneous systems are solved using different methods compared to homogeneous systems.

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The standard deviation of assembly time (in minutes) is approximately .33.

The standard deviation of a uniform distribution of assembly time is calculated using the following formula:

σ = √((b-a)^2 / 12),

where a is the lower boundary of the range of assembly time (6 minutes) and b is the upper boundary of the range of assembly time (10 minutes).

Substituting a = 6 and b = 10 into the formula yields:

σ = √((10-6)^2 / 12)

σ = √(16/12)

σ = √(1.33)

σ = .33

Therefore, the standard deviation of assembly time (in minutes) is approximately .33.

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Option A is a correct representation of the graph of the function,

g(x) = -1/3f(x).

When two parallel lines intersect, a two-dimensional coordinate plane called the cartesian plane is created. The horizontal line is the X-axis, while the vertical line is the Y-axis. If the sign of x is positive, the coordinate point (x, y) in the Cartesian plane indicates that the point is on the right of the origin; otherwise, it indicates that the position is on the left of the origin.

Given the graph of the function,

f(x) is the shape of a parabola so the graph is of a quadratic function.

and given g(x) = -1/3f(x)

graph of f(x) is on coordinates (0, 0), (1, 1), and (-1, 1)

so the function is f(x) = x²

so g(x) should lie in coordinates (0, 0), (1/3, -1/3), and (-1/3, -1/3)

the shape of g(x) will be the same as f(x), but due to the negative sign, the shape will be in opposite quadrants.

and g(x) is 1/3 time f(x) so the shape will evolve more as compared to g(x),

so the graph of Option A only follows the required condition.

Hence option A is correct.

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The car will spend 18 minutes to cover 18 km.

Proportions are defined as the concept where two or more ratios are set to be equal to each other.

Suppose we have two ratio p : q and r : s. If both these ratios are proportional, then we can write it as p : q = r : s or p/q = r/s

Given that,

Time taken to travel 105 km = 1 hr 45 min = 60 min + 45 min = 105 minutes

Time taken to travel 18 km = x

Using the concept of proportion,

105 / 105 = 18 / x

Cross multiplying,

105 x = 18 × 105

x = 18

Hence the time taken to travel 18 km is 18 minutes.

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Suppose the detector will sound the alarm if more than 2 milligrams of the dye are in your system. It will take 56 minutes for the visit of the doctor

The amount of radioactive dye remaining in your system after t minutes can be modeled as:

A(t) = 11 * (1/2)^(t/20)

where A(t) is the amount of dye remaining after t minutes. We want to find the time t when A(t) = 2 milligrams.

A(t) = 11 * (1/2)^(t/20) = 2

Solving for t:

(1/2)^(t/20) = 2/11

Taking the natural logarithm of both sides:

(t/20) = ln(2/11) / ln(1/2)

Multiplying both sides by 20:

t = 20 * ln(2/11) / ln(1/2)

Using a calculator or logarithm tables, we can estimate t to be approximately 56 minutes. So, your visit to the doctor would take about 56 minutes.

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The triangle JLK is transformed to J''K''L'' by a rotation of 90° anticlockwise and a translation of -2 units

The measure of the amount a figure is rotated about the center of rotation is called the angle of rotation. The angle of rotation is usually measured in degrees. We specify the degree measure and direction of a rotation.

90° clockwise rotation: (x,y) becomes (y,-x)

90° counterclockwise rotation: (x,y) becomes (-y,x)

180° clockwise and counterclockwise rotation: (x, y) becomes (-x,-y)

270° clockwise rotation: (x,y) becomes (-y,x)

270° counterclockwise rotation: (x,y) becomes (y,-x)

Given data ,

Let the triangle be represented as ΔJKL

Now , the coordinates of the triangle JKL is

J ( 2 , -4 ) , K ( 5 , -4 ) and L ( 2 , -2 )

And , the transformed triangle be represented as Δ J''K''L

Now , the coordinates of the triangle J''K''L'' is

J'' ( 2 , 2 ) , K'' ( 2 , 5 ) and L'' ( 0 , 2 )

The triangle JKL is first rotated by an angle of 90° counterclockwise rotation: (x,y) becomes (-y,x) to form J'K'L'

So , substituting the values in the equation , we get

The coordinates of the triangle J'K'L' is

J' ( 4 , 2 ) , K' ( 4 , 5 ) and L' ( 2 , 2 )

Now , when the triangle is translated -2 units to up , we get

So , the coordinates of the triangle J''K''L'' is

J'' ( 2 , 2 ) , K'' ( 2 , 5 ) and L'' ( 0 , 2 )

Hence , the transformed triangle is going through a rotation of 90° counterclockwise and a translation of -2 units

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Answer:

Either

90 degree rotation about point 0 composition translation of 0 units x, negative 2 units y

or

90 degree rotation about point 0 composition translation of negative 2 units x, 0 units y

Step-by-step explanation:

The answer above is correct.

