The number of conjugates of H in G is equal to the index [G:N(H)] of H in G.
To prove that the number of conjugates of H in G is |G:N(H)|, where N(H) is the normalizer of H in G, we need to show that there is a bijection between the set of conjugates of H in G and the set of left cosets of N(H) in G.
Let g be an element of G. Then the conjugate of H by g is given by gHg^(-1), which is the set of all elements ghg^(-1) for h in H. We need to show that every conjugate of H in G can be written in this form for some g in G, and that distinct elements g and g' give rise to distinct conjugates.
Let C be a conjugate of H in G. Then there exists some g in G such that C = gHg^(-1). Let N(H) denote the normalizer of H in G, which is the set of all elements of G that commute with every element of H. Since gHg^(-1) is a conjugate of H, we have gHg^(-1) = hHh^(-1) for some h in G. This implies that gh is in N(H), so gHg^(-1) = (gh)H(gh)^(-1) is a left coset of N(H) in G. Therefore, every conjugate of H in G can be written as a left coset of N(H) in G.
Now, we need to show that distinct elements g and g' give rise to distinct conjugates. Suppose that gHg^(-1) = g'Hg'^(-1) for some g, g' in G. Then g'^(-1)g is in the normalizer of H, so g'^(-1)gH = Hg'^(-1)g. This implies that g and g' belong to the same left coset of N(H) in G. Therefore, the number of conjugates of H in G is equal to the number of left cosets of N(H) in G, which is |G:N(H)| by the definition of index.
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this is worth 40 points so pls help! I need this ASAP.
I also need COMPLETE solution
Answer:
Shown below.
Step-by-step explanation:
Test Marks Tally Frequency Percentage
1 8 8/60 = 0.133
2 6 6/60 = 0.100
3 5 5/60 = 0.083
4 5 5/60 = 0.083
5 5 5/60 = 0.083
6 8 8/60 = 0.133
7 6 6/60 = 0.100
8 7 7/60 = 0.116
9 4 4/60 = 0.066
10 5 5/60 = 0.083
Total 59 59/60 = 0.983
For the Tally section, I believe you just fill in tally marks corresponding to the frequency. One of the observations in the table is 0, which is not a column in the frequency table.
The area of a rectangle is given as x2+5x+6. which expression represents either the length or widith of the rectangle. these are the answers, it has to be one of these (x-3) (x+1) (x+3) (x+6)
The expression which represents either the length or width is (x+3). The correct answer is option (c).
Given that the area of a rectangle which is given as x²+5x+6.
We have to find which expression represents either the length or width.
We are given an expression for the area. But we also know that the area of a rectangle is length times width. So the expression we were given, x²+5x+6 must be equal to the length of the rectangle times its width.
So, will find the factoring the expression we can see expressions for the length and the width.
Factoring x²+5x+6 we get (x+2)(x+3).
One of these factors is the width and the other is the length.
Hence, the expression represents either the length or width of the rectangle when the area of a rectangle is given as x²+5x+6 is (x+3).
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An acute angle θ is in a right triangle with sin θ = eight ninths. What is the value of cot θ? nine divided by the square root of seventeen square root of seventeen divided by eight eight divided by the square root of seventeen square root of seventeen divided by nine
Answer:
\(\frac{\sqrt{17} }{9}\)
Step-by-step explanation:
a^2 +b^2 =c^2 Use pythagorean theorem
8^2 +b^2 =9^2 Substitute in your known values
b=\(\sqrt{17} , -\sqrt{17}\)
b=\(\sqrt{17}\) A triangle leg cannot be a negative length
\(\frac{\sqrt{17} }{9}\) Find cosine of angle theta.
What is the equation of a line that passes through (0.8) and (3,6)?
Answer:
\(y=\frac{-2}{3}x+8\)
Step-by-step explanation:
Hi there!
