The resulting matrix is \( \left[\begin{array}{ll}0 & 0 \\ 0 & 0\end{array}\right] \).
we notice is that the resulting matrix is the zero matrix, which means that all of its elements are zero. This is because the matrices \( A \) and \( B \) are inverses of each other.
To calculate \( A B \), we multiply the elements in each row of \( A \) with the corresponding elements in each column of \( B \) and then add them together. This gives us the elements in the resulting matrix.
So, the first element in the resulting matrix is \( (4 * 1) + (2 * -2) = 4 - 4 = 0 \). The second element is \( (4 * -3) + (2 * 6) = -12 + 12 = 0 \). The third element is \( (2 * 1) + (1 * -2) = 2 - 2 = 0 \). And the fourth element is \( (2 * -3) + (1 * 6) = -6 + 6 = 0 \).
Therefore, the resulting matrix is \( \left[\begin{array}{ll}0 & 0 \\ 0 & 0\end{array}\right] \).
What we notice is that the resulting matrix is the zero matrix, which means that all of its elements are zero. This is because the matrices \( A \) and \( B \) are inverses of each other. When we multiply a matrix by its inverse, we get the identity matrix, which has ones on the main diagonal and zeros everywhere else. But in this case, since the matrices are 2x2, the identity matrix is just the zero matrix.
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what’s the inverse function of
f (x) = 2x+3
Answer:
[tex]f^{2} (x) = \frac{1}{2} x + \frac{3}{2}[/tex]Step-by-step explanation:
Answer:
[tex]f^{-1}[/tex] = [tex]\frac{x-3}{2}[/tex]
The inverse of a function is just the opposite of the function.
The following illustrates an application of optimization using parabolas.
A study found that the cost C per pupil of operating a high school in a certain country depends on the number n of students enrolled. The cost is given by
C = 70,000 − 500n + n2 dollars per pupil.
What enrollment produces the minimum cost per pupil?
n = students
The minimum cost per pupil is $7,500 when 250 students are enrolled.
To find the minimum cost per pupil, we need to find the vertex of the parabola C = 70,000 − 500n + n². The vertex of a parabola in the form y = ax² + bx + c is given by the formula x = -b/2a. In this case, a = 1, b = -500, and c = 70,000.
Plugging these values into the formula, we get:
x = -(-500)/2(1) = 500/2 = 250
So the minimum cost per pupil occurs when n = 250 students are enrolled.
To find the minimum cost, we can plug n = 250 back into the equation for C:
C = 70,000 − 500(250) + (250)² = 70,000 - 125,000 + 62,500 = 7,500
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Man this shi 40 points
The match of the terms and correct locations are:
1. A - Amplitude
2. B is compression
3. C is rarefaction
What are longitudinal waves?A longitudinal wave is a form of wave in which its direction of propagation is similar to the direction of vibration of the particles of the medium through which the wave is travelling. The waves generated by a stretched or compressed spiral spring produces longitudinal waves.
When a spiral spring is streched or compressed, on removal of the force a series of compression and rarefactions of the sections of the spring are produced. This sections vibrates in the direction of propagation of the waves produced.
Thus the match of the terms and correct locations are:
i. A - Amplitude
ii. B is compression
iii. C is rarefaction
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Using the quotient and reciprocal identities again, simplify the left side. \[ \begin{aligned} \frac{\sec x+\tan x \csc x}{\csc x} & =\frac{\sec x+\sec x}{\csc x} \\ & =\frac{2 \sec x}{\csc x} \end{al
The simplified form of the left side of the equation is $2 \tan x$.
The left side of the equation can be simplified using the quotient and reciprocal identities. The quotient identity states that $\tan x = \frac{\sin x}{\cos x}$ and the reciprocal identity states that $\sec x = \frac{1}{\cos x}$ and $\csc x = \frac{1}{\sin x}$. By substituting these identities into the equation, we can simplify the left side:
\[ \begin{aligned} \frac{\sec x+\tan x \csc x}{\csc x} & =\frac{\frac{1}{\cos x}+\frac{\sin x}{\cos x} \cdot \frac{1}{\sin x}}{\frac{1}{\sin x}} \\ & =\frac{\frac{1}{\cos x}+\frac{1}{\cos x}}{\frac{1}{\sin x}} \\ & =\frac{2 \cdot \frac{1}{\cos x}}{\frac{1}{\sin x}} \\ & =\frac{2}{\cos x} \cdot \frac{\sin x}{1} \\ & =\frac{2 \sin x}{\cos x} \\ & =2 \tan x \end{aligned} \]
Therefore, the simplified form of the left side of the equation is $2 \tan x$.
