To prove: The number of left cosets of a subgroup is equal to the number of its right cosets.
Proof: Let H be a subgroup of a group G. Let g be an element of G. Consider the map f: H→ gH defined by f(h) = gh for all h in H. We claim that f is a bijection from H to gH.
First, we show that f is injective. Suppose f(h1) = f(h2) for some h1, h2 in H. Then gh1 = gh2, which implies that h1 = h2, by left cancellation law. Therefore, f is injective.
Next, we show that f is surjective. Let gh be an element of gH. Then h is an element of G, since gH is a subset of G. Since H is a subgroup of G, it follows that gh is an element of gH. Therefore, f(h) = gh, which shows that f is surjective.
Hence, f is a bijection from H to gH. Therefore, the number of left cosets of H is equal to the number of right cosets of H.
can someone help me please
The matrix formed by performing the row operation 4R₁ + R₂ — R₂ on M will have R₁ = [1 0 3] and R₂ = [ -1 2 10]
What is a matrix row operationRow operations are a set of operations that can be performed on the rows of a matrix in order to transform it into a row equivalent matrix, which has the same solution set as the original matrix.
performing the row operation 4R₁ + R₂ — R₂ on M, we have;
4(1) + (-5) = -1 {row 2 column 1}
4(0) + 2 = 2 {row 2 column 2}
4(3) + (-2) = 10 {row 2 column 3}
Therefore, the matrix formed by performing the row operation 4R₁ + R₂ — R₂ on M will have R₁ = [1 0 3] and R₂ = [ -1 2 10]
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What is the meaning of "Finally [tex]s _{i}\circ s_{i}=s _{j}\circ s_{i}=1[/tex] hence [tex]s _{j}=s_{i}\circ r_{i-j}[/tex] and [tex]s _{i}=r_{i-j}\circ s_{j}[/tex]?
This statement describes the relationship between symmetries and rotations
Explaining the meaning of the statement as statedThis statement describes a relation between two symmetry operations, denoted by [tex]s_i[/tex] and [tex]s_j[/tex], and a rotation operation denoted by [tex]r_{i-j}[/tex]. The notation [tex]"s_i \circ s_i"[/tex] and [tex]"s_j \circ s_i"[/tex] denotes the composition of these operations, which means applying one operation after the other.
The statement says that [tex]s_i[/tex] and [tex]s_j[/tex] are both symmetries, and that they have a specific relationship with each other: when [tex]s_i[/tex] is composed with itself, it gives the identity operation (denoted by 1), and when [tex]s_j[/tex] is composed with [tex]s_i[/tex], it also gives the identity operation.
Then the statement concludes that this relationship implies that [tex]s_j[/tex] can be obtained by first applying [tex]s_i[/tex] and then applying a rotation operation [tex]r_{i-j}[/tex], and that [tex]s_i[/tex] can be obtained by first applying a rotation operation [tex]r_{i-j}[/tex] and then applying [tex]s_j[/tex].
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Jeannie designs jewelry. The figure shows a
pendant on a necklace Jeannie is making. It is
composed of three individual beads.
The larger triangular bead cost $1.52. The
rectangular bead costs $0.42, and the smaller
triangular bead costs $0.92.
What is the cost per square millimeter of the
pendant? Round your answer to the nearest
hundredth.
Answer: ≅ $0.02
Step-by-step explanation:
First, lets find the area of the large triangle
0.5 x 14 x 11 = 77 mm^2
Next lets find the area of the middle rectangle:
4 x 14 = 56 mm^2
Last lets find the area of the small triange:
0.5 x 14 x 3 = 21 mm^2
So the total area is: 77 + 56 + 21 = 154 mm^2
the total cost is given to be: 1.52 + 0.42 + 0.92 = $2.86
dividing the cost by the area to find the cost/mm:
2.86/154 ≅ $0.02
A woman earned wages of 33,900 receive 2600 and interest from savings account and contributed 3600 to tax deferred retirement plan she was entitled to a personal exemption of 3500 and her deductions totaling 5440 find her gross income adjusted income and taxable income
The woman's gross income, adjusted income and taxable income are:
gross income - $ 36, 500adjusted income - $ 32, 900taxable income -$ 23, 960How to find the types of income ?The gross income to the woman is:
= Wages + interest
= 33, 900 + 2, 600
= $ 36, 500
The adjusted gross income :
= Gross income - Retirement plan contribution
= 36, 500 - 3, 600
= $ 32, 900
The taxable income ;
= AGI - Personal exemption - Deductions
= 32, 900 - 3, 500 - 5, 440
= $ 23, 960
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3. Write the following using exponential notation:
(5.
