Answers
The answer of the given question based on explaining the meaning of symmetric group Sₓ on X the answer is given below,
What is Permutation?In mathematics, permutation is way of arranging set of distinct objects in particular order. A permutation of set is bijection from the set to itself, meaning that each element in set is mapped to a unique element, and every element in set is mapped to exactly once. For example, the set {1, 2, 3} can be permuted in six different ways: (1, 2, 3), (1, 3, 2), (2, 1, 3), (2, 3, 1), (3, 1, 2), and (3, 2, 1). Permutations have important applications in group theory, combinatorics, and cryptography.
The symmetric group Sₓ on X is a group of permutations of a set X, where Sₓ is the set of all possible bijections from X to X. In other words, the elements of Sₓ are all possible ways of rearranging the elements of X, while still maintaining the structure of the set. A permutation is a bijection that maps each element of X to a unique element of X.
The order of the symmetric group Sₓ on X is the number of elements in X, denoted by |X|. The symmetric group has important applications in group theory, algebraic geometry, and combinatorics. It is also a fundamental concept in the study of abstract algebra and is used to study the properties of permutations, symmetry, and groups.
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The symmetric group S_X on a set X is the group of all permutations of the elements in X.
Describe Bijective Function?A bijective function, also known as a bijection, is a type of function in mathematics where every element in the domain (input) is paired with a unique element in the range (output), and every element in the range has a corresponding element in the domain. In other words, a bijection is both injective (one-to-one) and surjective (onto).
A function f: X → Y is said to be bijective if:
Every element in X is paired with a unique element in Y (one-to-one or injective). This means that no two elements in X are mapped to the same element in Y.
Every element in Y has a corresponding element in X (onto or surjective). This means that every element in Y is mapped to by at least one element in X.
A permutation of X is a bijective function that maps each element of X to a unique element of X. The symmetric group S_X contains all possible permutations of the elements of X, and the group operation is function composition.
In other words, if X is a set with n elements, then the symmetric group S_X contains all possible bijections from X to itself, which means there are n! (n factorial) elements in S_X. Each element in S_X represents a unique way to permute the elements in X.
For example, let X = {1, 2, 3}. The symmetric group S_X on X contains the following six elements (permutations):
The identity permutation: (1, 2, 3)The permutation that swaps 1 and 2: (2, 1, 3)The permutation that swaps 1 and 3: (3, 2, 1)The permutation that swaps 2 and 3: (1, 3, 2)The permutation that cycles the elements in a clockwise direction: (3, 1, 2)The permutation that cycles the elements in a counterclockwise direction: (2, 3, 1)These six permutations form a group under function composition, which is the symmetric group S_X on X.
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Related Questions
find the coordinates of point p that is 3/4 of the way along the directed line segment from c(6,-5) to d(-3,4)
Answers
The coordinates of point P that is 3/4 of the way along the directed line segment from C(6, -5) to D(-3, 4) are (-0.75, 1.75).
To find the coordinates of point P that is 3/4 of the way along the directed line segment from C(6, -5) to D(-3, 4), we can use the following formula:
P = (1 - 3/4)C + (3/4)D
First, we find the vector CD = D - C:
CD = (-3, 4) - (6, -5) = (-9, 9)
Then we can plug in the values and simplify:
P = (1 - 3/4)C + (3/4)D
P = (1/4)(6, -5) + (3/4)(-3, 4)
P = (3/4)(-3, 4) + (1/4)(6, -5)
P = (-2.25, 3) + (1.5, -1.25)
P = (-0.75, 1.75)
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The circumference of a circle is five pi centimeters what is the area in square centimeters express your answer in terms of pi
Answers
Answer:
Step-by-step explanation:
circumference c=2πr=5π
[tex]r=\frac{5\pi }{2\pi } =\frac{5}{2}~cm \\area=\pi r^{2} =\pi (\frac{5}{2} )^2\\=\frac{25}{4} \pi \\=6.25 ~cm^2[/tex]
can someone help me please
Answers
Since 34 people bought the gum and there’s a total of 46 people or it could be
34/12 the number of people who saved the money Wich is = 2.83
Use the substitution method to solve the following system of equations: 3x + 5y = 3
x + 2y = 0
(1, 1)
(6, −3)
(6, 1)
(1, −3).
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Milly took a loan of N$900 with simple interest for as many years as the rate of interest. If she paid N$324 as
interest at the end of the loan period, what was the rate of interest?