Linear equations are typically organized in slope-intercept form: \(y=mx+b\) where m is the slope and b is the y-intercept (the value of y when the line crosses the y-axis)
1) Determine the slope (m)
\(m=\frac{y_2-y_1}{x_2-x_1}\) where the given points \((x_1,y_1)\) are \((x_2,y_2)\)
Plug in the given points (0,8) and (3,6)
\(m=\frac{6-8}{3-0}\\m=\frac{-2}{3}\)
Therefore the slope of the line is \(\frac{-2}{3}\). Plug this into \(y=mx+b\):
\(y=\frac{-2}{3}x+b\)
2) Determine the y-intercept (b)
\(y=\frac{-2}{3}x+b\)
The y-intercept occurs when x=0. One of the given points is (0,8), so therefore, the y-intercept is 8. Plug this into \(y=\frac{-2}{3}x+b\):
\(y=\frac{-2}{3}x+8\)
I hope this helps!
What value of x will make the equation below true?
х/6=15
Answer:
x+90
90/6=15
15=15
Step-by-step explanation:
HELP HERE PLESSS. :)
***
Answer:
is reflected across the line x=4
When Denine went to the pizza palace to order pizza for her party her friend Caleb noticed that for every 10 orders of cheese pizza there were 7 orders of pepperoni pizza, 5 orders of sausage pizza and 8 orders of mushroom pizza. If there were 35 pepperoni pizzas ordered how many total pizza were ordered? While waiting on the pizza something went wrong with the oven and 2 out of every 25 pizzas were burned. How many pizzas were burned? If 360 pizzas were ordered how many cheese and how many mushroom pizzas were ordered?
Using proportions, it is found that:
If there were 35 pepperoni pizzas ordered, 150 total pizzas were ordered.12 pizzas were burned.120 cheese pizzas and 96 mushroom pizzas were ordered out of 360 pizzas.What is a proportion?A proportion is a fraction of a total amount, and the measures in the context of a problem are found using basic arithmetic operations such as multiplication and division.
One application of proportions is for ratio problems, as fractions are built from the ratios to find the equivalent amounts.
Caleb noticed that for every 10 orders of cheese pizza there were 7 orders of pepperoni pizza, 5 orders of sausage pizza and 8 orders of mushroom pizza, hence the fraction of Pepperoni pizzas out of the total is given by:
Pepperoni = 7/(10 + 7 + 5 + 8) = 7/30 of the total.
If 35 pepperoni pizzas were ordered, the total number is found as follows:
7x/30 = 35
7x = 30 x 35
x = 30 x 5
x = 150 pizzas.
2 out of every 25 pizzas were burned, hence the number of burned pizzas is given by:
2/25 x 150 = 2 x 6 = 12 pizzas.
The cheese fraction is given by:
10/30.
Hence, out of 360 pizzas, the number is given by:
10/30 x 360 = 10 x 12 = 120 cheese pizzas
The mushroom fraction is given by:
8/30.
Hence, out of 360 pizzas, the number is given by:
8/30 x 360 = 8 x 12 = 96 mushroom pizzas
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or Questions 1-20, let vectors u = (2,1,–3), v = (5,4,2) and w=(-4,1,6) be given. Find each of the following. If the answer does not exist, explain why. 9. 2u + 3y – w. – 10. |u| 11. The angle in degrees between u and w. 12. A vector parallel to v, but of length 2.
To find 2u + 3v - w, we can perform vector addition and scalar multiplication:
2u + 3v - w = 2(2, 1, -3) + 3(5, 4, 2) - (-4, 1, 6)
= (23, 13, -6).
Therefore, 2u + 3v - w = (23, 13, -6).
To find |u|, we need to compute the magnitude (length) of vector u:
|u| = √(2^2 + 1^2 + (-3)^2)
= √(4 + 1 + 9)
= √14.
Therefore, |u| = √14.
To find the angle between u and w, we can use the dot product formula and the magnitude of vectors:
cosθ = (u ⋅ w) / (|u| |w|)
= ((2, 1, -3) ⋅ (-4, 1, 6)) / (√14 √(-4^2 + 1^2 + 6^2))
= (-8 + 1 - 18) / (√14 √53)
= -25 / (√14 √53).
