in aut(z9), let ai denote the automorphism that sends 1 to i where gcd(i, 9) 5 1. write a5 and a8 as permutations of {0, 1, . . . , 8} in disjoint cycle form. [for example, a2 5 (0)(124875)(36).]

Answers

Answer 1

To write a5 and a8 as permutations of {0,1,...,8} in disjoint cycle form, we can start by identifying the elements that are fixed by the automorphisms. For a5, the elements fixed by ai are 1 and 8, so we can write a5 as (18)(0234576). For a8, the elements fixed by ai are 1 and 4, so we can write a8 as (14)(0235786).

In the cyclic group aut(z9), the automorphisms are essentially the permutations of the elements of the group. The automorphism ai sends 1 to i, where i is an element that is relatively prime to 9. To write a5 and a8 as permutations of {0,1,...,8} in disjoint cycle form, we need to identify the elements that are fixed by these automorphisms. The elements that are fixed are those that are mapped to themselves by the permutation. Once we have identified these fixed elements, we can write the permutation as a product of disjoint cycles.

In conclusion, a5 can be written as (18)(0234576) and a8 can be written as (14)(0235786) in disjoint cycle form. These permutations represent the automorphisms that send 1 to i, where gcd(i,9)=5. Identifying the fixed elements of the permutation is an important step in writing the permutation in disjoint cycle form.

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Related Questions

Jacob has $100 in his savings account. The interest rate is 5% per year. How much interest will he earn in 1 year?​

Answers

Answer: $5


5% of 100 is 5, so it would be $5

Hope this helps! :)

Kelsey put 6 gallons of water in the cooler. How many 1-pint water bottles can be filled from the water in the cooler?

Answers

Answer:

48 pints

Step-by-step explanation:

1 gal=8 pints

Hope this helps

Helppp plssss this is due soooon

Answers

76;(/:14 volume of 6
C=2pi*r
So you have d
D=8 divided by 2=. r=4
So
2pi*4 = 25.13
And because it’s half circle
The
25.13 divided by 2 = 12.565
Answer is 12.565

Triangle A'B'C' is the image of triangle ABC after a sequence of rigid motions,

Answers

Answer:

The sequence are:

i. reflection about the y-axis

ii. 2 units translation downwards

iii. 1 unit translation to the right

Step-by-step explanation:

Rigid transformation is a process of producing the image of a given figure or shape by either reflection, rotation, dilation or translation method. Thus the orientation and size of the figure changes with respect tot the method applied.

For the given question, some sequence were applied to produce the image of ABC.

The sequence are:

i. reflection about the y-axis

ii. 2 units translation downwards

iii. a unit translation to the right

Which equation would you use to solve this problem: Laura bought 4 1/3 bushels of apples for $16. How much did each bushel cost? *

Answers

Answer: $3.69

Step-by-step explanation:

Laura bought 4 1/3 bushels of apples.

Firs convert this to an improper fraction for easier calculation:

= 13/3 bushels of apples.

If cost $16 altogether, individually they must cost:

= Cost / Quantity purchased

= 16 ÷ 13/3

= 16 * 3/13

= $3.69

Note: You can divide by a fraction by multiplying the inverse of that fraction.

A certain population is initially 8,951 but declines by 8% every second. Find an exponential formula that gives the population as a function of time. What will be the population after half of a minute?

Answers

9514 1404 393

Answer:

  734

Step-by-step explanation:

The growth factor is 1 -8% = 0.92. This is the base of the exponential formula. The multiplier is the initial value, so you have ...

  p = 8951×0.92^t

When t=30, this evaluates to ...

  p = 8951×0.92^30 ≈ 733.68

The population after half a minute will be about 734.

Can someone help me please

Answers

I got you it’s 625 you get that answer from 5•5•5•5

Answer:

625

Step-by-step explanation:

Of the following test scores, who do you think received the best score? The worst score? Why?

Carla : 3 out of 5

Desmond: 20 out of 25

Ignacio: 6.5 out of 10

Gina: 38 out of 50

Answers

Answer:

Desmond

Step-by-step explanation:

3 over 5 x 100% = 60%

20 over 25 x 100% = 80%

6.5 over 10 x 100% = 65%

38 over 50 x 100% = 76%

Desmond is the correct answer. Continue learning and hope u have a great day/night! :)

Kamila buys a notebook for $1.59 and pens for $0.29 each. She spends $5.07.
Define a variable that can be used to determine how many pens she bought.
Write an equation using the variable and solve to determine how many pens she bought.

Answers

Answer:

12 pens

Step-by-step explanation:

Let the variable that can be used to determine the number of pens that Kamila bought be represented by n.

