let p be a p-group. let a be a normal subgroup of order p. prove that a is contained in the center of p.
Answers
We have proved that if A is a normal subgroup of order p in a p-group P, then A is contained in the center of P.
To prove that a normal subgroup A of order p is contained in the center of the p-group P, we need to show that every element of A commutes with every element of P.
Let's denote the elements of A as a_1, a_2, ..., a_p, where p is the order of A. Since A is a normal subgroup of P, every conjugate of A is also a subgroup of P. Therefore, the conjugates of A must have the same order as A, which is p.
Now, let's take an arbitrary element g from P. We want to show that g commutes with every element of A. Consider the subgroup generated by g and A, denoted as ⟨g, A⟩. Since A is normal in P, ⟨g, A⟩ is a subgroup of P.
The order of ⟨g, A⟩ must be a divisor of the order of P. Since P is a p-group, its order is a power of p. Therefore, the order of ⟨g, A⟩ is also a power of p. However, A has order p, so the order of ⟨g, A⟩ must be either p or 1.
If the order of ⟨g, A⟩ is 1, it means that g commutes with every element of A. In this case, we have shown that A is contained in the center of P.
If the order of ⟨g, A⟩ is p, it means that ⟨g, A⟩ is a subgroup of P with the same order as A. Since A is a normal subgroup, it is the unique subgroup of order p in P. Therefore, ⟨g, A⟩ must be equal to A itself. This implies that g is an element of A.
Since g was an arbitrary element of P, we have shown that every element of P is also an element of A. Therefore, A is contained in the center of P.
In conclusion, we have proved that if A is a normal subgroup of order p in a p-group P, then A is contained in the center of P.
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Related Questions
If I go through the 1st 10 difference in mean data sets in Statkey, the p values for two sided tests that I got from the randomization tests were .05,0,.0058,.05.01,6e-4..0075, 204,3.6e-4,036 and a. Identify which of the tests are interesting at a false discovery rate of 0.01=Q
Answers
At a false discovery rate of 0.01 (Q = 0.01), the tests with p-values less than or equal to 0.0058 are considered interesting. This includes the third and ninth tests.
A false discovery rate (FDR) is the proportion of false discoveries among all discoveries made in statistical hypothesis testing. In this case, the FDR is set to 0.01 (Q = 0.01), which means that only 1% of the tests can be expected to be falsely identified as significant.
To determine which tests are interesting at a false discovery rate of 0.01, we need to compare the p-values obtained from the randomization tests in Statkey with the FDR threshold of 0.01. The tests with p-values less than or equal to the FDR threshold are considered significant.
In this case, the FDR threshold is 0.01, and the third and ninth tests have p-values of 0.0058 and 0.0036 respectively, which are less than or equal to the FDR threshold. Therefore, these two tests are considered interesting at a false discovery rate of 0.01.
The other tests have p-values that are greater than the FDR threshold and are therefore not considered interesting at this threshold. It is important to note that even though a test may not be interesting at a certain FDR threshold, it does not necessarily mean that the null hypothesis is true. It could be that the sample size is too small or the effect size is too small to detect a significant difference.
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How many years does it take an account with a principal of $400 and an annual simple interest of 2% to double?
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a web music store offers two versions of a popular song. the size of the standard version is megabytes (mb). the size of the high-quality version is mb. yesterday, the high-quality version was downloaded four times as often as the standard version. the total size downloaded for the two versions was mb. how many downloads of the standard version were there?
Answers
260 standard versions were downloaded and 520 high-quality versions were downloaded.
What is Equations ?A mathematical statement that demonstrates the equality of two mathematical expressions is the definition of an equation. Consider the equation 3x + 5 = 14, where 3x + 5 and 14 are two expressions that are separated by the symbol "equal." Mathematical variables are used in even the most fundamental and straightforward algebraic equations.
Let 'x' represent the number of standard version songs, then '2x' represents the number of high-quality version songs:
2.3x+4.4*2x=2886
Solve for x
x=260
260*2=520
So 260 standard versions were downloaded and 520 high-quality versions were downloaded.
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What goes after 2, 9, 11, 18, 20, 27
Answers
Answer:
29 goes after 27
Step-by-step explanation:
the patern is add 2, then add 7, repeat
Answer:
29
Step-by-step explanation:
From 2 to 9, it's adding 7.