The angle θ between u and w can be found using the inverse cosine function:
θ = arccos(-25 / (√14 √53)).
To find a vector parallel to v with length 2, we can normalize v to obtain a unit vector and then multiply it by 2:
v_unit = v / |v| = (5, 4, 2) / √(5^2 + 4^2 + 2^2)
= (5, 4, 2) / √45.
A vector parallel to v, but of length 2, is then:
2v_unit = 2 * (5, 4, 2) / √45
= (10/√45, 8/√45, 4/√45).
Therefore, a vector parallel to v, but of length 2, is (10/√45, 8/√45, 4/√45).
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PLEASE HELP!!! I NEED TO TURN THI IN SOON !!!
Question and instructions in the image below!!!
Will mark brainliest if correct!!!
Answer:
Im pretty sure its the 3rd one
Step-by-step explanation:
I did this a while ago
The cost C in dollars of manufacturing x bicycles at a production plant is given by the function shown below. C(x) = 3x2 - 1500x + 199,000 a. Find the number of bicycles that must be manufactured to minimize the cost. b. Find the minimum cost. a. How many bicycles must be manufactured to minimize the cost? bicycles
To find the number of bicycles that must be manufactured to minimize the cost, we need to determine the value of x that corresponds to the minimum point of the cost function C(x).
We can find this by taking the derivative of C(x) with respect to x and setting it equal to zero. Let's differentiate C(x):
C'(x) = 6x - 1500
Now we set C'(x) = 0 and solve for x:
6x - 1500 = 0
6x = 1500
x = 250
Therefore, the number of bicycles that must be manufactured to minimize the cost is 250 bicycles.
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there are 112 students going on a field trip to pan for gold if they are going in vans that hold 6 students eat how many Vans are needed how many students will ride each van that isn't full
Answer:
18 because it all the kids can fit in all the vans
please help me !!!!!
Answer:
Cheer up...٩(●˙—˙●)۶٩(●˙—˙●)۶٩(●˙—˙●)۶
Step-by-step explanation:
Hahahah
Answer:
:
To find the new function all you have to do is apply the operation in the order that is specified. In this case, subtract the two functions:
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A certain 300-term geometric sequence has first term 1337 and common ratio $-\frac12$. How many terms of this sequence are greater than 1
There are 6 terms in the sequence greater than 1.
What is a geometric series ?A geometric series is sum of infinite numbers which has a common ratio between its successive terms.
The missing common ratio value is -1/2
It is given in the question that
the number of terms in the sequence = 300
Sum = a₁ (1-rⁿ)/(1-r)
nth term is given by
aₙ = a₁r⁽ⁿ⁻ ¹⁾
1337(1/2)^(n - 1) = 1
(1/2)^(n - 1) = 1/1337
Applying log on both sides
log (1/2)^(n - 1) = log (1/1337)
(n - 1) log(1/2) = log(1/1337)
n = log (1/1337)/ log (1/2) + 1 ≈ 11.384
the 11th term is 1337(-1/2)^(10) ≈ 1.305
and
And the 12th term is 1337(-1/2)^11 = -.653
As the even terms are negative , they are less than 1 and , therefore the odd terms from 1 - 11 term will be positive and greater than 1.
Therefore there are 6 terms in the sequence greater than 1.
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Design DFA {w ∈ Σ ∗ | |w| ≥ 3 and the second symbol from the left end of w is different from the last symbol of w}. For example, 010100 is in the language, but 0001100 is not in the language.
The DFA assumes that the input string consists only of symbols from the alphabet Σ = 0, 1
To design a deterministic finite automaton (DFA) for the given language, to define the states, alphabet, transition function, initial state, and accepting states.
Let's assume the alphabet Σ consists of 0 and 1.
