To prove that the left cosets of H constitute a partition of G, we need to show that they satisfy two conditions:
1) Each element of G belongs to some left coset of H.
2) Any two distinct left cosets of H are disjoint.
Let g be any element of G. Then, by definition of a left coset, there exists an element h of H such that g = h·x for some x in G. Therefore, g belongs to the left coset H·x. Since this holds for any element g of G, we have shown that the left cosets of H cover all of G, satisfying the first condition.
Now, let H·x and H·y be two distinct left cosets of H. Suppose there exists an element z in both H·x and H·y.
Then, z = [tex]h_{1}[/tex]·x = [tex]h_{2}[/tex]·y for some [tex]h_{1}[/tex], [tex]h_{2}[/tex] in H.
Solving for x,
x = [tex]h_{1}^{-1}[/tex]· [tex]h_{2}[/tex] · y.
Since H is a subgroup, [tex]h_{1}^{-1}[/tex]· [tex]h_{2}[/tex] is also in H, and therefore x belongs to H·y.
Thus, H·x is contained entirely in H·y, and the two cosets cannot intersect.
This satisfies the second condition, and hence the left cosets of H constitute a partition of G.
A similar argument can be used to show that the right cosets of H also constitute a partition of G. This completes the proof.
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Can someone help me please
The resulting matrix will be in the form :
5 9 -4
0 -14 15
What is a matrix in mathematics ?A matrix is described as a rectangular array or table of numbers, symbols, or expressions, arranged in rows and columns, which is used to represent a mathematical object or a property of such an object.
To get a 1 in row 1, column 1, we perform the following elementary row operation:
R2 - 2R1 -> R2
This will subtract 2 times the first row from the second row and give us the result:
5 9 -4
0 -14 15
Matrices are useful for describing systems of linear or differential equations, as well as representing a linear application.
In conclusion, in a matrix function, the input and the output values are matrices.
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An ant crawled 2/8 yard from an ant mount. On which number line does point A represent the ants position after crawling 2/8 yard?
The number line on which point A represents the ant's position after crawling 2/8 yard would be a number line labeled in units of yards, with O representing 0 and A representing 1/4 yard to the right of O.
To decide the place of the insect subsequent to creeping 2/8 yard from the insect mount, we really want to address this distance on a number line.
Since 2/8 can be rearranged to 1/4, we can address the distance crept by the subterranean insect as 1/4 of a yard.
To develop a number line to address this distance, we can begin with the point addressing the subterranean insect mount (we should call it point O) and separate a distance of 1/4 of a yard to one side of O. This point, which we can name as point A, addresses the place of the insect subsequent to creeping 2/8 yard (or 1/4 yard) from the insect mount.
The number line would have units of yards, with the distance between every unit separated similarly. The point O would address 0 on the number line, and the point A would address 1/4 yard on the number line.
Thus, the number line on which point An addresses the insect's situation in the wake of creeping 2/8 yard would be a number line named in units of yards, with O addressing 0 and An addressing 1/4 yard to one side of O.
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The complete question is:
An ant crawled 2/8 yard from an ant mount. On which number line does point A represent the ants position after crawling 2/8 yard?
0.6/(-0.9- -0.5 x -0.3)
The value of the expression is -0.8
What is PEDMAS?PEDMAS can be described as a mathematical acronym that is used for the representation of arithmetic operations on the basis of how they are to be carried out sequentially in an equation.
The alphabet represents different operations. They are;
P represents parenthesesE represents exponentsD represents divisionM represents multiplicationA represents additionS represents subtractionFrom the information given, we have that;
0.6/(-0.9- -0.5 x -0.3)
Multiply the values
0.6/(-0.9 +0. 15)
add the values
0.6/0. 75
Now, divide the values
-0.8
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N Heracio's Computer Time Shopping Research 10% Videos 15% Homework 20% Games 20% Social dia 25% Heracio used the computer a total of 40 hours last week. How many more hours did Heracio use the computer to do homework than shop online?
Heracio used the computer 4 more hours to do homework than shop online.
How to solve the proportionTo find out how many more hours Heracio used the computer to do homework than shop online, we first need to calculate the number of hours he spent on each activity.
Let's start by calculating the number of hours Heracio spent on each activity:
Shopping: 10% of 40 hours = 4 hours
Videos: 15% of 40 hours = 6 hours
Homework: 20% of 40 hours = 8 hours
Games: 20% of 40 hours = 8 hours
Social media: 25% of 40 hours = 10 hours
Now, to find out how many more hours Heracio used the computer to do homework than shop online, we need to subtract the number of hours spent shopping from the number of hours spent on homework:
8 hours (homework) - 4 hours (shopping) = 4 hours
Therefore, Heracio used the computer 4 more hours to do homework than shop online.
