MBUL with diagonals BL and MU intersecting at point A is shown. Find the value of x that makes MBUL a kite if BA=3x-1, LA=17, MA=2x, and UA=23
The value of x that makes MBUL a kite is given as follows:
x = 6.
How to obtain the value of x?For MBUL to represent a kite, the following lengths have to be congruent:
BA and AL.
The lengths for this problem are defined as follows:
BA = 3x - 1.LA = 17.As the sides are congruent, the equation is given as follows:
BA = LA.
Hence the value of x that makes MBUL a kite is obtained as follows:
3x - 1 = 17
3x = 18
x = 18/3
x = 6.
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Solve the following system of equations:
-2x + 5y = −11
4x - 3y = 15
Answer: (x,y)=(3,-1)
Step-by-step explanation:
What is the quotient when the dividend is 40 and the divisor is 2.5?
Answer:
16.00
Step-by-step explanation:
400 divided by 25 is also 16, so divide that and it should be the same as 40 divided by 2.5
QUOTIENT-
The answer to a division problem
40/2.5 =
16
Consider the following three random experiments: Experiment 1: Toss a coin. Experiment 2: Toss a die. Experiment 3: Select a ball at random from an urn containing balls numbered 0 to 9. (a) Specify the sample space of each experiment. (b) Find the relative frequency of each outcome in each of the above experiments in a large number of repetitions of the experiment. Explain your answer.
The sample space of the tossed coin: head or Tail =[ HT ]
The sample space of the die : [1, 2, 3, 4, 5,6 ]
The sample space of the ball {0 , 1, 2, 3, 4, 5, 6, 7, 8, 9]
What is the relative frequency?experiment 1: In a large number of repetitions of the experiment, the relative frequency of each outcome (Heads or Tails) would be approximately 0.5 or 50%.
Experiment 2: In a large number of repetitions of the experiment, the relative frequency of each outcome (1 to 6) would be approximately 0.1667 or 16.67%.
Experiment 3: In a large number of repetitions of the experiment, the relative frequency of each outcome (0 to 9) would be approximately 0.1 or 10%.
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Given a simplified rate of (1.99), determine the percent change.
Therefore , the solution of the given problem of percentage comes out to be 19.9% is the percent change.
Define percentage.In mathematics, a percentage is any value that can be written as a proportion of 100. There are also sporadic uses of the abbreviations "pct.," "pct," or "pc." However, it is commonly indicated by the "%" mark. The proportional amount is flat and lacks any dimensions. Since percentages have a numerator of 100, they can be thought of as fractions. The cent symbol (%) must come after a number to denote that it is a percentage.
Here,
Given:
You can compute 1.99 as a percent of a given number x by dividing 1.99 by x and multiplying the outcome by 100.
For instance,
if 1.99 is expressed as a percentage of 10,
then
=> 1.99 x 100% = 19.9%
Therefore , the solution of the given problem of percentage comes out to be 19.9% is the percent change.
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Which of the following describes a situation in which it is reasonable to reach a cause-and-effect conclusion based on data from a statistical study?answer choices- The study is based on a random sample from a population of interest.- The study is observational, and the sample used is not a convenience sample.- The study is an experiment that uses random assignment to assign volunteers to experimental conditions (treatments).- It is never reasonable to reach a cause-and-effect conclusion based on data from a statistical study.- It is always reasonable to reach a cause-and-effect conclusion based on data from a statistical study.
The correct answer is: The study is an experiment that uses random assignment to assign volunteers to experimental conditions (treatments).
What is statistical study?A sample is an analytic subset of a larger population in statistics. The utilization of samples enables researchers to conduct investigations with more manageable data and more quickly. Randomly chosen samples exhibit little bias if they are large enough, but obtaining such a sample can be costly and time-consuming.
Here,
A study that uses random assignment to assign volunteers to experimental conditions (treatments) is considered the best design to establish cause-and-effect relationships. In this type of study, researchers can control the variables and minimize extraneous factors that could confound the results. By using random assignment, the volunteers in the experimental and control groups are similar on average, making it more likely that any observed differences between the groups are due to the treatments.
The correct answer is: The research is an experiment in which volunteers are randomly assigned to experimental settings (treatments).
