The partial order | on the set {1, 2, 3, ..., 10} does not have an antichain of size 6.
Does the partial order | on the set {1, 2, 3, ..., 10} have an antichain of size 6?To prove that the partial order | on the set {1, 2, 3, ..., 10} does not have an antichain of size 6, we can use a proof by contradiction.
Assume, for the sake of contradiction, that there exists an antichain A of size 6 in the partial order | on the set {1, 2, 3, ..., 10}. An antichain is a subset of elements in a partially ordered set where no two elements are comparable.
Since A is an antichain, for any two elements a, b ∈ A, neither a | b nor b | a. This means that any two elements in A are not comparable.
Now, let's analyze the size of A and the maximum number of elements that can be in an antichain of a partial order on a set of size n.
In a partial order, the maximum number of elements in an antichain is given by the length of the longest chain (a totally ordered subset) in the partial order. Let's find the length of the longest chain in the partial order | on the set {1, 2, 3, ..., 10}.
The longest chain in this case is a chain with all the elements in increasing order: 1 < 2 < 3 < ... < 10. This chain has a length of 10.
According to the theorem, Dilworth's theorem, which we are not using here, the maximum size of an antichain in a partial order is equal to the minimum number of chains in a chain decomposition of the partial order. In this case, the maximum size of an antichain would be equal to the minimum number of chains needed to cover all the elements of the partial order.
Since the length of the longest chain is 10, the minimum number of chains required to cover all the elements is also 10.
However, we assumed that there exists an antichain A of size 6. This contradicts the fact that the minimum number of chains needed to cover all the elements is 10.
Therefore, our initial assumption that there exists an antichain of size 6 is false.
Hence, the partial order | on the set {1, 2, 3, ..., 10} does not have an antichain of size 6.
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please help asap i am so confused
The table so fined below based on the information given about the function.
How to illustrate the information?The table based on the function given will be:
Plan A. Plan B
Monday. 10. 30
Tuesday. 20. 40
Wednesday. 40. 50
Thursday. 80. 60
Friday. 160. 70
A is illustrated as it's double minutes for each day. B is illustrated by adding 10min each day.
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Which of these absolute values is the greatest? a. |140| b. |-104| c. |104| d. |-20
Answer: a
/////////////////
Answer:
The correct answer is A.
Step-by-step explanation:
The absolute value of any number is always positive.
Quick algebra 1 assignment for 50 points!
Experts and Geniuses please help asap, TYSM!
Oh by the way this is just a section of the real assignment, the assignment calls for you to make an app that people can play to learn inverse variation & direct variation and stuff.
Hope that helps solve this! :)
Step-by-step explanation:
Direct variation is essentially a linear equation, where there is a constant rate. Direct variation can be applied to many things, and we can use it to represent how much money someone has in their bank account after "x" weeks if they're depositing a constant amount of money each week.
So a practical example would be: If someone just opened a bank account and deposits $50 every week, how many weeks will it take for them to have $400 in their account.
So the slope is given in the question, it's $50, since their depositing that constant amount each week. So this gives us the equation: [tex]y=50x[/tex] where x represents the amount of weeks. The y represents the amount of money they have, and since we want to find when this equals 400, we set the y=400, and then solve for x. This gives us the equation: [tex]400=50x[/tex]. Dividing both sides by 50 you get: [tex]8=x[/tex]. So it'll take 8 weeks to have $400 dollars, if you deposit 50 dollars each week.
If Robbie has twenty-five apples and he wants to share them equally with four other friends, how many apples must he give to each of his friends so that he will have the same number of apples as each of his friends
Answer:
5 apples
Step-by-step explanation:
4 friends + Robby = 5 people
25 apples in total ÷ 5 people
= 5 apples per person
2(-2-4) = use the distributive property to expand the expression below.
Answer:
-12
Step-by-step explanation:
First, solve in parentheses.
2(-2-4)
=
2(-6)
Next, multiply 2 by -6.
Which equals -12.
So therefore using the distributive property shown above, the answer would be -12.
