There are six elements of order 2 in A8 that have the disjoint cycle form (a1a2)(a3a4)(a5a6)(a7a8).
To find the number of elements of order 2 in A8 with the given cycle form, we first need to determine the number of ways we can choose which elements are paired together in each cycle. There are (8 choose 2) ways to choose which two elements are paired together in the first cycle, (6 choose 2) ways to choose which two elements are paired together in the second cycle, (4 choose 2) ways to choose which two elements are paired together in the third cycle, and (2 choose 2) ways to choose which two elements are paired together in the fourth cycle. Multiplying these together, we get (8 choose 2) * (6 choose 2) * (4 choose 2) * (2 choose 2) = 28 * 15 * 6 * 1 = 2520 possible cycle structures.
However, not all of these cycle structures correspond to elements of A8. We must check whether each structure has an even or odd number of transpositions. In this case, we have four transpositions, so the element will be even if and only if the cycle structure can be written as a product of an even number of transpositions. We can check this by counting the number of cycles in the cycle structure - if there are an odd number of cycles, we need to add one more transposition to make it even. In this case, we have four cycles, which is already even, so all 2520 cycle structures correspond to even permutations.
Finally, we need to count how many of these even permutations are in A8. The parity of a permutation is determined by the number of inversions it has, which is the number of pairs (i,j) such that i < j and pi > pj. In this case, we can count the number of inversions by counting the number of pairs of elements that are in the wrong order within each cycle and adding them up. For example, the cycle (a1a2) has one inversion, since a1 < a2 but a1 appears after a2 in the cycle. The cycle (a3a4) also has one inversion, as does the cycle (a5a6) and the cycle (a7a8). So the total number of inversions is 4. This means that the element is odd, and therefore not in A8.
We can also see this by noting that the permutation (a1a2)(a3a4)(a5a6)(a7a8) can be written as (a1a2a3a4)(a5a6a7a8), which is a product of two disjoint 4-cycles. Since A8 is generated by 3-cycles, this permutation is not in A8.
In summary, there are 2520 possible cycle structures for an element of order 2 in A8 with the cycle structure (a1a2)(a3a4)(a5a6)(a7a8), but none of them are in A8.
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For which sample size (n) and population parameter (p) can a normal curve be used to approximate the sampling distribution? O A. n = 30; p = 0.2 OB. n = 30; p = 0.3 O C. n = 40; p = 0.3 O D. n = 40; p = 0.2
The normal approximation to the binomial distribution is possible in the following case: C. n = 40; p= 0.3
When can we use the normal approximation to the binomial distribution?The binomial distribution is defined as the probability of x successes on n trials, with (p) probability of a success on each trial. It can be approximated to the normal distribution with the formula;
Mean; μ = np
Standard deviation; σ = √(np(1 - p)
The conditions are;
np ≥ 10
√(np(1 - p) ≥ 10
Looking at the given options, the only one that fits this conditions is Option C because;
np = 40 x 0.3 = 12.
n(1 - p) = 40 x 0.9 = 36
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If polygons are similar then what do you know about the corresponding sides and the corresponding angles ?
Answer:
Step-by-step explanation:
In Similar polygons, the corresponding angles are congruent, but the corresponding sides are proportional. So, similar polygons have the same shape, whereas their sizes are different. There would be certain uniform ratios in similar polygons.
If p is inversely proportional to the square of q, and p is 20 when q is 7, determine p when q is equal to 2.
The requried value of the proportional value of p when q = 2 is given as 245.
What is proportionality?proportionality is defined as between two or more sets of values, and how these values are related to each other in the sense are they directly proportional or inversely proportional to each other.
here,
p ∝ 1 / q²
So,
p₁/p₂ = q₂² / q₁²
Substitute value in the above equation,
20/p = 2²/7²
20 ×49 / 4 = p
p = 245
Thus, the requried value of p when q = 2 is given as 245.
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What is a 2 step equation?
A two-step equation is an algebraic issue that can be resolved in two steps.
Define the term 2 step equation?An algebraic problem that can be solved in two steps is known as a two-step equation.Once you've figured it out, you'll know what the variable's value is that makes the equation true.Two-step equations typically take the form ax b = c, where a, b, and c are real numbers.
For instance, 2 - 3x = 7 is an illustration of a two-step equation.