Answers
Answer:
Let's assume that the rate of interest is r (in decimals), and the time period is also r years. Then we can use the simple interest formula:
I = P * r * t
where I is the interest paid, P is the principal amount (the loan amount in this case), r is the rate of interest per year, and t is the time period in years.
Substituting the given values, we get:
324 = 900 * r * r
Simplifying, we get:
r² = 324/900
r² = 0.36
Taking the square root of both sides, we get:
r = ±0.6
Since the rate of interest cannot be negative, we can take r = 0.6. Therefore, the rate of interest is 0.6 or 60% per year.
18 Look at the two inequalities below.
3x + 2 > 14
10-x≤7
Which value of x makes both inequalities true?
(A) 2
(B) 3
(C) 4
(D) 5
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ANSWER :
Answer is D.
Thanks for the question today.
2.2 × 1.6 as a fraction multiplication expression PLEase hELP I'm gonna GET GROUNDED IF I DONT DO THIS QUESTION HELP FAST!
Answers
Answer:
88/25
Step-by-step explanation:
if you do 2.2 times 1.6 equals 3.52 and then a fraction.
Answer:
2.2 × 1.6 can be expressed as a fraction multiplication expression as follows:
(22/10) × (16/10)
Simplifying the expression by canceling out the common factor of 10, we get:
22 × 16 / 10 × 10
Multiplying the numerator and denominator, we get:
352 / 100
Simplifying the fraction by dividing both the numerator and denominator by 4, we get:
88 / 25
Therefore, 2.2 × 1.6 as a fraction multiplication expression is 88/25.
a rectangular prism with a volume of 20 in^3 is dialited with a scale facotr of 2. what is the volume of the new figure?
Answers
The volume of the new rectangular prism is 160 in³ after it has been dilated with a scale factor of 2.
In this case, the scale factor is 2, which means that the dimensions of the original figure will be multiplied by 2 to get the dimensions of the new figure.
Volume of rectangular prism = length x width x height
20 = l x w x h
Next, we need to find the new dimensions of the rectangular prism after it has been dilated by a scale factor of 2. We can do this by multiplying each dimension of the original rectangular prism by 2.
New length = 2 x l
New width = 2 x w
New height = 2 x h
Now we can find the volume of the new rectangular prism by using the same formula as before, but with the new dimensions:
Volume of new rectangular prism = (2 x l) x (2 x w) x (2 x h)
Simplifying this expression, we get:
Volume of new rectangular prism = 8 x (l x w x h)
We know that l x w x h is equal to the volume of the original rectangular prism, which is 20 in³. So we can substitute this value into the expression to get:
Volume of new rectangular prism = 8 x 20 in³
Volume of new rectangular prism = 160 in³
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A box containing 5 balls costs $8.50. If the balls are bought individually, they cost $2.00 each. How much cheaper is it, in percentage terms, to buy the box as opposed to buying 5 individual balls?
Answers
Answer: The total cost of buying 5 balls individually is $2.00 x 5 = $10.00.
The box costs $8.50, which means it is $10.00 - $8.50 = $1.50 cheaper to buy the box.
To calculate the percentage difference, we can use the formula:
% difference = (difference ÷ original value) x 100%
In this case, the difference is $1.50, and the original value is $10.00.
% difference = ($1.50 ÷ $10.00) x 100%
% difference = 0.15 x 100%
% difference = 15%
Therefore, it is 15% cheaper to buy the box than to buy 5 individual balls.
Step-by-step explanation:
there are 3/4 as many boys as girls in a class of fith-graders. if there are 35 students in the class how many are girls?
Answers
Therefore, there are 20 girls in the class of fifth-graders.
What is fraction?In mathematics, a fraction represents a part of a whole or a division of two numbers. It is written in the form of a numerator and a denominator separated by a horizontal bar (also known as a fraction bar). The numerator represents the number of equal parts being considered, while the denominator represents the total number of equal parts in the whole or the divisor of the division.
Here,
Let the number of girls in the class be represented by 'g'.