From 9 to 11, it's adding 2.
and so forth with the rest of them
11-18: 7
18-20: 2
20-27: 7
so it's a pattern rotating by adding 7 then by adding 2
so from 20 to 27, we added 7, so now you need to add 2.
27 + 2 = 29
so your answer is dun dun dun '29'
EXERCISE 8.2 a) 5x²-2r³+3 - 6x c) -2r²-2r²³-6-5r³ 1. Write down the constant term in each of these expressi
Answers
c) The constant term in the expression -2r²-2r²³-6-5r³ is -6.
Point A is located at (−2, 2), and point M is located at (1, 0). If point M is the midpoint of segment AB, find the location of point B.
(−0.5, 1)
(4, −2)
(−5, 4)
(−1, 1)
Answers
Answer:
B. (4, -2)
Step-by-step explanation:
Please see attachment.
Hope this helps!
If not, I am sorry.
Bread, gasoline, and ____ are examples of convenience products.(A) cars(B) furniture(C) newspapers(D) large appliances(E) a cruise
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The answer is (C) newspapers. Convenience products are low-cost consumer goods and services that are readily available and easily accessible to consumers.
These products are typically purchased frequently, with minimal effort and little thought or research. Examples of convenience products include bread, gasoline, newspapers, and other everyday items that consumers purchase without much consideration.
Cars, furniture, large appliances, and a cruise are not typically considered convenience products. These are generally higher-cost items that require more thought and research before purchase.
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you compute a two-sample z statistic and it comes out to equal 1.35. what is the p-value if you are doing a two-tailed test? enter a value between 0 and 100 corresponding to the percentage, e.g. if your p-value equals 2.4%, enter 2.4. any correctly rounded version will receive full credit.
Answers
The p-value for a two-tailed test with a two-sample z statistic of 1.35 is approximately 17.7%.
What is the p-value for a two-tailed test with a two-sample z statistic of 1.35?To determine the p-value for a two-tailed test using a two-sample z statistic of 1.35, we need to find the probability of observing a test statistic as extreme as 1.35 or more extreme in both tails of the distribution.
The p-value corresponds to the area under the curve beyond the observed test statistic in both tails. Since the test is two-tailed, we need to calculate the cumulative probability in both the left and right tails.
Using a standard normal distribution table or a statistical software, we can find the cumulative probability for the test statistic of 1.35. In this case, the area in one tail would be 1 - (cumulative probability of 1.35) = 1 - 0.9115 ≈ 0.0885.
Since we're conducting a two-tailed test, we need to consider both tails, so the total p-value is twice the value obtained from one tail.
P-value = 2 * 0.0885 = 0.177.
Converting this value to a percentage, the p-value is approximately 17.7%.
Therefore, the p-value for the two-tailed test with a two-sample z statistic of 1.35 is approximately 17.7%.
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Please help as soon as possible:)
Answers
Answer:
I think is SSS
Step-by-step explanation:
I haven't had to take geometry yet, but from my understanding, SSS means the all the side have the same ratio in both? They are all the same ration, just dilated to different sizes, so I think its SSS
Answer all parts (a)-(e) of this question. The utility of an agent who consumes x amounts of good 1 and y amounts of good 2 is given by the following utility function: U(x,y) = x²y The agent has an income of 12. The price of good 1 is 4 and the price of good 2 is 2. (a) Show that the agent's utility function is homogeneous of degree 3. (b) Explain why the budget constraint is 4x + y = 12 and draw its graph.
(c) Compute the marginal utility the agent derives from good 1 and the marginal utility she derives from good 2. (d) What is the agent's marginal rate of substitution? What is the slope of the budget constraint? (e) Derive the agent's optimal consumption bundle. Illustrate the bundle, along with the budget constraint and the relevant indifference curve, in a diagram on the (x,y) plane and sketch it in x, y space. Interpret the slope of the budget constraint.
Answers
(a) The utility function U(x, y) = x²y is homogeneous of degree 3 because if we multiply both x and y by a positive constant λ, the utility function becomes U(λx, λy) = (λx)²(λy) = λ³x²y. The function exhibits a degree of homogeneity equal to the exponent of λ, which in this case is 3.
(b) The budget constraint can be derived by equating the total expenditure to the agent's income. The price of good 1 is 4, so the expenditure on good 1 is 4x, and the price of good 2 is 2, so the expenditure on good 2 is 2y. Therefore, the budget constraint is given by 4x + 2y = 12. To graph this constraint, we plot x on the horizontal axis and y on the vertical axis. The resulting line has a slope of -2 and intersects the x-axis at x = 3 and the y-axis at y = 6.
