In every n-player tournament described in Exercise 12 of Section 2.4, there is at least one top player.
We will use the Well-Ordering Principle (WOP) to prove that in every n-player tournament, there is at least one top player.
Consider a tournament with n players.
Let's assume that there is no top player in the tournament.
This means that for every player x, there exists a player y who beats x and is beaten by another player z.
We can create a sequence of players: y1, z1, y2, z2, y3, z3, ..., yn, zn, where yi beats xi and is beaten by zi for every i from 1 to n.
Since there are only n players in the tournament, the sequence must repeat at some point due to the Pigeonhole Principle.
Let's say the sequence repeats with players ym and zm, where m < n.
Now, we have a subsequence: ym, zm, ym+1, zm+1, ..., yn, zn, y1, z1, y2, z2, ..., ym-1, zm-1, which is a cycle.
If we consider the players in the cycle from ym to zm-1, none of them can be a top player because they are all beaten by other players within the cycle.
However, we know that ym beats xm and zm-1 beats xm, so by the transitive property, ym must beat zm-1.
This means that ym is a top player, which contradicts our initial assumption.
Therefore, our assumption that there is no top player in the tournament is false.
By the WOP, there must be at least one top player in every n-player tournament.
This proof shows that in every n-player tournament described in Exercise 12 of Section 2.4, there is always at least one top player, as required.
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Trevor's Cafe has regular coffee and decaffeinated coffee. This morning, the cafe served 5 coffees in all, 4 of which were regular. What percentage of the coffees were regular? Write your answer using a percent sign (%)
Answer:
80%
Step-by-step explanation:
since there were 5 coffees but 4 out of it were regular
mathematically
that's 4/5
but to percentage
that's times 100
4/5×100
4×100 all divided by 5
400 divided by 5
80%
The function g is defined by the following rule. g(x) = 2x +1
The function g is defined by the following rule. g(x) = 2x +1 can be represented in the method given below-
How does this occur?
The function f with g is written as (fg)(x)=f(g(x)), and is understood as f of g of x. The function g will be used in place of any x in the function f, according to this statement (x)
f(x), where x is the input, is a common way to refer to a function. A function can be conceptualized as y = f in general (x).
x= -3 then g(-3) = 2(-3) + 1 = -5If x = -2 then g(-2) = 2(-2) + 1 = -3if x = -1 then g(-1) = 2(-1) + 1 = -1If x = 1 then g(1) then = 2(1) +1 =3This is how by taking various x value we can find the value of g(x) = 2x +1
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A fence post that is 5 feet tall casts a 2-foot shadow at the same time that a tree that is 26 feet tall casts a shadow in the same direction. Determine the length of the tree's shadow.
5.2 feet
10.4 feet
12.2 feet
15.4 feet
Answer:
10.4 feet
Step-by-step explanation:
26/5 = 5.2
5.2(2)=10.4
The length of the tree's shadow is 10.4 feet. Option B is correct.
What are Similar Triangles?Two triangles are said to be similar if their corresponding angles are congruent and the corresponding sides are in proportion .
We can use similar triangles to solve this problem.
The ratio of the height of the fence post to its shadow is the same as the ratio of the height of the tree to its shadow.
(height of fence post) / (length of fence post's shadow) = (height of tree) / (length of tree's shadow)
Substituting the given values, we get:
5 / 2 = 26 / x
where x is the length of the tree's shadow.
Cross-multiplying and solving for x, we get:
x = 26 × 2 / 5
= 10.4 feet
Therefore, the length of the tree's shadow is 10.4 feet.
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How do you convert base 10 to base 4?
Answer:
First, divide the number by the base to get the remainder. This remainder is the first, ie least significant, digit of the new number in the other base
Then repeat the process by dividing the quotient of step 1, by the new base. ...
Repeat this process until your quotient becomes less than the base
Step-by-step explanation:
I need help on filling in the blanks for these shapes
We can see here that the triangles have been attached to the corresponding angles and sides.
(a) ∠A ≅ ∠Y
∠B ≅ ∠Z
∠C ≅ ∠X
(b) Side AB ≅ Side YZ
Side AC ≅ Side YX
Side BC ≅ Side ZY
(c) ΔABC ≅ Δ YZX
What is congruent?Congruent refers to the state of two geometric figures or shapes having the same size and shape. Two figures are congruent if one can be superimposed on the other by a combination of rotation, reflection, and translation.
