What stays the same when you perform a rigid motion transformation?

The standard deviation of the given population is 7.72.

What is population?

All of the components of the data set are included in the population, as are parameters like mean and standard deviation that can be used to measure the population. The term "population" denotes the complete group of individuals, things, events, etc.

Given data,

                   53, 36, 36, 44, 31

We know that,

Standard deviation of a population is given by :

= √ [ ∑ ( X - ц )²/N

Where, X = each data point

            ц = mean of data of population

            N = No. of data points in population = 5

We need mean,

So, mean of data of population = (53 + 36 +36 +44 + 31)/5

                                                    = 40.

So, By applying formula :

SD = √ [ ∑ ( X - ц )²/N ]

      = √1 / 5 [ (40-53)² + (40-36)² + (40-36)² + (40-44)² + (40-31)²

      = √ ( 169 + 16 + 16 + 16 + 81 )/5

      = √298/5

      =7.72.

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The multiplicity of a root of a polynomial can be determined by the factorization of the polynomial.

If a root is repeated multiple times, then this root is said to have a higher multiplicity. For example, if a polynomial has the form a(x-r)^2, then the multiplicity of root r is 2. This is because the polynomial can be written as a(x-r)(x-r), and the root r is repeated twice.

To calculate the multiplicity of a root, the polynomial must be factored into its linear factors. The multiplicity of each root is then equal to the power of the corresponding linear factor. For example, if a polynomial is factored into (x-r)^3(x-s), the multiplicity of root r is 3 and the multiplicity of root s is 1.

In general, if a polynomial is written in the form [tex]a*(x-r1)^k1*(x-r2)^k2*...*(x-rn)^kn[/tex], then the multiplicity of root ri is ki. Therefore, the multiplicity of the roots can be calculated by factoring the polynomial and finding the power of the linear factors.

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For x = 5 and y = 3 the given triangles are congruent.

What is congruent triangles?

In any orientation, two triangles are said to be congruent if their three sides and three angles are equal.

Therefore, if two triangles have the same number of sides on each side, they are said to be congruent. Additionally, we can determine that they are congruent if we have a side, an angle between the sides, and then another side that is congruent, in that order: side, angle, side.

Let the given triangles are congruent.

So, their sides are equal.

⇒ x = y + 2         ..(1)

 3y = x + 4         ..(2)

Plug value of x in equation (2)

3y = (y + 2) + 4

3y = y + 6

2y = 6

 y = 3

Plug y = 3 in equation (1)

x = 3 + 2

x = 5

Hence, for x = 5 and y = 3 the given triangles are congruent.

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Answer:

(a) The percentage change is 82.35  . The change is decreasing.

(b) The percentage change is -37.80. The change is decreasing.

Step-by-step explanation:

(a) percentage change- the change between two values in percent is called a percentage change .

formula - final value-initial value /initial value *100

here , 62-34/34*100

since , the value is positive , the value is increasing .

(b) percentage change- the change between two values in percent is called a percentage change .

formula - final value-initial value /initial value *100

here , 22.88-36.79/36.79*100

since , the value is negative , the value is decreasing.

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Answer:

a) 82% Increase

b) -37% decrease

Step-by-step explanation:

a)

Percentage :-

= ((62-34) / 34) * 100

= 82.3529 ≈ 82% ------> increase

b)

Percentage:

= ((22.88-36.79) / 36.79) * 100

= -37.8 ≈ -37% ------> decreased

I hope my answer helps you

Range with three parameters: start, end, step.

Now, According to the question:

What are the 3 loops in Python?

The three types of loop control statements are:

What are the three parameters in range in Python?

The range() function in Python works by taking three inputs as parameters which are start_value, stop_value, and step value. The range() function returns an immutable sequence of numbers starting from the start_value, and increments the values by the value given in the step_value, and stops at the stop_value.

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4x + 8y ≤ -24 is the example of linear inequality in two variables.

Linear equations are one-degree equations. It is a straight-line equation. A linear equation with parameters a and b equal to zero has the conventional form ax + by + c = 0.

The graph of a two-variable inequality is the set of points that describe all solutions to the inequality. The coordinate plane is split in half by a boundary line created by a linear inequality, with one-half representing the solutions to the inequality.

It's a line with a shaded side on one side to show which xy pairings are the inequality's solutions.

For example -

Let us take a equation, 4x + 8y ≤ -24

Now, solve the above equation in the form of slope-intercept.

4x + 8y ≤ -24

or, 8y ≤ - 4x - 24

or, y ≤ -(1/2)x - 3

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Regional economic integration has facilitated trade among neighbors while allowing nations to concentrate on issues pertinent to their stage of development. Four forms of regional economic integration are possible. Zone of unrestricted trade. The most basic form of economic cooperation is this one.