[tex]\huge\text{Hey there!}[/tex]
[tex]\huge\textbf{What is the distributive formula?}[/tex]
[tex]\mathsf{a(b + c)}[/tex]
[tex]\mathsf{= a(b) + a(c)}[/tex]
[tex]\mathsf{= ab + ac}[/tex]
[tex]\huge\textbf{What is the equation?}[/tex]
[tex]\mathsf{2(-2 - 4)}[/tex]
[tex]\huge\textbf{What are we simplifying?}[/tex]
[tex]\mathsf{2(-2 - 4)}[/tex]
[tex]\mathsf{= 2(-2) + 2(-4)}[/tex]
[tex]\mathsf{= -4 - 8}[/tex]
[tex]\mathsf{= -12}[/tex]
[tex]\huge\textbf{How are you going to translate to}\\\\\huge\textbf{easier terms?}[/tex]
[tex]\mathsf{2(-2 - 4)}[/tex]
[tex]\mathsf{= 2(-6)}[/tex]
[tex]\mathsf{= -12}[/tex]
[tex]\huge\textbf{What is the ANSWER to the question?}[/tex]
[tex]\huge\boxed{\mathsf{-12}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]
Find the quotient: look at pic
Answer:
2y+6
Step-by-step explanation:
first, pull out the 2 from the top to separate the equation
second, factor out y
third, cancel out the common factor of y-1
fourth, remove the parenthesis from 2(y+3)
answer = 2y+6
One can convert temperature from kelvin into fahrenheit using the formula . what is the temperature in kelvin corresponding to f degrees fahrenheit?
One can easily convert the temperature using temperature conversion formula given below
K = [tex]\frac{5(F - 32)}{9} + 273.15[/tex]
where F = degrees in Fahrenheit
K = degrees in Kelvin
What is temperature conversion? The measuring units of the temperature recorded in a particular unit can be converted with the aid of a temperature converter. The degree of heat or cold that a solid, liquid, or gas has is expressed by its temperature. A thermometer is used to determine temperature. Although the SI unit for temperature is Kelvin (K), most people measure temperature in Centigrade or Celsius (°C) and Fahrenheit (°F).Know more about temperature conversion https://brainly.com/question/13421795
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The set $\{2, 4, 6, \dots, n\}$ contains the positive consecutive even integers from 2 through $n$. When one of the integers from the set is removed, the average of the remaining integers in the set is 28. What is the least possible value of $n$
The least possible value of n is 27.
According to the statement
We have given that the set which is {2,4,6,8.....n} and and one set is removed from them the average of remaining integers is 28.
Then
Firstly set contain n numbers
But after that set contain n-1 numbers after removal of 1 digit from them.
and average value of remaining digit is 28 then 28th term become after removal is
28th term =28*2
28th term = 56.
then
we use the formula to calculate n
n-1 =28
then the value of n become 27.
the least possible value of n is 27.
So, The least possible value of n is 27.
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(s^-6t^-2)^0 i know that the exponents equal zero but what would the answer 1 or s^0 t^o
Answer: 1
Step-by-step explanation: Any number raised to zero is always 1.
The perimeter of a rectangle is 99 ft, and the length is twice the width. what are its dimensions?
The dimension of the length and width of the rectangle with the given perimeter are 33ft and 16.5ft respectively.
What are the dimensions of the rectangle?Perimeter of rectangle is expressed as;
P = 2( l + w )
Given that;
Perimeter P = 99ftLet width w = xLength l = 2xWe substitute into the formular above.
P = 2( l + w )
99ft = 2( x + 2x )
99ft = 2x + 4x
99ft = 6x
x = 99ft/6
x = 16.5ft
Width = x = 16.5ft
Length = 2x = 2( 16.5ft ) = 33ft
Therefore, the dimension of the length and width of the rectangle with the given perimeter are 33ft and 16.5ft respectively.
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Model the situation with the sun of the polynomials. Then simplify their sum.
A rectangular picture frame has the dimensions shown in the figure. Write a polynomial that represents the perimeter of the frame.
Answer: 16x - 2
Step-by-step explanation:
The perimeter of a figure is the total length of all sides of the figure. Since this figure is a rectangle, opposite sides have the same length.
