A) A 3 × 4 matrix can have independent columns but not independent rows.
B) A 3 × 4 matrix can have independent columns but not independent rows.
C) If A is an mxn matrix and rank A = m, it follows that m ≤ n.
D) A nonsquare matrix can have its rows independent.
E) The null space of a 3 × 6 matrix cannot have dimension 2.
F) If A is 5x4 and null(A) = x for some column x ≠ 0, dim(im A) cannot be 2.
Matrix Linear Independence RulesA) A 3 × 4 matrix can have independent columns but not independent rows. This is because a column vector can be linearly independent, meaning no linear combination of other columns in the matrix can create it, but a row vector can't be linearly independent because it can always be written as a linear combination of the columns.
B) If A is 4 × 3 and rank A = 2, it cannot have independent columns but it can have independent rows. This is because if rank A = 2, the number of linearly independent columns is 2, which is less than the number of columns, meaning that not all columns can be linearly independent. However, since rank A = 2, the number of linearly independent rows is also 2, which is less than the number of rows, meaning that some rows can be linearly independent.
C) If A is an mxn matrix and rank A = m, it follows that m ≤ n. This is because the rank of a matrix is the maximum number of linearly independent columns, which cannot be greater than the number of columns.
D) A nonsquare matrix can have its rows independent and its columns independent, as long as the number of rows is not equal to the number of columns.
E) The null space of a 3 × 6 matrix cannot have dimension 2. This is because the dimension of the null space is always less than or equal to the number of columns of the matrix, which is 6 in this case.
F) If A is 5x4 and null(A) = x for some column x ≠ 0, dim(im A) cannot be 2. This is because the dimension of the image of A is equal to the rank of A, which cannot be less than the dimension of the null space. Therefore, dim(im A) must be greater than or equal to the dimension of the null space, which is at least 1.
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How many terms are there in the expression 7x² 5x 5 *?
The number of terms in the given expression "7x² +5x -5" is three terms .
An Algebraic Expression is defined as the expression that contains combination of constants and variables joined by mathematical operators .
For Example ; 2x + 3y .
The given Algebraic Expression is 7x² +5x -5 ;
we can see that the terms joined by the mathematical operators + and - ;
the given expression cannot be simplified further ,
So ,the first term is 7x² ;
the second term is 5x and the third term is 5 .
Therefore , the expression 7x² +5x -5 has three terms .
The given question is incomplete , the complete question is
How many terms are there in the expression 7x²+5x -5 ?
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There are three terms in the expression 7x² 5x 5.
The expression 7x² 5x 5 contains three terms. The first term is 7x² which is the product of 7 and x². The second term is 5x which is the product of 5 and x. The third term is 5 which is a constant term. All together, these three terms make up the expression 7x² 5x 5. The 7x² term is a quadratic term, since it contains a squared variable, while the 5x and 5 terms are linear terms, since they only contain a single variable. When these three terms are combined, the expression 7x² 5x 5 is formed.
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Professor Grok writes an arithmetic sequence with three terms. Calamitous Clod creates a geometric sequence with common ratio 2 by adding 2 to the second term and 11 to the third term. What is the first term of their sequences
Calamitous Clod creates a geometric sequence with common ratio 2 by adding 2 to the second term and 11 to the third term. The first term is 7.
Let the numbers are: a₁, a₂, a₃.
These three numbers form an arithmetic sequence, which means the differences between 2 consecutive terms are the same.
Hence,
a₃ - a₂ = a₂ - a₁
a₃ = 2a₂ - a₁ ..... (equation 1)
Calamitous Clod creates a geometric sequence with common ratio 2 by adding 2 to the second term and 11 to the third term.
Hence, the geometric sequence is:
a₁, a₂ + 2, a₃ + 11.
with common ratio = 2
common ration = (a₃ + 11) / (a₂ + 2) = 2
a₃ + 11 = 2a₂ + 4
a₃ = 2a₂ - 7 ..... (equation 2)
Substitute equation 2 into equation 1
2a₂ - 7 = 2a₂ - a₁
a₁ = 7
Hence,
The first term = a₁ = 7
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In a sequence diagram, a lifeline is identified by a _____ line.
a.curved
b.red
c.solid
d.dashed
A lifeline in a sequence diagram is a line that is used to represent an active object, such as a class, interface, or object, and is typically identified by a solid line.
