Enter the equivalent decimal.
9/9/25

A rotation matrix has two complex eigenvalues e−iθ and eiθ.

These are matched by complicated eigenvectors.

We are aware that the rotational axis is represented by the eigenvector with the eigenvalue 1 in it. how to demonstrate that the angle of rotation is represented by the complex eigenvalue.

It is simple to compare it with a rotation matrix for rotation about the x, y, or z axes, but how can one draw this conclusion for a general R that belongs to SO (3).

In linear algebra, a rotation matrix is a transformation matrix that is used to perform a rotation in Euclidean space. For example, using the convention below, the matrix rotates points in the xy plane counterclockwise through an angle θ with respect to the positive x axis about the origin of a two-dimensional Cartesian  Plane.

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12 students like chocolate and vanilla, if there are 55 people in the class.

In the given question, in a class, there are 30 students who like chocolate, 25 students who like vanilla, and 12 students who like neither.

If there are 55 people in the class, then we have to find how many students like chocolate and vanilla.

The number of students who like chocolate, n(C)=30

The number of students who like vanilla, n(V)=25

The number of students who like neither chocolate and vanilla, n(C∪V)′=12

Total number of students, n(U)=55

Now,

The number of students who like vanilla or chocolate;

n(C∪V) = n(U)-n(C∪V)’

n(C∪V) = 55-12

n(C∪V) = 43

Since, we have to find how many students like chocolate and vanilla, if there are 55 people in the class. So

n(C∩V)=n(C)+n(V)- n(C∪V)

n(C∩V)=30+25- 43

n(C∩V)=12

Hence, 12 students like chocolate and vanilla, if there are 55 people in the class.  

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Answer: 21 miles

Step-by-step explanation:

We know that it travels 2016 miles in 96 hours.

So we just need to get 2016 divided by 96 = 21 miles/ per hour

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Hence, the miles does the balloon travel in one hour is [tex]21[/tex] miles/ per hour.

What is the miles?

Mile is a customary unit used for measuring length or distance. More About Mile Mile is denoted by the symbol 'mi'.

Here given that,

A hot-air balloon travels [tex]2,016[/tex] miles in [tex]96[/tex] hours. It travels the same number of miles each hour.

As we know that it travels [tex]2016[/tex] miles just only in [tex]96[/tex] hours.

[tex]\frac{2016}{96}=21[/tex] miles/ per hour

Hence, the miles does the balloon travel in one hour is [tex]21[/tex] miles/ per hour.

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the f-test statistic to test the claim that the population variances are equal is F test = 2.54

We are given two samples

Standard deviation of the first sample = 2.1971

Standard deviation of the second sample = 7.32

F test statistic = Variance of the Larger sample/ Variance of the smaller sample

Variance = (Standard deviation)²

Variance for the first sample = 2.1971²

= 4.8272

Variance for the second sample = 7.32² = 53.5824

F test = 53.5824/4.8272

= 11.100

Therefore, the F test approximately = 11.100

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For the given data, a) The mass at the time t = 3 is 14.13 kg. and b) The mass remaining after 20 days is 10.05 kg.

What is radioactive decay?

The spontaneous breakdown of an atomic nucleus of a radioactive substance resulting in the emission of radiation from the nucleus is known as Radioactive decay.

The Radioactive Formula is given by

                     [tex]N = N_{0} e^{-\lambda T}[/tex]

Given, [tex]m(t) = 15e^{-0.02t}[/tex]

where m(t) is measured in kilograms

a) To find the mass at time t=3, then

m(3) = [tex]15e^{-0.02*3}[/tex] = [tex]15e^{-0.06}[/tex] = 14.13 kg

Therefore, the mass at the time t=3 is 14.13 kg.

b)  To find how much of the mass remains after 20 days,

m(20) = [tex]15e^{-0.02*20}[/tex] = [tex]15e^{-0.4}[/tex] = 10.05 kg

Therefore, the mass remaining after 20 days is 10.05 kg.

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In 700 years the population of Transylvania will double  

What is growth rate ?

the typical annual rate of population change during a particular period for a certain nation, region, or geographic area. In most cases, a factor of 100 is used to describe the ratio between the annual growth in population size and the total population for the year.

