Sylow's Theorem states that for any prime factor p of the order of a group G, there exists a Sylow p-subgroup of G. Let n_p denote the number of Sylow p-subgroups in G. Then, n_p is congruent to 1 mod p and n_p divides the order of G. In the case of G with order 312, the prime factorization of 312 is 2^3 * 3 * 13. By Sylow's Theorem, there exists a Sylow 2-subgroup of order 8, a Sylow 3-subgroup of order 3, and a Sylow 13-subgroup of order 13. Since 8 and 13 are coprime, the number of Sylow 2-subgroups and Sylow 13-subgroups must be 1. Thus, both subgroups are normal in G.
Sylow's Theorem is a powerful tool in group theory that enables us to analyze the structure of a finite group by studying its subgroups. A Sylow p-subgroup of a group G is a maximal p-subgroup of G, i.e., a subgroup of G of order p^k, where k is the largest integer such that p^k divides the order of G. Sylow's Theorem states that for any prime factor p of the order of a group G, there exists a Sylow p-subgroup of G. Moreover, any two Sylow p-subgroups are conjugate in G, which means that they are essentially the same from the perspective of the group structure. This fact can be used to prove important results such as the existence of normal subgroups in G.
In the case of G with order 312, Sylow's Theorem guarantees the existence of Sylow 2-subgroups, Sylow 3-subgroups, and Sylow 13-subgroups. The number of Sylow p-subgroups for each prime factor p is determined by the congruence n_p ≡ 1 mod p and the divisibility n_p | |G|. Since 8 and 13 are coprime, it follows that the number of Sylow 2-subgroups and Sylow 13-subgroups must be 1. This implies that both subgroups are normal in G, which means that they are invariant under conjugation by elements of G. The existence of normal subgroups is a fundamental property of group theory that has many applications in algebra, number theory, and geometry.
To know more about Sylow's Theorem visit:
https://brainly.com/question/29282070
#SPJ11
the figure it made of a square and right triangles. Find the area
PLZ help me
Answer:
720 inches squared
Step-by-step explanation:
for the square:
a = 24 x 24 = 576 inches squared
for the triangle:
36-24 =
a = 12 x 24 / 2
= 144 inches squared
576 + 144 = 720 inches squared
Answer:
720 inches squared
Step-by-step explanation:
i took test
Are the two expressions in the equation 2b + 5 + 1b = 3b + 5 equal or equivalent? How do you know?
Answer:
they are equal because while solving 2b+5+1b it will come 3b+5 so they are equal
Answer:
the equation are equivalent
Step-by-step explanation:
to know why, look at the pic above
what is the surface area of the cylinder with height 3km and radius 7km
Answer:
A=439.82 or A=439
Step-by-step explanation:
~~~~~~~~:)
What additional information would you need to prove
Answer:
A
Step-by-step explanation:
We use the Hypotenuse Leg Theorem
When we know the hypotenuse and a leg of a triangle.
We know The Hypotenuse (TO) so we need to know A leg of the triangle which the only leg is TM and OR.
which one of the following is NOT a polynomial option 1. x^2-2x+3 option 2. 11x-9. option 3. 3/y
Answer:
option 3
Step-by-step explanation:
√32+√42 ÷ √8 +√12 simplify
Note: It should be 48 instead of 42 because √42 cannot be simplified.
Given:
Consider the given expression is
[tex]\dfrac{\sqrt{32}+\sqrt{48}}{\sqrt{8}+\sqrt{12}}[/tex]
To find:
The simplified form of the given expression.
Solution:
We have,
[tex]\dfrac{\sqrt{32}+\sqrt{48}}{\sqrt{8}+\sqrt{12}}[/tex]
It can be written as
[tex]=\dfrac{\sqrt{16\times 2}+\sqrt{16\times 3}}{\sqrt{4\times 2}+\sqrt{4\times 3}}[/tex]
[tex]=\dfrac{4\sqrt{2}+4\sqrt{3}}{2\sqrt{2}+2\sqrt{3}}[/tex]
[tex]=\dfrac{4(\sqrt{2}+\sqrt{3})}{2(\sqrt{2}+\sqrt{3})}[/tex]
[tex]=\dfrac{4}{2}[/tex]
[tex]=2[/tex]
Therefore, the simplified form of the given expression is 2.
Donna paid $3 to rent shoes and then $1 for each game she played at a bowling alley. She spent a total of $8 at the bowling alley.
Which equation can be used to find the number of games Donna played?