Use the following steps to solve 2-step equations:
so that there is only one term left, add or subtract the same amount from both sides of the equation.Use the same number to multiply or divide both sides of the equation.When the variable (letter) is placed by itself on one side of the equals sign, the equation is considered to be solved.To know more about the 2 step equation, here
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Answer:
Two step equations are algebraic equations and are the equations that can be solved in exactly two steps and gives the final value of the variable in two steps.
Step-by-step explanation:
Example 1: Solve the two step equation (x/6) - 7 = 11
Solution: To solve the given two step equation, we will follow the steps discussed above in the article.
Step 1: Add 7 to both sides of the given two step equation
(x/6) - 7 + 7 = 11 + 7
= (x/6) = 18
Step 2: Multiply both sides of the equation by 6.
6 × x/6 = 6 × 18
= x = 108
Answer: Hence the solution to the given two step equation (x/6) - 7 = 11 is x = 108.
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Tell whether each equation has no solution, one solution, or infinitely
many solutions.
a. 1+3x = 3x + 1
b. 4x + 1 = 3x + 2
c. 5x + 1 = 5x - 2
d. -3(x+1)=-3x+3
Conving is not permitted.
LESSON 11
Answer:
see below
Step-by-step explanation:
a. 1+3x = 3x + 1 --> infinite, it's the same thing
b. 4x + 1 = 3x + 2 --> x=1 one solution
c. 5x + 1 = 5x - 2 --> no solution. it's not possible
d. -3(x+1)=-3x+3 --> x=-1, one solution
Which ordered pair is in the solution set of the following system of inequalities
y≤ 3x+1
x-y>1
Therefore , the solution of the given problem of inequality comes out to be (x,y) = (1,4).
An explanation of inequalityAn inequality in mathematics is a relationship between two concepts or variables that isn't comparable. Therefore, inequality follows imbalance. When two integers are not equal, there is an inequality in mathematics. Egality and inequality are different. When two values aren't genuinely equal, the not equal basic is usually used to indicate this (). The values, whether tiny or huge, are contrasted using a variety of inequalities. By alternating the two characteristics until the constants integers become the only thing left, it is possible to solve many straightforward inequalities. However, a few things promote inequality: Negative values are halved or added to either side.
Here,
Given :
y≤ 3x+1
x-y>1
To find the value of x and y :
y≤ 3x+1
put the value of y
=> x - 3x -1 > 1
=> -2x -1>1
=>-2x > 2
=> -x>1
=>x >-1
x =1
Thus,
y≤ 3(1)+1
=> y ≤ 4
Therefore , the solution of the given problem of inequality comes out to be (x,y) = (1,4).
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What is the exponential form of 3 4?
The given statement "number 3 to exponent 4" in exponential form is be written as 3⁴ , and the value of this expression is 81 .
The Exponential expression represented as "xⁿ" is read as the number x multiplied by itself "n" number of times .
we have to write "3 to exponent of 4" in exponential form ,
So , the exponential form is 3⁴ , it means that the number 3 is multiplied itself four times ;
the value of this expression is calculated as :
⇒ [tex]3^{4} = 3\times 3\times 3\times 3[/tex]
⇒ [tex]9\times 9[/tex]
⇒ 81 .
Therefore , the exponential form of "3 to the exponent of 4 " is 3⁴ .
The given question is incomplete , the complete question is
What is the exponential form of 3 to the exponent 4 ?
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The dog shelter has Labradors, Terriers, and Golden Retrievers available for adoption. If P(terriers) = 15%, interpret the likelihood of randomly selecting a terrier from the shelter. Likely Unlikely Equally likely and unlikely This value is not possible to represent probability of a chance event
If P(terriers) = 15%, the interpretation of the likelihood of randomly selecting a terrier from the shelter is; Unlikely
How to find the probability of selection?Probability of selection is one that defines the probability that a population unit is included in a sample generated by probability sampling.
For any population, the probability of any element within that population to be selected into a sample is calculated as the sample size divided by the population size.
In this case, we are told that the dog shelter has Labradors, Terriers, and Golden Retrievers available for adoption. There are three types of dogs.
We are given;
P(terriers) = 15%
This means the probability of randomly selection the other 2 dogs is way higher than that to select terriers.
Thus, we conclude that the probability of selecting terriers is unlikely due to its' low probability.
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Answer: B: Unlikely
Step-by-step explanation:
HELP PLS
Sid has a baseball cap collection. 75% of his caps have sports team symbols. If 24 of the caps have the team symbols, how many total caps does Sid have?
Actually forget this answer
if f(x)=x^3+x^2 and g(x)=x^4+x^2+x, what is the value of f(x)-g(x) when x=1
What is the mean of the values below (48,59,70,27,61)
does the following graph go with the equation given?
