find an expression for sin (5 theta) as a fifth degree polynomial in the variable sin(theta) ?

The proof that z lies on the x-axis is shown below

For z to lie on the x-axis, then the coordinate must be represented as (x, 0)

Given that

[tex]\frac{|z - 5i|}{|z + 5i|} = 1[/tex]

We start by simplifying the given expression using the definition of the modulus of a complex number:

So, we have

[tex]\frac{|z - 5i|}{|z + 5i|} = \frac{\sqrt{(x - 0)^2 + (y - 5)^2}}{\sqrt{(x - 0)^2 + (y + 5)^2}} = 1[/tex]

Where

z = x + yi or z = (x, y)

Squaring both sides of the equation above, we obtain:

[tex]\frac{(x - 0)^2 + (y - 5)^2}{(x - 0)^2 + (y + 5)^2} = 1[/tex]

This gives

[tex]\frac{x^2 + (y - 5)^2}{x^2 + (y + 5)^2} = 1[/tex]

By comparison, we have

[tex](y + 5)^2 = (y - 5)^2[/tex]

Set y = 0 to test the equation

So, we have

[tex](0 + 5)^2 = (0 - 5)^2[/tex]

25 = 25 --- true

The equation is true for y = 0

This means that

z = (x, 0)

Hence, z lies on the x-axis

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Answer: Since the perimeter of all the rectangles is equal (24 cm), the sum of the length and width of each rectangle must be equal for each rectangle. This is because the perimeter of a rectangle is equal to the sum of its lengths plus the sum of its widths, multiplied by 2.

For example, if the length of one rectangle is "l" cm and its width is "w" cm, then its perimeter would be 2l + 2w = 24 cm.

So, in general, we can write the equation: l + w = P/2, where P is the perimeter of the rectangle (in this case, P = 24 cm).

Therefore, the sum of the length and width of each rectangle is equal and constant, regardless of the individual values of the length and width. This means that as the length of a rectangle increases, its width must decrease by an equal amount to keep the sum constant. And vice versa.

In conclusion, the sum of the length and width of each rectangle is equal, and it is equal to half of the perimeter of the rectangle.

Step-by-step explanation:

If a poll is to be conducted in an elementary school by interviewing 50 students, the following samples have been described as either representative or not representative as follows:

a. The first 50 students leaving the cafeteria. Not representative

b. Fifty randomly chosen names from a computer-generated list of names of all students at the school. Representative

c. Ten students randomly chosen from each of the 5 areas of campus. Representative

d. Five students from 10 teachers' classes. Representative

A representative sample is a small collection from a larger group from which any information obtained will be as good as the larger group. While choosing a representative sample, the researcher should take care not to zone the participants from a given section of the population. This will cause the information to be skewed and not objective.

Selecting 50 students leaving a cafeteria will not be representative because this might only represent a section of the school that will be giving their response based on a certain mood.

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One way to manage your staff to manage complaints would be  to establish clear procedures for handling complaints and regularly train staff on these procedures.

Establishing clear procedures for handling complaints and training staff helps to ensure that all complaints are handled consistently and effectively, reducing the potential for misunderstandings or conflicts to arise.

Additionally, creating an open-door policy for staff to voice their concerns and providing regular opportunities for feedback can help to identify and address issues before they escalate into complaints. Regular communication and coaching can also help to build strong working relationships and foster a positive workplace culture, reducing the likelihood of complaints in the first place.

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If A, B and C be events relative to the sample space S, then the Venn diagram of the representing event has been plotted

Let A, B and C be events relative to the sample space S.

The sample space is the set of all possible outcomes of the experiment.

The Venn diagram is the pictorial representation of the sample space of the experiment by using the circles and the overlapping of the circles.

Here we have to plot the each representing events using the Venn diagram representation

Part a

The event is (A ∩ B)'

Plot the Venn diagram

Part b

The event is (A ∪ B)'

Plot Venn diagram

Part c

The event is (A ∩ C) ∪ B

Plot the Venn diagram

Therefore, the Venn diagram of the each event has been plotted

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The output value of y when input value x is -7:   -6

Function is a relation between a set of inputs and a set of outputs which are permissible. In a function, for particular values of x we will get only a single image in y. It is denoted by f(x).