5.5.5.5.5.5.5.5.5) (7.7.7.7.7.7.7.7.7.7.7.7.7.7)
Answer:
5.5.5.5.5.5.5.5.5 in exponential notation is 5^9
7.7.7.7.7.7.7.7.7.7.7.7.7.7 in exponential notation is 7^13
Therefore, (5.5.5.5.5.5.5.5.5) (7.7.7.7.7.7.7.7.7.7.7.7.7.7) in exponential notation is:
5^9 * 7^13
A scale drawing for an apartment is shown below. In the drawing, 3cm represents 4cm. Assuming the bedroom is rectangular, find the area of the real room
The calculated value of the area of the real room is 10.67 cm²
Finding the area of the real roomFrom the question, we have the following parameters that can be used in our computation:
In the drawing, 3cm represents 4cm
This means that
Scale factor = 4/3
Also, we have the dimension of the scale drawing to be
Dimension = 3cm by 2 cm
So, the area of the bedroom in the scale is
Area = 3cm * 2cm
For the actual room, we have
Area = 3cm * 2cm * (4/3)²
Evaluate the exponent
Area = 3cm * 2cm * (16/9)
Evaluate the products
Area = 10.67 cm²
This means that the real area is 10.67 cm²
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Write an equation of a circle with the given center and radius. center (3,4) and radius 6
(x-3)^2+(y-4)^2=36
(x-3)^2+(y-4)^2=6
(x+3)^2+(y-4)^2=36
(x+3)^2+(y-4)^2=6
Answer:
[tex] {(x - 3)}^{2} + {(y - 4)}^{2} = 36[/tex]
A cube has shaded shapes on three of its faces. Here is a net of the cube. Draw in the two missing shaded shapes.
The appropriate diagram to illustrate the cube is given.
What is a cube?A cube is a three-dimensional shape featureing six equal square faces, with its edges and vertices being of congruent length. It counts as one of the five platonic solids distinguished by all of its features having matching sizes.
The cube can be perceived as a special instance of a rectangular parallelepiped where all six are perfectly square in shape. In order to calculate the volume of such an ordinary cube, the number of its edge needs to be multiplied by itself thrice (V = a³).
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Use the unit circle to find exact value of the trig function
sin(135°)
Which of the following statements about the number line
is true?
A. Number lines can't help you compare numerals.
B. Numbers get larger as you move to the left on the
number line.
C. Numbers get smaller as you move to the left on the
number line.
D. Number lines end with the number 10.
Find the area of this triangular prism. Be sure to include the correct unit in your answer
The surface area of the prism is 360in²
What is surface area of prism?A prism is a solid shape that is bound on all its sides by plane faces.
The surface area of a prism is expressed as;
SA = 2B + ph
where h is the height of the prism and B is the base area , p is the perimeter of the base.
Base area = 1/2 × 5 × 12
= 5 × 6 = 30 in²
Perimeter of the base = 5+12+13
= 30 in²
height = 10 in
SA = 2 × 30+30× 10
= 60 + 300
= 360 in²
therefore the surface area of the prism is 360 in²
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help please
the triangle above has the following measures. q = 7cm m
Answer:
Put your calculator in degree mode.
sin(35°) = 7/r
r sin(35°) = 7
r = 7/sin(35°) = 12.2 cm
is 1 over 16 the same as 16 A: Yes B.NO
Answer:
1 over 16 is not the same as 16.
1 over 16 is a fraction, which means that it represents a part of a whole. It can be written as 1/16, which means one part out of a total of sixteen equal parts.
On the other hand, 16 is a whole number, which represents a quantity of sixteen units.
So, 1/16 is not equal to 16.
Step-by-step explanation:
A triangle is shown in the image 28 inches 32 inches 8 inches what is the area of the triangle
The area of the triangle is 128 square inches.
How to find the area of the triangle
To find the area of a triangle, you can use the formula:
Area = (1/2) * base * height
In this case, the base of the triangle is 32 inches and the height is 8 inches.
Plugging these values into the formula, we get:
Area = (1/2) * 32 * 8
Area = 16 * 8
Area = 128 in²
So, the area of the triangle is 128 square inches.