Worldwide integration of the markets. global integration of the economy. On the financial markets, the effects of globalization are being assessed. More than ever, people, companies, and sectors are linked. This facilitates linkages, which encourages specialization, innovation, and economic expansion.

These accords have made it possible for nations to trade successfully with one another today by removing trade and financial restrictions. actions taken to lower prices for consumers in the member countries of the bloc when tariffs are decreased

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Answer:

34 cm

Step-by-step explanation:

the gap in the middle is 2 cm because 9 - ( 4 + 3 ) = 2

4 + 2 + 2 + 3 + 3 + 6 + 9 + 5 = 34

The probability of the influenced voters, if The political scientist randomly surveyed 2509 voters, 709 said the advertisements did influence their vote, is 0.283.

The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true. An event's probability is a value between 0 and 1.

Given:

The political scientist randomly surveyed 2509 voters, n = 2509,

709 said the advertisements did influence their vote, S = 709,

Calculate the probability of influenced voter as shown below,

[tex]Probability = S / n[/tex]

Probability = 709 / 2509

Probability = 0.283

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The number of days when the two companies will have the same number of followers is 380 days.

The first step is to form linear functions that represent the information of the two companies. The form of the functions is:

Total followers = initial number of followers + (number of new followers x number of days)

The linear function that represents the online followers for the first company is:

Total followers = 95,000 + 100d

The linear function that represents the online followers for the second company is: Total followers = 350d

When the companies have the same number of followers the two above equations would be equal 95,000 + 100d = 350d

95,000 = 350d - 100d

95,000 = 250d

d = 95,000 / 250

d = 380

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Answer:

f is negative

(A) Given question can be represented in the system of linear equations as x + y = 360,

      y =3x

(B) 90 tickets were sold on Friday and 270 tickets were sold on Saturday.

There will be only one solution to this question.

(C) We have drawn the graph for the solution.

(D) We have justified our answers by using the substitution method.

What is a linear equation in two variables?

An equation is said to be a linear equation in two variables if it is written in the form of ax + by + c=0, where a, b & c are real numbers and the coefficients of x and y, i.e a and b respectively, are not equal to zero.

Let x number of tickets sold on Friday and y number of tickets sold on Saturday.

By using the given condition,

x + y = 360 ----------(I)

y =3x -------(II)

Put y = 3x in equation (I), we get

x + 3x = 360

4x = 360

  x = 90

Now put x = 90 in equation (I), and we get

90 + y = 360

y = 270

Hence, 90 tickets were sold on Friday and 270 tickets were sold on Saturday.

There will be only one solution to this question.

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transformations and rigid body symmetric transformations. Geometric figures' sizes and shapes are unaltered throughout a stiff transformation (also known as an isometric transformation).

A stiff transformation in mathematics, commonly referred to as a Euclidean transformation or a Euclidean isometric transformation, is a geometric transformation of Euclidean space that keeps the Euclidean distance between each pair of points. Transformations of rigid bodies can take the shape of rotations, translations, reflections, or any combination of these.

transformations and rigid body symmetric transformations. Geometric figures' sizes and shapes are unaltered throughout a stiff transformation (also known as an isometric transformation). a unique kind of metamorphosis when the characters' sizes or shapes are left unaltered.

Area = [tex]\sqrt{s(s - a)(s - b)(s - c) }[/tex]

and, here s = half the perimeter,

[tex](a + b + c)/2.[/tex]

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Answer:

Rounding down to the nearest whole number, we get 5 stories. The correct answer is, therefore (A) the 5th story.

Step-by-step explanation:

To solve this problem, we need to find the number of stories the ladder can reach by dividing the length of the ladder by the height of each story.

The longest ladder on the fire truck reaches 95 feet, and each story is 18 feet high, so the highest story that the ladder can reach is:

95 feet / 18 feet/story = <<95/18=5.28>>5.28 stories

Answer:

-----------------------------------

Hypotenuse of an isosceles triangle is √2 times the leg:

Answer:

D. 12 hours

Step-by-step explanation:

I am guessing that they want you to find the average time together, or the mean.

Add 18 hours and 6 hours together to get 24 hours.

To get the average, you have to divide the total hours by the amount people involved.

Since there are 2 groups (2 people) that have an outcome of 18 hours and 6 hours, 24 hours/2 people is a 12 hour average.

Answer:

Step-by-step explanation: Let x represent the number in the algebraic expression, then 6 less means the following:

x-6

The additive inverse of the number 8 is " -8 "  .

The Inverse (Additive) of the number is defined as the number that is added to a given number to make the sum zero ;

that means : If a number is added to its additive inverse, then the sum of both numbers becomes 0 .