(c) To compute the marginal utility of good 1, we take the derivative of the utility function with respect to x, which gives us MU₁(x, y) = 2xy. Similarly, the marginal utility of good 2 is given by MU₂(x, y) = x².
(d) The agent's marginal rate of substitution (MRS) represents the rate at which the agent is willing to trade one good for another while maintaining the same level of utility. It is given by MRS = MU₁/MU₂ = 2xy/(x²) = 2y/x. The slope of the budget constraint is equal to the negative ratio of the prices of the two goods, which is -4/2 = -2.
(e) To derive the agent's optimal consumption bundle, we need to find the combination of x and y that maximizes the agent's utility while satisfying the budget constraint. This occurs at the point where the indifference curve (representing constant utility) is tangent to the budget constraint. In this case, the indifference curve is U(x, y) = x²y, and the optimal consumption bundle can be found by solving the system of equations formed by the utility function and the budget constraint. The resulting bundle will depend on the specific values of x and y obtained. By plotting the bundle on the (x, y) plane along with the budget constraint and an indifference curve, we can visually represent the optimal consumption bundle. The slope of the budget constraint represents the rate at which the agent can trade one good for another while staying within the budget constraint.
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If (6^2)^p = 6^10, what is the value of p?
1.) 2
2.) 3
3.) 4
4.) 5
Answers
Answer:
Step-by-step explanation:
(6^2)^p = 6^(2p) = 6^10
2p = 10
p = 5
Two charged objects share a 44 n force between them. if one object has a charge of +4.0-6 c and is 3 cm from the second one. then the second charge is ___ e-6 c. round your answer to the nearest tenth. (100 cm = 1 m)
Answers
The charge of the second object is approximately 2.5 x 10⁻⁶C.
What is the charge of the second object in the given scenario?In the given problem, there are two charged objects experiencing a force of 44 N between them. One of the objects has a charge of +4.0-6 C and is positioned 3 cm away from the second object.
We need to determine the charge of the second object.
The force between two charged objects can be calculated using Coulomb's Law:
F = (k ˣ q1 ˣ q2) / r²,
where F is the force, k is the electrostatic constant (9 x 10⁹ N m²/C²), q1 and q2 are the charges of the objects, and r is the distance between them.
Plugging in the given values, we have:
44 = (9 x 10^9 ˣ 4.0⁻⁶ ˣ q2) / (0.03)².
Simplifying the equation, we find:
q2 = (44 ˣ (0.03)²) / (9 x 10⁹ ˣ 4.0⁻⁶).
Evaluating the expression, we get q2 ≈ 2.47 x 10⁻⁶C. Rounding to the nearest tenth, the charge of the second object is approximately 2.5 x 10⁻⁶C.
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Work out ( 4 × 10 7 ) + ( 7 × 10 5 ) Give your answer in standard form.
Answers
The sum of the numbers (4 × 10⁷) + (7 × 10⁵) in scientific notation is 4.07 × 10⁷.
Given numbers are,
(4 × 10⁷) and (7 × 10⁵).
We have to find the sum of the numbers.
In order to find the sum of the numbers in scientific notation, we have to take the common numbers outside.
Now,
4 × 10⁷ = 4× 10² × 10⁵
= 400 × 10⁵
(4 × 10⁷) + (7 × 10⁵) = (400 × 10⁵) + (7 × 10⁵)
= 407 × 10⁵
= 4.07 × 10⁷
Hence the sum is 4.07 × 10⁷.
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It cost Steve $135.75 to buy 15 albums from an online music store. How much did 1 album cost?
Answers
Answer: $9.05
Step-by-step explanation:
divide 135.75 by 15 in order to find the cost of one album.
135.75 / 15 = 9.05
answer: $9.05
what is the slope and line of y+3=4(x-1)
Answers
Answer: M=3
Step-by-step explanation:
The slope-intercept form is y=mx+b, where mis the slope and b is the y-intercept. y=mx+b
Simplify the right side.
A right triangle has a leg b=3 and a hypotenuse c=15
how long is the other leg?