Vertical line test:-

Whenever we want to check given expression is a function or not we can check it by a vertical line test, in this test we check for a single image of x , we are getting a single image or more.

If we get more images then it will not be a function.

For example, let us take, y² = 4ax

y = ±√4ax

For single value of x we get two values of y

Hence, it will not be a function.

Given that,

A graph of a function,

And input value x  = -7

output value y = ?

As it can be seen in the graph,

For input value x  = 0

output value of y = -2

Similarly,

for input value x  = -7

It can be seen in the graph that

the value of y = -6

Hence, the value of y is -6

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The 5th , 6th and 7th term of the arithmetic sequence is 1 , 13/16 and 10/16 respectively

An arithmetic progression is a sequence of numbers in which each term is derived from the preceding term by adding or subtracting a fixed number called the common difference "d"

The general form of an Arithmetic Progression is a, a + d, a + 2d, a + 3d and so on. Thus nth term of an AP series is Tn = a + (n - 1) d, where Tₙ = nth term and a = first term. Here d = common difference = Tₙ - Tₙ₋₁

Sum of first n terms of an AP: Sₙ = ( n/2 ) [ 2a + ( n- 1 ) d ]

Given data ,

Let the first term of the AP be a₁ = 1 3/4

Let the second term of the AP be a₂ = 1 9/16

So , the common difference of AP d = a₂ - a₁

On simplifying the equation , we get

The common difference d = 1 9/16 - 1 3/4 = ( 25/16 - 7/4 )

The common difference d = - ( 3/16 )

And , the nth term of the AP is a + (n - 1) d

So , the 5th term of the AP = ( 1 3/4 ) + ( 4 ) ( -3/16 )

On simplifying the equation , we get

The 5th term of the AP = ( 7/4 ) + ( -3/4 )

The 5th term of the AP = 4/4 = 1

Therefore , the value of A = 1

And , the 6th term of the AP = ( 1 3/4 ) + ( 5 ) ( -3/16 )

On simplifying the equation , we get

The 6th term of the AP = ( 7/4 ) + ( -15/16 )

The 6th term of the AP = 13/16

Therefore , the value of B = 13/16

And , the 7th term of the AP = ( 1 3/4 ) + ( 6 ) ( -3/16 )

On simplifying the equation , we get

The 7th term of the AP = ( 7/4 ) + ( -18/16 )

The 7th term of the AP = 10/16

Therefore , the value of C = 10/16

Hence , the arithmetic progression is solved

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P(B A)=P(B)

Step-by-step explanation:Given situation that two events occurred event A and event B event A has already occurredtherefore, there is no relationship between them event A and event B since, the probability of B does not depend on any activity of A therefore, P(B A)=P(B)

The probability that event B occurs, given that event A has already occurred is P(A) = P(A ∩ B) / P(B | A).

An event is the outcome of a chance experiment or a collection of similar outcomes.

As the sample space is a collection of all potential outcomes of a random experiment, it might be defined as every subset of that space.

When the event B is dependent on event A,

P(A ∩ B) ≠ P(A) x P(B)

When the event A comes before event B. So, the probability of B given A:

P(B | A) = P(A ∩ B) / P(A)

P(A) = P(A ∩ B) / P(B | A)

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Answer:

21

Step-by-step explanation:

(-9)([tex]-\frac{7}{3}[/tex]) = 63/3 = 21

Answer:

48 kicks

Step-by-step explanation:

If she shoots 40 times and misses 8, we can create a ratio to represent the number of total shots to the number of misses:

40/8 = 60/x X represents the amount she will miss if she takes 60 shots.

We can find the value of x by using cross multiplication:

480 = 40x. We can now isolate x by dividing both sides by 40:

X = 12.

Melinda will miss 12 out of 60 shots.

She will make 48 kicks.

For the given triangle, the value of 'a' would be 41.41 degrees.

What is cosine angle?

