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Therefore , the solution of trigonometry function comes out to be tan x tan(4x+18)

When it comes to trigonometry, the relationship between the rectangular line segment and The field is believed to have originated in the 1770s, most likely beginning in the third century through the fusion of astrophysics and mathematical sciences. Numerous mathematical equations and their possible uses in calculations are covered by precise mathematical techniques. The basis of trigonometry are the six basic trigonometric operations.

Here,

tan x tan 4x=1

cos 4X cos X - sin 4x sin x=0

cos 5x=0

5x=(n+1/2)π,n ∈ Z

x=(2n+1)/10 π,0 <x <π

π/10, 3π/10, 5π/10, 7π/10,9π/10 (5π/10 is not possible)

Thus, there are only four solutions.

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The area of a polygon with the given vertices is calculated by adding the areas of the individual triangles that make up the polygon.

A polygon is a closed figure in a plane consisting of a set of straight line segments connected end-to-end. The sides of a polygon are all of equal length, and the angles between them are all of equal measure. Polygons are one of the most fundamental shapes in geometry. They include triangles, squares, rectangles, hexagons, and many more.

The area of triangle WXZ is calculated as (1/2) × |XW × ZY|,

where XW is the vector from W to X and ZY is the vector from Z to Y.

In this example,

XW = (3, -2) and ZY = (-2, -4).

Therefore, the area of triangle

WXZ is (1/2) ×|(3, -2) × (-2, -4)| = (1/2) × 14 = 7.

The area of triangle XYA is calculated similarly,

where XY = (2, 3) and YA = (-2, -4).

Therefore, the area of triangle

XYA is (1/2) ×|(2, 3) ×(-2, -4)| = (1/2)× (-14) = -7.

The area of the polygon is calculated by adding the areas of the individual triangles, which in this example is 7 + (-7) = 0. Therefore, the area of the polygon with the given vertices is 0.

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The equation to model the given situation is 120 - 4.5t= 75 and the solution to the equation is 10 minutes.

An equation is a mathematical statement that is made up of two expressions connected by an equal sign. For example, 3x – 5 = 16 is an equation.

The balloon will reach an altitude of 75 meters above the ground.

Now, 120-75 =45 meters

Let t be the time to descends 45 meters

So, 120 - 4.5t= 75

= -4.5 t = 75-120

= -4.5t = -45

= t = -45/(-4.5)

= t = 10 minutes

Hence, the equation to model the given situation is 120 - 4.5t= 75 and the solution to the equation is 10 minutes.

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The correct order of match is 1-a, 2-b, 3-d and 4-c.

The term "conic" refers to a curve formed by the intersection of a right circular cone with a plane. In Euclidean geometry, it has distinctive features. The cone is split into two nappes, the upper nappe and the lower nappe, at its vertex.

A plane crosses the cone, and the resulting section is referred to as a conic section.

Given the equations,

the equation for parabola is given by

(y - b)² = 4p(x - a)

Vertex is (a,b)

equation 2 follows the same

x = -2(y - 4)² + 3

this is the equation for parabola.

Equation for ellipse is

(x − a)²/h² + (y − b)²/k² = 1

the equation x²/4 + (y - 8)²/144 = 1

(x/2)² + ((y - 8)/12)² = 1

the equation is same is equation for ellipse,

Equation for circle

(x - h)² + (y - k)² = r²

fourth equation

(x - 9)² + (y + 2)² = 7²

is same as equation of circle

Equation for hyperbola

(x − a)²/h² − (y − b)²/k²  = 1

equation (x - 3)²/5 - (y + 4)²/25 = 1

is same as equation of hyperbola.

Hence the correct order is a, b, d, and c.

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Answer:

Regular megagon

Step-by-step explanation:

Regular megagon is a shape called with 1000000000 sides.

The confidence interval is (22.68,29.52).

In statistics, a confidence interval describes the likelihood that a population parameter would fall between a set of values for a given percentage of the time. Confidence ranges that include 95% or 99% of anticipated observations are frequently used by analysts. Therefore, it can be concluded that there is a 95% probability that the true value falls within that range if a point estimate of 10.00 is produced using a statistical model with a 95% confidence interval of 9.50 - 10.50.

n = 10

x = 26.1

s = 4.2

Two-sided confidence interval :

CI = [tex](x-\frac{z*s}{\sqrt{n}},x+\frac{z*s}{\sqrt{n} } )[/tex]

    = [tex](26.1-\frac{2.576*4.2}{\sqrt{10}},26.1+\frac{2.576*4.2}{\sqrt{10}} )[/tex]

    = (26.1−3.42,26.1+3.42)

    = (22.68,29.52)

Hence, the confidence interval is (22.68,29.52).