Congruence is often denoted by the symbol “≅”. Congruence is a fundamental concept in Euclidean geometry, and it applies to many types of geometric figures, including lines, angles, triangles, and polygons.
We can see that the various angles and sides has been shown above.
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A chef can bake 15 pies in 1 hour. What is the rate of pies per minute?
Answer: The chef can bake (a) 0.25 pies/min.
Step-by-step explanation:
1 hour = 60 minutes
1 hour = 15 pies
15=60m
15/60 = 60/60 m
0.25 = m
The rate in pies per minute is 0.25. Therefore, option A is the correct answer.
Given that, a chef can bake 15 pies in one hour.
We need to find the rate in pies per minute.
What is the rate per minute?
Rate per minute was calculated by dividing the number of events observed by the observed minutes in the observation.
Simplify the rate by dividing each number by the greatest common factor.
Here, divide the number of pies by 60 minutes (1 hour=60 minute)
Now, 15/60=0.25 pies/min
The rate in pies per minute is 0.25. Therefore, option A is the correct answer.
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If a1 = 4 and an = -3an-1 - 4 then find the value of a3
The 3rd term in the given sequence is 45
What is sequence?A sequence is an enumerated collection of objects in which repetitions are allowed and order matters.
Given that, first and nth term of a sequence a₁ = 4 and aₙ = 3aₙ₋₁ + n
a₁ = 4
aₙ = 3aₙ₋₁ + n
So, a₂ = 3a₂₋₁ + 2
= 3a₁ + 2
= 3×4+2
= 14
Therefore,
a₃ = 3a₋₁ + 3
= 3a₂ + 3
= 14×3+3
= 45
Hence, a₃ = 45
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Why can’t astronomers take a picture of a black hole?
Gravity is so strong that even light cannot escape a black hole.
The nearest black hole is too far away to be seen.
There is no way to detect the locations of black holes.
Black holes are too large to photograph.
Answer:
A
Step-by-step explanation:
edge 2023
Which one of the following triangles has only 2 equal sides.(i) Equilateral triangle(ii) Scalene Triangle(iii) Isosceles Triangle
The correct option is (iii) Isosceles triangle is the one which has only 2 equal sides.
Every triangle is made up of three sides and three angles. A side is opposing an angle or a vertex if none of its ends is at the given angle's vertex. An angle is included between two sides if their common terminus is the angle's vertex.
Triangles are divided into one of three types based on the lengths of its sides: scalene, isosceles, or equilateral. A triangle is scalene if none of its sides are equal (of equal length). The triangle is isosceles if two or more of its sides are equal. A triangle is equilateral if all three of its sides are equal. By definition, all equilateral triangles are also isosceles.
Therefore, the correct answer is option (iii) Isosceles Triangle
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Write a story problem that will result in the problem 5 + (-12)
what is the difference between 880 an 580
The Chamber of Commerce of a city in central Florida is making brochure to attract tourists. They recorded the high temperatures (in degrees Fahrenheit) for a week in January to be 75, 72, 73, 56, 62, and 71. If you were a tourist planning to visit the area, which of these measures of central tendency would be the best to use as the most accurate indicator of the temperature for planning your wardrobe? Correct mean median mode range
The measure of central tendency that would be the best to use as the most accurate indicator of the temperature for planning your wardrobe is the mean.
What is the mean?The ratio between the sum of all observations and the total number of observations in a data set is known as the mean in statistics. A data set's mean (average) is calculated by adding all of the numbers in the set, then dividing by the total number of values in the set.
When a data set is ranked from least to greatest, the median is the midpoint. The number that appears most frequently in a data set is called the mode.
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solve each system by substitution
y=4x
x-2y=56
Answer:
-8
Step-by-step explanation:
Since it tells you that y=4x you can use that to replace y in the next equation so now it's
X-2(4x)=56
Distribute the -2
X-8x=56
Subtract -8x from x
-7x=56
Divide by -7
X=-8
Answer:
x=−8
y=−32
pspdwdpvprngbpnrpt
What is the formula for finding the distance between two parallel lines?
[tex]d=\frac{|c_2-c_1|}{\sqrt{a^2+b^2}}[/tex] is the formula used to calculate the distance between two parallel lines. This is derived from the slope-intercept equation.
The two lines that never cross over one another are referred to as parallel lines. When the separation between these two lines is considered constant, then these two lines are parallel.