Answer:If shoes are for all games in row, P = 2 + 3 g If not, P = 5 g ,with g the number of games
Explanation: The price depends:if shoes are included for the whole games, you just have to pay them once and then you have to pay
g g a m e s , so P ( g ) = 2 + 3 g Else, you have to pay g s h o e s and g b o w l p a r t y ,so
P ( g ) = 2g + 3 g⇔ P ( g ) = 5 g
Hope this helped hope you get a good score on your assignment/test/quiz/homework-Tay did this
help, look at picure
Answer:
x=3
Step-by-step explanation:
61/4=15 1/4
5(3)=15+(1/4)=15 1/4
find the unknown Angles in the given figure
Answer:
x = 50°, y = 50°
Step-by-step explanation:
⇒ x + x + 80° = 180°
⇒ 2x = 180° - 80° = 100°
⇒ x = 100°/2 = 50° ∴ y = x = 50°
Three pounds of flour are divided into 6 containers so that each container holds the same number of pounds of flour
Answer:
0.5 pounds per container.
Step-by-step explanation:
just divide 3 pound by 6 containers so it would be 3/6 which is equal to 1/2 which is the same as 0.5
There each container holds a number of pounds of flour which would be 0.5 pounds.
What is the division operation?In mathematics, divides left-hand operands into right-hand operands in the division operation.
If three pounds of flour are divided into 6 containers so that each container holds the same number of pounds of flour, we can find out how many pounds of flour each container holds by dividing the total amount of flour by the number of containers.
We can use the following equation to find out how many pounds of flour each container holds:
pounds of flour per container = total pounds of flour / number of containers
So, using this equation:
pounds of flour per container = 3 / 6
Apply the division operation, and we get
pounds of flour per container = 0.5
Each container holds 0.5 pounds of flour.
To learn more about the division operation click here :
brainly.com/question/25870256
#SPJ2
SMART PPL HELP HELP PLEAse
Answer:
help with what
Step-by-step explanation:
Answer:
did you mean to post a question?
Step-by-step explanation:
What is the Value of X
What is the Length of JM?
Answer:
JM = 17
x = 12
Step-by-step explanation:
The given triangles are similar with ASA rule if so then x + 5 must be equal to 2x - 7
x + 5 = 2x - 7 and 5 + 7 = 2x - x
12 = x
The length of JM
2x - 7 can be written as 2×12 - 7 = 17
4
1
(12−8×)=
3
2
(6×)
creo que es 32 por la cultura
Ayuda!
Necesito el inciso k) por 10 puntos
Answer:
x=47is your answer
3x-11=130(alternate angle)
3x=130+11
x=141/3=47
Find the missing side of each right triangle. Side c is the hypotenuse. Sides a and b are the legs. Leave your answers in simplest radical form.
A=11m,C=15m
Find b with writing it out like the picture above.
Answer:
Side b = 10.2 m (1 d.p.)
Step-by-step explanation:
11² = 121
15² = 225
225 - 121 = 104
√104 = 10.2 (1 d.p.)
Side b = 10.2m
(Full answer = 10.198039)
11² + 10.2² = 15²
Answer the photo below thanks
Answer: rotation
Step-by-step explanation:
2. The weather forecast calls for 12 cm of snow. How many inches
can you expect?
4. You have a 1.5 gal jug. How many litres will it hold?
5. Joe is travelling in the United States. A road sign indicates he is
228 mi from his destination. How many kilometres is Joe from
his destination?
Answer:
2. 1 inch
4. 5.68 liters(if we estimate)
5. 366.96 kilometers
Step-by-step explanation:
2. centimeters to inches
4. gallons to liters
5. miles to kilometers
Twelve students share 3 pizzas equally. What fraction of a pizza does each student
get?
Answer: 4/12
Step-by-step explanation: 4 over 12
SOMEONE PLEASE HELP ME AND ANSWER THIS QUESTION CORRECTLY I WILL MAKE YOU THE BRAINLIEST, GIVE YOU A GOOD RATE, PLEASE ASWER THIS ASAPPPPPPPPP!!!!!!!!!!! I NEED HELP ASAPPPPPPPPPPP!!!!!!!!!! ALSO PLEASE SHOW YOUR WORK ASAPPPPPPP!!!!!!!!!!!!
Answer:
tbh that doesnt make sense the easiest way to et the first one is to do 955 divided by 90.
Step-by-step explanation:
Paisley invests money in an account paying a simple interest of 8.9% per year. If she invests $80 and no money will be added or removed from the investment, how much will she have in one year, in dollars and cents?
it will be removed
Step-by-step explanation:
Fifteen disks with the given measurements are stacked on top of each other. Which expression does NOT give the volume of the cylinder that is formed?