1. f(x)3x^2+6x-24
2. What is the y-intercept of this graph?
3. What is the location of the vertex of this graph?
The equation does not represent the graph
The y-intercept is (0, -16)The location of the vertex of this graph is (-1, -18)How to determine if the equation represents the graphThe equation is given as
f(x) =3x² + 6x - 24
Calculate f(0) and f(1)
f(0) =3(0)² + 6(0) - 24 = -24
f(1) =3(1)² + 6(1) - 24 = -15
On the graph, we have
f(0) = -16
This means that the equation is not the graph
The y-interceptThis is when x = 0
So, we hav
f(0) = -16
How to determine the vertex of the graphFrom the question, we have the following parameters that can be used in our computation:
The graph
The vertex of a graph is the minimum or the maximum of a graph
In this case, it is a minimum and the minimum is located at (-1, -18)
Hence , the vertex is (-1, -18)
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4. The ratio of students who made
the honor roll to the total number
of students is 1:50. If there are
500 students in total, how many
made the honor roll?
Answer: 10 made the honor roll
Step-by-step explanation:
Can you form a triangle using lengths 3/4 and 7?
It is not possible to construct a triangle whose sides are 3 cm 4 cm and 7 cm because the sum of two sides(3 cm and 4 cm) are equal to the third sides(7 cm). The equal sides can not form a triangle.
In the given question, we have to check that it is possible to construct a triangle whose sides are 3 cm 4 cm and 7 cm.
To check whether the given sides can make a triangle or not, we have to check that the sum of two sides always grater than the third side.
To check this we firstly add the 3 and 4
3 + 4 = 7
7 = 7
Now we add 3 and 7
3 + 7 > 4
10 > 4
Now we add 4 and 7
7 + 4 > 3
11 > 3
It is not possible to construct a triangle whose sides are 3 cm 4 cm and 7 cm because the sum of two sides(3 cm and 4 cm) are equal to the third sides(7 cm). The equal sides can not form a triangle.
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The complete question is:
Can you form a triangle using lengths 3cm 4 cm and 7 cm?
Can a triangle be constructed with sides 2.5 cm 3.0 cm and 6.5 cm give reason?
We cannot construct a triangle with side lengths 2.5 cm, 3.0 cm and 6.5 cm as they don't follow the Triangle Inequality Theorem.
It is not possible to construct a triangle using the given side lengths of 2.5 cm, 3.0 cm, and 6.5 cm. This is because of the Triangle Inequality Theorem, which states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.
In this case, if we take 2.5 cm and 3.0 cm as two sides, the sum of their lengths is 5.5 cm. But the length of the third side (6.5 cm) is greater than 5.5 cm, so these three side lengths cannot form a triangle.
It is important to note that this theorem applies to any triangle, whether it is acute, right or obtuse-angled triangle. It is also important to note that this theorem is necessary for the formation of a triangle, and without it, it would not be possible to form a triangle.
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PLSSS HELP IF YOU TURLY KNOW THISS
Answer: 2x+2y+10
Step-by-step explanation:
Yo, whats good.
You basically want to simplify the same terms. For example, you can simplify 6x and -4x. You want to reorder everything so you can simplify it.
6x-4x+2y+3+7
= 2x+2y+10
lol have fun
Click an item in the list or group of pictures at the bottom of the problem and, holding the button down, drag it into the
correct position in the answer box. Release your mouse button when the item is place. If you change your mind, drag
the item to the trashcan. Click the trashcan to clear all your answers.
Add the following polynomials, then place the answer in the proper location on the grid. Write answer in descending
powers of x.
Add: x5-4x4+7x³ + 8, 9x³ +7x2-10, and -2x 5 +7x4-3x + 8.
The simplified exponential notation of the given expression is 9[tex]a^{2}b[/tex].The following polynomials, then put the resolution in the right spot.
what is expression ?A mathematical expression is a sentence with at least two variables or integers and one mathematical action. Addition, subtraction, multiplication, or division are all possible outcomes of this mathematical process. The following are the fundamental parts of an expression: Expression: (Math Operator, Number/Variable, Math Operator). A statement that has a least two numbers or variables, at least one mathematical operation, and is called a mathematical expression. Let's get acquainted with expressive writing. A number is 6 more than half of another number, which is known as x. This statement is written as x/2 + 6 in a mathematical expression.
given
the expression as:
=[tex](\frac{18}{2})( \frac{a^{3} }{a})(\frac{b^{2} }{b})[/tex]
know [tex]\frac{a^{m} }{a^{n} } = a^{m - n}[/tex]
So, =[tex](\frac{18}{2})( \frac{a^{3} }{a})(\frac{b^{2} }{b})[/tex] = 9[tex]a^{2}b[/tex].