Price of a notebook = $1.59

Price a pen = $0.29

Total amount spent = $5.07

But,

1.59 + 0.29 n = 5.07

So that,

0.29 n = 5.07 - 1.59

0.29 n  = 3.48

n = [tex]\frac{3.48}{0.29}[/tex]

  = 12

Therefore, Kamila bought 12 pens.

Help I will be marking brainliest!!!!

A. 55.33
B. 156.16
C. 72
D. 61.16

Answers

Answer:

do RN/RM first which will be 95/73 which is 1.30 and use this to multiply 47 which is 47*1.3   61.1

ANSWER = D.

I first got the variable of 1.3 which is multiply that by RM to get RN and then useing that logic you multiply 1.3 by MP to get QN

MARK ME BRAINLIEST

Draw a rhombus with diagonals 4 and 6. What is the area of the rhombus?

Answers

first of all you have to draw a rhombus

area (d+d)/2

(4+6)/2

5

Simplify each of the following.
7^2 x 7^3

Answers

9514 1404 393

Answer:

  7^5 = 16,807

Step-by-step explanation:

The applicable rule of exponents is ...

  (a^b)(a^c) = a^(b+c)

__

Here, we have a=7, b=2, c=3, so ...

  (7^2)(7^3) = 7^(2+3) = 7^5 = 16,807

A number, n, decreased by 5, is equal to 3 times the number plus 1. Determine the number.

Answers

Answer:

-3

Step-by-step explanation:

A number, n, decreased by 5:   n - 5

3 times the number +1 = 3*n + 1 = 3n + 1

3n +1 = n -5

Subtract 1 from both sides

3n = n - 5 - 1

3n = n - 6

Subtract 'n' from both sides

3n - n = -6

      2n = -6        {Divide both sides by 2}

       n = -6/2

      n = -3

The number = - 3

Please hellppp meeeee

Answers

Answer:

Slope = -1

Explanation:

Basically, your rise will be going 1 box up (an arrow upwards) and your run would be 1 box to the left (an arrow to the left). This will give you :-

1/-1 = -1

Hope this helps, thank you :) !!

Answer:

-4/3

Step-by-step explanation:

Please help, I have ask it 5 times. Please.

Answers

LM are congruent to HI , GM are congruent to LJ

Answer:

Pair 1: GM and LJ

Pair 2:HI and LM

Step-by-step explanation:

The markings on the line show which lines are congruent to each other. This means that line HI and ML are congruent because they have similar markings. And you could say the same for line JL and MG because it has 2 lines that mark it as congruent to eachother.

So basically your answers are GM and LJ as one pair and HI and LM as another

A farmer has one square mile of land. If he divides his land into square fields that are 1/2 mile long and 1/2
[tex] \frac{1}{2} \times \frac{1}{2} [/tex]
wide, how many fields will he have?​

Answers

Answer:

1/4

Step-by-step explanation:

Which decimal is largest?
0.49
0.45
0.48

Answers

Answer:

0.49

Step-by-step explanation:

Answer:

0.49

Step-by-step explanation:

its 0.01 larger than 0.48

its 0.04 larger than 0.45

A game consists of randomly choosing a bag (labelled 1, 2 or 3) out of a choice
of 100, and then again randomly, picking a ball (red or black) from it.
Each bag has the same total number of balls (10).
Bag options
Ball options
a) Complete the tree diagram.
0.6 Red
b) Work out the probability that a player
will select a red ball.
0.4 -Black
0.35
0.2
Red
0.45
2.
0.8
Black
c) The same player is going to play the
game 200 times consecutively.
How many black balls should he
expect to pick?
0.7
Red
3
0.3
Black

Answers

Answer:

A=0.2

b=0.2 x 0.7=0.14

0.45 x 0.2=0.09

0.44

c=112

Step-by-step explanation:

What is the volume of the following rectangular prism pls pls pls pls pls pls pls pls p

Answers

Answer:

Step-by-step explanation:

V = l * w * h

l = 2

h = 2

w = 7/3

Volume = 2 * 2 * 7/3 = 28/3 = 9 1/3 or 9.3333

While eating lunch, Douglas noticed that 15 students chose to eat chicken and 19 chose to eat pizza. What is the ratio of students in his class who chose to eat chicken to the total number of students?

Answers

15 : 34 is the correct answer15 + 19 = 3415 ate chicken34 total students (assuming everybody ate either pizza or chicken)Please let me know if I am wrong.