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. Line y = 2x + 1 is
transformed by a dilation
with a scale factor of 2 and centered at (3, 5). Is
the image the same line or a parallel line? How do
you know?
Suppose vector d = vector a - vector b where vector vector a has components ax = 4, ay = 5 and vector vector b has components bx = -4, by = -4
The vector representing D = A - B has following values,
1. x- component of vector D = 9 and y- component of vector D = 9.
2. Magnitude and direction of vector D is equal to 12.73 and 45° above the positive x-axis.
Here, Vector D= A-B __(1)
Components of vector A are,
Ax=5
Ay=5
Components of vector B are,
Bx= -4,
By= -4
1. Subtract the x- and y-components of vector B from vector A, respectively by substituting in (1) we get,
Dx = Ax - Bx
= 5 - (-4)
= 5 + 4
= 9
Dy = Ay - By
= 5 - (-4)
= 5 + 4
= 9
2. Magnitude of vector D, use the Pythagorean theorem,
|D| = √(Dx² + Dy²)
= √(9² + 9²)
= √(162)
≈ 12.73
Direction of vector D, use trigonometry.
Angle θ represents vector D makes angle with positive x-axis is ,
θ = tan⁻¹(Dy / Dx)
= tan⁻¹(9 / 9)
= tan⁻¹(1)
= 45°
Therefore, required value of the vectors are,
1. x- and y-components of vector D are 9 and 9, respectively.
2. Magnitude of vector D is 12.73, and direction is 45° above the positive x-axis.
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The above question is incomplete , the complete question is:
Suppose D= A-B where vector A has components Ax=5, and Ay=5 and vector B has components Bx= -4, By= -4.
1. What are the x- and y- components of vector D?
2. What are the magnitude and direction of vector D?
What is the domain and range of y = log(-x + 3) - 1?
Answer:
The argument of the logarithmic function should be greater than zero.
Thus, for y = log(-x + 3) - 1 to be real-valued, we need:
-x + 3 > 0
or
x < 3
So, the domain of the function is all real numbers less than 3.
To find the range, let's consider the behavior of the logarithmic function.
As x approaches 3 from the left, the argument of the logarithm approaches zero from the negative side, which means the logarithm approaches negative infinity.
As x approaches negative infinity, the argument of the logarithm becomes very large and negative, which means the logarithm approaches negative infinity.
Therefore, the range of the function y = log(-x + 3) - 1 is all real numbers.
Step-by-step explanation:
On average, a clothing store gets 120 customers per day. What is the probability that the store will have fewer than 12 customers in the first two hours? (Assume the store is open 12 hours each day. Round your answer to four decimal places. )
The probability that clothing store have fewer than 12 customers in first 2 hours is 0.0003.
We know that, the store is open for 12 hours and gets an average of 120 customers per day, the expected number of customers in a 2-hour period can be calculated as:
The Expected number of customers in 2 hours = 120×(2/12) = 20 customers,
We, use the Poisson distribution to find the probability of having fewer than 12 customers in the first two hours.
The Poisson distribution is given by : P(X = k) = (e^(-λ) × λ^k)/k! ;
where X = random variable (the number of customers), λ = expected value of X (in this case, λ = 20), k = number of customers we want to calculate the probability for, and k! is the factorial of k.
To find the probability of having fewer than 12 customers in the first 2 hours, we need to calculate the probability for k = 0, 1, 2, ..., 11 and add up the probabilities.