Answers
Answer:
sqrt(216) = 6×sqrt(6) ≈ 14.6969
Step-by-step explanation:
Pythagoras :
c² = a² + b²
with c being the Hypotenuse.
so, we have
15² = a² + 3²
225 = a² + 9
a² = 225 - 9 = 216
a = sqrt(216) = sqrt(4×54) = sqrt(4×9×6) = 2×3×sqrt(6) =
= 6×sqrt(6)
Answer:
The length of the other leg is 14.697
Step-by-step explanation:
a^2 +b^2= c^2
Please answer correctly !!!!!!!!!!!!!! Will mark brainliest !!!!!!!!!!!!!!!!!!!
Answers
Answer:
222 okkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkk
Answer:
138°.
Step-by-step explanation:
Extend one of the lines that forms the angle. You should get a triangle. Because the topmost and bottoms lines are straight, one of the angles has to equal 180-111, which is 69°(nice). The opposite angle to that has to also be that size. Since the topmost and bottomost lines are parallel the alternate interior angle to the 111° outside of the triangle would also equal 111°. So, because it's a straight line, the angle next to it, which is inside the triangle, is once again 69°(nice). Then, since you have 2 angles of the triangle you can add them together and subtract their sum from 180°, that should be 42°. One of the lines that 42° is on is also one x is on, so 42°+x=180°. Using this, you can find that x should be about 138°, I think.
i need help plsQuestion 2(Multiple Choice Worth 2 points) (Likelihood MC) In an experiment with a bag of marbles, P(green) = three fourths. Interpret the likelihood of choosing a green marble. Likely Unlikely Equally likely and unlikely This value is not possible to represent probability of a chance event. 25 points rewarded
Answers
Step-by-step explanation:
i don't know sorry i didnt understand
compute p(s90,000 ≤ 29, 500); express the result in decimals.
Answers
The probability of a normal distribution with a mean of 90,000 and a standard deviation of 29,500 being less than or equal to 29,500 is approximately 0.0202.
To compute this probability, we can use the standard normal distribution and transform the values accordingly:
z = (x - mu) / sigma
where:
x = 29,500
mu = 90,000
sigma = 29,500
Substituting the values, we get:
z = (29,500 - 90,000) / 29,500 = -2.0347
Using a standard normal distribution table or calculator, we can find that the probability of a value being less than or equal to -2.0347 is approximately 0.0202.
Therefore, the probability of a normal distribution with a mean of 90,000 and a standard deviation of 29,500 is less than or equal to 29,500 is approximately 0.0202.
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In a study, the data you collect is the average weight of newborn babies in ounces.What is the level of measurement?nominalordinalintervalratio
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The level of measurement for the data collected in the study (the average weight of newborn babies in ounces) is interval.
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Interval data is a type of quantitative data, meaning it can be measured numerically and is used when the order or magnitude of the data is important. Unlike ordinal data, the difference between two values is the same regardless of where it falls in the scale.
For example, if two newborn babies weighed 5 and 10 ounces respectively, the difference between the two is 5 ounces. This 5-ounce difference would be the same no matter what order the babies were in. This is an example of interval data.
Another example of interval data would be temperature. When comparing temperatures, the difference between 60 and 70 degrees is the same as the difference between 70 and 80 degrees.
Interval data can be graphed on a line graph. It can also be used in calculations, such as the mean and standard deviation, as the data is numerical and can be averaged.
To summarise, the data collected in the study (the average weight of newborn babies in ounces) is interval data as it is numerical and the difference between two values is the same regardless of where it falls in the scale.
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IM STUCK i need help WITH THIS PROBLEM THE NUMBER 4 will give brainly
Answers
Answer:
Ok say your social life is on that scale, Now the moment you walk into school your life is A which means it hasn't made it anywhere..now as you progress your love life goes up and becomes a B soon you grow popular and hit C as your results sky rocket..suddenly something you do affects that maybe a bad grade or something you did to someone then your social life drops dramatically to a D and soon crumbling to an E.
~ Zachary Mark brainliest if you want Thanks <3 Have a nice day!!!
Answer:
The depth of water in a stream bed over time
Step-by-step explanation:
if sample evidence is inconsistent with the null hypothesis, we ___ the null hypothesis.
Answers
If sample evidence is inconsistent with the null hypothesis, we reject the null hypothesis.
Rejecting the null hypothesis means that we have found significant evidence that the observed data is unlikely to have occurred by chance alone, assuming the null hypothesis is true. It suggests that there is a significant difference or relationship present in the population being studied. This decision is based on the principles of hypothesis testing and statistical inference, where we set a significance level and compare the observed data to the expected outcomes under the null hypothesis.