In mathematics, the cosine of an angle is a trigonometric function that relates the ratio of the adjacent side of a right triangle to the hypotenuse.

More formally, the cosine of an angle is defined as the ratio of the length of the adjacent side of a right triangle to the length of the hypotenuse. It is denoted by the symbol cos and is calculated using the following formula:

cos(theta) = adjacent side / hypotenuse

where theta is the measure of the angle in radians or degrees.

By using the cosine definition,

cosθ = adjacent side/Hypotenuse

cos(a) = 45/50

[tex]a = cos^{-1}(\frac{45}{60})[/tex]

a = 41.41°

Hence, for the given triangle, the value of 'a' would be 41.41 degrees.

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On solving the provided question, we can say that Area of Rhombus is 24 cm²

A rhombus is an equal-sided quadrilateral in Euclidean plane geοmetry. The term "equilateral triangle" alsο refers to a quadrilateral whose sides are of the same length. A parallelοgram has a unique variation knοwn as a rhombus. In a rhombus, the οpposite sides and angles are parallel and equal.

A rhombus's diagοnal is split in half by a right angle, and each of its sides is the same length. Rhombic diamοnds and diamonds are other names for rhοmbuses. The length οf every side is the same. Diagοnals are equal in a rhοmbus. At a 90° angle, parallel lines split in half, 180 degrees is the sum of adjacent angles.

By distance formula

BD = [tex]\sqrt{(-2-4)^2 + (-1-5)^2}[/tex]

BD = [tex]\sqrt{36 + 36}[/tex]

BD = 6√2

similarly,

AC = 4√2

and, Area = 1/2 × (product of diagonals)

Area of Rhombus = 1/2 × 6√2 × 4√2 = 24 cm²

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The more basic function that has been shifted, reflected, stretched, or compressed to create q(x) = -1/x + 1 is the function f(x) = 1/x.

The transformation applied to f(x) to obtain q(x) is divided into several steps:

Reflection: The negative sign in front of 1/x reflects the graph of f(x) across the x-axis, causing the y-values to change sign.

Vertical shift: Adding "+1" to -1/x raises the graph of f(x) by one unit.

Horizontal shift: Although there is no explicit horizontal shift in q(x), we can see that the graph of q(x) has a vertical asymptote at x=0, whereas the graph of f(x) does not. This means that the graph of q(x) has been shifted to the right by one unit.

The more basic function that has been shifted, reflected, stretched, or compressed to create q(x) = -1/x + 1 is the function f(x) = 1/x.

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68 students said that Mr.Lopez should buy jumbo chocolate chip cookies.

What is a circle graph?

A pie chart, often known as a circle chart, is a visual representation of the various values of a specific variable or a means to summarise a set of nominal data (e.g. percentage distribution). This kind of chart consists of a circle with numerous segments.

Let's say the total number of students = X.

From the circle graph, we can say that 15% of students chose cinnamon twists and their count is 12.

Which means that

[tex]X*\frac{15}{100}=12\\ X=80[/tex]

Therefore the total number of students is 80.

Among the 80 students except for 12 students, the remaining students asked for jumbo chocolate chip cookies.

Which is equal to 80-12=68.

Therefore 68 students said that Mr.Lopez should buy jumbo chocolate chip cookies.

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The original markup price that will lead to a markup on cost of 25 % would be $ 1. 68 per pound

To find the marked up price, first, find the amount that is a 25 % markup on cost to be :

= ( 100 pounds x 79 cents per pound ) x ( 1 + 25 %)

= 79 x 1. 25

= $ 98. 75

The 40 % sold would bring in:

= 40 % x 100 x 0. 79

= $ 31. 60

The amount left to be raised is:

= 98. 75 - 31. 60

= $ 67. 15

The markup price on the rest of the mushrooms is:

= 67.15 / ( 100 - 40 % - 20 %)

= $ 1. 68 per pound

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The revenue corresponding to break even condition for selling x units is $4.28.

An evaluation of the model's accuracy in estimating the link between X and y is done using a cost function. In most cases, this is represented as a difference or distance between the projected value and the actual value. The price element (you may also see this referred to as loss or error.)