A lifeline in a sequence diagram is a graphical element used to depict the active objects in an interaction or sequence diagram. The lifeline is typically represented as a solid line running from the top of the diagram to the bottom, which represents the object's lifetime. The lifeline is used to show the messages that are sent and received between objects, as well as the sequence in which they occur. Additionally, the lifeline is often used to represent any changes of state in the objects, such as method calls, data values, and more. By depicting the lifelines of the active objects in a sequence diagram, it is possible to gain a better understanding of the interactions between the objects, and how they are related.
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A recipe for making 18 cookies requires 3/4 cup of sugar. How much sugar would be needed to make two dozen cookies using the same recipe
Answer:
18x=.75*24
18x=18
x=1 cup is needed for 2 doz. cookies.
Step-by-step explanation:
Therefore, the amount of sugar needed to make two dozen cookies is 1 cup. Explore all similar answers.
Given the equation of a linear function
Answer:
1/2x - 2 = Graph D, with the x intercept as 4, and the y intercept at
Answer:
D
Step-by-step explanation:
f(x) = mx + b
f(x) = 1/2 x - 2
m is the slope (1/2) and b is the y-intercept (b) -2.
Only graphs C and D cross the y axis at -2 . That is the point (0, -2)
The slope is 1/2. That means a rise of 1 space up and a run of 2 spaces left.
If you start at the point (0,-2) and go up 1 space and 2 spaces right, you end up back on the line at the point (4,0).
The wholesale price for a chair is $112. A certain furniture store marks up the wholesale price by 27%. Find the price of the chair in the furniture store. Round your answer to the nearest cent, as necessary
Answer:
$142.2
Step-by-step explanation:
First we know that we have $112
Then we calculate 112+27% and we get 142.24
Round that up and you get $142.2
Using permuatation.solve the questions regarding combinations and permutations. 1. using the digits 1, 2, 3 and 5, how many 4 digit numbers can be formed if i) the first digit must be 1 and repetition of the digits is allowed. ii) the first digit must be 1 and repetition of the digits is not allowed.
The number of possible outcomes for each case is given as follows:
i) 64 outcomes.
ii) 6 outcomes.
How to obtain the number of possible outcomes?The combination is composed by four digits, and each digit is independent of other digits, meaning that the Fundamental Counting Theorem is used to obtain the possible number of combinations.
The Theorem states that the total number of combinations is given by the multiplication of the number of outcomes for each digit.
For item i, as repetition is allowed, the first digit assumes a value of 1, hence there is only one possible outcome, while each of the remaining three digits can assume three values, hence the number of combinations is given as follows:
N = 4 x 4 x 4 = 4³ = 64 combinations.
When repetition is not allowed, and the number starts with the number one, we have that:
The second digit can assume three outcomes.The third digit can assume two outcomes.The fourth digit can assume a single outcome.Hence the number of combinations is obtained as follows:
N = 1 x 3 x 2 x 1 = 6 combinations.
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Which statement best describes the area of Triangle ABC shown below? A triangle ABC is shown on a grid. The vertex A is on ordered pair 4 and 6, vertex B is on ordered pair 6 and 1, and the vertex C is on ordered pair 2 and 1. (1 point) a It is twice the area of a rectangle of length 4 units and width 5 units. b It is one-half the area of a rectangle of length 4 units and width 5 units. c It is twice the area of a square of side length 5 units. d It is one-half the area of a square of side length 5 units.
The solution is Option B.
The area of the triangle is A = 10 units which is one-half the area of a rectangle of length 4 units and width 5 units
What is a Triangle?A triangle is a plane figure or polygon with three sides and three angles.