Growth rate equals Absolute Change divided by Previous Value. Calculate the percentage of change: Percent of change = Growth rate x 100 is the formula that may be used to calculate the percent of change.

To calculate in how many years the population of Transylvania double

= 70 / 0.1

= 700 years

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Answer: $117

Step-by-step explanation: 1st subtract 3 then divide by 2 then subtract 3 again and divide by 2 again

The standard deviation of the number of days absent is found as 1.1616.

For the stated question-

Number of Days Absent/Probability

Thus, the mean is found as;

Mean = (0x0.60) + (1x0.20) + (2x0.12) + (3x0.04) + (4x0.04)

Mean = 0.72

Standard deviation σ = (0-0.72)² x 0.60 + (1-0.72)² × 0.20 + (2-0.72)² × 0.12 + (3-0.72)²  × 0.04 + (4-0.72)² × 0.04

Standard deviation  = 1.1616

Thus, the standard deviation of the number of days absent is found as 1.1616.

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The complete question is-

A company is studying the number of monthly absences among its 125 employees. The following probability distribution shows the likelihood that people were absent 0, 1, 2, 3, 4, or 5 days last month.

Number of Days Absent/Probability

0 0.60

1 0.20

2 0.12

3 0.04

4 0.04

5 0.00

What is the standard deviation of the number of days absent?

Answer:

1) [tex]\dfrac{1}{2}[/tex]

2) [tex]\dfrac{7}{10}[/tex]

3) [tex]\dfrac{7}{8}[/tex]

Step-by-step explanation:

Any decimal can be written as a fraction by just putting the given number over 1.

For example, take the first problem.

0.5 can be written as:

[tex]\dfrac{0.5}{1}[/tex]

Then, to simplify it, multiply both the top and bottom by 2.

[tex]\dfrac{0.5 \times 2}{1 \times 2}[/tex]

[tex]= \dfrac{1}{2}[/tex]

The reason this doesn't change the value of the fraction is because any number over itself is 1. Look at the 2's we just multiplied by in the numerator and denominator. We are really just multiplying the entire fraction by 2/2, which equals 1. Here's a way of writing the above step that makes it clearer:

[tex]\dfrac{0.5}{1} \times \dfrac{2}{2}[/tex]

[tex]=\dfrac{1}{2}[/tex]

So, the answer to the first problem is [tex]\dfrac{1}{2}[/tex].

We can repeat these steps for the second problem.

[tex]0.7 = \dfrac{0.7}{1}[/tex]

But this time, multiply by 10/10 instead of 2/2. Remember that 10/10 is still equal to 1.

[tex]= \dfrac{0.7}{1} \times \dfrac{10}{10}[/tex]

[tex]= \dfrac{7}{10}[/tex]

So, the answer to the second problem is [tex]\dfrac{7}{10}[/tex].

Finally, repeat the steps from the previous problems.

[tex]0.875 = \dfrac{0.875}{1}[/tex]

But this time, multiply by 1,000/1,000.

[tex]= \dfrac{0.875}{1} \times \dfrac{1,000}{1,000}[/tex]

[tex]= \dfrac{875}{1,000}[/tex]

And this time, some extra simplification is necessary. Divide by 25/25.

[tex]= \dfrac{875}{1,000} \div \dfrac{25}{25}[/tex]

[tex]= \dfrac{35}{40}[/tex]

Then, divide by 5/5.

[tex]= \dfrac{35}{40} \div \dfrac{5}{5}[/tex]

[tex]= \dfrac{7}{8}[/tex]

So, the answer to the third problem is [tex]\dfrac{7}{8}[/tex].

There are two ways of reflection.

Along x-axis:

(x, y) – (x, -y)

Along y-axis:

(x, y) - (-x, y)

The transformation of f(x) to g(x) is,

f(x) is reflected over the x-axis and then shifted 3 steps to the right.

There are two ways of reflection.

Along x-axis:

(x, y) – (x, -y)

Along y-axis:

(x, y) - (-x, y)

We have,

f(x) = x

g(x) = -x + 3

g(x) is the transformation of f(x).

