How do you simplify i^100?

Divide by the norm of 1+i and apply De Moivre's theorem to find that (1 +i)^20 = − 1024 in standard form.

De Moivre's theorem presents a formula for calculating powers of complex numbers. By first studying what occurs when we multiply a complex number by itself, we may have a better understanding of de Moivre's theorem. This demonstrates that when squaring a complex number, the argument is multiplied by two and the absolute value is squared.

DeMoivre's Theorem, which unites complex numbers with trigonometry, is one of the most significant and practical theorems in the study of complex numbers. Obtaining correlations between trigonometric functions of various angles is also useful. The famous mathematician De Moivre, who made several contributions to the subject of mathematics, particularly in the fields of probability theory and algebra, is honored in the name of the theorem. The solution is attached below.

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The probability that the card will be a spade or a club 50%

Probability in math is referred as  how likely an event is to occur, or how likely it is that a proposition is true.

Here we have given that a card is drawn from a standard deck of 52 playing cards.

And we need to find  the probability that the card will be a spade or a club and we have to express your answer as a fraction or a decimal number rounded to four decimal places.

While we looking into the given question, we have identified the the total number of cards is 52.

And the number of spade cards = 13 and the number of club cards = 13

Therefore, the total number of spade and club cards

=> 13 + 13

=> 26

Therefore, the probability of getting a spade or  a club from a single draw is,

=> 26/52

When we simplified this one, then we get,

=> 0.5

When we convert this into percentage then we get

=> 50%.

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Answer:

The middle of A and C

Step-by-step explanation:

Definition of Midpoint

The total number of possible ways to complete the test would be 2048.

Total number of questions = 11

Each equation has two possible answers (either true or false).

We need to find the total number of ways in which the test can be​ completed.

the total number of possible ways to complete the test= 2×2×2×2×2×2×2×2×2×2×2

the total number of possible ways to complete the test=

2¹¹

Therefore the total number of possible ways to complete the test is 2048.

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The weighing of the balance scale required to find a lighter counterfeit coin among four coins, is twice.

In just two balance scale weighs, it is feasible to identify which of four coins is the lighter fake coin. Here is one approach:

Then, weigh the two groups against one another after splitting the four coins into two groups of two coins each. The lighter counterfeit currency must belong to the group that is lighter than the other if there are two groups. If the two groups of coins weigh the same, then one of the two remaining coins must be the lighter counterfeit coin.

Weigh the two coins from the lighter group (or the two still present, if the first step was unsuccessful) against one another.

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The expression can be rewritten as, by taking the common factor, 9 x³y³(2x - 4y), so option C is correct.

Common factors are those that apply to two or more different integers. To put it another way, a common factor is a number that will divide a group of two numbers exactly.

Given:

18 x⁴y³− 36x³y⁴

Factorize the above expression,

9 × 2 x⁴y³ - 9 × 4x³y⁴

Take common 9 x³y³

9 x³y³(2x - 4y)

Therefore, the expression can be rewritten as, by taking the common factor, 9 x³y³(2x - 4y).

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This study was conducted to test the effects of dietary supplementation of feed grade L - Met on growth performance.

Given :

based on this scatterplot , we observe that there are 6 groups of turkeys, each group receiving a different amount of methionine supplement (ranging from 0% to 44%).

Initial BW of birds did not differ among treatments. Weight gain of birds during 28 d feeding period increased ( P < 0.05 ) from 690 to 746 g ( an average of 0.33 % DL-Met and L-Met ) as dietary Met supplementation regardless of Met source increased from 0 to 0.33%. However, the source of Met did not affect the weight gain of birds.

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Consequently, the function's average rate of change is -11.

A mathematical expression, rule, or law that describes the relationship between two independent variables and one dependent variable In mathematics, functions exist everywhere, and they are crucial for creating physical links in the sciences.

The function is given by .

The ratio of the dependent variable's change to the independent variable's change is referred to as the rate of change.

f(x)=[tex]x^{2}[/tex]-6x+6

x ranges from -7 to 2, with 2 being the highest value.

=> f(-7) = 49 + 42 + 6 = 97.

=> f(2) =- 12 + 6+4 = -2.