To break even (R = C) we have:

7.8 √x + 22,000 = 13.82x

Substitute the value of x = u² thus:

7.8u +22000 = 13.8u²

13.8u² - 7.8u - 22000 = 0

The quadratic formula is given as:

u = -b ± √b² - 4ac / 2a

u = -(-7.8) ± √(-7.8)²- (4)(13.82)(22000) / 2(13.82)

u = 7.8 ± 7.8 / 27.64

u = 7.8 + 7.8 / 27.64

u = 0.56

Back substituting the value of u:

x = u²

x = (0.56)²

x = 0.31

Substituting the value of x is R:

R = 13.82 (0.31)

R = 4.28

Hence, the revenue corresponding to break even condition for selling x units is $4.28.

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The 52nd term of the arithmetic sequence -3, 12, 27, ..... is equal to 762.

Mathematically, the nth term of an arithmetic sequence can be calculated by using this expression:

aₙ =  a₁ + (n - 1)d

Where:

Next, we would determine the common difference as follows.

Common difference, d = a₂ - a₁

Common difference, d = 12 - (-3)

Common difference, d = 12 + 3

Common difference, d = 15

Substituting the given parameters into the formula, the 52nd term of this arithmetic sequence is given by;

a₅₂ = a₁ + (52 - 1)d

a₅₂ = -3 + (51)(15)

a₅₂ = -3 + 765

a₅₂ = 762.

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The equation for option 1 is y = 3.5x + 7.5 and option 2 is y = 5.5x. Option 1 will be the least expensive. The solution has been obtained by using the slope-intercept form.

What is slope-intercept form?

The graph of the equation y = mx + b is represented by a line with a slope of m and a y-intercept of b. The slope-intercept representation of the linear equation is employed, and the values of m and b are real numbers.

We are given two options.

Using slope-intercept form, we get the equations as

Option 1

It requires monthly fee of $7.50 which means this is the y-intercept and $3.50 per game which means this is the slope.

So, the equation is y = 3.5x + 7.5

Option 2

Slope = (33 - 16.5)/ (6 - 3)

Slope = 16.5/ 3

Slope = 5.5

The y-intercept for this is 0.

So, we get the equation as y = 5.5x.

Fee for renting 5 games

As per option 1: y = 3.5(5) + 7.5 = $25

As per option 2: y = 5.5(5) = $27.5

Hence, option 1 will be the least expensive.

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Blake needs a wooden dowel that is 2 1/6 feet long. Blake needs to cut off 7.4167 feet from the dowel.

What are arithmatic operations?

Arithmetic operations is a branch of mathematics, that involves the study of numbers, the operation of numbers that are useful in all the other branches of mathematics. It basically comprises operations such as Addition, Subtraction, Multiplication, and Division.

To find out how much Blake should cut off the dowel, we need to subtract the length of the dowel from the required length.

The length of the dowel is -5 1/4 feet, which can be written as -5.25 feet.

The required length is 2 1/6 feet, which can be written as 2.1667 feet (rounded to four decimal places).

To find out how much needs to be cut off, we can subtract the length of the dowel from the required length:

2.1667 ft - (-5.25 ft) = 7.4167 ft

Therefore, Blake needs to cut off 7.4167 feet from the dowel.

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Find the value of day/dx when X = 1 and when Y = 1. I would like to answer correct but Find the value of day/dx when X = 1 and when Y = 1.Find the value of day/dx when X = 1 and when Y = 1.Find the value of day/dx when X = 1 and when Y = 1.Find the value of day/dx when X = 1 and when Y = 1.Find the value of day/dx when X = 1 and when Y = 1.Find the value of day/dx when X = 1 and when Y = 1.Find the value of day/dx when X = 1 and when Y = 1.Find the value of day/dx when X = 1 and when Y = 1.Find the value of day/dx when X = 1 and when Y = 1.

Based on the information provided, the passage that explains the citation is "The outcome...is situational irony..." (option A).