States:
Start state (S)
Second symbol different state (D)
Accepting state (A)
Rejecting state (R)
Alphabet:
Σ = {0, 1}
Transition function (δ):
δ(S, 0) = D
δ(S, 1) = D
δ(D, 0) = A
δ(D, 1) = A
δ(A, 0) = R
δ(A, 1) = R
δ(R, 0) = R
δ(R, 1) = R
Initial state:
S
Accepting states:
A
Rejecting states:
R
The DFA is designed such that it transitions to the "Second symbol different state" (D) if it encounters either 0 or 1 as the first symbol. From the "Second symbol different state" (D), it transitions to the "Accepting state" (A) if it encounters 0 or 1 as the second symbol. Once it reaches the "Accepting state" (A), it transitions to the "Rejecting state" (R) for any subsequent symbols, ensuring the length of the string is at least 3 and the second symbol from the left end is different from the last symbol.
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A running circuit is in the shape of a triangle with lengths of 6km, 6.5km and 7km. What are the sizes of the angles (in minutes) between each of the sides?
A triangle is an example of a class of figures referred to as plane shapes. It has three straight sides and three internal angles which sum up to \(180^{o}\). The measures of the internal angles of the triangle given in the question are A = \(52.6^{o}\), B = \(59.4^{o}\), and C = \(68^{o}\).
A triangle is an example of a class of figures referred to as plane shapes. It has three straight sides and three internal angles which sum up to \(180^{o}\).
Considering the given question, let the sides of the triangle be: a = 6 km, b = 6.5 km, and c = 7 km.
Apply the Cosine rule to have:
\(c^{2}\) = \(a^{2}\) + \(b^{2}\) - 2ab Cos C
So that;
\(7^{2}\) = \(6^{2}\) + \((6.5)^{2}\) - 2(6 * 6.5) Cos C
49 = 36 + 42.25 - 78Cos C
78 Cos C = 78.25 - 49
= 29.25
Cos C = \(\frac{29.25}{78}\)
= 0.375
C = \(Cos^{-1}\) 0.375
= 67.9757
C = \(68^{o}\)
Apply the Sine rule to determine the value of B,
\(\frac{b}{Sin B}\) = \(\frac{c}{Sin C}\)
\(\frac{6.5}{Sin B}\) = \(\frac{7}{Sin 68}\)
SIn B = \(\frac{6.5 *Sin 68}{7}\)
= 0.861
B = \(Sin^{-1}\) 0.861
= 59.43
B = \(59.4^{o}\)
Thus to determine the value of A, we have;
A + B + C = \(180^{o}\)
A + \(59.4^{o}\) + \(68^{o}\) = \(180^{o}\)
A = \(180^{o}\) - 127.4
= 52.6
A = \(52.6^{o}\)
Therefore the sizes of the internal angles of the triangle are: A = \(52.6^{o}\), B = \(59.4^{o}\), and C = \(68^{o}\).
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The average high temperatures in degrees for a city are listed. 58, 61, 71, 77, 91, 100, 105, 102, 95, 82, 66, 57if a value of 98° is added to the data, how does the mean change?a. the mean increases by 8.2°. b. the mean decreases by 8.2°. c. the mean increases by 1.4°. d. the mean decreases by 1.4°.
Answer:
b
Step-by-step explanation:
Help me with this you get 50 points
Answer:
4.13 by the power of -8 is equal to 0.0000000413 in decimals!
and 0.04 by the power of -5 is equal to 4 by the power of -7 which is equal to 0.0000004 in decimals
Step-by-step explanation:
10 to the power of 1 is 10
10 to the power of 0 is 1
10 to the power of -1 is 0.1
and so on
but here is the quotient:
0.10325
when you divide a number, they flip over and become a number as big as 2500000 TIMES 0.0000000413
1/0.0000004 is 2500000, not 4000000
giving you the answer 0.10325
The percentage of measurements that are above the 39th percentile is.
The percentage of measurements that are above the 39th percentile is 61%.
To calculate the percentage of measurements above the 39th percentile, we need to find the complement of the percentile value. The 39th percentile represents the value below which 39% of the measurements fall. Therefore, the complement of the 39th percentile is the percentage of measurements above that value. Since the total percentage adds up to 100%, subtracting 39% from 100% gives us the percentage of measurements above the 39th percentile, which is 61%.