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The probability that all three are female is  0.281

2030⋅1929⋅18282030⋅1929⋅1828 = 0.281

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Answer: get yio colors straightv

Step-by-step explanation:

If the circle's center is in one of the foci, the inverse of the hyperbola is a Limaçon with an inner loop.

A hyperbola is a particular kind of smooth curve that lies in a plane and is classified by its geometric characteristics or by equations for which it is the solution set.

A hyperbola is made up of two mirror images of one another that resemble two infinite bows.

These two sections are known as connected components or branches.

The hyperbola's equation is expressed as (y−k)2b2−(x−h)2a2=1.

The transverse axis is defined by b, the conjugate axis by a, and the center is defined by (h,k).

The section of a line that a hyperbola's vertices form.

The inverse of the hyperbola is a Limaçon with an inner loop if the circle's center is in one of the foci.

Therefore, if the circle's center is in one of the foci, the inverse of the hyperbola is a Limaçon with an inner loop.

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Therefore , the solution of the given problem of algorithm comes out to be incomputable. is another word for undecidable.

A calculation or problem-solving procedure is known as an computation or algorithm. Algorithms serve as a thorough set of instructions that direct hardware- or software-based routines through a sequence of planned actions step by step. In all areas of IT, algorithms are commonly employed.

Here,

If it is impossible to develop an algorithm that reliably returns a true or false result for each input value, the problem is said to be undecidable.

The category of inherently unknowable questions, a subtype of insoluble problems, only includes questions that ought to receive a yes-or-no response .

Thus ,incomputable. is another word for undecidable.

Therefore , the solution of the given problem of algorithm comes out to be incomputable. is another word for undecidable.

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The sum of 2.3 and 1.94, that is 2.3 + 1.94 is 4 wholes, 2 tenths and 4 hundredths, which can be written in decimal form as 4.24.

Therefore the answer is 4.24.

The first number, 2.3, can be broken down into 2 wholes and 3 tenths.

The second number, 1.94, can be broken down into 1 whole, 9 tenths and 4 hundredths.

To add the two numbers together, we first add the wholes: 2 + 1 = 3.

Next, we add the tenths: 3 + 9 = 12

Since we cannot have more than 9 tenths in a whole, we must regroup 12 tenths as 1 whole and 2 tenths.

We add the regrouped tenths to the number of wholes: 3 + 1 = 4

After regrouping, we have 4 whole and 2 tenths.

Now we add the hundredths: 0 + 4 = 4

Thus the sum is 4 wholes, 2 tenths and 4 hundredths, which can be written in decimal form as 4.24.

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The circumference of the base of figure 2 is 5π inches, and the area of the base of figure 2 is 6.25π square inches

You can presume that the cylinders are proportionate because they are comparable.

9/5 = 4.5/x would be the equation to be used for the calculation.

The radius of 2.5 is obtained by dividing and multiplying by crosses.

Figure 1's circumference will be:

Circumference = 2 * 2.5 = 5π

The area for figure 2 is as follows:

Area = (2.5)² = 2.5 * 2.5 = 6.25π

As a result, the base of figure 1 has a 5π inches circumference.

The base of figure 2 has a 6.25π square inch area.

The base of figure 1 has a 5π inch circumference.

The base of figure 2 has a 6.25π square inch area.

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The factors of 5x as calculated from the data given is found to be as 5, x and  1 .

On factorizing 5x we can write it as ,

5 x 1 x x .

Therefore the factors are 5 , 1 and x.

There are some integers which are positive and can divide a number completely leaving no remainders. Such integers are known as factors for a number. If we want to get a product by multiplying two numbers , we will have to multiply two factors. Each number is a multiplier of itself.

The prime factor is the factor of a given number that is also a prime number. Factors are numbers that are multiplied together to produce another number.

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Each state is given a specific amount of "votes" under the "Electoral College" system. The amount of "votes" each state receives is proportionate to its size.

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A)There are 88 trader sell only one fruit.

B) There are 46  trader sell only two fruit.

Since there are three sets, use the formula

n (A∪O∪M) = n(A) + n(O) + n(M) - n(A∩O) -n(O∩M) - n(A∩M) + n(A∩O∩M)

A represents apple traders = 40

O represents orange traders = 46

M represents mangoes traders = 50

A∪O∪M = total traders = 100

A∩O = 14

O∩M = ?

