What is the meaning of "a subset that is closed under multiplication is not necessarily a subgroup"?

What Is The Meaning Of "a Subset That Is Closed Under Multiplication Is Not Necessarily A Subgroup"?

Answers

Answer 1

In abstract algebra, a subset of a group is considered a subgroup if it satisfies certain conditions. One of these conditions is closure under the group operation (i.e., multiplication).

What is abstract algebra?

Abstract algebra is a branch of mathematics that studies algebraic structures, which are sets with operations (such as addition, multiplication, or other binary operations) defined on them that satisfy certain axioms or properties. Algebraic structures can be extremely diverse and abstract, ranging from familiar structures such as the integers, rational numbers, and real numbers, to more complex structures such as groups, rings, fields, and modules.

If we take any two elements from the subset and multiply them together, the result must also be in the subset. However, a subset that is closed under multiplication is not necessarily a subgroup.

To see why this is the case, consider the set {1, -1} under multiplication. This set is closed under multiplication, since 1 * 1 = 1 and (-1) * (-1) = 1, which are both in the set. However, this set is not a subgroup of the group of real numbers under multiplication, because it does not contain an identity element (i.e., an element that behaves like a "neutral" element under multiplication). In this case, the identity element is 1, which is in the larger group but not in the subset {1, -1}. Therefore, {1, -1} is not a subgroup, even though it is closed under multiplication.

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Related Questions

Select the word from the following list that best describes each situation.

1. You deposit money in a savings account, and every year the amount of
money in the account increases by 2.5%.

2. For every car sold, a car salesman is paid 6% of the car's price.

3. Someone who eats at a restaurant pays an extra 20% of the food price. This
extra money is kept by the person who served the food.

4. An antique furniture store pays $200 for a chair, adds 50% of that amount,
and sells the chair for $300.

5. The normal price of a mattress is $600, but it is on sale for 10% off

6. For any item you purchase in Texas, you pay an additional 6.25% of the
item's price to the state government.

A Tax
B. Commission
C. Discount
D. Markup
E Tip or gratuity
F. Interest

Answers

Answer:

F

B

E

D

C

A

Step-by-step explanation:

Which expressions are equal to 0 when x=-1? Check all that apply.

Which expressions are equal to 0 when x=-1? Check all that apply.

Answers

Answer:

The answer A,B,C

Question 2
No calculations are necessary to answer this question.
3/01
3/02
$1.7420 $1.7360
Date
July GBP Futures
Contract Price
O long; long
Based on the closing prices of July GBP Futures Contract over the 3-day period in March 20XX as shown above, you shou
position on 3/01 and a position on 3/02.
O long; short
O short; short
3/03
short; long
$1.7390

Answers

The given information does not provide any clear indication for determining the position that should be taken on 3/01 and 3/02. Without additional information, it is not possible to make a decision. The table only displays the closing prices of the July GBP Futures Contract on different days, and it is unclear what trading strategy or what scenario is being considered. Additional information about the goals and objectives, the market conditions, and other relevant factors would be necessary to make a decision about trading positions.

\(\frac{5}{\sqrt{2} }\)

Answers

Answer:yesStep-by-step explanation:

yes


Jamie went out to her grandfather's farm.
Her grandfather has pigs and chickens on his farm.
She noticed that there were a total of 26 heads and
68 feet among them. How many chickens and how
many pigs did her grandfather have?

Answers

Answer:

8 pigs

Step-by-step explanation:

Since every animal has only 1 head, a total of 26 heads suggests that there are 26 animals in total.

Suppose all animals are chickens.

Total no. of feet = 26 chickens × 2 feet

                           = 52 feet

Difference in total no. of feet = 68 feet - 52 feet

                                                = 16 feet

Difference in no. of feet each animal has

= 4 feet (a pig) - 2 feet (a chicken)

= 2 feet

∴ No. of pigs = 16 feet ÷ 2 feet

                      = 8 pigs

how to solve 2x + 2 = -10

Answers

Answer:

x = -4

Step-by-step explanation:

\(2x+2=-10\)

Subtract 2 on both sides

\(2x=-8\)

Divide by 2 on both sides

\(x=-4\)

Answer:

x = -6

Step-by-step explanation:

2x + 2 = -10

      -2 =  -2

2x = -12

2x divided by 2 is x. -12 divided by 2 is -6.

x = -6

PLEASE HELP ME
The function f(x) = -2(4)^x+1 +140
represents the number of tokens a child has x hours after arriving at an arcade.
What is the practical domain and range of the function?
If necessary, round to the nearest hundredth.
The practical domain of the situation is ?
The practical range of the situation is ?
PLEASE SEE PHOTO FOR FUNCTION

PLEASE HELP METhe function f(x) = -2(4)^x+1 +140 represents the number of tokens a child has x hours

Answers

The function f(x) = -2(4)ˣ⁺¹ +140 represents the number of tokens a child has x hours after arriving at an arcade. The practical domain and range of the function are x ≥ 0 and The practical range of the situation is [140, ∞).