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The table represents the quadratic functions f(x) and g(x).
x f(x) g(x)
−8 16 4
−4 4 1
0 0 0
4 4 1
8 16 4
What transformation of f(x) will produce g(x)?
g of x equals one fourth times f of x
g of x equals f of the quantity of one fourth times x end quantity
g(x) = 4f(x)
g(x) = f(4x)
The transformation of f(x) that will produce g(x) is given as follows:
g(x) = f(x)/4.
How to obtain the function g(x)?If we observe at the table, we have that each value of g(x) is one fourth of the value of the function f(x).
Hence the transformation of f(x) that will produce g(x) is given as follows:
g(x) = f(x)/4.
The transformation means that the function g(x) is a vertical compression by a factor of 4 of the function f(x).
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Marla, Jamie, and Sarah have each led their book club’s monthly meeting. Jamie has led 2/6 of the meetings, and Sarah has led 1/6 of the meetings. What fraction of the meetings has Marla led?
Step-by-step explanation:
1-2/6-1/6= 3/6
= 1/2
Marla has led 1/2 of the meetings
Find the sine, cosine, and the tangent of the acute angle A of the triangle. Express each answer as a fraction in simplest form.
Answer:
Step-by-step explanation:
sina=12/20=0.6
cosa=16/20=0.8
tana=0.6/0.8=0.75
Which one of the following is a rule of multiplication?
A.The order in which you multiply two whole numbers
changes the product.
B.The product of a whole number and 1 is never the
same whole number.
C.The product of a whole number and zero is the same
whole number.
D.The way you group numbers in a series of
multiplication problems doesn't change the final
product.
Answer:
D.The way you group numbers in a series of
multiplication problems doesn't change the final
product.
I need help finding the answer to this question
Answer: I believe it would be 2/5.
Step-by-step explanation:
Reduction means the fraction is reduced to it's simplest form.
7/7=1
2/5=2/5
15/13=1 2/13
See as the '2/5' does not change in reduction.
So, '2/5' would be your answer.
Hope this helps! :)
Assume that the speed of automobiles on an expressway during rush hour is normally distributed with mean of 62 mph and a standard deviation of 5 mph.
What percent of cars are traveling slower than 55 mph?
About 8.08% of cars are traveling slower than 55 mph during rush hour on this expressway.
To solve this problemUsing the provided mean and standard deviation, we must standardize the value of 55 mph before determining the equivalent area under the standard normal distribution curve.
The standardized value, or z-score, is calculated as:
z = (x - μ) / σ
Where
x is the value we want to standardize (in this case, 55 mph) μ is the mean (62 mph)σ is the standard deviation (5 mph)Plugging in the values, we get:
z = (55 - 62) / 5 = -1.4
The area under the usual normal distribution curve to the left of z = -1.4 must now be determined. Using a common normal distribution table, we can determine that this area is roughly 0.0808.
Therefore, about 8.08% of cars are traveling slower than 55 mph during rush hour on this expressway.
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The right triangle on the right is a scaled copy of the right triangle on the left. Identify the scale factor. Express your answer as a fraction in simplest form.
7
7
22
The scale factor for this right triangles is equal to 5/4.
What is a scale factor?In Mathematics, the scale factor of any geometric figure can be determined by dividing the dimension or side length of the new figure (image) by the dimension or side length of the original figure (pre-image):
Scale factor = Dimension of new figure (image)/Dimension of original figure (pre-image)
By substituting the given dimensions into the formula for scale factor, we have;
Scale factor = image dimension/pre-image dimension
Scale factor = 15/12 = (25/4)/5
Scale factor = 5/4.
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Missing information:
The question is incomplete and the complete question is shown in the attached picture.
The trinomial: x² - 5x +11 is not factorable. Explain why this is.
Answer:
Step-by-step explanation:
I cannot find 2 numbers that multiply to the last term (+11) and add to middle term (-5)
So it can't be factored that way.
After further inspection. i try to plug it into b²-4ac from the quadratic formula.
b=-5
c=11
(-5)²-4(1)(11)
= -19 you can never get a negative under the square root. so this quadratic will produce 2 imaginary solutions. so it is not factorable.
a group of students were asked if they are in the math club and if they are in the literature club. Partial results are shown in the table. What is the value of x+y?
Hence Option A. 22 is correct.
How to solveOf the students in the maths club , 67% are not in the literature club.