According to the problem, the number of boys is 3/4 as many as the number of girls. This means:
Number of boys = (3/4) * number of girls
Number of boys = (3/4) * g
The total number of students in the class is given as 35. So we have:
Number of girls + Number of boys = Total number of students
g + (3/4)g = 35
Simplifying the equation, we get:
(7/4)g = 35
Dividing both sides by 7/4, we get:
g = 20
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fill in the blank. Find the kinetic energy of the following particles that each have a de Broglie wavelength of 0.50 nm.? (a) photons ____eV = 2480eV
Answers
The kinetic energy of particle with a de Broglie wavelength of 0.50 nm is 82.6 eV.
The given de Broglie wavelength of 0.50 nm corresponds to photons. The formula for the kinetic energy of a particle with a given de Broglie wavelength λ is given by:
K = (hc/λ) - mc^2
where h is Planck's constant, c is the speed of light, and m is the rest mass of the particle.
For photons, the rest mass is zero, so the formula simplifies to:
K = hc/λ
Plugging in the given wavelength of 0.50 nm, we get:
K = (6.626 × 10^-34 J s × 3.00 × 10^8 m/s) / (0.50 × 10^-9 m)
K = 1.3252 × 10^-17 J
Converting to electronvolts (eV), we use the conversion factor 1 eV = 1.602 × 10^-19 J:
K = (1.3252 × 10^-17 J) / (1.602 × 10^-19 J/eV)
K = 82.6 eV (rounded to three significant figures)
Therefore, the kinetic energy of photons with a de Broglie wavelength of 0.50 nm is 82.6 eV (rounded to three significant figures).
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Show that,the sum of an infinite arithmetic progressive sequence with a positive common difference is +∞.
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The sum of the arithmetic progressive sequence will be +∞, for common difference as positive that is d >0.
Explain about the arithmetic progression?The difference between every two successive terms in a sequence is the same; this is known as an arithmetic progression (AP).
A good example of an arithmetic progression (AP) is the series 2, 6, 10, 14,..., which follows a pattern in which each number is created by increasing 4 to the previous term. This annual income of a worker whose pay rises by a predetermined amount of $5000 each year serves as a real-world illustration of an AP.
The expression for an arithmetic progression:
a is the first term
l is last term
d is common difference
n is total number of terms
Sn = the sum of term
A.P = a,a+d,a+2d,a+3d,…, a+(n-1)d
l = a+(n-1)d
Sum formula:
Sn=n/2 [a+(n-1)d]
Or, Sn=n/2 [a+l]
Thus, the sum of the arithmetic progressive sequence will be +∞, for common difference as positive that is d >0.
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in one of his experiments conducted with animals, thorndike found that cats learned to escape from a puzzle box:
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In one of his experiments conducted with animals, Thorndike found that cats learned to escape from a puzzle box is increased gradually
To quantify the learning process, Thorndike used a mathematical formula known as the Law of Effect equation. The equation is:
B = f(log S1/S2)
where B represents the strength of the behavior, S1 represents the satisfaction of the positive consequence, and S2 represents the degree of frustration or negative consequence.
In the context of Thorndike's puzzle box experiment, the Law of Effect equation can be used to describe how the cat's behavior changed over time as it learned to escape the puzzle box more quickly and efficiently. Initially, the cat's behavior was weak because it did not know which actions would lead to a positive outcome.
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Use the power of a power property to simplify the numeric expression.
(91/4)^7/2
Answers
Using the power property to simplify the expression (9¹⁺⁴)⁷⁺², we have 9^7/8
Using the power property to simplify the numeric expression.
Given the expression
(9¹⁺⁴)⁷⁺²
To simplify this expression using the power of a power property, we need to multiply the exponents:
(9¹⁺⁴)⁷⁺² = 9(¹⁺⁴ ˣ ⁷⁺²)
Simplifying the exponents in the parentheses:
(9¹⁺⁴)⁷⁺² = 9⁷⁺⁸ or 9^7/8
Therefore, (9¹⁺⁴)⁷⁺² simplifies to 9^(7/8).
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What is the slope from (-8, 9) to (-4,6)
Answers
Answer:
m = -3/4
Step-by-step explanation:
Calculation of the Slope of a line
The information provided about the line is that the line passes through the points (-8, 9) to (-4,6)
Therefore, the first step consists in computing the slope. The formula for the slope is:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
Now, by plugging the corresponding numbers is , we get that the slope is:
[tex]m=\frac{y_2-y_1}{x_2-x_1}=\frac{6-9}{-4-(-8)} =\frac{6-9}{-4+8} =-\frac{3}{4}[/tex]
So then, we find that the slope is [tex]m=-\frac{3}{4}[/tex] and that the line passes through the point [tex](-8,9)[/tex].