When f(x) is reflected along the x-axis we get,

g(x) = -x

Now,

g(x) is shifted 3 steps to the right we get,

g(x) = -x + 3

Thus,

The transformation of f(x) to g(x) is,

f(x) is reflected over the x-axis and then shifted 3 steps to the right.

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After solving the given expression the values for x will be equal to x = 1 and x = 13.

Mathematical actions are called expressions if they have at least two terms that are related by an operator and include either numbers, variables, or both. Adding, subtraction, multiplying, and division are all reflection coefficient operations. A mathematical operation such as reduction, addition, multiplication, or division is used to integrate terms into an expression.

As per the given information in the question,

The given equation is,

(x - 7)² = 36

x - 7 = √36

x = ±6

Then the values for x will be,

x1 = 6 + 7 = 17

x2 = -6 + 7 = -1

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Answer:

  yes

Step-by-step explanation:

You want to know if the sides are congruent in a triangle with congruent angles.

The Law of Sines tells us the sides of a triangle are proportional in length to the sines of the opposite angles.

If the angles are congruent, their sines are equal, and the sides are congruent.

A triangle with congruent angles has all angles 60°. Such a triangle is called an equilateral triangle. The name "equilateral" refers to the fact that the sides are the same length.

Answer:  10.169

Step-by-step explanation: To add decimals like this we have to line up them in order.

2.859

+

7.31 =

10.169

Above I have to line them up in order.

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The value of x is -7.

An equation is an expression that shows the relationship between two or more numbers and variables. A system of equations is two or more equations that can be solved to get a unique solution. the power of the equation must be in one degree.

We are given the equation as

[tex]8^{x + 3} = 2 ^{x - 5}[/tex]

Solving the equation as;

[tex]8^{x + 3} = 2 ^{x - 5}\\\\2^{3(x + 3)} = 2 ^{x - 5}[/tex]

Then we have;

3x + 9 = x - 5

2x = -14

x = -7

The value of x is -7.

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Answer:

315 children attend the play.

Answer:

c=315

Step-by-step explanation:

we know c is equal to 21a so we can insert it into the second equation

a+21a=330

22a=330

/22. /22

a=15

now we inset a to find c

21(15)=c

315=c

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Answer:

  rectangle, square, triangle

Step-by-step explanation:

Given the coordinates of the vertices of a rectangle, triangle, and square, you want to sort them in order of increasing perimeter.

In general, the length of a side can be found using the distance formula:

  d = √((x2 -x1)² +(y2 -y1)²)

This shows you that if the x-coordinates are the same, the distance is the positive difference of the y-coordinates, and vice versa.

The attachment shows the side lengths for the figures, computed using this formula. Each row shows the distance from the point on that row to the point on the next row. (You will notice the last point is a copy of the first point.)

The perimeter of each figure is the sum of the side lengths. This is the number below the Distance column in each of the tables.

In increasing order, the perimeters are ...

__

Additional comment

When the computations are repetitive, it is often convenient to let a spreadsheet do them. The formula can be entered once and copied where needed. The problem then reduces to one of data entry, which you generally have to do for any but mental arithmetic.

Answer:

Step-by-step explanation:

Answer:

Step-by-step explanation:

sus

The maximum number of electrons in an atom that can have the given sets of quantum numbers n=4 is 32.

In the given question we have to find the maximum number of electrons in an atom that can have the given sets of quantum numbers n=4.

As we know that;

A negatively charged subatomic particle known as an electron can either be free or attached to an atom (not bound). One of the three main types of particles within an atom is an electron that is bonded to it; the other two are protons and neutrons. The nucleus of an atom is made up of electrons, protons, and neutrons altogether.

So the maximum number of electrons in an atom is;

Number of Electron = 2*n^2

Number of Electron = 2*(4)^2

Number of Electron = 2*16

Number of Electron = 32

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The value of ''- X'' will be;

⇒ - X = 19

What is Number line?

Number line is a horizontal line where numbers are marked at equal intervals one after another form smaller to greater.

Given that;

X is 19 units to the left of 0.

Now,

Since, X is 19 units to the left of 0.