The given function is f(x) = -2(4)ˣ⁺¹+ 140, which represents the number of tokens a child has x hours after arriving at an arcade.

To determine the practical domain and range of the function, we need to consider the constraints and limitations of the situation.

For the practical domain, we need to identify the valid values for x, which in this case represents the number of hours the child has been at the arcade. Since time cannot be negative in this context, the practical domain is x ≥ 0, meaning x is a non-negative number or zero.

Therefore, the practical domain of the situation is x ≥ 0.

For the practical range, we need to determine the possible values for the number of tokens the child can have. Looking at the given function, we can see that the term -2(4)ˣ⁺¹represents a decreasing exponential function as x increases. The constant term +140 is added to shift the graph upward.

Since the exponential term decreases as x increases, the function will have a maximum value at x = 0 and approach negative infinity as x approaches infinity. However, due to the presence of the +140 term, the actual range will be shifted upward by 140 units.

Therefore, the practical range of the situation will be all real numbers greater than or equal to 140. In interval notation, we can express it as [140, ∞).

To summarize:

- The practical domain of the situation is x ≥ 0.

- The practical range of the situation is [140, ∞).

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Translation are always

Answers

Answer:

The same shape but in a different location

Step-by-step explanation:

hope i helped u today:)

PLZ HELLPPP
what is 20% of $8.38

Answers

Answer:

$1.676 but you can round it to $1.68

Step-by-step explanation:

Answer: About $1.68

Step-by-step explanation:

I just used a calculator but you would do:

20 ?

—— ——

100 $8.38

Then you would cross multiply 20x8.38 which gives you 167.6 then you’d divide by 100 and get 1.676 and round up to 1.68!

An insurance data scientist is researching a certain stretch of a rural highway where drivers are never pulled over. The mile markers in the solution of the following inequality, where x represents the mile marker along the highway.\(2x - 18 \geqslant 122 \: or \: 5x + 15 \ \textless \ 250\)

Answers

the given inequalities are

2x - 18 ≥ 122 .....................(1)

5x + 15< 250 ....................(2)

now we solve equation (1),

2x - 18 ≥ 122

2x ≥ 122 + 18

2x ≥ 140

x ≥ 140/2

x ≥ 70

now we solve equation (2)

5x + 15< 250

5x < 250 - 15

x < 235/5

x < 47

so the value of x less than 47 and more than equal to 70.

A wireless keyboard is 10/12 foot long. The area of the wireless keyboard is 5/24 square foot. What is the width of the wireless keyboard, in feet? Enter the answer as a fraction in lowest​

Answers

Answer:

1/4 ft

Step-by-step explanation:

A = l x w

5/24 = 10/12 x w

Solve for w

5/24 divided by 10/12 = w

Take inverse of 10/12 and multiply

5/24 times 12/10

1/4

how many solutions are there 14x + 6 = 2(5 + 7x) - 4

Answers

Answer:

infinitely many solutions

Step-by-step explanation:

14x + 6 = 2(5+7x)-4

14x + 6 = 10 + 14x - 4

14x + 6 = 14x + 6

infinitely many solutions because both sides of the equation are equal

Find the midpoint of the segment with the given endpoints.
(-1,1) and (-1,9)

Answers

Answer:

(-1, 5)

Step-by-step explanation:

The midpoint of a line segment is given by the formula:

\(\boxed{\text{Midpoint}=(\frac{x_1+x_2}{2} ,\frac{y_1+y_2}{2} )}\)

Using the formula above,

midpoint of segment

= \((\frac{-1-1}{2},\frac{1+9}{2})\)

= \((\frac{-2}{2},\frac{10}{2})\)

= (-1, 5)

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Sundeep mixed 300 mL of water with 100 mL of sugar. She says "the total volume is
300 mL + 100 mL = 400 mL." Do you agree with Sundeep? Explain why or why not.

Answers

No, I don't agree with Sundeep. The mixture wont simply add up

How to show the volume will not be 400 ml

When two liquids are mixed together, their volumes don't simply add up to equal the total volume of the mixture.

When sugar is mixed with water, the total volume of the mixture is usually slightly greater than the volume of the water alone, because the sugar particles take up space between the water molecules.

The volume of the mixture will be equal to the sum of the individual volumes only if the two liquids are completely immiscible, meaning they don't mix together at all. In this case, the total volume of the mixture will be equal to the sum of the volumes of water and sugar, which is 400 mL.