A Triangle has three vertices and the sum of the interior angles add up to 180°
Let the Triangle be ΔABC , such that
∠A + ∠B + ∠C = 180°
The area of the triangle = ( 1/2 ) x Length x Base
For a right angle triangle
From the Pythagoras Theorem , The hypotenuse² = base² + height²
if a² + b² = c² , it is a right triangle
if a² + b² < c² , it is an obtuse triangle
if a² + b² > c² , it is an acute triangle
Given data ,
Let the triangle be represented as ΔABC
Let the coordinates of the triangle ABC be
The coordinate of A = A ( 4 , 6 )
The coordinate of B = B ( 6 , 1 )
The coordinate of C = C ( 2 , 1 )
Now , the base of the triangle B = 4 units
The height of the triangle H = 5 units
And , The area of the triangle = ( 1/2 ) x Length x Base
Substituting the values in the equation , we get
The area of the triangle = ( 1/2 ) x 4 x 5
The area of the triangle = 10 units
Now , one-half the area of a rectangle of length 4 units and width 5 units
Substituting the values in the equation , we get
Area of rectangle = ( 1/2 ) Length x Width
Area of rectangle = ( 1/2 ) 4 x 5
Area of rectangle = 10 units
Hence , the area of triangle is 10 units
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How do u do this? (Answers pls)
The expression are given as;
x + y : positive.
y - x : negative.
x - y : positive.
y + (-x) :negative.
What is an expression?Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
The Numbers constants, variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbol; which can also be used to indicate the logical syntax's order of operations and other features.
We are given that the x and y are two numbers on the number line
y = negative number.
x = positive number
Therefore, the expression are;
x + y
The expression is positive.
y - x
The expression is negative.
x - y
The expression is positive.
y + (-x)
The expression is negative.
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14
Kayla has 10 quarters, 9 dimes, and 8 nickels
in her pocket. If she pulls out one coin
without looking, what type of coin is she
most likely to pull out?
Answer: The quarter
Step-by-step explanation:
The quarter is larger and there are more quarters than there are any other coins in her pocket.
Ruby is designing a new board game, and is trying to figure out all the
possible outcomes. How many different possible outcomes are there if
she flips a coin, rolls a fair die in the shape of a cube that has six sides
labeled 1 to 6, and spins a spinner with three equal-sized sections
labeled Walk, Run, Stop?
Answer:
Submit Answer
attempt 1 out of 2
The maximum possible outcome for the situation is 36.
What is Probability?The number of favorable events to all the events in an experiment is the ratio that makes up the probability formula. Theoretical probability, Experimental probability, and Axiomatic probability are the three categories into which probability can be divided.
We have been Given that Ruby is designing a new board game and is trying to figure out all the possible outcomes.
Ruby flips a coin, rolls a fair die in the shape of a cube that has six sides labeled 1 to 6, and spins a spinner with three equal-sized sections labeled Walk, Run, Stop.
we know that there are 3 things happening simultaneously and favorable moments will be chosen by all three.
Thus, Maximum possible outcome are;
2 x 6 x 3 = 36
Therefore, For the given, 36 outcomes are available in total.
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sylvester the slug travelled across four tree branches each tree branch was 9.01 meters 12.31 meters 19.5 meter and 25.92 meters what was the total distance sylvester travelled
By adding all the distances of the branches, we will conclude that Sylvester traveled a distance of 66.74 meters.
What is the total distance that Sylvester traveled?We know that Sylvester is a slug, and it travels for four branches, such that the length of each branch is:
9.01 meters12.31 meters19.5 meters25.92 metersTo get the total distance that Sylvester travels, we just need to add these 4 numbers, then we will get:
Total distance = 9.01 m + 12.31m + 19.5m + 25.92m
Total distance = 66.74 meters.
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show that the bisectors of angles of a parallelogram form a rectangle.
Answer:
LMNO is a parallelogram in which bisectors of the angles L, M, N, and O intersect at P, Q, R, and S to form the quadrilateral PQRS. Hence the angle bisectors of a parallelogram form a rectangle as all the angles are right angles; we conclude that it IS RECTANGLE. Hence proved.
Alex, an eighth grader, and Eric, a seventh grader, need to determine who came closer to their grade’s state record for the triple jump. Alex jumped 38 feet 11 2/3 inches and Eric jumped 36.89 feet. Who was closer to the state record if the eighth-grade record is 40.17 feet, and the seventh-grade record is 38 feet 1 3/5 inches?
Alex came closer to their grade’s state record for the triple jump.
What is algebra?
The area of mathematics known as algebra is used to help express issues or circumstances into mathematical expressions.
Here, we have
Given:
Alex jumped 38 feet 11 2/3 inches the eighth-grade record is 40.17 feet.
Let's see how closer Alex jumped.