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6x^2 − 5x + 6 = 6x + 3
Answer:
x=1/3;3/2
Step-by-step explanation:
6x^2-5x+6 = 6x+3
-6 -6
6x^2 -5x = 6x - 3
+5x +5x
6x^2 = 11x -3
6x^2 + 11x - 3 = 0
(3x-1)(2x-3)=0
3x-1=0
3x=1
x=1/3
2x-3=0
2x=3
x=3/2
whats the liner expression for 2h - 1 and 3h + 4
The linear expression for 2h - 1 and 3h + 4 is 5h + 3. The solution has been obtained by using the arithmetic operations.
What are arithmetic operations?
According to mathematicians, the four fundamental operations, also referred to as "arithmetic operations," can be used to describe all real numbers. Division, multiplication, addition, and subtraction are the four mathematical operations that result in the terms quotient, product, sum, and difference, respectively.
We are given two expressions as 2h - 1 and 3h + 4.
On adding both, we get
2h - 1 + 3h + 4 = 5h + 3
Hence, the linear expression for 2h - 1 and 3h + 4 is 5h + 3.
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URGENT PLS HELP
stats standard deviation
The sample standard deviation of the given data will be 10.058.
What is a standard deviation?It is the measure of the dispersion of statistical data. Dispersion is the extent to which the value is in a variation.
[tex]\rm \sigma = \sqrt{\dfrac{\Sigma (x_i - \mu)^2}{n}}[/tex]
The table is given below.
M f Mf M²f
15 8 120 1,800
25 18 450 11,250
35 20 700 22,050
45 13 585 26,325
55 7 385 21,175
The variance is given as,
Var = 1 / (66 - 1) [82600 - 2240² / 66]
Var = 101.16
Then the standard deviation is given as,
SD = √ Var
SD = √101.16
SD = 10.058
The sample standard deviation of the given data will be 10.058.
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Logan says, “140 millilitres is more than 1.2 litres”. Is he right?
A unit can be used for measurement, and is commonly found in mathematics to describe length, size, etc.
First, because we are dealing with different units here, we need to know how many milliliters are in a litre.
1000 milliliter = 1 litreSo, an equation we can use is:
1 litre × 1000 = the amount in millilitersIf we look at 1.2 litres, we can now convert it to milliliters.
1.2 × 1000 = 1200Comparing 1200ml to 140ml, we can see that 1200ml is bigger.
Therefore, 1.2 litres are greater.
An experienced roofer with Stark Vegas roofing company can install a new roof in 24
hours. Together with a new trainee they can install a new roof in 15 hours. How long
would it take the trainee working by himself to install a new roof? Round to the nearest
tenth.
Answer:
40 hours
Step-by-step explanation:
This is an example of a work-rate-time problem
Since the experienced roofer can finish the job in 24 hours, his rate of work would be 1/24 (of the roof) per hour
Let the time taken by the trainee alone be x hours
His rate of work = [tex]\dfrac{1}{x}[/tex]
Together they finish the roof in 15 hours
So combined work rate = [tex]\dfrac{1}{15}[/tex]
Since combined rate = sum of individual rates we get
[tex]\dfrac{1}{24} +\dfrac{1}{x} = \dfrac{1}{15}[/tex]
Move 1/24 to the right side:
[tex]\dfrac{1}{x} = \dfrac{1}{15} - \dfrac{1}{24}[/tex]
[tex]\dfrac{1}{x} =\dfrac{24 - 15}{24\cdot 15} = \dfrac{9}{360}\\\\[/tex]
Taking reciprocals on both sides
[tex]x = \dfrac{360}{9} = 40 \;hours[/tex]
An animal shelter needs to buy 8 pounds of cat food for every cat
they have. Complete the following table of cats to pounds of cat food.
the food needed for 10 cats will be 80 pounds.
What is the arithmetic operation?
The four fundamental operations of arithmetic are addition, subtraction, multiplication, and division of two or more quantities. Included in them is the study of numbers, especially the order of operations, which is important for all other areas of mathematics, including algebra, data management, and geometry. The rules of arithmetic operations are required in order to answer the problem. Arithmetic is an elementary part of mathematics that consists of the study of the properties of the traditional operations on numbers
An animal shelter needs to buy 8 pounds of cat food for every cat
they have.
So per pound, it food needed for 10 cats will be 8*10 = 80 pounds.
Hence the food needed for 10 cats will be 80 pounds.