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A triangle is shown in the image. A triangle with a height of 8 inches. The height is perpendicular to the base labeled 32 inches. The side from the top of the perpendicular side to the base is labeled 28 inches. What is the area of the triangle? 256 in2 224 in2 128 in2 112 in2
pls pls help me with answer(correct it)
Screenshot below i have no idea how to solve this
Answer:
x^1/4 + 8x^1/4 + 12
Step-by-step explanation:
Using the FOIL method, we get x^1/4 + 8x^1/4 + 12
The mass of 12 packets of flour and 8 packets of salt is 19 kg. When 7 packets of flour are removed, the mass became 9.9 kg. Find the mass of each packet of salt in kilogram.
Answer:
1.235 kg
Step-by-step explanation:
Let's assume that each packet of flour and salt weighs the same.
When we remove 7 packets of flour, we are left with 5 packets of flour and 8 packets of salt. The total number of packets is 13 and their total mass is 9.9 kg.
Therefore, the average mass of each packet is 9.9 kg ÷ 13 = 0.76 kg.
Since we know that 12 packets of flour and 8 packets of salt have a total mass of 19 kg, we can subtract the mass of the 12 packets of flour (12 × 0.76 kg = 9.12 kg) from the total mass to find the mass of the 8 packets of salt:
19 kg - 9.12 kg = 9.88 kg
Finally, we can divide the mass of the 8 packets of salt by the number of packets to find the mass of each packet:
9.88 kg ÷ 8 = 1.235 kg
Therefore, each packet of salt weighs approximately 1.235 kg.
A waitress sold 11 ribeye steak dinners and 14 grilled salmon dinners, totaling $551.11 on a particular day. Another day she sold 15 ribeye steak dinners and 7 grilled salmon dinners, totaling $581.47. How much did each type of dinner cost?
Answer:
A ribeye steak dinner costs $32.23 and a grilled salmon dinner costs $14.04.
Step-by-step explanation:
Let's use variables to represent the cost of each dinner. Let's say that the cost of a ribeye steak dinner is "r" and the cost of a grilled salmon dinner is "s".
From the first day's sales, we know:
11r + 14s = 551.11From the second day's sales, we know:
15r + 7s = 581.47We now have two equations with two variables, which we can solve using elimination or substitution.
Let's use elimination. If we multiply the first equation by 15 and the second equation by 11, we can eliminate the "r" variable:
165r + 210s = 8266.65165r + 77s = 6396.17Subtracting the second equation from the first, we get:
133s = 1870.48Dividing both sides by 133, we get:
s = 14.04So a grilled salmon dinner costs $14.04.
We can substitute this value back into one of the original equations to solve for "r". Let's use the first equation:
11r + 14(14.04) = 551.1111r + 196.56 = 551.1111r = 354.55r = 32.23So a ribeye steak dinner costs $32.23.
Therefore, a ribeye steak dinner costs $32.23 and a grilled salmon dinner costs $14.04.
Find the approximate area of the shaded region below, consisting of a right triangle with a circle cut out of it. Use 3.14 as an
approximation for pi.
a. 1.254 square meters
b. 312 square meters
c. 2, 822 square meters
d. 314 square meters
Answer:
(a) 1.254 square metersStep-by-step explanation:
We are given a figure, consisting of a right triangle with a circle cut out of it.
To Calculate : area of the shaded region below,
First Let's find the Area of the right triangle:
Area(triangle) = 1/2 × Base × Height
= 1/2 × 56 × 56
= 1/2 × 3136
= 3136/2
= 1568 m².
Now, We are diameter of the circle = 20 m
Radius of the circle = 20/2 = 10 m
Area of circle = πr²Acc. to question we have to use 3.14 as an
approximation for pi.
Area (circle) = 3.14 × 10 × 10
Area (circle) = 3.14 × 100
Area (circle) = 314 m²
Area of shaded region = Area of triangle - Area of circle =
= 1568 m² - 314 m²
= 1.254 square meters
Therefore, The approximate area of the shaded region is 1.254 square meters.
Option (a) is the required answer.
The volume of a juice box is about 24 cubic inches.
Find the average rate of change of g(x)= 4x^2+3 on the interval [-4,1]
The rate of change is 4/1
Please help Thanks
there is a FRACTION symbol two variable symbols y and x
I need to write an equation
The required equation of line is y = 2x
What is equation of line?A straight line's equation is y=mx+c, where m denotes the gradient and c denotes the height at which the line crosses the y-intercept, also known as the y-axis.
According to question:Given points:
(1,2) and (2,4)
then
[tex]Slope of line = \frac{4-2}{2-1}= 2[/tex]
then
y-2 = 2(x-1)
y = 2x - 2 + 2
y = 2x
Thus, required equation of line is y = 2x
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Consider the line 6x-7y = 4. What is the slope of a line parallel to this line? What is the slope of a line perpendicular to this line?