Therefore, the perimeter of the picture frame can be modeled by
[tex]6x+3+2x-4+6x+3+2x-4[/tex]
Moving all like terms together, we get
[tex]6x+2x+6x+2x+3-4+3-4[/tex]
Finally, combining these terms, we get
[tex]16x -2[/tex]
3x^2=7x solve the equation
Answer:
3x^2 - 7x =0
x(3x-7) = 0
3x - 7 = 0
3x =7
x= 7/3
Please explain the answer before, and also help with number line!
The solution to the given inequality is x < -6
For the number line, an open circle will be drawn on the value of -6 and the arrow pointing to the left side.
Number line and inequalityGiven the inequality expression as shown
6x + 6 < -30
Subtract 6 from both sides
6x < -30 - 6
6x < -36
Divide through by 6
x < -36/6
x < -6
For the number line, an open circle will be drawn on the value of -6 and the arrow pointing to the left side.
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In convex pentagon $ABCDE$, angles $A$, $B$ and $C$ are congruent and angles $D$ and $E$ are congruent. If the measure of angle $A$ is 40 degrees less than the measure of angle $D$, what is the measure of angle $D$
In a convex pentagon, the measure of angle D is 132°.
What is convex pentagon?If a planar polygon has all the line segments connecting any given pair of its points, it is said to be convex pentagon.
Properties of a Convex Polygon are-
Any polygon whose inner angles are all smaller than 180 degrees is said to be convex.A concave polygon is one in which at least one of the angles is bigger than 180°.A convex polygon's diagonals are located inside the polygon.A polygon is considered convex if the line connecting every pair of its points lies entirely within it.Calculation for the measure of angle D.
The sum of the interior angles = 540°
Let A, B , C = D - 40
And let E = D
So we have
A + B + C + D + E = 540
(D - 40) + (D - 40) + (D - 40) + D + D = 540
5D - 120 = 540
5D = 660
D = 660 / 5
D = 132°
Therefore, the measure of angle D is 132°.
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The organizers of a community fair set up a small Ferris wheel for young children. The table shows the heights of one of the cars above the ground for different rotations of the wheel. The function below, where a
and b are constants, models the height of the Ferris wheel car at a rotation of x radians. What are the values of a and b?
The value of a is 6 and the value of b is 7
How to determine the values of a and b?The function is given as:
h(x) = a . sin(x - π/2) + b
From the table of values, we have:
x = π/2 when y = 7
So, we have:
a . sin(π/2 - π/2) + b = 7
Evaluate the difference
a . sin(0) + b = 7
Evaluate the value of sin(0)
a . 0 + b = 7
Evaluate the product of a and 0
b = 7
Substitute b = 7 in h(x) = a . sin(x - π/2) + b
h(x) = a . sin(x - π/2) + 7
From the table of values, we have:
x = π when y = 13
So, we have:
a . sin(π - π/2) + 7 = 13
Evaluate the difference
a . sin(π/2) + 7 = 13
Subtract 7 from both sides
a . sin(π/2) = 6
Evaluate sin(π/2)
a . 1 = 6
Divide both sides by 1
a = 6
Hence, the value of a is 6 and the value of b is 7
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1 1/6 + (x/3 · 1/4) = 1 3/4
solve for x
Answer:
x = 7Step-by-step explanation:
1 1/6 + (x/3 · 1/4) = 1 3/4
solve for x
1 1/6 + x/12 = 1 3/4
1 1/6 - 1 3/4 = -x/12
-7/12 = -x/12
-7 = -x
x = 7
----------------
check
1 1/6 + (7/12 * 1/4) = 1 3/4
1 1/6 + 7/48 = 1 3/4
1 15/16 = 1 3/4
1 3/4 = 1 3/4
the answer is good
slope:
y-intercept:
PLSPLSPLS HELP
Answer:
Slope: 1
Y-intercept: -1
Step-by-step explanation:
The line passes the y-axis at -1, the rise/run, which is used to calculate the slope is 2/2, and it equals to 1, so the slope is 1.
I hope it helps! Have a great day!
bren~
PLEASE HELP 50 POINTS
Step-by-step explanation:
The initial velocity of a particle moving along x−axis is u (at t=0 and x=0) and its acceleration a is given by a=kx.Select the correct answer.