So , that means to find the additive inverse of "8" , we have to find the number such that on adding it to 8 , we get the sum as 0 .

let the additive inverse of 8 be = x ;

So , x + 8 = 0 ;

x = -8 .

So , putting the value in above equation,  8 - 8 = 0 .

Therefore , the additive inverse is "-8" .

The given question is incomplete , the complete question is

What is the additive Inverse of 8 ?

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A geometric sequence with a common ratio of 2 is E . F( n ) = 5 * 2^n where n = 1 , 2 , 3 .

Given :

A. -5 , -3 , -1 , 1 , 3

common ratio r = -3/-5

it is not the option

B . 0.0625 , 0.125 , 0.25 , 0.5 , 1

Common ratio :

r = 0.125 / 0.0625

= 0.5

it is not the option .

C. a[tex]_n[/tex] = 1/2 * [tex]a_{n-1}[/tex] where a1 = 2

a2 = 1/2 * a1

= 2/2

= 1

common ratio = 1/2

it is not the option

D. a[tex]_n[/tex] = [tex]a_{n-1}[/tex] + 2 where a1 = 3

a2 = a1 + 2

= 3 + 2

= 5

common ratio = 5/3

it is not the answer

E. F( n ) = 5 * 2^n where n = 1 , 2 , 3

a1 = 5 * 2^1

= 10

a2 = 5 * 2^2

= 20

common ratio = 20 / 10

r = 2

It is the correct option.

F. f ( n ) = n^2 where n = 1 , 2 , 3

a1 = 1^2

a2 = 2^2

= 4

common ratio = 4/1 = 4

it is not the correct option.

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Full question :

Which of these is, or describes, a geometric sequence with a common ratio of 2? select two answers that are correct.

A. -5 , -3 , -1 , 1 , 3

B . 0.0625 , 0.125 , 0.25 , 0.5 , 1

C. a[tex]_n[/tex] = 1/2 * [tex]a_{n-1}[/tex] where a1 = 2

D. a[tex]_n[/tex] = [tex]a_{n-1}[/tex] + 2 where a1 = 3

E. F( n ) = 5 * 2^n where n = 1 , 2 , 3

F. f ( n ) = n^2 where n = 1 , 2 , 3

The time period is T = √[(4π^2mA^2)/mw^2A^2].

In the given question, we have to calculate this time and hence the period.

By conservation of energy :

1/2*mw^2A^2 = 1/2*mv^2+1/2*mw^2x^2

V^2 = w^2(A^2−x^2)

V = w√(A^2-x^2)

dx/dt = w√(A^2-x^2)

[tex]\frac{dx}{\sqrt{A^2-x^2}}[/tex] = w*dt

[tex]\frac{dx}{A\sqrt{(1-(x/A)^2}}[/tex] =w*dt

put (x/A)^2 = v

dx/A=dv

[tex]\int_{0}^{1} \frac{dv}{\sqrt{1-v^2}} = \int_{t=Io}^{t=t}w\times dt[/tex]

[tex][sin^{-1}(1)-sin^{-1}0]=wt[/tex]

π/2=wt

t= π/2w

[∴w=2π/T]

t= πT/2*2* π

t=T/4

Where T is time period

F = -kx

a = -k/m*x

ma = -kx

a = -w^2x

(standard equation of S.H.H)

w = √(k/m)

T = 2π/w

T = 2π√(m/k)

[k = mw^2]

T = √[(4π^2mA^2)/mw^2A^2]

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The elements in sets are separated by commas so they can be read easily.

Instead of describing the constituents of a set, a set-builder notation describes them. The elements are listed, for instance, in the set {5, 6, 7, 8, 9}. We interpret the collection of all x such that x is a counting number between 4 and 10 as the collection of all x.

In mathematics, a set is a logically arranged group of items that can be represented in either set-builder or roster form. Sets are typically denoted by curly brackets {}; for instance, A = {1, 2, 3, 4} is a set.

The sequence of elements (separated by commas) between the curly braces " and "in mathematics form an unordered group of elements known as a set. For instance, the domesticated animals {cat, cow, dog} , the odd numbers {1, 3, 5, 7, 9} and the alphabets {a, b, c, d, e} are all sets. So they can be read or interpreted easily.

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To find the height of an isosceles triangle, we square the length of one of the equal sides and subtract the square of half the base, and the area can be easily calculated if the height  and the base are known. Multiplying the height with the base and dividing it by 2, results in the area of the isosceles triangle.

isosceles triangle

an isosceles triangle is a triangle that has two sides of equal length. Sometimes it is specified as having exactly two sides of equal length, and sometimes as having at least two sides of equal length.