In summary, the percentage of measurements that are above the 39th percentile is 61%. This means that 61% of the measurements are higher than the value corresponding to the 39th percentile.
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What is the percentage of measurements that fall above the 39th percentile?
Please help, this is a simple question I don't know:
What type of function is this?
Answer:
Quadratic
Step-by-step explanation:
write one-half times a number minus 4. use x as a variable
Answer:
\(\frac{1}{2}\)x-4
Step-by-step explanation:
Answer:
1/2 (x)-4
Step-by-step explanation:
Hopes this helps
What is less than .59
A. 0.07
B. 0.4
C. 0.6
D. 0.55
A. 0.07
Explaination:
if you were to say these are money.
0.59 would be 59 cents. 0.07 would be 7 cents.
59 is greater then 7 cents. so A is your answer
Answer:
0.07,0.4,.55 are all less than.59
Step-by-step explanation:
0.6 stands for 0.60 so it is the only one that is more than .59.
A square garden has sides 100 ft long. You want to build a brick path along a diagonal of the square. How long will the path be? Round your answer to the nearest
foot.
The length of the diagonal of the square rounded to the nearest foot is 141.2 feet.
What are the dimensions of a square?The area of a square is a product of it's any two sides or a product of diagonals divided by two. If the side has a length then the diagonal is a√2.
The perimeter of a square is the sum of the lengths of all the sides.
Given, A square garden has sides 100 ft long.
Now, If we draw a diagonal it becomes a right-angled triangle with a height of 100 ft and a base of 100 feet.
Therefore, By applying Pythagoras' theorem we have,
The length of the diagonal is = √(100² + 100²).
= √(10000 + 10000).
= √(20000) feet.
= 141.42 Or 141 feet.
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In Exercises 11-14, find a point P where the line intersects the given plane or decide that the line does not intersect the plane.
11.
x=1+2t
y=3−t, x+y−z=2
z=5+4t
A point P the line intersects the plane or decide that the line does not intersect the plane is: (x, y , z) = [-9/5 , 22/5 , -3/5]
Equation of Line in 3D:Suppose we have equation of line :
\(\frac{x-x_1}{l}=\frac{y-y_1}{m}=\frac{z-z_1}{n}=t\) and the equation of the plane ax + by + cz = d.
Here are the step to solve the point of intersection:
Step 1: Solve the values of x, y, and z in term of t
Step 2: Plug in the values x, y, and z in the equation of the plane and solve the value of t
Step 3: Plug in the value of t and solve the values x, y, and z.
The equation of line is: x=1+2t , y=3−t, z=5+4t
Plug in the values of x, y, and z in the equation of plane :
x + y + z = 2
1 + 2t + 3 - t + 5 + 4t = 2
9 + 5t = 2
5t = 2 - 9
5t = -7
t = -7/5
Plug in the value of t and find the point of intersection:
(x , y , z) = (1 + 2t , 3 - t, 5 + 4t)
(x , y , z) = [ (1 + 2× \(\frac{-7}{5}\)), (3 - (\(\frac{-7}{5}\))), (5 + 4 ×\(\frac{-7}{5}\))]
(x, y , z) = [-9/5 , 22/5 , -3/5]
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suppose there is a 1.2°F drop in temperature for every thousand feet that an airplane climbs into the sky. if the temperature on the ground is 56.9°F, what will be the temperature when the plane reaches an altitude of 8,000 ft?
We have a linear model, that relates temperature with altitude.
The first senctence gives us a clue about tha rate of change (the slope) of temperature in function of the altitude.
We can write the slope, in °F/1000 ft, as:
\(m=-1.2\)The temperature on the ground, where h=0, is 56.9 °F, so we can write the equation of the line as:
\(T(h)=-1.2h+56.9\)When the altitude is 8,000 ft, h=8 and T is:
\(T(8)=-1.2\cdot8+56.9=-9.6+56.9=47.3\)The temperature at 8,000 ft will be 47.3 °F.