As a result, the distance between two lines can be determined by considering their perpendicular distance. The two parallel lines can be written using the slope-intercept form as y = mx + c₁ and y = mx + c₂, respectively.
Then, the formula to calculate distance is given by, [tex]d=\frac{|c_2-c_1|}{\sqrt{a^2+b^2}}[/tex]. Here, the intercepts of the two lines are c₁ and c₂, and a and b are the constants or integers.
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Which two points on the number line represent numbers that can be combined to make zero?
B and D
A and B
C and D
A and C
Answer:
B and D
Step-by-step explanation:
-2+2=0
What ordered pairs are the solutions of the system of equations shown in the graph below?
Answer: (-4, 1) (-8, 9)
Explanation: These points are where the two functions meet
Can you draw a triangle with sides of length 2cm 3cm and 7cm?
It is not possible to construct a triangle whose sides are 2 cm 3 cm and 7 cm because the sum of two sides(2 cm and 3 cm) are smaller than third sides(7 cm).
In the given question, we have to check that it is possible to construct a triangle whose sides are 2 cm 3 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 2 and 3
2 + 3 < 7
5 > 7
Now we add 2 and 7
2 + 7 > 3
9 > 3
Now we add 3 and 7
7 + 3 > 2
10 > 2
It is not possible to construct a triangle whose sides are 2 cm 3 cm and 7 cm because the sum of two sides(2 cm and 3 cm) are smaller than third sides(7 cm).
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Ellie is 1.75 meters tall. At 3 p.m., she measures the length of a tree's shadow to be 20.25 meters. She stands 16.2 meters away from the tree, so that the tip of her shadow meets the tip of the tree's shadow. Find the height of the tree to the nearest hundredth of a meter.
To find the height of the tree, we can use the tangent of the angle between the top of the tree and the tip of Ellie's shadow to find the height of the tree.
Tangent(theta) = Opposite / Adjacent
Opposite = height of tree
Adjacent = distance between Ellie and the tree
Tangent(theta) = height of tree / 16.2
We know that:
Tangent(theta) = 20.25 / 16.2
We can solve for the height of the tree by multiplying both sides of the equation by 16.2:
height of tree = Tangent(theta) * 16.2
height of tree = (20.25 / 16.2) * 16.2height of tree = 20.25
So, the height of the tree is 20.25 meters to the nearest hundredth of a meter.
Answer: the height of the tree is 20.25 meters to the nearest hundredth of a meter.
Step-by-step explanation:
What is the y-intercept of y =- 2 5?
Comparing the given expression with the slope-intercept form, the intercept value is calculated. And the value is -2/5.
A line's slope gives information about its steepness or indicates how much y rises as x rises. The equation is typically written as y=mx+b in slope-intercept form. The slope in this equation is represented by the letter m, and the y-intercept is represented by the letter b. The y-intercept is calculated in the subsequent step by comparing the given expression with this.
The given expression is y =- 2/5. Comparing this expression with y=mx+b, we get, m=0, x=0, and b=-2/5. Therefore, the required y-intercept is -2/5.
The complete question is -
What is the y-intercept of y =- 2/5?
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what is the square root 15v to the 4th power times square root of 2v
the square root 15v to the 4th power times square root of 2v to the 3rd power is 15v^2 x 2v^3, or 30v^5.
What is square root?The square root of a number is a value that, when multiplied by itself, produces the original number. For example, the square root of 16 is 4 because 4 x 4 = 16. In mathematics, the square root of a number is written as a radical symbol, with the number inside the radical symbol. The square root symbol is also known as the radical symbol or radix.
To calculate this, first take the square root of 15v to the 4th power, which is 3v. Then take the square root of 2v to the 3rd power, which is 2v.
Finally, multiply 3v and 2v together to get the final answer of 30v^5.
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Complete questions as follows-
What is the square root 15v to the 4th power times square root of 2v to the 3rd power?
Use the quadratic formula to find the solutions to the quadratic equation
below.
x-5x-4 = 0
O A. x =
O
-5+√41
2
B. x = 5±√41
O c. x =
C.
-5+√/29
D. x = 5√2
Answer:
A, B
Step-by-step explanation:
[tex]x^2-5x-4=0 \\ \\ x=\frac{5 \pm \sqrt{(-5)^2-4(1)(-4)}}{2}[/tex]
On simplifying, the correct answers are A and B.