The slope of a line parallel to this line is 6/7.
The slope of a line perpendicular to this line is -7/6.
What are parallel lines?In Mathematics and Geometry, parallel lines can be defined as two (2) lines that are always the same (equal) distance apart and never meet.
In Mathematics and Geometry, two (2) lines are parallel under the following conditions:
Slope, m₁ = Slope, m₂
Based on the information provided about this line, we have the following equation in standard form;
6x - 7y = 4
By making y the subject of formula, we have:
7y = 6x - 4
y = 6x/7 - 4
In Mathematics and Geometry, a condition that is true for two lines to be perpendicular is given by:
m₁ × m₂ = -1
6/7 × m₂ = -1
6m₂ = -7
Slope, m₂ = -7/6
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Helppppppp anyoneeee?
Answer:
( -6, 6)
Step-by-step explanation:
Explain by using an example why you need to multiply when converting from a larger unit to a smaller unit
Multiplying is necessary because each larger unit contains a certain number of the smaller units and we need to account for that conversion factor.
Why is multiplication necessary with examples?For example, when converting from meters to centimeters where we know that 1 meter is equal to 100 centimeters.
To convert 3 meters to centimeters, we need to multiply by the conversion factor of 100 which gives us:
= 3 meters * 100 centimeters/meter
= 300 centimeters
So, without the multiplication, we would not account for the fact that each meter contains 100 centimeters. This principle applies to all conversions from larger units to smaller units and it is important to remember to ensure accurate conversions.
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Calculate standard deviation for the following by direct and shortcut method.assume mean as 32
Serial no.of workers
1
2
3
The standard deviation for the given distribution is 8.739 using either the direct method or the shortcut method.
How to find the standard deviation?Standard deviation is defined as a measure of how spread out numbers are. It is also referred to as the square root of the Variance, and then the Variance is the average of the squared differences from the Mean.
To calculate the standard deviation for the given distribution, we will utilize either the direct method or the shortcut method.
Direct method:
Calculate the mean wage (F) for the distribution:
Mean = (20 + 22 + 27 + 30 + 31 + 32 + 35 + 45 + 40 + 48)/10
Mean = 34
Calculate the differences between each wage and the mean wage:
20 - 34 = -14
22 - 34 = -12
27 - 34 = -7
30 - 34 = -4
31 - 34 = -3
32 - 34 = -2
35 - 34 = 1
45 - 34 = 11
40 - 34 = 6
48 - 34 = 14
Square each of the differences:
(-14)² = 196
(-12)² = 144
(-7)² = 49
(-4)² = 16
(-3)² = 9
(-2)² = 4
1² = 1
11² = 121
6² = 36
14² = 196
Add up the squared differences: 196 + 144 + 49 + 16 + 9 + 4 + 1 + 121 + 36 + 196 = 756
Divide the sum of the squared differences by the number of workers: 756/10 = 75.6
Take the square root of the result to get the standard deviation:
√75.6 = 8.739
Shortcut method:
The mean wage (F) for the distribution:
(20 + 22 + 27 + 30 + 31 + 32 + 35 + 45 + 40 + 48)/10 = 34
The sum of the squares of the differences between each wage and the mean wage:
(20 - 34)² + (22 - 34)² + (27 - 34)² + (30 - 34)² + (31 - 34)² + (32 - 34)² + (35 - 34)² + (45 - 34)² + (40 - 34)² + (48 - 34)² = 756
Divide the sum by the number of workers: 756/10 = 75.6
Take the square root of the result to get the standard deviation:
Standard deviation = √75.6 = 8.739
Therefore,
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Complete question is:
Calculate standard deviation for the following
distribution by direct and shortcut method.
Assume mean as 32.
Serial No. of Workers
1
2
3
4
5
6
7
8
9
10
Wage (F)
20
22
27
30
31
32
35
45
40
48
Commutative property
Answer:
Commutative property of addition: Changing the order of addends does not change the sum. For example, 4 + 2 = 2 + 4 4 + 2 = 2 + 4 4+2=2+44, plus, 2, equals, 2, plus, 4. Associative property of addition: Changing the grouping of addends does not change the sum
Total score:
of 15 points
(Score for Question 1: of 5 points)
1. The diagram shown is two intersecting lines. The measure of 22 is 29
2
(a) What is the measure of 24? How do you know? Explain your answer in complete sentences.
(b) Suppose the measure of 3 can be represented by (3x - 8)*. What equation can be written to solve for the value of x?
(c) What is the value of x? Show all work.