How do I solve? I don’t understand
Answers
Step-by-step explanation:
Use the 110 to find the 70 degree angle (they form a straight line = 180°)
then 70 + 64 + R angle = 180° ( sum of angles of a triangle)
then : R angle = 46°
then the R angle + 2x-10 = 90° ( because the two lines are perpendicular)
(2x -10)° + 46 ° = 90 °
x = 27
Consider two agents, Alice and Bob, who have utility functions 0.3x3 + 0.72A if xa > XB (0.314 +0.72B if XB > XA UA(2A, 2B) = UB(XA, XB) 4X A – 32B if XB > IA -0.32A + 1.3xB if x A > XB If Alice is the dictator in the dictator game with a $10 endowment, then she will offer Bob (A) $0; (B) $5; (C) $2; (D) $10.
Answers
The utility that maximizes the possible utility of both the agents Alice and Bob is equal to option D. $10.
Compare Alice's utility from each option and choose the one that maximizes her utility.
Let us consider each option,
If Alice offers Bob $0, her utility will be,
If XA > XB then
UA (XA , XB )= 0.3x3 + 0.72A
UA(10,0)
= 0.3(10)³ + 0.72(10)
= 307.2
If Alice offers Bob $5, Bob's utility will be,
UB(10,5)
= 0.314 + 0.72(5)
= 0.314 + 3.6
= 3.914
And Alice's utility will be,
UA(5,10)
= -0.32(5) + 1.3(10)
= 11.4
Total utility for both Alice and Bob will be,
UA(5,10) + UB(10,5)
= 11.4 + 3.914
= 15.314
If Alice offers Bob $2, Bob's utility will be,
UB(10,2)
= 0.314 + 0.72(2)
= 1.754
And Alice's utility will be,
UA(2,10)
= -0.32(2) + 1.3(10)
= 12.4
So the total utility for both Alice and Bob will be,
UA(2,10) + UB(10,2)
= 12.4 + 1.754
= 14.154
If Alice offers Bob $10, Bob's utility will be,
UB(10,10)
= 0.314 + 0.72(10)
= 7.514
And Alice's utility will be,
UA(10,10)
= 0.3(10)³ + 0.72(10)
= 307.2
So the total utility for both Alice and Bob will be,
UA(10,10) + UB(10,10)
= 307.2 + 7.514
= 314.714
Therefore, utility which maximizes the total utility for both Alice and Bob is given by option (D) $10.
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In circle � W, � � = 3 WX=3 and m ∠ � � � = 8 0 ∘ ∠XWY=80 ∘ . Find the length of � � ⌢ XY ⌢ . Express your answer as a fraction times � π. X W Y Answer: Length of X Y ⌢ = Length of XY ⌢ =
Answers
The Length of arcXY is 4π/3
Define the term Circle identities?The Circle identities refer to a set of fundamental identities in trigonometry that relate the six trigonometric functions of an angle in a right-angled triangle.
Given, (radius) WX =3, it means, r = 3
given, m∠XWY = 80°
So, the length of arc XY;
arcXY = [tex]\frac{80}{360}* 2\pi r[/tex] (by formula: length of arc)
arcXY = [tex]\frac{2}{9}* 2\pi *3[/tex]
arcXY = [tex]\frac{4}{3}\pi[/tex]
Therefore, the Length of arcXY is 4π/3
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Complete question-
in a class if 108 students, 60 like football, 53 like Tennis and 10 like neither. calculate the number of students who like football but not tennis
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Answer:
60 - 10 = 50
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A rectangle has a length 2 m less than twice its width. When 5 m are added to the width, the resulting figure is a square with an area of 144m2. Find the dimensions of the original rectangle.
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When 5 meters are added to the width, the resulting figure is a square with an area of 144 square meters. This means that the new width is w + 5 meters, and the new length is also w + 5 meters (since it's a square). We can write an equation for the area of this square:
(w + 5)^2 = 144
Simplifying the equation, we get:
w + 5 = 12
w = 7
Now that we know the width of the original rectangle, we can use the expression we came up with earlier for the length:
length = 2w - 2 = 2(7) - 2 = 12
Therefore, the dimensions of the original rectangle are 7 meters by 12 meters.