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For y=f(x)=7x^3, x=5, and Ax=0.06 find
A) Ay for the given x and Ax values,
B) dy=f’ (x)dx,
C) dy for the given x and Ax values
The functions and equations y = f(x) = 7·x³, x = 5, Δx = 0.06, indicates that we get;
a) Δy = 31.879512
b) dy = 21·x²dx
c) dy = 31.5
What is a function?A function is a rule that maps input variables to output variables in a relationship in which an input is assigned to exactly one output.
a) The value of the function y = f(x) = 7·x³
The value of x = 5
Value of the change in x, Δx = 0.06
The change in y, Δy is therefore;
Δy = f(x + Δx) - f(x), from which we get;
Δy = f(5 + 0.06) - f(5) = f(5.06) - f(5)
Δy = f(5.06) - f(5)
Plugging in the values of x = 5.06, and x = 5 in the function f(x), we get;
f(5.06) = 7 × (5.06)³ = 906.879512
f(5) = 7 × 5³ = 875
Therefore; Δy = f(5.06) - f(5) = 906.879512 - 875 = 31.879512
Δy = 31.879512
b) dy = f'(x)dx
f'(x) is the derivative of the function f(x)
dy/dx = f'(x) = 3 × 7 × x² = 21·x²
dy/dx = f'(x) = 21·x²
dy = f'(x)dx = 21·x²dx
dy = 21·x²dx
c) dy for the given x and Δx values can be found by plugging in x = 5 and dx = Δx = 0.06 in the equation, dy = 21·x²dx, as follows;
dy = 21 × 5²× 0.06 = 31.5
dy = 31.5
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Can anyone help me? Find m
Answer:
m∠Y = 60°WY = 7 inStep-by-step explanation:
Given triangle WXY with sides WX = 7 in and XY = 7 in and angle X = 60°, you want the measure of angle Y and the length of side WY.
Isosceles triangleThe equal given side measures tell you that their opposite angles (W and Y) have equal values. Those values will be such that the total of all angles is 180°:
W +Y +X = 180°
Y +Y +60° = 180° . . . . . . . . . . . use given values; substitute Y for W
Y = (180° -60°)/2 = 60° . . . . . . . subtract 60°, divide by 2
All of the angles in this triangle have the same measure, so it is an equilateral triangle. All of the sides have the same measure, too.
angle Y = 60°
WY = 7 inches
__
Additional comment
It is helpful to recognize that an isosceles triangle with a vertex angle of 60° is an equilateral triangle. That recognition lets you write down the answer with no further work.
What type of variable is a coin flip?
The coin flip is random variable.
What is probability?
Simply put, probability measures how probable something is to occur. We can discuss the probabilities of various outcomes, or how likely they are, whenever we are unsure of how an event will turn out. Statistics is the study of events subject to probability.
The likelihood that a population parameter will be less than a given value when the null hypothesis is true is expressed as the p-value, also known as a probability value or a measure of significance, for a particular statistical model.
A variable at random The value of the variable X is subject to chance. Imagine that you flip a coin. If the coin lands on its head, you win one dollar; otherwise, you lose one. You can never predict how much money you'll make from one coin toss.
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The coin flip is random variable.
What is probability?
Simply put, probability measures how probable something is to occur. We can discuss the probabilities of various outcomes, or how likely they are, whenever we are unsure of how an event will turn out. Statistics is the study of events subject to probability.
The likelihood that a population parameter will be less than a given value when the null hypothesis is true is expressed as the p-value, also known as a probability value or a measure of significance, for a particular statistical model.
A variable at random The value of the variable X is subject to chance. Imagine that you flip a coin. If the coin lands on its head, you win one dollar; otherwise, you lose one. You can never predict how much money you'll make from one coin toss.
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Will mark BRAINLY ASAP
Solve the quadratic x2+10x=−25.
-10
10
5
-5
A stone is projected vertically so that its position above ground level after t
seconds is given by h(t)=100t−5t2
meters, t≥0
.
Which one of the following is the maximum height the stone can reach?
Answer: The height of the stone after time "t" is given by the function h(t) = 100t - 5t^2, where t is in seconds. To find the maximum height, we need to find the value of t for which the height is greatest.
To do this, we can take the derivative of h(t) with respect to t, which gives us the rate of change of height with respect to time. Then, we can set this derivative equal to 0 and solve for t. The value of t that satisfies this condition will be the time at which the height is at its maximum.
h'(t) = 100 - 10t
Setting h'(t) = 0, we get:
100 - 10t = 0
10t = 100
t = 10
So, the maximum height is h(10) = 100 * 10 - 5 * 10^2 = 100 - 500 = -400 meters.