11 2/3 inches = 22* 0.083 = 1.826
38+ 1.826 = 39.826
40.17 - 39.826 = 0.344
Eric, a seventh grader, jumped 36.89 feet. The seventh-grade record is 38 feet 1 3/5 inches.
1 3/5 inches = 8/5*0.083 = 0.1328
38 + 0.1328 = 38.1328
Eric jump was
38.1328 - 36.89 = 1.2428
0.344 is smaller than 1.2428.
Hence, Alex came closer to their grade’s state record for the triple jump.
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What kind of data might be displayed on a pie chart ?
Answer: nomial data
Step-by-step explanation:
At a concession stand, a family buys 3 slices of pizza, 2 drinks, and one bag of chips for $10. Another family bought 2 slices of pizza, 4 drinks, and a bag of chips for $9.50. If a bag of chips cost 50 cents then how much does a slice of pizza cost?
The cost of a slice of pizza is $2.5.
What are Linear Equations?Linear equations are equation involving one or more expressions including variables and constants and the variables are having no exponents or the exponent of the variable is 1.
Let x be the price of 1 slice of pizza and y be the price of a drink.
Cost of a bag of chips = 50 cents = $0.5
A family buys 3 slices of pizza, 2 drinks, and one bag of chips for $10.
Another family bought 2 slices of pizza, 4 drinks, and a bag of chips for $9.50.
We have two linear equations,
3x + 2y + 0.5 = 10 or 3x + 2y = 9.5
2x + 4y + 0.5 = 9.5 or 2x + 4y = 9
So we have
3x + 2y = 9.5
2x + 4y = 9
Multiplying throughout the first equation with 2 and subtracting the second equation from the resultant equation, we get
[2(3x + 2y) - (2x + 4y) = (2 × 9.5) - 9
6x - 2x = 10
4x = 10
x = 2.5
Hence $2.5 is the cost of a slice of pizza.
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Find each missing measure.
Answer:
< is angle, Dont be confused
m<1= 51
m<2=39
m<3=90
m<4=51
m<5= 17
m<6= 129
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How many 3 digit numbers greater than 500 are odd?
There are 28 numbers in total that are odd numbers greater than 500 with no digit being repeated.
First, there are 18 odd numbers with four digits, and all of them are greater than 500. To see that, starting from the end of the number, there are 3 options for the last digit, 3 for the second last, 2 for the second digit, and 1 for the first digit. Multiplying one gets 3*3*2*1=18.
Second, for numbers with 3 digits, in order to be greater than 500, it must start either with 5 or with 6. If it starts with 5, there are 2 options for the last digit and 2 options for the second digit.
Thus, there are 4 different numbers in this case. Finally, if it starts with 6, then there are 3 options for the last digit and 2 options for the second digit. Thus, there are 6 different numbers in this case.
Complete question: How many different odd numbers greater than 500 can be made using some or all of the digits 1,3,5 and 6 with no digit being repeated?
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As per the permutations, there as 36 three digit numbers that are greater than 500 and which are odd one also.
The term permutation in math is defined as the way of arranging objects or numbers in order.
Here we have given that we have to identify the 3 digit numbers greater than 500 are odd
Let us make three digit numbers 1st
Here we know that if we want odd number at end then one number from three numbers can come there so
=> 3P1
Then the rest of the two numbers don't matter so
Then it can be written as
=> 3P2
Then the overall combination is written as
=> 3P1 * 3P2=18
Here now let us make four digit numbers
Then the digit odd again and it can be written as
=> 3P1
Here also the rest of the order Doesn't matter so
then it can be written as
=> 3P3 =6
Then the four digit value is
=> 3p1 * 3p3= 18
Therefore, the overall count is written as
=> Overall = 18+18= 36
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(a) What is the coefficient of x^4y^{12} in the expansion of (-4x+2y)^{16}
(b) What is the coefficient of x^4y^8z^7 in the expansion of (-4x+2y-1z)^{19}?
A. The coefficient of x^4y^{12} in the expansion of (-4x+2y)^{16} is -8192.
B. The coefficient of x^4y^8z^7 in the expansion of (-4x+2y-1z)^{19} is -134217728.
For the first question, we can use the binomial theorem to expand the expression. The binomial theorem states that
(a+b)^n = C(n,0)a^nb^0 + C(n,1)a^{n-1}b^1 + C(n,2)a^{n-2}b^2 + ... + C(n,n)a^0b^n
Where C(n,k) = n!/(k!(n-k)!)