A∩M = 15

A∩O∩M = 10

B) Substitute values into the formula

100 = 40 + 46 + 50 - 14 - 15 - O∩M + 10

100 = 146 - 29 - O∩M

100 = 117 - O∩M

Make O∩M subject of formula

O∩M = 100 -117

O∩M = 17 traders

Now,

n(A∩O) -n(O∩M) - n(A∩M)

= 14 + 17 + 15

= 46

Therefore, the number of traders that sells two fruits  are 46.

A) oranges n(O)

= 46-(4+10+ x)

= 32

Again,

mangoes n(M).

= 50-(5+10+x)

= 35

Now,

apple n(A)

= 40-(4+10+5)

= 21

Now, adding all of them we get:

n(o) + n(M) + n(A) = 32 + 35 + 21

                            = 88

Therefore, 88 trader sells only two fruit

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The meaning of the 4! ( factorial ) in mathematics is equal to                    ( 4 × 3 × 2 × 1 ).

As given in the question,

Given expression in mathematics is written as :

4! ( factorial )

In standard form meaning of the n! ( factorial ) is given by multiplication of all the terms in decreasing order till 1.

It is expressed as:

n! = n × ( n - 1 ) × ( n - 2 ) × ( n - 3 ) × ........× 3 × 2 × (n - (n - 1) ).

Apply this formula for 4! ( factorial ) we get,

4! ( factorial )

= 4 × ( 4 - 1 ) × ( 4 - 2 ) ×( 4 - 3)

= 4 × 3 × 2 × 1

= 12

Therefore, the meaning of 4! ( factorial ) in mathematics is given by

4 × 3 × 2 × 1 .

The above question is incomplete , the complete question is :

What does 4! ( factorial ) mean in mathematics?

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The 7 stepd in problem-solving examples are:

Step 1: Read through the problem

Step 2: Draw diagram

Step 3: Assign variable to each unknown

Step 4: Translate information into an equation

Step 5: Check the equation

Step 6: Use algebra rules to solve the equations

Step 7: Check the final answer.

We know that the word problems are required to translate the real world problem into mathematical terms.

Everything mentioned in the word problem is important.

The seven necessary steps in problem solving examples:

Step 1: Read the problem throughly

Step 2: Draw picture / diagram / arrow diagram related to example

Step 3: Assign an alphabate to each unknown value

Step 4: Translate information into an equation

Step 5: Check the types equation

Step 6: solve the equations using algebra rules

Step 7: Check the final answer.

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According to probability, if both families want to sit together, they can be seated in a row a maximum of two times.

The direction that each person is facing is crucial when arranging the people.

In order to determine how many ways they can be seated in a row if both families want to sit together, imagine that two families with four members each attend a movie theatre.

Given that the arrangement is important, we will apply the permutation rule. We'll divide the remaining four into two groups of four each.

There are two different ways to arrange the groups so they can sit together.

2! = 2 * 1

2! = 2ways

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We will plot the graph for a LN function by keeping in mind that the domain must be greater than 0.

LN means natural logarithm. LN function denotes natural logarithm function. It has also another name, logarithm of base e.

It is expressed as

y = ㏑x that is the inverse of                            

the natural base exponential function

y = ex

If we have a logarithm function, f(x) = y = ln x

while plotting with the above function, ln x can be found for only the positive value of x and there is no value of ln x for negative values.

The properties of the graph of the LN function are following.

The domain of the LN function is only the real numbers that means x > 0.

The ranges of the LN function are all real number.

The coordinate of x intercept of the LN function is (1, 0).

The graph of LN function will be such that it will never touch the Y axis although it always approaches to it.

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Using the Central Limit Theorem for proportions, the correct option is:

E. The statistic is biased.

In plain English, what is the central limit theorem?

According to the central limit theorem, even if a population isn't normally distributed, you may still obtain sufficiently big samples from it and have the samples' means be distributed normally.

What is the central limit theorem and why is it significant?

Because of the Central Limit Theorem, we can confidently assume that the sampling distribution of the mean will be normally distributed in most situations.

                  Since a normal distribution is assumed, we can benefit from statistical methods, as we will see in the section after this one.