Consider these functions:
f(x) = 4x³ - 10
g(x) = 3x - 4/2
What is the value of g(f2))?
Answer:
3x - 4/2
Step-by-step explanation:
2 result(s) for "f(x) = 4x³ - 10 g(x)
Having trouble can someone help me solve this
The function f(x) is vertically compressed to form g(x)
How to compare both functions?The functions are given as
f(x) =x^2
g(x) =3x^2
Substitute f(x) =x^2 in g(x) =3x^2
g(x) =3f(x)
This means that the function f(x) is vertically compressed to form g(x)
See attachment for the function g(x)
Also, both functions have the same domain and range
The complete table is:
x -2 -1 0 1 2
g(x) 12 3 0 3 12
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What is the standard deviation of the data set? 6.5, 11.2, 13, 6.3, 7, 8.8, 7.4
Using it's concept, the standard deviation of the data-set is of 2.39.
What are the mean and the standard deviation of a data-set?The mean of a data-set is given by the sum of all values in the data-set, divided by the number of values.The standard deviation of a data-set is given by the square root of the sum of the differences squared between each observation and the mean, divided by the number of values.The mean of the data-set in this problem is given by:
M = (6.5 + 11.2 + 13 + 6.3 + 7 + 8.8 + 7.4)/7 = 8.6.
Hence the standard deviation is:
[tex]S = \sqrt{\frac{(6.5-8.6)^2+(11.2-8.6)^2+(13-8.6)^2+(6.3-8.6)^2+(7-8.6)^2+(8.8-8.6)^2+(7.4-8.6)^2}{7}} = 2.39[/tex]
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142857/500000 simplified
Using your own examples, explain why all statements are sentences but not all sentences are statements. Clearly indicate which type of non-statement you have used in each case. (Your response should be between 500 and 600 words).
Answer:
0.285714 -> 0.29
Step-by-step explanation:
A can of popcorn is to be packed in a box for shipping as shown. The can is 18
inches tall and has a radius of 7 inches. The box is 19 inches tall and has a square
base with sides of length 15 inches. All empty space around the can is to be filled
with packing material. How many cubic inches of packing material will be needed?
The amount of packing material is 1506 cubic inches
How to determine the amount of packing material?The given parameters are:
Can
Radius, r = 7 inches
Height, h = 18 inches
Box
Base dimension, l = 15 inches
Height, h = 19 inches
The volume of the can is:
[tex]V = \pi r^2h[/tex]
So, we have:
[tex]V_1 = 3.14 * 7^2 * 18[/tex]
[tex]V_1 = 2769[/tex]
The volume of the box is
[tex]V =l^2h[/tex]
So, we have:
[tex]V_2 =15^2 * 19[/tex]
[tex]V_2 =4275[/tex]
The amount of packing material is;
Amount = V2 - V1
This gives
Amount = 4275 - 2769
Evaluate
Amount = 1506
Hence, the amount of packing material is 1506 cubic inches
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The distance from the Sun to Mercury is approximately 57910000 km.
Assuming Mercury has a circular** orbit around the Sun, find the distance Mercury travels in orbiting the Sun through an angle of 2.65 radians.
Mercury travels a distance of 153 461 500 kilometers on its orbit.
How much distance did Mercury travel on its orbit?
The statement indicates that Mercury has a circular orbit and indicates the central angle covered by translation. The distance traveled is found by definition of circular arc:
s = (2.65 rad) · (57 910 000 km)
s = 153 461 500 km
Please notice that the radius of translation is the distance from the Sun to Mercury.
Mercury travels a distance of 153 461 500 kilometers on its orbit.
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-x^2 +x+6=0 (Please solve by completing the square, and show steps)
The solution to the equation using the completing the square are 2 and -3
Quadratic equationThese are equation that has a leading degree of 2. Given the equation below
-x^2 +x+6=0
This can also be written as
x^2-x-6 = 0
Complete the square
x^2-x = 6
x^2-x+ (1/2)^2 = 6 + (1/2)^2
(x-1/2)^2 = 6 + 1/4
(x+1/2)^2 = 25/4
x+1/2 = ±√25/4
x = 5/2 -1/2 or -5/2-1/2
x = 4/2 or -6/2
x = 2 and -3
Hence the solution to the equation using the completing the square are 2 and -3
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Find the sum of the primes between 100 and 200, inclusive, that are 1 or 2 more than a perfect square.