The average rate of change is

f(-7)-f(2)/-7-2

=> 97-(-2)/-9

=> 99/-9

=> -11

Consequently, the function's average rate of change is -11.

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Answer: 7

Step-by-step explanation: You would multiply 70 by 10 to get 700, then divide it by 100 to get 7. So, it would be 7 dollars.

Answer: 7

Step-by-step explanation:

The simplified form of the given expression is 3x+5y+4. Here only the constants are simplified since there are no like terms in the expression.

The given expression which is to be simplified is 6+3x-6+4+5y.

Here to simplify the given expression, we need to add or subtract the like terms.

In the given expression, the variables x and y.

They are unlike terms. So, we cannot add or subtract them. But there are three constants. Then, we can add or subtract them.

Thus, the simplified expression for the given expression is

6+3x-6+4+5y = 3x+5y+4

Here 6 and -6 are added so that we get 0.

Hence the answer is 3x+5y+4.

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The value of y will be 104 using direct proportion property between x and y.

What is direct proportion ?

Direct proportion is the relation between two quantities where ratio of these two is equal to a constant.

It is represented by proportional symbol , "∝"

Let's consider constant is m.

For given que,

As y and x are in direct proportion,

y ∝ x

or x ∝ y

eliminating the proportionality,

y = x*m where m is any constant.

y/x = m

Given when y = 64 , then x = 8

So, m = 64/8

          = 8

And when x = 13 then y = ?

y/13 = 8

y = 13*8

  = 104

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Answer: slope = -1

Step-by-step explanation:

count number down vs number it takes to get back to the line.

For example, 1 down, 1 across

The expected number of defective shirts produced by the factory on Friday is of:

42 shirts.

The expected number of defective shirts produced by the factory on Friday is obtained as the multiplication of the sample proportion by the total number of shirts produced on Friday.

The manager of a clothing factory checks a random sample 500 shirts for defects he finds that 8 are defective, hence the sample proportion is given as follows:

p = 8/500 = 0.016.

The factory produces 2625 shirts on Friday, hence the expected number of defective shirts is given as follows:

E(X) = 0.016 x 2625 = 42 shirts.

The problem is incomplete and could not be found on any search engine, hence we suppose that it asks for the expected number of defective shirts produced by the factory on Friday.

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The surd expression 1 + [√2 / (3 - √2)²]  can be simplified as (61 + 11√2/ 49) where a is 61/49 and b is 11/49

When evaluating an expression, the first step is to identify the operators and operands in the expression. The operators are the symbols that direct the operation. The operands are the values or variables that the operators act upon. Once the operators and operands are identified, the expression can be evaluated by applying the order of operations to the expression. This includes performing operations inside parentheses first, then multiplication and division, followed by addition and subtraction.

In the case of a surd expression, the same process should be followed. However, it is important to note that surds can be simplified using the rules of indices. This means that surds with the same base value can be combined using addition and subtraction.

In the give problem, we have

1 + [√2 / (3 - √2)²] can be written in the form a + b√2

1 + [√2 / (3 - √2)²] can be simplified using a calculator to give us a value of;

1 + [√2 / (3 - √2)²] = (61 + 11√2/ 49)

In this expression, a = 61/49, b = 11/49

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Answer:

the range of possible weights for the letters is 98-105 ounces.

Step-by-step explanation:

To determine whether 101 ounces is a reasonable estimate for the weight of 25 letters that each weigh between 3.92 ounces and 4.2 ounces, we need to calculate the range of possible weights for the letters.

The minimum weight for the letters is 25 * 3.92 ounces = 98 ounces. The maximum weight for the letters is 25 * 4.2 ounces = 105 ounces. Therefore, the range of possible weights for the letters is 98-105 ounces.

Since 101 ounces falls within this range, it is a reasonable estimate for the weight of the letters.

The probability of the indicated event is  1/110.

P(2red, pink) = P(2red, pink)/P (pink)

There are a total of 1 ways to get 2 red and pink, for a total of 1 possible triples. P(2red and pink) = 1/220 P(pink) = Number of ways to get 1 pink = 1*11*10 Number of potential triples = 220 P(1 pink in 3) = 110/220 = 1/2 ———-

P(2red | pink) = (1/220)/(1/2) = 2/220 = 1/110 ————————————————

Cheers,

Stan H.