Answer:

The next number in the sequence is 17/15.

Step-by-step explanation:

From the graph of the system of equations y = 3x - 8 and 6x - 2y = 10, there is no solution

An equation is an expression that uses mathematical operations to show the relationship between numbers and variables. Types of equations are linear, quadratic, cubic and so on.

The standard form of a linear equation is:

Ax + By = C

Where A, B and C are constants

The slope intercept form of a linear equation is:

y = mx + b

Where m is the slope and b is the y intercept

The slope of the line passing through points (x₁, y₁) and (x₂, y₂) is:

m = (y₂ - y₁) / (x₂ - x₁)

Given the system of equations:

y = 3x - 8        (1)

and:

6x - 2y = 10     (2)

From the graph of the equations, there is no solution

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Answer: The last one; is the one closest to the keyboard.

Step-by-step explanation: Its D because after I looked at the range, I looked at the median, which is 22, and D is the only one that had that as its median. I hope this helped!

a) The proportion of the population that is less than 18 is 0.3085.

b) The probability that a randomly chosen value is greater than 25 is 15.39%, which is not equal to 2.6667 as stated in the question.

a) To find the z-score corresponding to the value of 18, we can use the standard normal formula:

z = (18 - mu) / sigma

Where mu is the mean and sigma is the standard deviation of the population.

To find the proportion of the population that is less than 18, we can use the cumulative distribution function (CDF) of the standard normal distribution.

The CDF gives us the proportion of the population that is less than a given value.

For a standard normal distribution, we can use a standard normal table or a calculator to find the CDF.

Using the standard normal table, or a standard normal calculator,

we find that the CDF of the standard normal distribution at z = -0.6309 is 0.3085.

So, the proportion of the population that is less than 18 is 0.3085.

b) To find the z-score corresponding to the value of 25, we can use the standard normal formula:

z = (25 - mu) / sigma

Using a standard normal calculator or table,

we find that the z-score for 25 is 1.0538.

The proportion of the population that is greater than 25 is 1 - the CDF of the standard normal distribution at z = 1.0538.

Using a standard normal calculator or table, we find that the CDF of the standard normal distribution at z = 1.0538 is 0.8461.

So, the proportion of the population that is greater than 25 is 1 - 0.8461 = 0.1539.

To find the probability that a randomly chosen value is greater than 25, we can multiply 0.1539 by 100% to get 15.39%.

Therefore, the probability that a randomly chosen value is greater than 25 is 15.39%, which is not equal to 2.6667 as stated in the question.

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Refer to the images attached (answers are circled). Let me know if you have any questions.

Step-by-step explanation:

hope you can see the awful green

Answer:

13.14cm

Step-by-step explanation:

lets start by finding the length of AD

90 + 65=155...........180-155= 25

x/sin 25= 7/sin 90

xsin90=7sin 25

x= 2.96cm=AD

Now lets find DC

we shall find DB first;

x/sin65=7/sin90

xsin90=7sin65

x=6.34cm...=DB

Now lets use Pythagoras theorem to find DC

12²-6.34²=√103.80

DC=10.18cm

Add AD and DC

2.96+10.18= 13.14cm

AC=13.14cm

The  height of the pyramid is 6cm

a three dimensional shape can be defined as a solid figure or an object or shape that has three dimensions—length, width, and height.

Given that Six square-based pyramids fit exactly onto the six faces of a cube of side 4 cm.

The volume of the object formed is 256 cm³.

We need to find the  height of each of the pyramids.​

The total volume can be calculated as

Total volume= cube volume+6 one pyramid volume

cube volume=4³=64

pyramid volume=1/3.4²h=16/3h

64+6.16h/3=256

64+32h=256

Subtract 64 on both sides

32h=256-64

32h=192

Divide both sides by 32

h=6

Hence, the  height of the pyramid is 6cm

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The correct answer is option b) Bacteria in samples 2 and 3 mutated quickly to adjust to temperature change.