When you cite information from other sources or authors, there are three elements that should be included:

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Answer:

Prepaid expenses are payments made in advance for goods or services that will be received or used in the future. These expenses are considered assets on a company's balance sheet because they provide future economic benefits. Examples of prepaid expenses include rent payments made in advance, insurance premiums, and prepaid service contracts. They are recorded as an asset on the company's balance sheet until the expense is incurred, at which point it is recognized as an expense on the income statement.

Step-by-step explanation:

Answer:

This is not math...

Step-by-step explanation:

Credit scores are made of credit history, payment history, debt ratio, and types of credit which is therefore denoted as option A.

This is referred to as a numerical expression based on a level analysis of a person's credit files, to represent the creditworthiness of an individual.

It is a prediction of how likely you are to pay a loan back on time based on information from your credit reports and has different components such as the credit history, payment history, debt ratio, etc.

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Answer:

LCD → 468

Step-by-step explanation:

[tex]\frac{5}{18} = \frac{5}{18} * \frac{26}{26} = \frac{130}{468}[/tex]

[tex]\frac{11}{12} = \frac{11}{12} * \frac{39}{39} = \frac{429}{468}[/tex]

[tex]\frac{6}{13} = \frac{6}{13} * \frac{36}{36} = \frac{219}{468}[/tex]

Hence, the least common denominator for these three fractions would be 468.

The value of x from the given triangle is approximately 19.10.

Triangle can be defined in which it consists of three sides , three angles and sum of three angles is always 180 degrees.

We can use the Pythagorean theorem to find the value of x. The theorem states that in a right-angled triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the lengths of the other two sides. Mathematically, it can be represented as follows:

c² = a²+ b²

where c is the length of the hypotenuse, and a and b are the lengths of the other two sides.

In this problem, c = 25, and we need to find the value of x which is the length of one of the other two sides. Let's call the other side y. Then, we can write the equation as follows:

25² = x² + y²

We are also given that the angle between x and y is 41 degrees. We can use trigonometry to find the value of y. The sine function gives us the ratio of the opposite side to the hypotenuse, so we can write:

sin(41) = y/25

Therefore, y = 25 * sin(41). Now that we have the values of x and y, we can substitute them in the equation derived from the Pythagorean theorem:

25² = x² + (25 * sin(41))²

Solving for x, we get:

x = √(25²- (25 * sin(41))²)

Using a calculator, we get that sin(41) = 0.661437827766148.

Now, we can substitute this value in the equation:

x = √(25² - (25 * sin(41))²)

x = √(25² - (25 * 0.661437827766148)²)

x = √(25² - (16.0359050108801)²)

x = √(625 - 256.132749101278)

x = √(368.867250898722)

x = 19.10

Hence, The value of x is approximately 19.10

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The mean for this population is 55. The variance and standard deviation for this population are 94.8 and 9.74

The data is given for five families and their children are tested to see how many words they can speak in Swahili.

Toddler     Number of words(X)        X - M         (X - M)²

   A                        47                          - 8                64

   B                        73                           18               324

   C                        56                            1                  1

   D                        46                          -9                 81

   E                        53                          -2                  4

                                                                              424

Mean of the population(M) = (∑X)/n

                                             = (47 + 73 + 56 + 46 + 53)/5

                                             = 275/5 = 55

Variance f population (σ²) = (X - M)²/n = 474/5 = 94.8

Standard deviation of population(σ) = √94.8 = 9.74

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Another way to find 4x2x5 is to multiply two of the digits and multiply the last digit with the product of two.

Multiplication is when you take one number and add it together a number of times. Example: 5 multiplied by 4 = 5 + 5 + 5 + 5 = 20. We took the number 5 and added it together 4 times. This is why multiplication is sometimes called "times".

Given are three numbers multiplied, 4x2x5, we need to find the another way to solve it,

So,

4x2x5 = 40

So, in another method,

Multiply 4 and 2, we get, 8 as product, now multiply the product 8 to the last number 5,

8x5 = 40

Hence, the another way to find 4x2x5 is to multiply two of the digits and multiply the last digit with the product of two.

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The question is incomplete solved for:

Find the another method to solve 4x2x5