To determine the likelihood, apply the procedure below: Find an event with a single result in Step 1. 2. Determine the total number of possible results. Step 3: Subtract the number of fortunate occurrences from the total number of potential outcomes.

You can attempt to find the indicated probability using a variety of equations. The normal distribution model and the standard normal distribution are two techniques that you could choose to adopt since they are both frequently used to calculate suggested probability precisely.

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Therefore by solving the question from the equation we get ,total money he has now is $(m+100)/2

equation, a declaration of equivalence between two expressions with variable- and/or number-filled expressions. In essence, equations are questions, and efforts to discover a method for answering them have fueled the growth of mathematics. Equations range in complexity from straightforward addition-and-multiplication equations in mathematics through differential equations, exponential equations that use exponential expressions, and integral equations.

Here,

He got $m for his birthday

therefore he spent half the money the money left =m/2

and he got extra $50

Thus

total money he has now is = m/2 +50

or m+100/2

Therefore ,total money he has now is $(m+100)/2

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Answer: (4, 10)

Step-by-step explanation:

The first number, 4, is the number on the x axis, the horizontal axis. The second number 0 is the number on the y axis, the vertical axis.

If you move up you would moving on the y axis, therefore the second number, 0, would change.

You moved 10 units so starting at 0 move up 10 units. 0 + 10 = 10

Now you're at (4, 10)

Moving this barrel up a ramp required around 339.41 foot-pounds of labour from Alexa.

W = F.d

When the dot product is expanded, we get:

W=Fd cos(Ф)

We can plainly see from the given statement that:

applied force = F = 120 pounds

d = 4 feet for displacement.

F's angle with the horizontal is Ф = 45 degrees.

When the formula's values are substituted, we obtain:

W = 4 * 120 * cos (45)

W equals 339.41 foot pounds.

This indicates that lifting the barrel up this ramp required roughly 339.41 foot-pounds of labour from Alexa.

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The complete question is-

Alexa is pushing a construction barrel up a ramp 4 feet long into the back of a truck. She is using a force of 120 pounds in a horizontal direction and the ramp is 45 degrees from the horizontal. How much work is Alexa doing?

Answer:

Step-by-step explanation:

men = 2x

women = 3x

2x+3x=135

5x=135

x=27

27(2)=men

54 men

The width of the parking lot is 78 m

We have been given the perimeter of a rectangular parking lot which is equal to 350 m.

We know the perimeter of a rectangular plot is 2 X (width of the plot ) + 2 X (length of the parking lot ).

And the length of the parking lot is given as 97 m.

2 X (width of the plot ) +2 X (length of the parking lot ) =350 m

2 X (width of plot ) + 2 X 97 =350

2 X (width of the plot ) =156 m

width of the plot = 78 m

Hence the width of the plot is 78 meters.

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The width of this rectangular parking lot is equal to 78 meters.

In Mathematics and Geometry, the perimeter of a rectangle can be calculated by using this mathematical equation (formula);

P = 2(L + W)

Where:

By substituting the given side lengths into the formula for the perimeter of a rectangle, we have the following:

P = 2(L + W)

350 = 2(97 + W)

175 = 97 + W

Width, W = 175 - 97

Width, W = 78 meters.

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Q1 If you averaged every person in the population, the result would be Mu, but the mean of a sample, or xbar, would be the average value discovered in the sample.

Q2 For the group being tested, each point in a sample distribution represents a potential outcome variable.

Q3 The random condition is very important because it simplifies the sample and prevent possible bias in the sampling.

Q4 To make sure that the observations in the sample are nearly independent, it is crucial to evaluate the 10% condition before calculating probability involving x.

Q5 The big counts criterion ensures that there are more successes than failures for a normally distributed set of results. The need for big numbers is np ≥10 and n(1-p) ≥10.

Q6 For a variety of reasons, finding unbiased estimates for those seeking asylum may be challenging. First, because of persecution, these people are escaping their country.

Q7 there is less spread for larger sample than that of lower sample.

The probability distribution of a statistic acquired from a bigger sample size taken from a certain population is known as the sampling distribution.

Based on the data they have available, sampling distributions are useful tools used by researchers to estimate and draw conclusions about a wider population of interest.