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Determine the measure of the third angle in a triangle when the other two angles total 165 degrees.

Answers

Answer:

15

Step-by-step explanation:

180-15

Hello!

the sum of the angles in the triangle = 180°

so the 3rd angle = 180° - 165° = 15°

The answer is 15°

Calcular los 3/5 de los 2/3 de las 3/4 de 560

Answers

For the fractions, the calculation of 3/5 of 2/3 of 3/4 of 560 is equal to 168.

How to solve fractions?

To calculate 3/5 of 2/3 of 3/4 of 560, break it down step by step:

Step 1: Calculate 3/4 of 560:

3/4 × 560 = (3 × 560) / 4 = 1680 / 4 = 420

Step 2: Calculate 2/3 of the result from Step 1:

2/3 × 420 = (2 × 420) / 3 = 840 / 3 = 280

Step 3: Calculate 3/5 of the result from Step 2:

3/5 × 280 = (3 × 280) / 5 = 840 / 5 = 168

Therefore, 3/5 of 2/3 of 3/4 of 560 is equal to 168.

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The figure below shows parallel lines cut by a transversal. Which statement is true about angles 1 and 2?

A. Angles 1 and 2 are complementary because they are a pair of corresponding angles.
B. Angles 1 and 2 are congruent because they are a pair of corresponding angles.
C. Angles 1 and 2 are complementary because they are a pair of alternate interior angles.
D. Angles 1 and 2 are congruent because they are a pair of alternate interior angles.​

The figure below shows parallel lines cut by a transversal. Which statement is true about angles 1 and

Answers

Answer:

The answer is B. they are congruent because they are a pair of corresponding angles.

Answer:

B)

Step-by-step explanation:

Angles 1 and two are corresponding angles, because if you were to move the top line down, the two angles would be in the exact same spot.

This year you earned $75,500. Last year you earned $72,400. What was the rate of change on your earnings since last year

Answers

Answer:

4.28%

Step-by-step explanation:

We Know

Last year you earned $72,400

This year you earned $75,500

What was the rate of change in your earnings since last year?

We Take

(75,500 ÷ 72,400) x 100 ≈ 104.28%

Then We Take

104.28 - 100 = 4.28%

So, the earning increased by about 4.28%.

11 of 3011 of 30 Questions





















Question
A baker makes peanut butter cookies and chocolate chip cookies.

She needs 2 cups of flour and 34
cup of butter to make one batch of peanut butter cookies.
She needs 3 cups of flour and 1 cup of butter to make one batch of chocolate chip cookies.
If the baker has 26 cups of flour and 9 cups of butter, how many batches of each type of cookie can she make?

Answers

The baker can only make peanut butter cookies and cannot make any chocolate chip cookies with the given amount of ingredients.

Let's denote the number of batches of peanut butter cookies as "x" and the number of batches of chocolate chip cookies as "y."

From the given information, we can set up the following system of equations:

For the flour:

2x + 3y = 26

For the butter:

34x + y = 9

To solve this system of equations, we can use the substitution method or the elimination method. Let's use the elimination method:

Multiply the first equation by 17 (to make the coefficients of x in both equations the same):

34x + 51y = 442

Now we have the system of equations:

34x + y = 9

34x + 51y = 442

Subtract the first equation from the second equation:

34x + 51y - (34x + y) = 442 - 9

50y = 433

Divide both sides by 50:

y = 433/50

Since the number of batches of cookies cannot be fractional, we need to find a whole number solution for y. However, in this case, y is a fraction, indicating that the given amount of butter is not sufficient to make even one batch of chocolate chip cookies.

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Please really need answer would greatly be appreciated and mark brainliest.

Please really need answer would greatly be appreciated and mark brainliest.

Answers

Answer:

8ft of ground is covered, 8ft of metal and about 2 feet wide, it can hold 10ft of water i think

Answer:

Step-by-step explanation:

8 feet

In ΔGHI, \text{m}\angle G = (8x+14)^{\circ}m∠G=(8x+14)

, \text{m}\angle H = (3x-6)^{\circ}m∠H=(3x−6)

, and \text{m}\angle I = (x+16)^{\circ}m∠I=(x+16)

. Find \text{m}\angle G.m∠G.