Ursula is looking at data about educators’ salaries in different cities in the country (in thousands of dollars). For which data set would the mean be the best measure of center? 48, 44, 41, 50, 38, 42, 92, 39 48, 14, 42, 53, 49, 51, 55, 43 55, 52, 60, 65, 56, 63, 68, 58 72, 78, 67, 81, 80, 76, 29, 70
Answers
There are no very large or small numbers inside the range of 38 to 92. The first data set [tex]48, 44, 41, 50, 38, 42, 92, 39.[/tex] is the one for which the mean would serve as the most accurate indicator of the center.
What are mean, median, and average?By adding every value in a collection and dividing by the total number of values, you may get the mean. The median is the value that falls in the center when a group of values are arranged from smallest to greatest. The value that appears the most frequently in the set is the mode.
How does the mean become used?The mean may be used as a benchmark for all observations since it can be used to reflect the typical value.
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certain can of soda contains 60 milligrams of caffeine. The caffeine is
eliminated from the body at a rate of 15% per hour. What is the half-life of the
caffeine? That is, how many hours does it take for half of the caffeine to eliminated
from the body?
Answers
Answer:
3.33 hours
Step-by-step explanation:
you have a total of 60mg, it is asked how much hours it takes to remove half the caffeine which is 30mg
1 hour removes 15%, 15% of 60 is 9g
(15/100×60) = 9
now it removes only 9g in an hour, we have to find out how long (hours) it'll take to remove 30g
30÷9= 3.33 hours
I need help with this question.. :')
Answers
The equation of the line passing through A and B is y = (4/5)x - (2/5).
What is the line example's equation?A straight line's general equation is y = mx + c, where m is the gradient and y = c is the value at which the line intersects the y-axis. The y-axis intercept is denoted by the number c. A straight line with gradient m and intercept c on the y-axis has the equation y = mx + c.
The point-slope form of a linear equation can be used to find the equation of the line passing through points A and B:
y - y1 = m(x - x1) (x - x1)
where m denotes the slope of the line, (x1, y1) denotes the coordinates of point A or B, and (x, y) denotes the coordinates of any other point on the line.
To calculate the slope, we can use points A (3, 2) and B (8, 6).
m = (y2 - y1) / (x2 - x1) = (6 - 2) / (8 - 3)\s= 4 / 5
So the equation for the line connecting A and B is:
y - 2 = (4/5)(x - 3) (x - 3)
This equation can be simplified by multiplying both sides by 5:
5y - 10 = 4x - 12
Then we can rearrange it to form the slope-intercept equation, y = mx + b:
5y = 4x - 2
y = (4/5)x - (2/5)
As a result, the equation for the line connecting A and B is y = (4/5)x - (2/5).
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STUDY SKILLS 7. State ONE way in which each of the examination writing skills below could effectively assist you when writing your examinations. 7.1 Read the question 7.2 Plan the response 7.3 Answer the questions (3 x 1) (3)
Answers
What are examination writing skills?
Examination writing skills refer to a set of abilities that are essential for effective and successful writing in an exam context.
These skills include reading the question carefully, planning your response, writing a clear and concise answer, using appropriate terminology, providing evidence to support your argument, and presenting your answer in a logical and organized manner.
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Complete question:
State one way in which each of the examination writing skills below could effectively assist you when writing your examinations:
Read the questionPlan the responseAnswer the questionsFind the generating functions and the associated sequences of: (x+4) ^ 4
Answers
Using binomial theorem, the generating function is G(x) = x^4 + 16x^3 + 96x^2 + 256x + 256 while the associated sequence of (x+4)^4 is {1, 16, 96, 256, 256}.
What is the generating functions and associated sequences of the functionTo find the generating function of (x+4)^4, we expand it using the binomial theorem:
[tex](x+4)^4 = C(4,0)x^4 + C(4,1)x^3(4) + C(4,2)x^2(4^2) + C(4,3)x(4^3) + C(4,4)(4^4)[/tex]
where C(n,k) denotes the binomial coefficient "n choose k".
Simplifying the terms, we get:
[tex](x+4)^4 = x^4 + 16x^3 + 96x^2 + 256x + 256[/tex]
Therefore, the generating function of (x+4)^4 is:
[tex]G(x) = x^4 + 16x^3 + 96x^2 + 256x + 256[/tex]
The associated sequence can be read off by finding the coefficients of each power of x:
The coefficient of x^k is the k-th term of the sequence.In this case, the sequence is given by the coefficients of G(x):a₀ = 256a₁ = 256a₂ = 96a₃ = 16a₄ = 1To find the generating function of (x+4)^4, we expand it using the binomial theorem:
(x+4)^4 = C(4,0)x^4 + C(4,1)x^3(4) + C(4,2)x^2(4^2) + C(4,3)x(4^3) + C(4,4)(4^4)
where C(n,k) denotes the binomial coefficient "n choose k".