Q1 If you averaged every person in the population, the result would be Mu, but the mean of a sample, or xbar, would be the average value discovered in the sample.

Q2 For the group being tested, each point in a sample distribution represents a potential outcome variable.

Q3 The random condition is very important because it simplifies the sample and prevent possible bias in the sampling.

Q4 To make sure that the observations in the sample are nearly independent, it is crucial to evaluate the 10% condition before calculating probability involving x.

Q5 The big counts criterion ensures that there are more successes than failures for a normally distributed set of results. The need for big numbers is np ≥10 and n(1-p) ≥10.

Q6 For a variety of reasons, finding unbiased estimates for those seeking asylum may be challenging. First, because of persecution, these people are escaping their country.

Q7 there is less spread for larger sample than that of lower sample.

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kiloliter

One thousand liters is called a kiloliter. A kiloliter is equal to 264.172 gallons. One liter is equal to 0.264172, so if you want to find how many gallons there are in 1 kiloliter, just multiply 0.264172 by 1000

Answer:

1000 liters  

Step-by-step explanation:

Irrational numbers are numbers that cannot be expressed as a ratio of integers and have digits that go on forever without repeating.

Irrational numbers are a type of real number which cannot be represented as a simple fraction. These numbers could be expressed in decimals but not in the form of fractions i.e., they cannot be written as the ratio of integers. Irrational numbers have endless non-repeating digits after the decimal point, hence cannot be expressed as terminating or repeating decimals. For example, when taking the square root of a number that is not a perfect square, it is going to be irrational number.

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Answer:

1/2

Step-by-step explanation:

16/64 (divide the numerator and denominator by 4)

-> 4/8 (divide the numerator and denominator by 4)

-> 1/2

1085 different combination of 3 movie she can rent.

What is linear equations?

Linear equations is a type of equation that is in between two variables that gives a straight line.

The calculation of  number of different combinations of 3 films she can rent if she needs at least two documentaries is shown below:-

=N×(2× documentry and 1 horror movies)+N×(3 documentry)

=(6C1)×(15C2)+(6Co)×(15C3)

= 630 + 455

= 1,085

Therefore for calculating the number of different combinations of 3 films she can rent if she needs at least two documentaries we simply applied the above formula and here we consider one number in the question as it shows the double number.

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Complex number equal to (5 + 12i) − (9i^2 − 6i), for i = √ -1 is 14 + 18i.

Complex numbers are the numbers that are expressed in the form of a+ib where, a,b are real numbers and  ‘i’ is an imaginary number called “iota”. The value of i = (√-1)

Given number is (5 + 12i) − (9i^2 − 6i).

We know that i^2 = -1.

Using this we get number = 5+12i+9+6i

                                           = 14+18i

So the required number is 14 + 18i.

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The value of a is 42.

Simply use cross multiplication :

The process of multiplying numbers in the shape of a fraction is called cross multiplication. Cross multiplying, also known as cross multiplication, is the process of multiplying the numerator of one fraction by the denominator of the other fraction on the other side of an equal symbol. Cross multiplication is a method for comparing fractions.

Both fractions with like and unlike parts are multiplied across. When employing the cross-multiplication procedure, we multiply the denominators as well as the numerators when a fraction is dissimilar, or when the denominators of two fractions are not alike.

[tex](15-a)/3=-9[/tex]

or, [tex]15-a=-9*3[/tex]

or,[tex]-a=-27-15[/tex]

or, [tex]a=42[/tex]

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The pie chart is shown in the attached image. 30% of the pet owners responded with a price of $25

A pie chart is a circular graph that is divided into slices to illustrate numerical proportion

Given the data of 2,500 pet owners as shown below:

Number of People    Price

500                              $10

350                               $15

750                                $20

550                                $25

350                                 $0 (not interested)

To create a pie chart, you need to find the percentages of each price as follows:

For  $10:  percentage = 500/2500 × 100  = 20%

For  $15:  percentage = 350/2500 × 100  = 14%

For  $20:  percentage = 750/2500 × 100  = 30%

For  $25:  percentage = 550/2500 × 100  = 22%

For  $0:  percentage = 350/2500 × 1000  = 14%

Use the percentages to create a piechart as shown in the image attached

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