If the evidence contradicts the null hypothesis beyond a reasonable doubt, we reject it in favor of an alternative hypothesis.
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If a matrix is diagonalizable then it is invertible.
a. True
b. False
Answers
If a matrix is diagonalizable then it is invertible is False.
A matrix can be diagonalizable but not invertible. For example, the zero matrix (a matrix where all entries are 0) is diagonalizable but not invertible.
What is diagonalizable metrix?
A diagonalizable matrix is a square matrix that can be transformed into a diagonal matrix through a similarity transformation. In other words, a matrix A is diagonalizable if there exists an invertible matrix P and a diagonal matrix D such that A = PDP⁻¹.
Geometrically, diagonalizable matrices represent linear transformations that stretch or shrink the space along a set of independent directions, which are called eigenvectors. The diagonal entries of the diagonal matrix D correspond to the eigenvalues of A, which represent the scaling factors along these directions.
Not all matrices are diagonalizable. A matrix is diagonalizable if and only if it has a sufficient number of linearly independent eigenvectors. In particular, symmetric matrices are always diagonalizable, and non-diagonalizable matrices are often associated with non-invertible linear transformations or defective geometric structures.
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Complete question is: If a matrix is diagonalizable then it is invertible is False.
: Find the indicated probability. Round your answer to 6 decimal places when necessary. A card is drawn at random from a well-shuffled deck of 52 cards. What is the probability of drawing a face card or a 5? Select one: O A4 13 O B. 16 O C. 48 52 OD 13
Answers
The probability of drawing a face card or a 5 is 4/13. Option a is correct.
A card is drawn at random from a well-shuffled deck of 52 cards. To find the probability of drawing a face card or a 5, we need to count the number of cards in a deck that are face cards or 5s and divide that by the total number of cards in a deck.
There are 16 such cards (12 face cards and 4 5s) in a deck and 52 total cards. So the probability of drawing a face card or a 5 is:
16/52 which can be simplified to 4/13.
The probability is 4/13. Option a is correct.
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a cube has one side that measures 6 cm what is the volume? And no this is not the same question
Answers
Answer: 216cm
Step-by-step explanation:
volume = 6×6×6 =216 cm
Emerson makes 8 cups of snack mix. She puts all the snack mix into plastic bags. She puts 3 1/2 cups of the mix into each bag. How many plastic bags does Emerson need?
Answers
Emerson needs 3 bags in total to hold all of her snack mix .
To determine the number of plastic bags that Emerson needs, we have to divide the total amount of snack mix by the amount of snack mix in each bag.
Emerson made 8 cups of snack mix, and she puts 3 1/2 cups of mix into each bag. We can write this as a mixed number: 3 1/2 = 7/2. So Emerson puts 7/2 cups of mix into each bag.
To find out how many bags Emerson needs, we divide the total amount of mix by the amount of mix in each bag:
8 cups ÷ (7/2 cups per bag) = 16/7 bags
We can simplify 16/7 by dividing the numerator and denominator by 1 (the greatest common factor of 16 and 7)
16/7 ÷ 1/1 = 16/7 x 1/1 = 16/7
So Emerson needs 16/7, or approximately 2.29, bags. Since she can't use a fraction of a bag, she will need to round up to the nearest whole bag. Therefore, Emerson needs 3 bags in total to hold all of her snack mix.
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Jennifer invests $8,353 in a retirement account with a fixed annual interest rate of8% compounded 4 times per year. What will the account balance be after 15 years?
Answers
Answer:
Amount after 15 years = $27,406.45 (Approx.)
Step-by-step explanation:
Given:
Amount invested p = $8,353
Rate r = 8% = 0.08/4 = 0.02 per year (4 times)
Number of interest compounded n = 15 year x 4 = 60 times
Find:
Amount after 15 years
Computation:
A = p[1+r]ⁿ
Amount after 15 years = 8,353[1+0.02]⁶⁰
Amount after 15 years = 8,353[1.02]⁶⁰
Amount after 15 years = $27,406.45 (Approx.)
What is the answer ???
Answers
What is 4.89 + ? = 11.26
Answers
Answer:
The answer is 6.37.
Step-by-step explanation:
Please pick me as brainlest answer
Answer:
6.37
Step-by-step explanation:
11.26 - 4.89 = 6.37
Hope this help ;)
2x-y=3 x+3=4 solve by substitution
Answers
x=1
2(1)-y=3
2-y=3
-y=1
y=-1
y=-1 is the answer