So, we have,
⇒ P(X < 12) = e⁻²⁰×(20⁰/0!) + e⁻²⁰×(20¹/1!) + ... + e⁻²⁰×(20¹¹/11!);
On solving, We get,
⇒ P(X < 12) = 0.0003,
Therefore, the required probability is 0.0003.
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HELPPP!!!!
What should be reason 2 in the following proof?
The reason that should be used to complete statement 2 "∠2 and ∠3 are supplementary" is linear pair postulate.
What is the linear pair theorem?In Mathematics, the linear pair theorem is sometimes referred to as linear pair postulate and it states that the measure of two angles would add up to 180° provided that they both form a linear pair.
This ultimately implies that, the measure of the sum of two adjacent angles would be equal to 180° when two parallel lines are cut through by a transversal.
According to the linear pair theorem, we have the following supplementary angles:
∠2 + ∠3 = 180°
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Pls help me it’s to go from lease value to the greatest and closest to zero!
According to the information, the expressions that would match the descriptions would be both expressions have the same result, so it doesn't matter which description they are associated with. both are the largest and the smallest value.
How to find the correct expressions for the descriptions?To find the correct descriptions that match the expressions we must look at the graph. In this case q and n represent two numbers on the number line. In this case, to relate them to a description we must find the number to which they refer:
q = -1n = -4The expression q - n would be equal to -1 - 4 = -5The expression n - q would be equal to - 4 - 1 = -5In accordance with the above, we could say that the descriptions would look like this:
Closest to zero = qLeast value = q - nGreatest value = n - qIn this case, both expressions have the same result, so it doesn't matter which description they are associated with. both are the largest and the smallest value.
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A ferry traveled
1
6
6
1
start fraction, 1, divided by, 6, end fraction of the distance between two ports in
3
7
7
3
start fraction, 3, divided by, 7, end fraction hour. The ferry travels at a constant rate.
At this rate, what fraction of the distance between the two ports can the ferry travel in one hour?
The ferry travels at constant rate is 7/18 miles/hour
What is Division method?Division method is used to distributing a group of things into equal parts. Division is just opposite of multiplications.
For example, dividing 20 by 2 means splitting 20 into 2 equal groups of 10.
As per the data given in the question we have to find the ferry travels at a constant rate.
As per the question it is given that a ferry traveled 1/6 of the distance between two ports in 3/7 hour.
Now, Ferry travelled 1/6 miles of distance between two ports in 3/7 hours
Hence, Rate of Ferry is equal to distance travelled over time taken.
Rate of ferry = 1/6 ÷ 3/7
Now we calculate it.
Rate of ferry = 1/6 × 7 / 3 miles/hour
Rate of Ferry = 7/18 miles/hour
Hence, The ferry travels at constant rate is, 7/18 miles/hour.
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About 71 % of the residents in a town say that they are making an effort to conserve water or electricity. 110 residents are randomly selected.
1) Mean:
2) Standard Deviation:
3) What is the probability that the proportion of sampled residents who are making an effort to conserve water or electricity is greater than 80%?
About 71 % of the residents in a town say that they are making an effort to conserve water or electricity. 110 residents are randomly selected. The mean is 0.71. Standard Deviation is 0.043. The probability that the proportion of sampled residents who are making an effort to conserve water or electricity is greater than 80% is 0.0183.
1) Mean:
The mean of a proportion is simply the proportion itself, so the mean is 0.71.
2) Standard Deviation:
The standard deviation of a proportion is given by the formula:
σ = √(p(1-p)/n)
where p is the proportion, and n is the sample size. Plugging in the values given in the question:
σ = √(0.71(1-0.71)/110)
σ = 0.043
3) To find this probability, we need to use the normal distribution. We will use the z-score formula:
z = (x - μ) / σ
where x is the proportion we are interested in (0.8), μ is the mean (0.71), and σ is the standard deviation (0.043). Plugging in the values:
z = (0.8 - 0.71) / 0.043
z = 2.09
Using a z-table, we find that the probability of getting a z-score greater than 2.09 is 0.0183. So the probability that the proportion of sampled residents who are making an effort to conserve water or electricity is greater than 80% is 0.0183.
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PNDM got dilated about the origin and formed P' N' D' M'. Write the dilation rule.