Answers

Answer:16

Step-by-step explanation:

The measure of the angle m<G is 118 degrees

The sum of an interior angle of a triangle is 180 degrees

Given the following angles of a triangle:

m∠G=(8x+14)

m∠H=(3x-6)

m∠I=(x+16)

Since the sum of angle is 180 degrees, hence;

m∠G + m∠H + m∠I = 180

8x + 14 + 3x - 6 + x + 16 = 180

12x + 24 = 180

12x = 180 - 24

12x = 156

x = 156/12

x = 13

Get the measure of angle m<G

m<G = 8x + 14

m<G = 8(13) + 14

m<G = 104 + 14

m<G = 118 degrees

Hence the measure of the angle m<G is 118 degrees

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Which linear inequality is graphed with y >x-2 to
create the given solution set?
Oy>x+1
O y Oy>x-1
O y

Answers

The inequality y > x - 2, plotting the inequality using geogebra online graphing tool, the solution is attached.

Inequality

Inequality is an expression that is used to show the non equal comparison of two or more numbers and variables.

Given the inequality y > x - 2, plotting the inequality using geogebra online graphing tool, the solution is attached.

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The inequality region is represented by the inequality y < x + 1.

We have to given that,

To find the inequality set which is graphed with y > –x – 2 to create the given solution set.

Now, One of the line is having the y intercept -2 and slope -1 having the equation y = -x -2.

Since, The shaded region is having the inequality y>-x-2.

The other line is having the y intercept 1 and slope of 1.

Hence equation of line is,

⇒ y = x + 1.

And, The shaded part is above the line .

Hence, The inequality region is represented by the inequality y < x + 1.

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Complete question is,

Which linear inequality is graphed with y > –x – 2 to create the given solution set?

A=y > x + 1

B=y < x – 1

C=y > x – 1

D=y < x + 1

Which linear inequality is graphed with y &gt;x-2 tocreate the given solution set?Oy&gt;x+1O yOy&gt;x-1O

Joanna ran a mile in physical education class after resting for 1 hour her heart rate was 60 beats per minute if her heart rate decreased it by 2/5 what was her heart rate and merely after she ran the mile

Answers

Answer:Since 2/5 is basically a part of a whole, you would have to divide 60 by 20. You would get thirty. Thirty times five is 150.

Step-by-step explanation:

Part 2: Kristen is paid $8.25 per hour. How much would her paycheck be for 39 hours? Show your work

Answers

$321.75, just multiply the 2 numbers

The Kristen's paycheck for 39 hours is $321.75.

What is the unitary method?

The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.

Given that, Kristen is paid $8.25 per hour.

Paycheck for 39 hours

= 39×8.25

= $321.75

Therefore, the Kristen's paycheck for 39 hours is $321.75.

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Select the correct answer.
If a six-sided die is rolled 30 times, how many times can you expect to get a 6?
OA 3
OB.
5
OC. 6
OD 10
PL HELP WILL MARK BRAINLY 10 POINTS

Answers

Answer:

5 times

Step-by-step explanation:

1/6·30=5

so your answer is b)5

Can i have a brainliest please or 10 points?

Given the quadratic function

Given the quadratic function

Answers

The vertex is (-4,-3)

The axis of symmetry is x=-4

and the transformations are:

Given the quadratic function

There are 16 left-handed students in Ms. Tatum's class. The other 20 students in her class are right-handed.
What is the percentage of the class who are left-handed? Explain your answer.

Answers

Answer:

I'm pretty sure the answer is about 44%

Step-by-step explanation:

Can anyone help? Its on plato precalc sem A

Can anyone help? Its on plato precalc sem A

Answers

B or C I’m not sure :/

help ugent!
12 + 2 + 2 + 2 + 2 + 2 ^ 2=

Answers

\(24.\)

Step-by-step explanation:

\(12 + 2 = 14.\)

\(14 + 2 = 16.\)

\(16 + 2 = 18.\)

\(18 + 2 = 20.\)

\(20 + {2}^{2} = 24.\)

Note:- 2² = 2×2 = 4. So, 2² = 4.

Answer:

24

make sure you calculate the answer next time!

What is (3x7 + 7x5 - 3x² + 7) + (x7 - 3x5 + 2x³ + 3)?

Answers

Answer:

Hope this helps ;) don't forget to rate this answer !

Step-by-step explanation:

To solve this problem, we need to perform the indicated operations in order. The first step is to simplify the expressions inside the parentheses.

(3x7 + 7x5 - 3x² + 7) + (x7 - 3x5 + 2x³ + 3)

= (21x + 35x - 3x² + 7) + (7x - 15x + 2x³ + 3)

The next step is to combine like terms within each parentheses:

= (21x + 35x - 3x² + 7) + (7x - 15x + 2x³ + 3)

= (56x - 3x² + 7) + (-8x + 2x³ + 3)

Finally, we can add the two expressions:

= (56x - 3x² + 7) + (-8x + 2x³ + 3)

= 56x - 3x² - 8x + 2x³ + 3 + 7

= 56x - 3x² - 8x + 2x³ + 10

The final answer is 56x - 3x² - 8x + 2x³ + 10.

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