From the given graph it is seen that sample 1 is not showing any growth or decline despite of the temperature change. One cannot ascertain its gene expression. On the other hand, Sample 2 shows a slight change from 4cm² to 7cm² bacteria count and Sample 3 shows a wide change as per temperature change from 8cm² to 12cm². Hence it can be said that samples 2 and 3 mutated to adjust to the temperature compared to sample 1 which showed no changes.

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Complete Question

the graph below shows the growth of three samples of the different bacteria on Petri dishes incubated over 24 hours as the temperature was increased 10 degrees every eight hours: (Graph in the figure attachment) which statement best explains the data trend observed in the bacteria samples?

a) All bacteria samples grow better at higher temperatures.

b) Bacteria in samples 2 and 3 mutated quickly to adjust to temperature change.

c) Temperature changes do not affect gene expression for growth in sample 1.

d) Bacteria in sample 1 will eventually die out at higher temperatures.

Answer:

[tex]f^{-1}(x)=\sqrt[4]{x}+2 \qquad \textsf{for $x \geq 0$}[/tex]

Step-by-step explanation:

Given function:

[tex]f(x)=(x-2)^4[/tex]

The domain of the given function is restricted:  

Therefore, the range of the given function is also restricted:  

To find the inverse of a function, swap x and y:

[tex]\implies x=(y-2)^4[/tex]

Rearrange the equation to make y the subject:

[tex]\implies \sqrt[4]{x}=y-2[/tex]

[tex]\implies y=\sqrt[4]{x}+2[/tex]

Replace y with f⁻¹(x):

[tex]\implies f^{-1}(x)=\sqrt[4]{x}+2[/tex]

The domain of the inverse of a function is the same as the range of the original function.  Therefore, the domain of the inverse function is restricted to {x : x ≥ 0}.

Therefore, the inverse of the given function is:

[tex]f^{-1}(x)=\sqrt[4]{x}+2 \qquad \textsf{for $x \geq 0$}[/tex]

Let x be the length of the bottom of the triangle. Then, the second side has a length of more than x * k, where k is some number greater than 1. And the third side has a length of more than x.

The perimeter of the triangle can be represented by the expression:

P = x + (x * k) + (x + y), where y is a positive number that represents the difference between the length of the third side and the length of the bottom of the triangle.

Simplifying the expression:

P = x * (1 + k) + (x + y) = x * (k + 1) + y.

This expression represents the perimeter of the triangle in terms of the length of the bottom of the triangle and the unknown values

In a convex hexagon, if the area of the hexagonal region is 2116 (√2 + 1), then the value of AB is 46.

A convex hexagon is a hexagon in which all of the inner angles and all of the vertices have to be smaller than 180 degrees. There are both regular and irregular convex hexagons. Inside a convex hexagon, there are no angles. More specifically, no internal angle will exceed 180 degrees. Any internal angle which exceeds 180 degrees is concave.

Let the side length be x.

So, the diagonal BF = √(AB^2 + A F^2) = √(x^2 + x^2) = x√2.

Then, the areas of the triangles AFB and CDE in total equals (x^2 / 2) * 2, and the area of the rectangle BCEF equals x * x√2 = x^2 √2.

Now, let the equation be:

2116 (√2 + 1) = x^2√2 + x^2

And by simplifying the above equation, we will get:

2116 (√2 + 1) = x^2 (√2 + 1)

2116 = x^2

By taking root both sides, then it will be:

x = 46

Hence, the value of AB is 46.

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Although part of your question is missing, you might be referring to this full question: In a convex hexagon ABCDEF, all six sides are congruent, ∠A and ∠D are right angles. And ∠B, ∠C, ∠E and ∠F are congruent. The area of the hexagonal region is 2116 (√2 + 1). Find AB.

The solution is the given triangles are similar to each other due to S-S-S rule.

A triangle is a polygon with three edges and three vertices. It is one of the basic shapes in geometry. A triangle with vertices A, B, and C is denoted \triangle ABC. In Euclidean geometry, any three points, when non-collinear, determine a unique triangle and simultaneously, a unique plane.

here, we have,

From the given figure we get,

triangle ABC & HIJ

we get,

AC = 2* HI

AB= 2*IJ

BC = 2* HJ

so, the scale factor = 2

Hence, The solution is the given triangles are similar to each other due to S-S-S rule.

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