Applying this to the given expression, we get:
(-4x+2y)^{16} = C(16,0)(-4x)^{16}(2y)^0 + C(16,1)(-4x)^{15}(2y)^1 + C(16,2)(-4x)^{14}(2y)^2 + ... + C(16,16)(-4x)^0(2y)^16
The coefficient of x^4y^{12} is the coefficient of the term -4x^42y^{12} in this expansion, which is
C(16,4)(-4)^42^{12} = C(16,4)(-256)4096 = C(16,4)(-256)*4096 = -8192
For the second question, the same logic can be applied to:
(-4x+2y-1z)^{19} = C(19,0)(-4x)^{19}(2y)^0(-1z)^0 + C(19,1)(-4x)^{18}(2y)^1(-1z)^0 + C(19,2)(-4x)^{17}(2y)^2(-1z)^1 + ... + C(19,19)(-4x)^0(2y)^0(-1z)^19
The coefficient of x^4y^8z^7 is the coefficient of the term -4x^42y^8(-1z)^7 in this expansion, which is C(19,4)(-4)^42^8*(-1)^7 = C(19,4)256256*-1 = -134217728
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What percentage of the shape is pink?
Write your answer using a percent sign (%).
Answer:
Step-by-step explanation:
The percentage of pink is 13%.
w(n) = −2n – 2; Find w(9)
Answer:
w(n)= -20
Step-by-step explanation:
w(9)=-2(9)-2
= -18-2
=-20
Answer:
w(9) = -20
Step-by-step explanation:
w(n) = −2n – 2
w(9) = −2(9) – 2
w(9) = -18 - 2
w(9) = -20
Tiana fills a basket with apples. The empty basket weighs 1.07 pounds. The basket full of
apples weighs 6.93 pounds in all. How many
pounds of apples are in the basket?
Answer:
5.86 lbs
Step-by-step explanation:
6.93 - 1.07 = 5.86
You subtract the weight of the basket from the weight of the basket full of apples to get the weight of just the apples
Does anyone know how to solve this? I’ve been hanging a rough time figuring it out
A man has a collection of stamps made up of 5 cent stamps and 8 cent stamps. There are three times as many 8 cent stamps as 5 cent stamps. The total value of all the stamps is $3.48. How many of each stamp does he have?
If a man has a collection of stamps made up of 5 cent stamps and 8 cent stamps and there are three times as many 8 cent stamps as 5 cent stamps. The number of each stamp he have is: 5 cent stamp is 12, 8 cent stamp is 36.
How to find the number of each stamp?Let x represent 5 cent = 0.05x + 0.08 = 3.48
Let y represent 8 cent = 3x
Hence,
0.05x + 0.08(3x)= 3.48
0.05x + 0.24x = 3.58
Combine like terms
0.29x = 3.58
Divide both side by 0.29x
x = 3.58/0.29
x =12 (5 cent stamps)
Now let solve for y
y =3x
y =3(12)
y = 36 (8 cent stamps)
Therefore the number of each stamp he have is: 5 cent stamp is 12, 8 cent stamp is 36.
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Strat
1. Brenna cuts wood for a fire. She can cut a log into thirds in 10 min.
How long would it take Brenna to cut a similar log into sixths?
Brenna would take 20 min to cut the same wood into sixths.
What are equation models?The equation model is defined as the model of the given situation in the form of an equation using variables and constants.
Here,
Let x be the rate at which Brenna cuts the wood in a single piece,
So, She can cut a log into thirds in 10 min.
x = 3/10
x = 0.3 cuts per minute for single wood,
Now,
time took to cut the same wood into 6 pieces
= 6 / x
= 6 / 0.3
= 20 min
Thus, Brenna would take 20 min to cut the same wood into sixths.
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Match each drawing on the left with its word description on the right. Some of the answer choices on the right may not be used.
Answer: below :)
Step-by-step explanation:
1. Line AB
2. Ray AB
3. Line segment AB
4. Ray BA
-4a - 12 factorisation
Answer: -4(a+3)
Step-by-step explanation:
You can take out -4 from -4 and -12
Answer:
-4(a+3)
Step-by-step explanation:
Right on edge!