(x,y) -->
Since PNDM got dilated about the origin and formed P' N' D' M', the dilation rule is (x, y) → (2x, 2y).
What is scale factor?In Geometry, the scale factor of a geometric figure can be calculated by dividing the dimension of the image (new figure) by the dimension of the pre-image (original figure):
Scale factor = Dimension of image (new figure)/Dimension of pre-image(original figure)
Substituting the given parameters into the scale factor formula, we have the following;
Scale factor = Dimension of image/Dimension of pre-image
Scale factor = 4/2
Scale factor, k = 2.
Therefore, the dilation rule is given by:
(x, y) → (kx, ky)
(x, y) → (2x, 2y)
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Zach's plants grew 2 feet in 7 weeks.
How many centimeters did Zach's plants grow?
1 ft = 0.3 m
1 m = 100 cm
Enter your answer in the box.
( ) cm
Using the unitary method, we found that Zach's plants grew 60cm in 7 weeks.
What is meant by the unitary method?The unitary method is a strategy for problem-solving that involves first determining the value of a single unit and then multiplying that value to determine the required value. Therefore, the goal of this method is to establish values in relation to a single unit. Always write the things that need to be calculated on the right side and the things that are known on the left side to simplify things. The unitary approach must be applied whenever we need to determine the ratio of one quantity to another.
Given that the height the plant grew in 2 weeks = 2 feet
We are asked to convert it into centimetres.
This can be done using the unitary method.
Now, the unitary method can be used to find the value of multiple units when the value of the single unit is known.
Here we are given,
1 ft = 0.3 m
But we need feet and centimetre relation.
So we use the metre and centimetres relation.
1m = 100cm
Using the unitary method,
0.3m = 0.3* 100 = 30 cm
So,
1 feet = 0.3m = 30 cm
Then,
2 feet = 30 * 2 = 60 cm
Therefore using the unitary method, we found that Zach's plants grew 60 cm in 7 weeks.
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Please help me! I'm horrible at math!
Answer:
I think the answer is C. 65 m
Step-by-step explanation:
Answer:
L=22
Step-by-step explanation:
For the area of a rectangle you have to multiply the width by the length.
This problem would look like L*W=A. Being that you already have the area and the width, you would just have to fill in for these.
L*6.5=143
Then just follow the rules of PEMDAS to sole for L. In this case this would be dividing 6.5 by both sides.
L=22
What term refers to the achievements that will take a person awhile to meet? A. backwards goals B. short-term goals C. long-term goals D. visualization
Answer:
C is the answer
five students each wrote an expression to represent the perimeter of the given rectangle [3x+3x) +(4x+4x)+( 3+3)
Answer:
The given rectangle is not fully defined, as it is missing some measurements such as the length and width. Without this information, it is not possible to accurately calculate the perimeter of the rectangle.
However, assuming that the missing measurement is the width of the rectangle, then the expressions given by the five students would be:
2(3x + 4x + 3) = 14x + 6
2(6x + 6) + 2(4x + 6) = 20x + 24
2(3x + 3) + 2(4x + 3) = 14x + 12
2(6x + 3) + 2(4x + 3) = 20x + 12
2(6x + 3x) + 2(3 + 4x) = 18x + 10
Note that all expressions follow the formula for the perimeter of a rectangle, which is P = 2l + 2w, where l is the length and w is the width of the rectangle.
15.F(x)=−529, F(x)=x^2+33; h(x)=∣x∣−233 ; g(x)=2x
The values of F(x), h(x), and g(x) when x=3 are 42, -230, and 6, respectively.
The given functions are F(x)=−529, F(x)=x^2+33, h(x)=∣x∣−233, and g(x)=2x.
To find the value of F(x) when x=3, we can substitute x=3 into the equation F(x)=x^2+33 and solve for F(x):
F(x)=x^2+33
F(3)=3^2+33
F(3)=9+33
F(3)=42
Similarly, to find the value of h(x) when x=3, we can substitute x=3 into the equation h(x)=∣x∣−233 and solve for h(x):
h(x)=∣x∣−233
h(3)=∣3∣−233
h(3)=3−233
h(3)=-230
And to find the value of g(x) when x=3, we can substitute x=3 into the equation g(x)=2x and solve for g(x):
g(x)=2x
g(3)=2(3)
g(3)=6
Therefore, the values of F(x), h(x), and g(x) when x=3 are 42, -230, and 6, respectively.