Since the height cannot be negative, the maximum height the stone can reach is 100 meters.
Step-by-step explanation:
Your Shadow measures 8 ft your father's Shadow is 9 ft if you are 5.5 ft how tall is your father in inches? I need problem wrote out please.
Check the picture below.
Write the answer is (x,y) form
The translation in the form (x,y) is (-3, -10)
How to determine the translation that maps from T to T'?In geometry, translation is a type of transformation that moves each point of a figure to a new location, while preserving the shape and size of the figure. A translation is defined by a displacement vector, which specifies the direction and magnitude of the movement.
T is the initial position of the object and T' is the image (new position) of the object after translation. We can use this equation:
T + translation = T'
translation = T' - T
translation = (6, -2) - (9, 8)
translation = (6-9, -2-8)
translation = (-3, -10)
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1. What is the approximate volume of the sugar container? Show your work. (2 points)
2. What is the approximate height of the rice container? Show your work. (2 points)
3. Compare the heights of the sugar container and the rice container. Next, compare their volumes. How many times as large is the volume of the rice container compared to the volume of the sugar container? Explain your answer. (2 points)
4. In the formula V = Bh, B is the area of the base. Use this formula to calculate the volume of the flour container. (2 points)
5. Compare the volumes of the containers. Which container has the greatest volume? Which has the smallest volume? (2 points)
PLS HELP I WILL GIVE BRAINLIST
The greatest volume and smallest volume container is of rice and flour.
What is the volume of a right circular cylinder?Suppose that the radius of considered right circular cylinder be 'r' units.
And let its height be 'h' units.
Then, its volume is given as:
[tex]V = \pi r^2 h \: \rm unit^3[/tex]
Right circular cylinder is the cylinder in which the line joining center of top circle of the cylinder to the center of the base circle of the cylinder is perpendicular to the surface of its base, and to the top.
Given;
Sugar container radius and height is 2.5in and 8.5inch
Rice container radius and volume is 2.5in and 235.3inch^3
Sugar container area of base and height is 12.26in and 4inch
Now,
1. volume= pi*r*r*h
=3.14*2.5*2.5*8.5
=166.8125
2. volume= pi*r*r*h
235.3=3.14*2.5*2.5*h
h=11.98in
3. volume= base*h
=12.26*4
=49.04in^3
Therefore, the volume of flour container is 49.04in^3.
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carry out the following matrix multiplications. for each problem, say what the function represented by each matrix does to the standard basis vectors and what the product of the two matrices would do to these vectors.
The row in the original matrix and the column in the primary matrix must match. Hence, the matrix product has the first matrix's number of rows and the second matrix's number of columns.
A matrix is exactly what?Read an overview of this subject. a collection of numbers lined up in rows or columns to form a flat array is called a matrix. The atoms, or units, of the matrix are the integers.
The matrix theory is what?The study of squares is the main focus of the mathematical field known as matrix theory. It started out as a branch of linear algebra but quickly expanded to cover topics in graph theory, algebra, combinatorics, and statistics.
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Juan's mother gave him a recipe for trail mix. What is the order of the ingredients from least to greatest?3/4 cup raisins1/3 cup almonds2/3 cup peanuts1/2 cup cereal
The answer to question of trail mix in ascending order would be, 1/2 cup cereal, 3/4 cup raisins, 1/3 cup almonds, 2/3 cup peanuts.
The order of ingredients from least to greatest for Juan's trail mix recipe is: 1/2 cup cereal, 3/4 cup raisins, 1/3 cup almonds, and 2/3 cup peanuts. Juan's mother provided the recipe which consists of a combination of dried fruits, nuts, and cereal. The recipe calls for 1/2 cup of cereal, which is the least amount of any of the ingredients. The next ingredient is 3/4 cup of raisins, followed by 1/3 cup of almonds, and finally 2/3 cup of peanuts, which is the greatest amount of any of the ingredients. These ingredients can be combined and enjoyed as a snack.
Hence the answer is, 1/2 cup cereal, 3/4 cup raisins, 1/3 cup almonds, 2/3 cup peanuts.