Answer:
298
Step-by-step explanation:
All perfect squares from 100-200 inclusive:
100, 121, 144, 169, 196
100+1=101, 101 is prime
121+2=123, 123=41*3 so its not prime
144+1=145 145=29*5 so its not prime
169+2=171 171=9*19 so its not prime
196+1=197, 197 is prime
101+197=298
Notice that I excluded all even numbers because they are obviously composite.
The bars in a _____________ do not touch since data is ______________.
A. bar graph ; continuous
B. bar graph ; discrete
C. histogram ; continuous
D. histogram ; discrete
Answer:
b
Step-by-step explanation:
Bat Graphs represent discrete data. They are spaced and don't touch to represent a discrete value.
Histograms represent continuous data. They are close and connected to represent variation in continuous data.
A group of friends wants to go to the amusement
park. They have no more than $420 to spend on
parking and admission. Parking is $8.75, and
tickets cost $25.75 per person, including tax.
Which inequality can be used to determine x, the
maximum number of people who can go to the
amusement park?
Answer:
The maximum amount of people that can go to the amusement park is 15.
Step-by-step explanation:
First you create an equation to represent the question
8.75+25.75x≤420
You put the less than or equal to sign because 420 is the maximum amount of money.
Now you just solve the equation.
25.75x≤420-8.75
25.75x≤411.25
x≤411.25/25.75
x≤15.9708738
Then you have to round down because you cant have .9 of a person.
So x≤15
Then, Check your solution
8.75+(25.75 x 15)≤420
8.75+386.25≤420
395≤420
That is true. But to make sure that is the maximum add another 25.75
395+25.75≤420
420.75≤420
This is equation is false so, our answer is correct.
The maximum amount of people that can go to the amusement park is 15.
The piece of music that I am learning is 60 measures long. There are 13 beats in every measure, and every eighth note lasts for 1 beat. The last 17 measures of this piece are the finale. In every measure of the finale, there are 7 eighth notes played at middle C. If middle C never occurs in this piece outside of the finale, for what fraction of the whole piece do I play middle C
[tex]\frac{119}{780}[/tex] fraction of the whole piece you play middle C.
What is a fraction?A fraction is a portion of a whole or, more broadly, any number of equal parts. In everyday English, a fraction represents the number of pieces of a specific size, such as one-half, eight-fifths, or three-quarters. A common, vulgar, or simple fraction consists of a numerator above a line and a non-zero denominator below (or after) that line. Numerators and denominators are also employed in uncommon fractions such as compound fractions, complex fractions, and mixed numerals.To find for what fraction of the whole piece do you play middle C:
Since 7 out of every 13 beats in the finale are played at middle C, [tex]\frac{7}{13}[/tex] the finale is played at middle C.
The finale is 17 measures out of a 60-measure piece or [tex]\frac{17}{60}[/tex] of the whole piece.
[tex]\frac{7}{13}[/tex] of [tex]\frac{17}{60}[/tex] is [tex]\frac{7}{13}[/tex] x [tex]\frac{17}{60} = \frac{119}{780}[/tex]
Therefore, [tex]\frac{119}{780}[/tex] for a fraction of the whole piece you play middle C.
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The pen is 2 cm shorter than the scale. if the scale is 7 inches long. how long is the pen?
The pen is [tex]15.78[/tex] centimeters long when scale is [tex]7[/tex] inches long and pen is [tex]2cm[/tex] shorter then the scale.
How to find the how much long is the pen ?
Scale is [tex]7 inches[/tex] long and
We know that
[tex]7inches=17.78cm[/tex]
And pen is [tex]2cm[/tex] shorten then the scale
So the length of the pen is
[tex]=17.78-2\\=15.78cm[/tex]
[tex]=6.21 inches[/tex]
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