There are two right angle triangles, triangle ABC and Triangle EDF. Measure of angle ACB and angle EFD are 90. Side AB is congruent to side ED, Side AC is congruent to side DF. What theorem can be used to show that ABC ≅ DEF?

Answers

Answer:

SAS theorem

Step-by-step explanation:

Given

Triangles ABC and DEF

[tex]AB = ED[/tex]

[tex]AC = DF[/tex]

[tex]\angle ACB = \angle EFD = 90^{\circ}[/tex]

Required

Which theorem shows the similarity between both triangles

The following can be deduced from the given parameters.

[tex]AB = ED[/tex] ===> Equal Sides

[tex]AC = DF[/tex] ===> Equal Sides

[tex]\angle ACB = \angle EFD = 90^{\circ}[/tex] ===> Equal Angle

This implies that two sides and 1 angle of both triangles are equal.

Hence, the theorem to use is the SAS theorem.

Vertical angles are a pair of opposite angles made by two intersecting lines and the angles are _________. *
2 points
Equal to each other
Equal to 90°
Equal to 180°
Equal to 360°

Answers

Answer:

[tex] \boxed{ \large{ \underline{\tt{Equal \: to \: each \: other}}}}[/tex]

Step-by-step explanation:

When two lines interesect , the angles formed opposite to each other are called vertically opposite angles. Vertically opposite angles [ V.O.A ] are always equal to each other.

Refer to the attachment! In the given figure , [tex] \angle[/tex] p and [tex] \angle[/tex] s are opposite to [tex] \angle[/tex]r and [tex] \angle[/tex]q respectively. Therefore [tex] \angle[/tex]p and [tex] \angle[/tex]r are vertical angles. Similarly , [tex] \angle[/tex]s and [tex] \angle[/tex]q are also vertical angles.

Hence , Our final answer : Vertical angles are a pair of opposite angles made by two intersecting lines and the angles are equal to each other .

Hope I helped ! ツ

Have a wonderful day / night ! ♡

# [tex] \underbrace{ \large{ \tt{Carry \: On \: Learning}}}[/tex] !!▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁

At the circus, a clown is shot from a cannon. This situation can be modeled by the function: h = – 16t2 + 45t + 15, where 'h' is height in feet and 't' is time in seconds. Height of the clown

Answers

Answer:

t = 3.11 seconds

Step-by-step explanation:

Given that,

At the circus, a clown is shot from a cannon. This situation can be modeled by the function :

[tex]h = -16t^2 + 45t + 15[/tex]

Where

'h' is height in feet and 't' is time in seconds

We need to find how long did it take for the clown to reach his highest point. It can be calculated as follows :

[tex]-16t^2 + 45t + 15=0[/tex]

We need to solve for t. It can be calculated as follows :

[tex]t=\dfrac{-45\pm \sqrt{45^2-4(-16)(15)} }{2(-16)}\\\\t=-0.301\ \text{and}\ 3.11\ s[/tex]

So, the required time is 3.11 seconds.

A line passes through point (-2, 5) and has a slope of 5/2.
Write an equation in Ax + By = C form for this line.
Use integers for A, B, and C.

Answers

Answer:

5x-2y=-20

Step-by-step explanation:

y-y1=m(x-x1)

y-5=5/2(x-(-2))

y-5=5/2(x+2)

y-5=5/2x+10/2

y-5=5/2x+5

y=5/2x+5+5

y=5/2x+10

y-5/2x=10

-5/2x+y=10

2(-5/2x+y)=2(10)

-10/2x+2y=20

-5x+2y=20

5x-2y=-20

Write 6 ,7,8,9 or 10 and 12

Answers

Answer:

9

Step-by-step explanation:

a. On the map of Arkansas shown, find the actual distance between Clarksville and Little Rock. Use a ruler to measure.​

Answers

Answer:

1cm/20mi = 4cm/x

1x = 80

x = 80

The answer is 80 miles

Find the median:51,53,49,51,53,50,54,56​

Answers

Answer:

52

Step-by-step explanation:

Answer:

52

Step-by-step explanation:

49, 50, 51, 51, 53, 53, 54, 56

the middle are (51,53) and when u have 2 numbers in the middle u add them up and divide by two which gives us 52:)

Can someone solve this please?

Answers

Answer: x = 1/2

Step-by-step explanation:

how long is a 75% of a 24 hour day

Answers

Answer:

18 hours

Step-by-step explanation:

because 6 x 3 = 18!

2. A bacteria population is modeled by the equation p(n)= 10,000.2", where h is the number of hours since
the population was measured.
About how long will it take for the population to reach 100,000?

Answers

Answer: its 3 the answer is 3

Step-by-step explanation:

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