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Match each formula on the left side to an equivalent formula on the right side A=BC+D
We can see that matching each formula on the left side to an equivalent formula on the right side, we have:
A = BC + D ------ B = A - D/C
A = B + CD ------ B = A - CD
A = BD - C ------- B = A + C/D
A = CD - B ------- B = CD - A
What is formula?A formula is a mathematical expression that represents a set of instructions for solving a specific problem or calculating a desired value. It often uses symbols and variables to represent values, and can include operations such as addition, subtraction, multiplication, and division.
Formulas can be used in a variety of fields, including physics, chemistry, finance, and engineering.
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Let f(x)=6x2+18x. Answer the following questions. 1. Find the x intercepts of the parabola. Intercepts (separate with commas): x=2. Find the vertex of the parabola. Write the vertex as a point (a,b) where a and b are numbers.
The x-intercept is -3 and the vertex of the parabola is (-1.5, -13.5).
What is vertex?The intersection of two lines, two line segments, or any other suitable arrangement of rays, segments, and lines that results in two straight "sides" coming together at one location is known as an angle's vertex.
The x coordinate of the vertex is given as:
x = -b/2a= -18/ 2(6)= - 1.5
The y coordinate of the vertex is given as:
y = f(- 1.5)
f(- 1.5) = 6(- 1.5)² + 18(- 1.5) = 13.5 - 27= -13.5
Hence, the vertex of the parabola is (-1.5, -13.5).
The x intercept is found by substituting the value of y = 0 in the function:
0 = 6x² + 18x
0 = 6x (x + 3)
x + 3 = 0
x = -3
Hence, the x-intercept is -3 and the vertex of the parabola is (-1.5, -13.5).
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Which function is the same as y = 3 cosine (2 (x + StartFraction pi Over 2 EndFraction)) minus 2?
y = 3 sine (2 (x + StartFraction pi Over 4 EndFraction)) minus 2
y = negative 3 sine (2 (x + StartFraction pi Over 4 EndFraction)) minus 2
y = 3 cosine (2 (x + StartFraction pi Over 4 EndFraction)) minus 2
y = negative 3 cosine (2 (x + StartFraction pi Over 2 EndFraction)) minus 2
The function as the same as y = 3 cosine (2 (x + Start Fraction pi Over 2 End Fraction)) minus is y = -3 sin(2(x + π/4)) - 2 Option B
How to find the function?Sine and cosine have the following relationship:
cos(θ) = sin (π/2 - θ)
y = 3 cos(2 (x + π/2)) - 2
y = 3 cos(2x + π) - 2
Let θ = 2x + π,
therefore using Sine and cosine have the following relationship:
cos(2x + π) = sin (π/2- (2x + π))
= sin (π/2 - 2x - π)
= sin (-2x - π/2)
= sin (-2(x + π/4))
but sin(-θ) = -sin (θ)
Therefore:
sin (-2(x + π/4)) = -sin (2(x + π/4))
= - sin (2(x + π/4)) = cos(2x + π)
y = 3 cos(2x + π) - 2 = 3[ - sin (2(x + π/4))] -2
y = -3 sin (2(x + π/4)) -2
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Given A= {{4,1,6},{-7,5,3},{9,-3,3}}
Observe that the first column plus twice the second column equal the third column. Find a nontrivial solution Ax=0
The nontrivial solution to the equation Ax = 0 is x = [1, 1, 1]^T.
What is the nontrivial solution?
To find a nontrivial solution to the equation Ax = 0, where A is the given matrix, we need to find a vector x that satisfies the equation and is not the trivial solution x = 0.
We can start by using the observation that the first column plus twice the second column equal the third column:
4x1 - 7x2 + 9x3 = 0
x1 + 2x2 - 3x3 = 0
6x1 + 3x2 + 3x3 = 0
Applying row reduction to the matrix A, we find:
{{4,1,6},{-7,5,3},{9,-3,3}}
{{1,1/2,-3/2},{-7,5,3},{9,-3,3}}
{{1,1/2,-3/2},{0,11/2,15/2},{0,11/2,15/2}}
The rank of the matrix A is 2, which is less than the rank of the matrix of the system of linear equations, which is 3. This means there is a nontrivial solution to the equation Ax = 0.
One such nontrivial solution can be found by setting x3 = 1 and solving for x1 and x2:
x1 + 2x2 - 3(1) = 0
x1 + 2x2 = 3
x1 = 3 - 2x2
Setting x2 = 1, we find:
x1 = 3 - 2(1) = 1
x2 = 1
x3 = 1
Hence, a nontrivial solution to the equation Ax = 0 is x = [1, 1, 1]^T.