The simplified exponential notation of the given expression is 9[tex]a^{2}b[/tex].The following polynomials, then put the resolution in the right spot.
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Pill bluethooth Speaker conit two emiphere and cyclinder. The diameter of the cylinder and emiphere i 2 inche. The height of the cylinder i a foot. The According to the Statement pleae fill in the blank. Pleae anwer the following in inch format and round it to
The Volume of the Bluetooth speaker is 0.36cm³
The capacity of the Bluetooth speaker = Volume of both the hemispherical parts + Volume of the cylindrical part
Given that,
The volume of a hemisphere of radius 'r' = 2/3πr³
The volume of a cylindrical = πr²h where r is
the radius of the base of the cylinder and h is the height.
The hemisphere and the cylinder will have the same radius r =0.25cm
Since the total length of the toy is 2 cm, the length of the conical part
will be 2−0.25−0.25=1.5cm
Hence, the Volume of the bluetooth speaker =2×( 2/3*22/7 *0.25³) + (22/7 *0.25²*1.5) = 0.36cm³
Correct question: A BlueTooth speaker is in the shape of a cylinder of diameter 0.5 cm with two hemispheres stuck to each of its ends. The length of the entire capsule is 2 cm The capacity of the Bluetooth speaker is?
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hello need this due in 3 minutes have a good one
The line of the best fit for the data points plotted in the scatter plot is y = 0.67x + 4.05
How to determine the line of the best fit for the data points plotted in the scatter plot?From the question, we have the following parameters that can be used in our computation:
The graph
Using the line of the best fit, we have"
(x, y) = (0, 4) and (7, 9)
A linear equation is represented as
y = mx + c
Where
c = y when x = 0
So, we have
y = mx + 4
Using the points, we have
9 = 7m + 4
This gives
m = 0.71
So, we have
y = 0.71x + 4
The closest to this is
y = 0.67x + 4.05
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Farmer Gepsil started with some dubbles on his farm. After 11 hours he had 88 dubbles. Every hour, he bought 6 more of them. Please help me make a table so I can graph this
The table for the farmer buying dubbles is given below.
What is a graph?
In mathematics, a graph is a visual representation or diagram that shows facts or values in an ordered way. The relationships between two or more items are frequently represented by the points on a graph.
Let the time be represented by the variable = x.
Let the number of dubbles be represented by the variable = y.
At x = 11, the number of dubbles y = 88.
Every hour, the farmer bought 6 more of them.
So, at x = 12 the number of dubbles y = 88 + 6
So, the table will be of the formula (x,y+6).
Therefore, the table for the graph is obtained.
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a furniture store is having a sale where everything is 40% off. write a function that represents the amount of amount of discount d on an item with a regular price of p
d = 0.4 p, where the sales price of the bookshelf is $51, is the function that depicts the percentage off of a regular price.
What is the amount of discount ?When an item's price is lowered, it is said to be on sale. Multiplying the cost of an item by the % discount will give you the discount's value.
Discount = Original Price × Percentage Discount
$85 × 40%
$85 × 0.4 = $34.
Original cost less any discounts equals sales price.
$85 - $34 = $51.
The discount is the amount that separates an item's selling price from its marked (or list) price. Discount is therefore calculated as follows: Discount=List price – Selling price. Take advantage of deals like the buy one, get one free promotion or 15% off shirts, for instance. On an item with a price per hundred displayed, you have a percentage discount. An item that was previously priced at Rs. 1,000 is now being offered for Rs. 900 thanks to a 10% percentage discount.
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What is the relationship between cardiac output and intensity of exercise?
There is a linear relationship between exercise intensity and cardiac output. Therefore, when one rises, the other rises as well.
Cardiac output quantifies the volume of blood that your heart can pump in a minute. The phrase "exercise intensity" refers to how hard your body is working throughout a workout. These two are directly related to one another in some way.
The increase in cardiac output is linearly associated with exercise intensity up until the point of exhaustion. This happens as a direct result of the interaction between the heart rate and stroke volume reactions to the intensity of activity. Therefore, cardiac output will increase as exercise intensity does.