Hence, The value of X = - 19

So, We get;

The value of - X = - (- 19)

                         = 19

Thus, The value of ''- X'' will be;

⇒ - X = 19

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Answer:

it would have a 50% or 0.5 probability of rolling an even number on the dice

Step-by-step explanation:

A dice has six numbers, three have them are odd and three are even so we would calculate it as 3/6.

Answer:

The Tiger has the better record, because the Leo won 5 games out of 8 and the Tiger won 7 games out of 11. When we change both denominator to the same number, the Leo's is 55/88 and the Tiger is 56/88, so the Tiger has the better record

The distance the jet can fly in 9 hours is 1950 miles.

The distance the jet can fly in 6 hours is 1300 miles.

The first step is to determine the rate of the jet. The rate measures how fast the jet travels with respect to time. It is the total distance travelled divided by the total time.

Rate = distance / time

Rate  = 650 / 3

Rate  = 216.67 miles per hour

Distance travelled = rate x time

Distance travelled in 9 hours  = 216.67 miles per hour x 9 = 1950 miles

Distance travelled in 6 hours = 216.67 miles per hour x 6 = 1300 miles

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Answer:

y = 5x

Step-by-step explanation:

the equation of variation in which y varies directly as x is

y = kx ← k is the constant of variation

to find k use the given y = 21.25 when x = 4.25

21.25 = 4.25k ( divide both sides by 4.25 )

5 = k

y = 5x ← equation of variation

Answer:

6pi

Step-by-step explanation:

1.) Figure out the total circumference of the circle. The circumference of a circle is equal to 2*pi*r, which is equal to 8pi.

2.) Figure out the portion of the circle that the arc is by using the angle. Since the angle is 90 degrees, and the total measure in a circle is 360 degrees, that means that the cut out part is 90/360, which is 1/4 of the circle.

3.) Now, since the cut out part is 1/4, that means that the remaining part is 3/4 of the circle.
4.) Now, we multiply 8pi * 3/4, which is equal to 6pi.

The probability of having 2 boys and 1 girl would be  [tex]\frac{3}{8}[/tex]

What is Probability?

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 number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.

Given that:

family with 3 children.

Condition: Girl is as likely as a boy at each birth.

s will be the sample space.

The sample space has 8 elements:

s = {bbb, bbg, bgb, bgg, gbb, gbg, ggb, ggg}

n(s) =  [tex]\frac{1}{8}[/tex]

We need 2 boys and 1 girl, regardless of order,

sample space for 2 boys and 1 girl, regardless of order would be 3.

s = 3

Then, probability will be

      [tex]Probability \ of\ having\ 2 \ boys\ and \ 1\ girl =\frac{3}{8}[/tex]

Hence, The probability of having 2 boys and 1 girl would be  [tex]\frac{3}{8}[/tex]

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Answer:

12. impact

13. environment

14. unique

15, destination

16. provide

17. designed

19. local

20. conservation

Step-by-ste1p explanation:

ur welcome

Answer:$17.50 remaining

Step-by-step explanation: 0.25 x 30 = 7.50

7.50 - 25.00 = $17.50 remaining

Answer:

$17.5

Step-by-step explanation:

B = 25 -0.25(30)

B = 25 - 7.5

B = 25.0 - 7.5

B = $17.5

Answer:

215.1x

Step-by-step explanation:

2.151x(102)

=2.151*x*100

=215.1*x

=215.1x

Answer:

The answer would be 215.1x

Step-by-step explanation:

2.151 x 10^2 = 215.1x

10^2 = 100

Then multiply 100 and 2.151x

100 x 2.151x = 215.1x

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

15/8 quart of grape juice is needed for 15/4 quart of sparkling water.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

The recipe for sparkling grape juice calls for 1(1/2) quart of sparkling water and 3/4 quart of grape juice,

This means,

1(1/2) quart of sparkling water = 3/4 quart of grape juice

3/2 quart of sparkling water = 3/4 quart of grape juice

Multiply 15/6 on both sides.

15/6 x 3/2 quart of sparkling water = 15/6 x 3/4 quart of grape juice

15/4 quart of sparkling water = 15/8 quart of grape juice

Thus,

15/8 quart of grape juice is needed for 15/4 quart of sparkling water.

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