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A washer 4mm wide is to be made as indicated in the drawing. Find the area of the washer in term of the outer radius ( in expanded form ).
This question is related to special products. Please help if you can.
The required area of the washer is 8πr - 16π square millimeter.
How to find area of circle?A = π r², where r is the circle's radius, is the formula for calculating a circle's surface area. The square unit, such as m², cm², in², etc., is the unit of area.
Circle Area Formulas;
Area is equal to π r², where r stands for radius.
Area is equal to ( π /4) d², where d stands for diameter.
Area is equal to C²/4 π where C stands for circumference.
According to question:The area of a washer with outer radius "r" and inner radius "r-4" can be found as follows:
Area = π * (outer radius² - inner radius²)
= π * (r² - (r-4)²)
= π * (r² - r² + 8r - 16)
= 8πr - 16π square millimeter.
Thus, required area of washer is 8πr - 16π,Option(B) is correct.
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vector a has a magnitude 5.00 and points in a direction 60.0degrees clockwise from the negative y axis. what are the x and y components of vector a.
A is directed along negative X and Y axes respectively having magnitudes 3.214 and 3.83 units respectively.
A vector is an object that, as we all know, possesses both magnitude and direction. We must determine a vector's length in order to determine its magnitude. Vector quantities include things like velocity, displacement, force, momentum, etc. However, scalar quantities like as speed, mass, distance, volume, temperature, etc. exist. In contrast to vectors, which
have both magnitude and direction, scalars only have magnitude.
Magnitude of vector A = |A| = 5 units
We know, the negative Y-axis is an angle of 270° counterclockwise with a positive X-axis.
θ = Angle of vector A with positive X-axis = (270° - 40°) = 230°
So, x component of vector A = Ax = |A| * cos 230° = |A| * cos (180° + 50°) = |A| * (- cos 50°) = 5 * (-0.6428) = -3.214
And, y component of vector A = Ay = |A| * sin 230° = |A| * sin (180° + 50°) = |A| * (- sin 50°) = 5 * (-0.766) = -3.83
Since Ax and Ay both are negative relative to positive X and Y axes respectively; so, the x and y components of vector A are directed along negative X and Y axes respectively having magnitudes 3.214 and 3.83 units respectively.
the complete question is -
Vector img has a magnitude 5.00 and points in a direction 40.0° clockwise from the negative y axis.What are the x and y components of vector img .
A)Ax = 3.83 and Ay = 3.21
B)Ax = 3.83 and Ay = -3.21
C)Ax = -3.21 and Ay = -3.83
D)Ax = -3.21 and Ay = 3.83
E)Ax = 4.29 and Ay = 2.16
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Choice A: $0.10 on January 1, $0.20 on January 2, $0.40 on January 3, $0.80 on January 4, doubling the amount each day, or
Choice B: $5.00 on the first day, $10.00 on the second day, $15.00 on the third day, getting $5.00 more each day.
Which of the choices can be defined using an exponential function? explain
Step-by-step explanation:
Choice A.
Choice A is exponentially because the amount is double each day. In other words each day the amount gets larger. One day it increased by 10 cents, the next day 20 cents, the next day 40 cents and so on... eventually it'll be a day where it increases by a million cents.
Choice B is not exponentially, it is linearly because each day the amount increase stays the same. One day is $5.00 more, the next day it's $5.00 more, the next day it's $5.00 more... and so on.
Because of that, we can get rid of those two choice B options.
Both Choice A's look the same. The only difference is that one has a 2 and the other doesn't. That 2 indicates that we're doubling. Makes sense because that's what we associate with doubling.
Making the second Choice A the correct formula.
show that in any set of six classes there must be two that meet on the same day, assuming that no classes are held on weekends.
There must be two that meet on the same day, assuming that no classes are held on weekends.
What is Set?
Sets are groups of clearly defined objects or elements in mathematics. A set is denoted by a capital letter, and the cardinal number of a set is enclosed in a curly bracket to indicate how many members there are in a finite set.
According to question:Let us show that in any set of six classes, each meeting regularly once a week on a particular day of the week, there must be two that meet on the same day, assuming that no classes are held on weekends.
Since there are 5 working days by a week and 6 classes, by Pigeonhole Principle there must be two that meet on the same day.
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