Answer:
•(Score for Question 2: _ of 5 points)
2. Draw a right triangle with side lengths of 6, 8, and 10 units. For full credit, be sure to include appropriate labels and symbols where necessary. © Stride, Inc. All rights reserved. No reproduction without written consent of Stride, Inc.
Answer:
•Score for Question 3:
_ of 5 points)
3. At a park, a statue has a ring-shaped brick path around it. The outer edge of the brick path is a circle with a radius of 13 m. The inner edge of the brick path is a circle with a radius of 8 m.
Brick path
13 m
8 m
Statue
(a) Write and simplify an expression for the exact area of the brick path. Show all work.
(b) Find the approximate area of the brick path. Use 3.14 to approximate r. Show all work.
The measure of angle ∠4 is 29°, the equation is 3x = 159 and the value of x is 53
The right angle using the given lengths is attachedThe exact area is 105π square meters and the approximate area is 330 square metersThe two intersecting linesGiven that, we have
∠2 = 29°
(a)
Angles 2 and 4 are vertical angles
So, we have
∠4 = 29°
(b) and (c)
We have
∠3 = (3x - 8)°
Angles 3 and 4 are angles on a straight line
So, we have the equation to be
3x - 8 + 29 = 180
Solving for x, we have
3x = 159
Divide by 3
x = 53
This means that the equation is 3x = 159 and the value of x is 53
The right angle with the given lengthsIn this section, we have the following side lengths
Lengths = 6, 8 and 10
This means that
Side lengths = 6 and 8
Hypotenuse = 10
Next, we create the right angle using the given lengths of the legs and the hypotenuse
Calculating the area of the brick pathHere, we have
R = 13
r = 8
The exact area is calculated as
A = π(R² - r²)
So, we have
A = π(13² - 8²)
Evaluate
A = 105π
For the approximate area, we have
A = 105 * 22/7
A = 330
This means that the exact area of the brick path is 105π square meters and the approximate area is 330 square meters
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A subscription to a live streaming program normally costs $29 but is on sale for 25% off. An 8% tax is added at checkout. What is the total cost?
$7.25
$21.75
$23.49
$39.15
A subscription to a live streaming program normally costs $29 but is on sale for 25% off. An 8% tax is added at checkout then the total cost is $23.49.
To calculate the total cost, first, we find the discounted price of the subscription. A 25% discount on $29 is calculated by multiplying $29 by 0.25 (25% as a decimal), which gives us a discount of $7.25. Subtracting the discount from the original price, we get the discounted price of $29 - $7.25 = $21.75.
Next, we need to add the 8% tax to the discounted price. To calculate the tax amount, we multiply $21.75 by 0.08 (8% as a decimal), which gives us $1.74. Adding this tax amount to the discounted price, we get the total cost as $21.75 + $1.74 = $23.49.
Step 1: Calculate the discount amount:
Discount = 25% of $29
Discount = 0.25 * $29
Discount = $7.25
Step 2: Find the discounted price:
Discounted Price = Original Price - Discount
Discounted Price = $29 - $7.25
Discounted Price = $21.75
Step 3: Calculate the tax amount:
Tax Amount = 8% of Discounted Price
Tax Amount = 0.08 * $21.75
Tax Amount = $1.74
Step 4: Calculate the total cost:
Total Cost = Discounted Price + Tax Amount
Total Cost = $21.75 + $1.74
Total Cost = $23.49
So, the total cost after applying the 25% discount and adding an 8% tax at checkout is $23.49.
- Discount = 0.25 * $29 = $7.25
- Discounted Price = $29 - $7.25 = $21.75
- Tax Amount = 0.08 * $21.75 = $1.74
- Total Cost = $21.75 + $1.74 = $23.49
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The questions I need answered are in the picture… help plsss
The graph of the linear equation y = (1/2)*x + 3 can be seen in the image at the end.
How to graph the linear equation?Here we want to graph the linear equation:
y = (1/2)*x + 3
To graph it we need to find a few points on the line, graph them on a coordinate axis and then draw a line that connects them.
The first point that we can use is the y-intercept, it is what we get when we evaluate in x = 0.
y = (1/2)*0 + 3
The point is (0, 3)
Then we can get other points by evaluating in different values of x, for example, if x = 2
y = (1/2)*2 + 3 = 1+ 3 =4
If x = 4
y = (1/2)*4 + 3 = 2 + 3 = 5
So we have the points (2, 4) and (4, 5)
Now just graph all these points on a cordinate axis and connect them with a line, you will get a graph like the one in the image below.
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