The table shows values for functions f(x) and g(x). x 1 3 5 7 9 11 f(x) 7 10 0 5 5 7 g(x) 7 3 5 0 5 11. Which answers are solutions to the equation f(x)=g(x)? A. 1 B. 3 C. 5 D. 9 F. 10
The solutions to the equation f(x) = g(x) are the values of x that make f(x) and g(x) equal. Looking at the table, we can see that f(x) = g(x) for x = 7 and x = 5. Therefore, the solutions to the equation f(x) = g(x) are C. 5 and D. 9. Answer choices A. 1 and F. 10 are not solutions to the equation as f(1) ≠ g(1) and f(10) is not given in the table. Answer choice B. 3 is also not a solution as f(3) ≠ g(3).
Write an equation for the given ituation, and enter the rate of change (in total page read) a your anwer. Jenny read 30 page per hour. She ha already read 83 page today
We are given that Jenny can read 30 pages per hour and she has already read 83 pages. This portrays that it took 2 hours and 46 minutes to complete reading 83 pages.
What is Rate of Change?The pace at which one value within a function changes in proportion to another is known as the average rate of change. The slope of a graphed function is typically calculated using the average rate of change.
The average rate of change of a function corresponds to the slope of the line connecting two endpoints of a certain interval (known as the secant line). This is the equation for the average rate of change.
Average rate of change = change in y / change in x
The change in y-values is the numerator and the changes in x-values is the denominator of the function's average rate of change. After simplifying, we'll take the x and y values of the second point away from those of the first point.
How to solve?
Jenny reads 30 pages in an hour
i.e., she reads 10 pages in 20 minutes
and, 3 pages in 6 minutes
Therefore, it took her 30 * 2 hr+ 10 * 2min + 6min i.e., 2 hours 46 minutes
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answer to –1.7+5.2(5.5+–10.8a)
Answer:
26.9 - 56.16a
Step-by-step explanation:
-1.7 + 5.2(5.5 - 10.8a)
use the distributive property
-1.7 + 28.6 - 56.16a
combine like terms
-1.7 + 28.6 = 26.9
26.9 - 56.16a
plz mark as brianliest if correct!!!
In the recent year, 51.9 billion aluminum cans were recycled. About how many cans per week is this?
The number of cans that are recycled is approximately 1 billion cans in 1 week.
What is the fundamental principle of multiplication?Multiplication is the mathematical operation that is used to determine the product of two or more numbers. If an event can occur in m different ways and if following it, a second event can occur in n different ways, then the two events in succession can occur in m × n different ways.
Given that 51.9 billion aluminum cans were recycled.
Therefore, the rate of recycled the can is;
51.9 billion / 1 year
We know that 1 year has 52 weeks
Then
51.9 billion / 1 year x 1 year / 52 weeks
= 51.9 (1) billion / 1 (52 ) weeks
= 51.9 billion/ 52 weeks
= 1 billion/ 1 week
Hence, the number of cans that are recycled is approximately 1 billion cans in 1 week.
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recursively define the set of binary strings with more 0s than 1s.
0>1,If a function f is constructed recursively, at least one of its values, f(x), must be defined in terms of f(y), where x>y.
What do binary strings mean?A series of bytes make up a binary string. A binary string is used to store non-traditional data, including images, as opposed to a character string, which typically holds text data. The quantity of bytes in a binary string determines its length. The CCSID for a binary string is 65535.Binary refers to this system of 1s and 0s. Because of the way they are made, computers only speak in binary. A computer is nothing more than a sizable number of switches. On those curiously engraved boards inside the computer, there are millions of microscopic electronic switches.If a function f is constructed recursively, at least one of its values, f(x), must be defined in terms of f(y), where x>y. A procedure P is defined recursively if its action, P(x), is defined in terms of another action, P(y), where x>y.Explanation:
0>1.
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Sara's office recycled a total of 12 pounds of paper over 4 weeks. How many weeks will it take Sara's office to recycle a total of 48 pounds of paper?
Answer:
16
Step-by-step explanation:
12 pounds: 4 weeks
48 pounds: 16 weeks