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Answer:

Below

Step-by-step explanation:

Picture  is     .12   x  .08  m

    2 m / .08 m = 25

    2.4 m / .12 m = 20    <===== limiting factor   ( 20 is less than 25)

      so it would be   20 * (.12)      X      20(.08)   =  3.84 m^2

There are 333 numbers less than 1000 that are divisible by 3.

To find this, you can divide 1000 by 3 to get 333 with a remainder of 1. Since the numbers less than 1000 that are divisible by 3 do not include 1000, you subtract 1 from 333 to get 332. However, 0 is also divisible by 3, so you should add 1 to 332 to get 333 as the final answer.

When a number divides evenly (i.e., leaves no residue), it is said to be divisible. For instance, since 2 can be divided by 34 equally, 34 may be divided by 2. 34 is not divisible by 3 since doing so would leave us with a remainder.

A whole number is said to be divisible by three according to the three-digit rule of division if the sum of all of its digits is precisely divided by three. Without actually doing division, it is possible to establish whether a number may be divided by three.

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Answer:

x = 8

Step-by-step explanation:

In a triangle, if two angles are congruent, then the opposite sides are congruent.

Since you are told that angles A and C are congruent, then their opposite sides, BC and AB are congruent.

That makes BC = AB.

3x - 3 = 2x + 5

x = 8

Answer:

a. $660

b. $3660

Step-by-step explanation:

a. 1.1% = 1 years

   22% = 20 years

22% = 0.22

Take 3000 times 0.22 = $660

So, they will earn $660 interest in 20 years

b. $3000 + $660 = $3660

$3660 is their account balance after 20 years

The sample space of rolling a 6 sided number cube is the set of all possible outcomes of rolling the number cube. The sample space for a 6 sided number cube is the set of numbers 1,2,3,4,5, and 6.

When rolling a 6 sided number cube, the sample space is the set of all possible outcomes, which are the numbers from 1 to 6. This means that the sample space includes each of the six numbers, with no bias towards any particular number. Each of the six numbers has an equal chance of being obtained when rolling the number cube.

The sample space of a 6 sided number cube is also known as a discrete sample space, since all of the possible outcomes are predetermined and known. The sample space of a 6 sided number cube is finite and can be easily calculated by listing all the possible outcomes. Since there are 6 possible outcomes, the sample space consists of 6 elements.

The sample space of a 6 sided number cube can be easily visualized by imagining a six-sided die being rolled and each side being labeled with a number from 1 to 6. This demonstrates that the sample space of a 6 sided number cube is a discrete sample space, and each of the six numbers has an equal chance of being obtained.

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1/2+9/10+m+n=2 is true when m and n have values { (m, n) : m = 3/5 - n, ∀ n and m ∈ R }.

What is number?

An arithmetic value known as a number is used to calculate and represent a quantity.

Given, 1/2+9/10+m+n=2

m+ n = 2 - 1/2 - 9/10

m+ n = 3/5

m = 3/5 - n

So, If n= 0, m = 3/5

Hence, we can define as { (m, n) : m = 3/5 - n, ∀ n and m ∈ R }

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Answer:

one solution because when you isolate the x terms:

2x-3x=0 and you combine like terms

-x=0

and divide by negitive one because -x is (-1)(x)

you get x=0

Step-by-step explanation:

Answer:

One solution

Step-by-step explanation:

It appears this problem has no solution, buttt let's look closer.

2x and 3x are like terms, meaning they can be added and subtracted because they both have x!

So let's combine these like terms and see what we get...

2x = 3x

0 = 3x -2x

0 = 1x

x = 0 / 1

x = 0

The only solution is 0! No other number is possible.

As per the rational root theorem, the actual root of the polynomial is  - 5/2

The term polynomial refers the algebraic expression in which the exponents of all variables should be a whole number

Here we have given that  f(x) = 6x⁴ + 5x³ – 33x² – 12x + 20.  and we need to find which is an actual root of f(x).

In order to find the root for the polynomial we have to apply each value as the replacement of x in the polynomial.

And then we have to find in which one makes the polynomial result as zero.

First we have to take the value of x as -5/2, then the polynomial equation be like,

Here we have to substitute x=-5/2, then we get

=> f(-5/2) = 6(-5/2)⁴ + 5(-5/2)³ - 33(-5/2)² - 12(-5/2) + 20

=> f(-5/2) = 6(625/16)-5(125/8)-33(25/4)+30+20

when we simplify this one then we get,

=> f(-5/2)=(1,875-625-1,650+400)/8

=>  f(-5/2)=0/8

Here we know that if we zero by any number we get the result as zero.

Therefore, f(-5/2)=0 then x=-5/2 is a root of f(x)

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Answer:

its A

Step-by-step explanation:

Just took the test