Determine the measures of all unknown angles and side lengths of δpqr. round side lengths to the nearest hundredth. m∠r = ° pr ≈ pq ≈
The measures of all unknown angles and side lengths of δpqr of m∠R = 50 degrees, PR ≈ 5.74 cm, after solving the Pythagorean theorem equation, and PQ ≈ 8.53 cm, after solving the Law of Cosines equation.
In order to determine the measures of all unknown angles and side lengths of ΔPQR, we can use the properties of a triangle. In particular, we can use the fact that the sum of the angles in a triangle is 180 degrees and the Pythagorean theorem.
We know that m∠P + m∠Q + m∠R = 180, so we can use this equation to find m∠R, m∠R = 180 - m∠P - m∠Q = 180 - 99 - 31 = 50To find the length of PR, we can use the Pythagorean theorem. PR = √(PQ² + QR²) = √(PQ² + (11cm)²)To find the length of PQ, we can use the Law of Cosines on the triangle, PQR, PQ² = PR² + QR² - 2PRQRcos(P) = (PR)² + (11cm)² - 2PR11cos(99)You can use the above information to find the value of PR and PQ using trigonometric functions and/or squares.
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The question is -
Determine the measures of all unknown angles and side lengths of ΔPQR. Round side lengths to the nearest hundredth.
m∠R =
PR ≈
PQ ≈
Which of these values for p and a will cause the function f(x)=pa^x to be an exponential growth.
Option C. p= 1/6; a= 8 values for p and a will cause the function [tex]f(x) = Pa^x[/tex] to be exponential growth.
An exponential growth function is a function in which the variable x is the exponent of the base. In the function, [tex]f(x) = Pa^x,[/tex] the variable x is the exponent and the constant a is the base. For the function to be an exponential growth function, the base must be greater than 1.
In option A, P=6 and a=1/8. The base is less than 1 (1/8 < 1) so this function is not an exponential growth function.
In option B, P=6 and a=1. The base is equal to 1, which is not greater than 1, so this function is not an exponential growth function.
In option C, P=1/6 and a=8. The base is greater than 1 (8 > 1) so this function is an exponential growth function.
In option D, P=1/6 and a=1/8. The base is less than 1 (1/8 < 1) so this function is not an exponential growth function.
Therefore, the only option that causes the function [tex]f(x) = Pa^x,[/tex] to be an exponential growth function is option C. P=1/6; a=8.
Complete Question:
Which of these values for P and a will cause the function [tex]f(x) = Pa^x[/tex] to be an exponential growth function?
A. P=6; a = 1/8
B. P = 6; a = 1
C. P= 1/6; a=8
D. p= 1/6; a= 1/8
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P= 1/6; a=8
Is a exponential growth function, because a > 1 and P is not zero
Now, According to the question:
We know that
The equation of a exponential growth function is given by:
[tex]f(x)=pa^x[/tex]
where
P is the initial value or y-intercept (this vale cannot be equal to zero)
a is the base of the exponential function ( in a exponential growth function the value of a is greater than 1)
Verify each case
case A) P=6; a = 1/8
Is not a exponential growth function, because a < 1 (is a decay exponential function)
case B) P=6; a = 1
Is not a exponential function
case C) P= 1/6; a=8
Is a exponential growth function, because a > 1 and P is not zero
case D) P=1/6; a = 1/8
Is not a exponential growth function, because a < 1 (is a decay exponential function)
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The complete question is this:
Which of these values for P and a will cause the function f(x) = Pa^x to be an exponential growth function?
A. P=6; a = 1/8
B. P = 6; a = 1
C . P= 1/6; a=8
D. p= 1/6; a= 1/8
Which of the following are measures of central tendency? Check all that apply.
A.The median
B.A sample statistic
C.The mode
D.The lowest value
E. The mean
All the measures of central tendency are, The median, The mode, and The mean.
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
There are some measures,
A. The median
B. A sample statistic
C. The mode
D. The lowest value
E. The mean
We know that;
The four measures of central tendency are mean, median, mode and the midrange.
Here, mid-range or mid-extreme of a set of statistical data values is the arithmetic mean of the maximum and minimum values in a data set.
Hence, All the measures of central tendency are, The median, The mode, and The mean.
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