Missing information:
[tex]r = 3cm[/tex]
[tex]h = 1cm[/tex]
Options:
(a) [tex]\pi * 3^2 * 15[/tex] (b) [tex]\pi * 3* 15^2[/tex]
(c) 15 times the volume of the disk
(d) The height of the stack multiplied by [tex]\pi r^2[/tex]
Answer:
(b) [tex]\pi * 3* 15^2[/tex]
Step-by-step explanation:
Given
15 identical disks
[tex]r = 3cm[/tex]
[tex]h = 1cm[/tex]
Required
Determine the odd option
The volume of 1 disk is:
[tex]V_1 = \pi r^2h[/tex]
[tex]V_1 = \pi * 3^2 * 1[/tex]
The volume of 15 is:
[tex]V_{15} = 15 * V_1[/tex]
[tex]V_{15} = 15 * \pi * 3^2 * 1[/tex]
[tex]V_{15} = \pi * 3^2 * 15[/tex]
The above equation represents (a), (c) and (d)
Because:
(a): [tex]V_{15} = \pi * 3^2 * 15[/tex]
(c) 15 * volume of the disk: [tex]V_{15} = 15 * V_1[/tex] = [tex]V_{15} = \pi * 3^2 * 15[/tex]
(d) height * [tex]\pi r^2[/tex] = h * [tex]\pi r^2[/tex] = [tex]15 * \pi * 3^2 * 1[/tex] = [tex]V_{15} = \pi * 3^2 * 15[/tex]
Hence, (b) is the odd option
(1x)/(2)=12
PLEASE SHOW THE WORK!!!
Answer:24
Step-by-step explanation:
simplify 1 * x to x
x/2=12
multiply both sides by 2
x=12 * 2
simplify 12 * 2 to24
x=24
Brandon buys a radio for $43.75 in a state where the sales tax is 7%.
Part 1 out of 2
How much does he pay in taxes? If necessary, round to the nearest cent
Answer:
Tax: $3.06
Step-by-step explanation:
7% of 43.75 = 0.07 × 43.75 = 3.0625
43.75 increase 7% =
43.75 × (1 + 7%) = 43.75 × (1 + 0.07) = 46.8125
Radio: $43.75
Tax: $3.06
Total: $46.81
At a store closing, a universal discount rate is applied to all items. If the original price of an item was $27.00 and the price
after the discount is $16.20, what is the discount rate at the store?
Answer:
Step-by-step explanation:
Your answer
40% discount
Mark it as Brainlist. Follow me for more answer.
Solve for x
X=4
3/2x+8=-1
Yep here we go again :
In the diagram below lines HA and BC are parallel. If angle GEC = 135 what is angle HDF?
If you don't know the question, or not sure, please don't answer it!
Whoever answers it right gets brainliest.
Step-by-step explanation:
Angle HDF is also 135 degrees as well. Alternate exterior angles are congruent.
Helppppppppppppppppp
Answer:
The answer will be 24
Step-by-step explanation:
Hope this Helped
Answer:
24
Step-by-step explanation:
Rodrigo practiced playing the guitar 15 1/3 hours over the past 3 weeks. He practiced for 5 1/4 hours during the first week and 5 2/3 hours during the second week.
Answer:
[tex]4 \frac{5}{12}[/tex]
Step-by-step explanation:
The computation of the number of hours practiced on the third week is given below:
= Total hours over the past 3 weeks - first week - second week
[tex]= 15 \frac{1}{3} - 5 \frac{1}{4} -5 \frac{2}{3}\\\\= \frac{46}{3} - \frac{21}{4} - \frac{17}{3}\\\\= \frac{184 - 63 - 68}{12} \\\\= \frac{53}{12}\\\\= 4 \frac{5}{12}[/tex]
Answer: is is correct
Step-by-step explanation:
The frequency, f, in Hz, at which a simple pendulum rocks back and forth is given by 1 , 2 g f π l = where g is the strength of the gravitational field at the location of the pendulum, and l is the length of the pendulum. a. Find the frequency of a pendulum whose length is 1 foot and where the gravitational field is approximately 32 ft/s2 b. The strength of the gravitational field on the moon is about 1 6 as strong as on Earth. Find the frequency of the same pendulum on the moon.
Answer:
a. 0.9 Hz b. 0.37 Hz
Step-by-step explanation:
The frequency of the simple pendulum f = (1/2π)√g/l where g = acceleration due to gravity and l = length of pendulum
a. Find the frequency of a pendulum whose length is 1 foot and where the gravitational field is approximately 32 ft/s2
To find f on Earth, g = 32 ft/s² and l = 1 ft
So, f = (1/2π)√(g/l)
f = (1/2π)√(32 ft/s²/1 ft)
f = (1/2π)√(32/s²)
f = (1/2π)(5.66 Hz)
f = 0.9 Hz
b. The strength of the gravitational field on the moon is about 1/6 as strong as on Earth.. Find the frequency of the same pendulum on the moon.
On the moon when acceleration due to gravity g' = g/6,
f = (1/2π)√(g'/l)
f = (1/2π)√(g/6l)
f = (1/2π)√[32 ft/s²/(6 × 1 ft)]
f = (1/2π)√(32/s²)/√6
f = (1/2π)(5.66 Hz)/√6
f = 0.9/√6 Hz
f = 0.37 Hz
What is the correct vocabulary term for a number variable product or quotient in an expression