Simplifying the terms, we get:
(x+4)^4 = x^4 + 16x^3 + 96x^2 + 256x + 256
Therefore, the generating function of (x+4)^4 is:
G(x) = x^4 + 16x^3 + 96x^2 + 256x + 256
The associated sequence can be read off by finding the coefficients of each power of x:
The coefficient of x^k is the k-th term of the sequence.
In this case, the sequence is given by the coefficients of G(x):
a₀ = 256
a₁ = 256
a₂ = 96
a₃ = 16
a₄ = 1
Therefore, the associated sequence of (x+4)^4 is {1, 16, 96, 256, 256}.
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Will tracks the high and low tempters in his town for five days during a cold spell in January his results are shown in the table below
Answers
Days when change in temperature more than 10° F are Option B)Tuesday and E) Friday.
Define change in temperaturecalculating the difference by deducting the end temperature from the initial temperature. The temperature difference is therefore 75 degrees Celsius - 50 degrees Celsius = 25 if something begins at 50 degrees Celsius and ends at 75 degrees Celsius.
Change in temperature on Monday from High to low
=15-10=5°F
Change in temperature on Tuesday from High to low
=8-(-4)=12°F
Change in temperature on Wednesday from High to low
=-2-(-5)=3°F
Change in temperature on Thursday from High to low
=-3-(-7)=4°F
Change in temperature on Friday from High to low
=-1-(-12)=11° F
Days when change in temperature more than 10° F are Tuesday and Friday.
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The Complete question is attached below:
What is the difference of the value of the two y= 2X plus 1X plus 3Y equals 10
Answers
y = 2x + 1...so sub in 2x + 1 for y in the other equation
x + 3y = 10
x + 3(2x + 1) = 10
x + 6x + 3 = 10
x + 6x = 10 - 3
7x = 7
x = 1
y = 2x + 1
y = 2(1) + 1
y = 2 + 1
y = 3
the difference : there can be 1 possible answer for this..
y - x = 3 - 1 = 2
Amelia knits 7 sweaters and 9 scarves to give to her friends. She uses 9 balls of yarn to make each sweater and 4 balls of yarn to make each scarf. How many balls of yarn does Amelia use in all?
Answers
Amelia uses 99 balls of yarn in all to make the sweaters and scarves.
What is addition ?
Addition is a basic mathematical operation that combines two or more quantities to find a total or a sum. It is denoted by the symbol "+" and is usually taught in elementary school. In addition, the order of the numbers does not matter, meaning that you can add them in any order and still get the same result. For example, 3 + 5 is the same as 5 + 3, and the answer is 8 in both cases.
According to the question:
To find the total number of balls of yarn that Amelia uses, we can start by finding the total number of balls of yarn she uses to make the sweaters and scarves separately, and then add those amounts together.
To make 7 sweaters, Amelia uses 7 x 9 = 63 balls of yarn.
To make 9 scarves, Amelia uses 9 x 4 = 36 balls of yarn.
Adding these together, we get:
63 + 36 = 99
So, Amelia uses 99 balls of yarn in all to make the sweaters and scarves.
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You roll one six-sided die. A friend looks at the number and tells you that it is an odd number. What is the probability that you rolled a 3?
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Answer: 1/3 chance or 33.33333%
Step-by-step explanation: There are only 3 odd numbers on the die, 1,3,5 so there is a 1/3 chance it is 3
I need help with this
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The angles can be named with one letter are 2.
What is angles?Angles are a type of geometric shape which are formed when two straight lines intersect at a point. They are measured in degrees, usually between 0 and 360. Angles can be classified as acute, right, obtuse, straight and reflex, and the sum of any three angles in a triangle will always equal 180 degrees. Angles can be used in various ways, from providing stability in construction work to helping to identify other shapes. They can also be used to measure the size and shape of objects and to calculate distances and areas on maps. Angles are an important part of mathematics, geometry and trigonometry, and are used in a variety of applications in science and engineering.
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