So the number of students in Maths club =
[ ( Number of students in maths club but not in the literature club) / 67 ] * 100 % = [ 16 / 67 ] * 100% = 24 (Rounded)
Hence, Number of students in maths club and in the literature club =
x = Total Number of students in Maths club - Number of students in maths club but not in the literature club
x = 24 - 16 = 8
Of the students not in the maths club , 78% are not in the in the literature club.
So, Of the students not in the maths club , 100% - 78% = 22% are in the literature club.
So the number of students not in the Maths club =
[ ( Number of students not in the maths club and in the literature club) / 22 ] * 100 %
= [ 4 / 22 ] * 100% = 18.18 = 18 (Rounded)
Hence, Number of students not in the maths club and not in the literature club =
y = Total Number of students not in the Maths club - Number of students not in the maths club and in the literature club
y = 18 - 4 = 14
So, x + y = 8 + 14 = 22.
Hence Option A. 22 is correct.
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Which statement concerning the equation x² - 1 = x is true?
1. Its discriminant is 0, so it has no solution.
2. Its discriminant is 5, so it has two real solutions.
3. Its discriminant is 0, so it has one real solution.
4. Its discriminant is -3, so it has two complex solutions.
Answer:
The equation x² - 1 = x can be rewritten as x² - x - 1 = 0. We can use the quadratic formula to find the solutions:
x = (-b ± sqrt(b² - 4ac)) / 2a
In this case, a = 1, b = -1, and c = -1. So:
x = (1 ± sqrt(1 - 4(1)(-1))) / 2(1)
x = (1 ± sqrt(5)) / 2
Therefore, the equation has two real solutions, and the discriminant is positive. The answer is 2. Its discriminant is 5, so it has two real solutions.
What type of transformation is modeled?
The type of transformation modeled in the graph is Reflection across y-axis.
How many different coordinate transformations are there?The three different kinds of coordinate transformation are listed below. The motor's three-phase current and voltage are transformed by the Clark transformation from their original natural coordinates to two-phase static coordinates determined with reference to the stator.
What is the transformational rule?Because the domain or range values of the function f(x) have changed, rules of transformations assist in changing f(x) to a new function f'(x). With the use of these transformational rules, the function can be stretched or compressed as well as transformed vertically or horizontally.
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Boyd's board shop grt a shipment of 92 new skateboards wheels. Boyd assembles the skateboards and puts 4 of the new wheels on each board. You can use a function to describe the number of new wheels Boyd has left after assembling x skateboards
The function to describe the number of new wheels Boyd has left is f(x) = 92 - 4x
From the question, we have the following parameters that can be used in our computation:
Shipment of 92 new skateboards wheels. 4 of the new wheels on each board.After assembling x skateboards, we have
f(x) = Shipmnet - Rate * x
Substitute the known values in the above equation, so, we have the following representation
f(x) = 92 - 4 * x
Evaluate
f(x) = 92 - 4x
Hence, the function is f(x) = 92 - 4x
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Solve for X. *
-48-x=-39
Answer:
x = - 9
Step-by-step explanation:
-48 - x = -39
Add 48 on both sides
-x = 9
Divided both sides by -1
x = - 9
So, the answer is x = - 9
Solve for x. Round to the nearest tenth, if necessary.
Answer:
x=38.6
Step-by-step explanation:
x=b/cos(alpha)
x=30/cos(39⁰)
x=38.602
q
5cm
X =
X
8cm
4cm
cm
Answer:
2.5 cm
Step-by-step explanation:
The small arrow is 1/2 the side of the large arrow. 1/2 of 5 is 2.5 or 2 1/2.
Helping in the name of Jesus.
The height y(in feet) of a ball thrown by a child isy=−114x2+2x+3
where x is the horizontal distance in feet from the point at which the ball is thrown.
(a) How high is the ball when it leaves the child's hand? (Hint: Find y
when x=0)
Your answer is y=____
(b) What is the maximum height of the ball? _____
(c) How far from the child does the ball strike the ground?_____
One respondent said they watched 10 movies. This seems to be an
symmetrical
This graph is
skewed
to the
left
because the data is stacked on the left with a "tail" going to the right.
Most people watched
[ Select ]
movies
The graph seems to be a left symmetrical distribution and most people watched action movies
Calculating the skewness of the graphFrom the question, we have the following parameters that can be used in our computation:
The graph (see attachment)
From the graph, we have the following readings and observations
The movie with the highest frequency is Action moviesThe data is stacked on the right with a "tail" going to the left.Using the above as a guide, we have the following conclusions
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Write the word form of the number in standard decimal form for: three and fifty-four thousandths
Answer: 350.214
Step-by-step explanation:
Find the measure of EB
The measure of angle subtended by the arc EB is 96 ⁰.