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Answer:

Step-by-step explanation:

Cost of 1 pen = 20 rupees

Cost of 4 pens = 20 x 4 = 80 rupees

Cost of 1 pencil = 5 rupees

Cost of 5 pencils = 5 x 5 = 25 rupees

Cost of 1 box = 60 rupees

Cost of 2 boxes = 60 x 2 = 120 rupees

therefore, total cost = 80 + 25 + 120  = 225 rupees

To simplify 3 ratios, divide each part of the ratio with the same amount and keep diving numbers in the ratio until they are as small as possible but they remain as whole numbers.

To simplify or reduce a fraction, first, we need to find a common factor between the ratio numbers. When we have multiple ratio numbers, we must find a common factor between all of them.

The greatest factor between all the ratio numbers (greatest common factor) will be utilised to divide or reduce the ratios down to their lowest form.

For example reduce the ratio 350: 250: 125

The first step is to determine a common factor between all of the ratio numbers. In this example, we can see that all of the numbers end in either 5 or 0. This means that each number should have 5 as a factor.

If numbers are large and we are not sure of the greatest common factor between them all, we can reduce by a common factor and then reduce again.

Now divide each number by 5 and see what we get.

350/5: 225/5: 125/5

70: 45: 25

When we divide each one by 5 again, we can see that each number again ends in 5 or 0 which means that 5 is still a factor of each number.

Now divide each number by 5 again and get a final ratio of 14: 9: 5.

70/5: 45/5: 25/5

14: 9: 5

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Odd degree polynomials can have no real roots.

A polynomial of even degree can have any number from 0 to n distinct real roots. A polynomial of odd degree can have any number from 1 to n distinct real roots.

polynomials

A polynomial is defined as an expression which is composed of variables, constants and exponents, that are combined using mathematical operations such as addition, subtraction, multiplication and division.

Real root

A real root is a solution to an equation which is also a real number.

Real number

Real numbers are numbers that include both rational and irrational numbers. Rational numbers such as integers (-2, 0, 1), fractions(1/2, 2.5) and irrational numbers such as √3, π(22/7), etc., are all real numbers.

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The average tuition for two randomly chosen in-state and out-of-state students is around $1,508 less than the mean of $6,348.75.

Mean Deviation

The average deviation from the mean value of the provided data set is determined using the mean deviation, which is defined as a statistical metric.

Given

μS = $6,348.75

σS = $1508.48

The average sum of the tuition fees is $6348.75

As a result, it follows:

The standard deviation of the tuition for in-state students is measured as a difference from 6348.75.

The standard deviation for out-of-state students gauges how their tuition is different from 1508 in total.

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Answer:

PF

Step-by-step explanation:

Since the triangles are congruent, meaning they are the same shape, we can just match the lines between the two triangles. In triangle ABC, the line AC is the hypotenuse of the triangle. So, we need to find the hypotenuse of the triangle PDF. Looking, we can see the hypotenuse of the triangle PDF is the line, or side, PF.

Hope this helped!

The sprinkler should be set to rotate through  the angle 6.42 degrees.

What is an angle?

Two lines intersect at a location, creating an angle. An "angle" is the term used to describe the width of the "opening" between these two rays. Angles are used in the design of buildings, roadways, and sports venues by engineers and architects.

r =  50 yards

Area, A = 140 square yards

Θ = angle

A= (Θ /360) πr²

140 = (Θ /360) * 3.14 * 50*50

Θ = (140*360)/(3.14*25*100) = 6.42 degrees

The sprinkler should be set to rotate through  the angle 6.42 degrees.

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The value of q in the given equation x²- 5x + q = 0 will be 4.

A polynomial is a mathematical equation that solely uses the operations addition, subtraction, multiplication, and non-negative integer exponentiation of variables. Variables are sometimes known as indeterminates in mathematics. Polynomials come in various varieties. Monomial, binomial, and trinomial, respectively.

given an equation x²- 5x + q = 0 and the question states that it has a root that is equal to 2

Since 2 is the root of this quadratic equation it will satisfy the equation

Substituting the values in the equation

4 - 5*2 + q = 0

q = 6

Equation will be

x²- 5x + 6 = 0

The root of the given equation using the fraction method

x²- 3x - 2x + 6= 0

(x -2)(x - 3) = 0

The root of the given equation are 2 and 3

Therefore, In the given equation x²- 5x + q = 0 the value of q will be 4.

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Answer:

1. 4x3<7×3

12×2<21×2

24×4<42×4

96×9<168×9

864<1512

2. 11+3>-2+3

14+3>1+3

17_4>4-4

13>0

3. -2/leg-2

-18/leg-18

4. -4<8

0<2