What is the rule of the sequence 2 4 6?
The rule of the sequence 2 4 6 is that each term is obtained by adding 2 to the previous term.
In an arithmetic sequence, the rule is that each term is obtained by adding a fixed value (common difference) to the previous term. In this case, the common difference of the sequence 2 4 6 is 2. So, 2 is added to the first term (2) to get the second term (4), and 2 is added to the second term (4) to get the third term (6).
It is also possible to express the rule of the sequence by using the formula of an arithmetic sequence, which is a_n = a_1 + (n-1)d, where a_1 is the first term, d is the common difference, and n is the number of the term.
In this case, a_1 = 2, d = 2, so the rule of the sequence is a_n = 2 + (n-1)2 = 2n, where n is the number of the term.
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1. The function that describes the rigid motion could be (x, y) -
A. (2x, y).
C. (y,-22).
B. (x - 3,y).
D. (x,3).
What is the exponential form of 5 * 5 * 7 * 7 * 7?
The exponential form of 5 * 5 * 7 * 7 * 7 is [tex]5^{2}[/tex] * [tex]7^{3}[/tex] . Exponential form can be written from the prime factorization of the number.
To get the exponential form of a number we have to write the prime factorization of that number. Prime factorization of the number is that number written as a product of prime numbers or as a product of powers of prime numbers. A basic exponential function from its definition is of the form f(x) = b x, where 'b' is a constant and 'x' is a variable. generally it refers to the positive valued function of a real variable. We can find the prime factorization of a number using factor trees, which are tools used to repeatedly break a number into products until all of the factors are prime numbers.
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in 2009 the average weekly wage of men exceeded that of a woman by $162. the sum of their average wages equaled $1476. write and solve a system of equations to determine the average wage of men and of women in 2009
8.3 points
What is the leading coefficient in the polynomial 2v³ +4v² + 1?
2
4
1
3
The leading coefficient in the polynomial 2v³ +4v² + 1 will be A. 2
How can you determine a polynomial's leading coefficient?The term with the highest power of x is the leading term in a polynomial. As an illustration, the leading term in 7 + x + 3x² is 3x².
The leading coefficient is the number in front of the variable with the highest power
A polynomial's leading coefficient is the coefficient of the leading term. The leading coefficient in the aforementioned illustration is 3.
In this case, this will be 2v³. The coefficient is 2.
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Find the missing values so that the area of the product is equal to the
area of its sum.
On solving the provided question, we can say that here, in the equation = (2x+3y)(3y-3)=12x+3y-15. so the missing values are = 3y
What is equation?A mathematical equation is a formula that joins two statements and uses the equal symbol (=) to indicate equality. A mathematical statement that establishes the equality of two mathematical expressions is known as an equation in algebra. For instance, in the equation 3x + 5 = 14, the equal sign places the variables 3x + 5 and 14 apart. The relationship between the two sentences on either side of a letter is described by a mathematical formula. Often, there is only one variable, which also serves as the symbol. for instance, 2x – 4 = 2.
here, in the equation
(2x+3y)(3y-3)=12x+3y-15
so the missing values are
3y
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In the triangle below, with right angle Q, suppose that m/R= (3x+2) and m/S= (2x+18).
Find the degree measure of each angle in the triangle.
summarize how the high temperature in this city changed over the 15 days
The temperature in this city changed by 7.5 degrees Celcius
How to determine the temperature changeFrom the question, we have the following parameters that can be used in our computation:
Rate of change = 0.5 degree Celcius daily
Number of days = 15
Using the above as a guide, we have the following:
Total change = Rate of change * Number of days
Substitute the known values in the above equation, so, we have the following representation
Total change = 0.5 * 15
Total change = 7.5
Hence, the total change is 7.5 degrees
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Complete question
The temperature of a City changes by 0.5 degree Celcius daily in the month of February. Summarize how the high temperature in this city changed over the 15 days
What are these two problems fully simplified?
Answer:
1. 3/2 x m^5 x n
2. 54 x m^11 x n^9
Need help right now please I don’t understand why this question is so hard
Answer:
A:33
B:22
C:74
Step-by-step explanation:
A:
2x2x2=8
5x5=25
8+25=33
B:
7x7=49
3x3x3=27
49-27=22
C:
8x8=64
square root of 100 is 10
64+10=74
i hope this helps :)