What is the measure of arc angle EB?The measure of angle subtended by the arc EB is calculated by applying the following formula.
Based on the angle of intersecting chord theorem, the theory states that, the angle formed by the intersection of two chords at the circumference of a circle is equal to half of the difference between the arc angles of the two chords.
We will have the following equation;
m∠ECB = ¹/₂( 7x + 6 - (4x + 16))
25 x 2 = 7x + 6 - 4x - 16
50 = 3x - 10
60 = 3x
x = 60/3
x = 20
The measure of arc angle EB is calculated as follows;
m∠EB = 4x + 16
m∠EB = 4(20) + 16
m∠EB = 96 ⁰
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Please help me i am so confused
The interval that will have the highest frequency will be: C. 11 - 15.
Which interval will have the highest frequency?The interval that will have the highest frequency will be 11 - 15. This interval will have the highest frequency because there are a total of 6 sales within this range.
The other intervals have sales that are 5 and below. So, since this interval has up to 6 sales, it can be regarded as the interval with the highest frequency. Frequency refers to how often something occurs. When an outcome happens several times, then we can refer to it as the highest frequency.
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18 m
Bookwork code: N93
Tyler wants to cover this prism in glitter.
If 80 g of glitter is needed to cover each m², how much glitter will he
need to cover the prism completely?
23 m
allowed
10 m
3,517 XP
25 m
Allie Eggleton MENU
14m
Tyler will need a amount of 79,200 grams (or 79.2 kilograms) of glitter to cover the prism completely.
To calculate the amount of glitter needed to cover the prism completely, we first need to find the total surface area of the prism.
The prism consists of five faces: two rectangular faces with dimensions 18 m x 10 m, two triangular faces with base 18 m and height 10 m, and one rectangular face with dimensions 18 m x 25 m.
The total surface area of the prism can be calculated by adding the areas of all the faces together:
Total Surface Area = 2(18 m x 10 m) + 2(0.5 x 18 m x 10 m) + 18 m x 25 m
Total Surface Area = 360 m² + 180 m² + 450 m²
Total Surface Area = 990 m²
Given that 80 g of glitter is needed to cover each m², we can now calculate the total amount of glitter needed:
Total Glitter = Total Surface Area x Glitter per m²
Total Glitter = 990 m² x 80 g/m²
Total Glitter = 79,200 g
Therefore, Tyler will need 79,200 grams (or 79.2 kilograms) of glitter to cover the prism completely.
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Question 12: The base and height of the rhombus are given. Apply a formula to find the area of the rhombus
Jim bought a pair of shoes for $50 and laces for $1. If the sales tax is 7%, how much tax must he pay?
(a) $3.57
(c) $0.36
(b) $350
(d) $35.70
Jim must pay tax $3.57.
The correct answer is (a) $3.57.
To calculate the sales tax that Jim must pay, we need to find 7% of the total cost of the shoes and laces.
The total cost of the shoes and laces is $50 (shoes) + $1 (laces) = $51.
To calculate the sales tax, we multiply the total cost by the tax rate:
Sales tax = 7% of $51
[tex]= 0.07 \times $51[/tex]
= $3.57.
Therefore, Jim must pay $3.57 in sales tax.
The correct answer is (a) $3.57.
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if you help I would be so thankful
Answer:
I put the answer on the attachment please look
please help me with this problem
Answer:
X = 81
Y = 729
Step-by-step explanation:
Basically I simplified each expression by making both logarithms as one then converting it from logarithm to exponential (I hope you know how to do it, you must).. I then obtained 2 final equations labeled as equation 1 and equation 2. From there on its just Maths but I hope you understand what I did
Find f(g(1)) and g(f(1))
F(x)=x^2+2;g(x)=2x-5
Answer:
Step-by-step explanation:
Given the functions f(x) = x^2 + 2 and g(x) = 2x - 5, we can find f(g(1)) and g(f(1)) by evaluating the inner function first and then using its result as the input for the outer function.
First, let’s find f(g(1)). We start by evaluating the inner function g(1):
g(1) = 2 * 1 - 5 = -3
Now we can use this result as the input for the outer function f(-3):
f(g(1)) = f(-3) = (-3)^2 + 2 = 9 + 2 = 11
Next, let’s find g(f(1)). We start by evaluating the inner function f(1):
f(1) = 1^2 + 2 = 3
Now we can use this result as the input for the outer function g(3):
g(f(1)) = g(3) = 2 * 3 - 5 = 6 - 5 = 1
So, f(g(1)) = 11 and g(f(1)) = 1.