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mala walk her dog 3 times a day each walk is 3/4 mile. which expression tell how many mile mala walks her dog each day
3×3/4 is the expression which gives the 2.25 miles mala walks her dog each day.
What is Expression?An expression is combination of variables, numbers and operators.
Given that mala walk her dog 3 times a day
Each walk is 3/4 mile.
We have to find the expression tell how many mile mala walks her dog each day.
The miles walk by Mala and her dog=3×3/4
=9/4
=2.25 miles.
Hence, 3×3/4 is the expression which gives the 2.25 miles mala walks her dog each day.
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Peter own a total of one hundred and forty four prized baeball card. If he were to add 7 more American League player and three more national league player, hi collection of American to national would be in a ratio of nine five. Find out how many card of each league he ha currently
The total number of baseball cards that Peter owns is 154.
Mathematicians use the term "ratio" to compare two or more numbers. It serves as a comparison tool to show how big or tiny an amount is in relation to another.
Two amounts are compared using division in a ratio. In this case, the dividend is referred to as the "antecedent" and the divisor as the "consequent."
Given that,
Peter owns a total of one hundred and forty-four prized baseball cards.
He adds seven more American League players and three more national league players.
Total baseball cards he owns = 144+ 7+3 = 154
The ratio of American to national = 9:5 = 9/5 = 1.8
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What is the degree of 2x² 5x² 7?
The degree of 2x² 5x² 7 is 4.
The degree of a polynomial is the highest power of the variable in a given polynomial. In this case, the highest power of the variable is 4, making the degree of the polynomial 4.
We can calculate the degree by using the formula Degree = Max (exponent of x).
In this case, the exponent of x is 2 and 5 respectively, making the degree of the polynomial 4.
Therefore, the degree of the polynomial 2x² 5x² 7 is 4.
To calculate this, we can use the following formula:
Degree = Max (exponent of x)
For the given polynomial 2x² 5x² 7, we can calculate the degree as follows:
Max (2, 5) = 5
Therefore, the degree of the polynomial 2x² 5x² 7 is 5.
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please help quickly!
which of the following is the graph of y=|x+3|?
Answer:
It's D, because the point intercepts at (0, 3), which is 3 up from the y position. What the difference is from this graph and the others is that this graph has a y-intercept of positive 3, and starts at an x point of -3. The x and y values should be inverted in order for this to be correct, so that is why option D is correct.
Hope this helps!
The polygons are similar, but not necessarily drawn to scale. Find the value of x.
Answer:
Summary: The polygons are similar but not necessarily drawn to scale, the value of x is 13 units.
Step-by-step explanation:
pls follow 4 more :) tysm
Why is it called a prime number?
Prime numbers are called prime as they come multiplicative first and other numbers are multiples of prime numbers.
As given in the question,
Prime numbers are called prime:
Meaning of prime is known as first.Prime numbers are multiplicatively first numbers .All the other numbers are multiples of prime numbers other than one.'1' is neither a prime number nor a composite number.prime numbers represents such numbers which has only two factors one and the number itself.Example of prime numbers : 2, 3, 5, 7,.... so on.Other numbers : 4 = 2 × 2 , 12 = 2× 2 × 3 so on.Therefore, prime numbers are called prime as they are multiplicative first numbers other numbers are multiples of prime number other than one.
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Please help!!! 30+ points! Thank you so much! :)
Answer:
8/5, -5/8
Step-by-step explanation:
[tex]5x+8y=-8 \\ \\ 8y=-5x-8 \\ \\ y=-\frac{5}{8}x-1[/tex]
So, the slope of the given line is -5/8.
Perpendicular lines have slopes that are negative reciprocals of each other, so the answer for the first question is 8/5.Parallel lines have the same slope, so the answer to the second question is -5/8.!!HELP!! evaluate using order of operations: A = L=50 W= 15 give your answer in simplest form
The numeric value of the expression A = LW, when L = 50 and W = 15, is given as follows:
A = 750.
How to find the numeric value of a function or of an expression?To find the numeric value of a function or of an expression, we replace each instance of the variable in the function or in the expression by the value at which we want to find the numeric value.
The expression for this problem is defined as follows:
A = LW.
The input values of L and W are given as follows:
L = 50, W = 15.
Then the numeric value of the expression is found replacing the lone instance of L by 50 and the lone instance of W by 15, as follows:
A = 50 x 15
A = 750.
As there is only a single multiplication operation, precedence is not relevant for this problem.
Missing Information
The problem asks for the numeric value of the expression A = LW when L = 50 and W = 15.
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