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Write a quadratic function f whose zeros are -2 and 9 .
To write a quadratic function f whose zeros are -2 and 9 , we have to factor the function by (x+2) and (x-9).
How to find the quadratic function of f?A quadratic function is a second-degree mathematical function whose graph is a parabola. The general form of a quadratic function is given by f(x) = ax² + bx + c, where a, b and c are constants and a cannot be equal to zero. The variable x represents the input of the function and f(x) represents the output or result of the function. To find the quadratic function of f we first need to multiply these factors, like this:
f(x)= (x+2) (x-9)Expanding the product, we have:f(x)= x²-7x-18So the quadratic function whose zeros are -2 and 9 is:
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Match each number with its name
Answer:
1,254 - whole number; 0.13 - terminating; 0.123456789... - non-terminating/non-repetitive; 0.143143143... - repeating decimal
Step-by-step explanation:
A whole number is a number without any decimals or fractions. A terminating number is one that has an end. A non-terminating number is one that continues on forever. A repeating number is one that has the same pattern and continues on forever.
what is the median of 1, 1, 2, 3, 7, 9, 10, 10, 15, 17, 19
Answer:
9
Step-by-step explanation:
The median is the number in the middle of a set of numbers.
Our set of numbers: 1, 1, 2, 3, 7, 9, 10, 10, 15, 17, 19
In this case the median is 9
Which graph models function m?
x- 0 1 2 3 4 5
m(x)- -9 -4 -1 0 -1 -4
245% of what number is 49
Answer: 20
Step-by-step explanation:
49 ÷ 245 %
convert the percentage to decimals
49 ÷ 2.455
calculate the product or quotient
20
Please give me brainliest
Answer:20
Step-by-step explanation:
Let's denote the number we are looking for as "x".
We can set up the equation:
245% of x = 49
We can convert 245% to the decimal form by dividing by 100:
2.45 * x = 49
To solve for x, we can divide both sides of the equation by 2.45:
x = 49 / 2.45
x = 20
Therefore, 245% of 20 is equal to 49.
Please please help will mark BRAINLIEST due tomorrow,!!!!! PLEASE PLEASE THANK YOU (PICTURE ATTACHED)
The solution for the inequality in this problem is problem is given as follows:
v ≤ 81.
What are the inequality symbols?The four inequality symbols, along with their meaning, are presented as follows:
> x: greater than x.< x: less than x.≥ x: at least x.≤ at most x.The inequality is given as follows:
5v/9 ≤ 45.
v ≤ 45 x 9/5
v ≤ 9 x 9
v ≤ 81.
Hence the solution is composed by the numbers to the left of 81, with a closed interval at x = 81.
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raina bulit a rectangular fence around her pigpen that had a length of 325 feet and a width of 185 feet. what is the perimeter of raina's pigpen?
The perimeter of Raina's pigpen is 1020 feet.
What is Perimeter?Perimeter is the total distance around the edge of a two-dimensional shape. It is the sum of the lengths of all sides of the shape. Perimeter is typically measured in units such as inches, feet, meters, or centimeters, depending on the system of measurement being used.
To find the perimeter of the rectangular pigpen, we need to add up the lengths of all four sides. The formula for the perimeter of a rectangle is:
perimeter = 2 * length + 2 * width
Plugging in the values we know, we get:
perimeter = 2 * 325 + 2 * 185
perimeter = 650 + 370
perimeter = 1020
Therefore, the perimeter of Raina's pigpen is 1020 feet.
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Solve the equation in exponential form Y^x = 65 / 177 A. Log 65/177 X= y B. log x 65/177 = y C. Log 65/177 y = x D. Log y 65/177 = X
Therefore, the correct answer is C. Log 65/177 y = x.
The correct answer is C. Log 65/177 y = x.
To solve the equation in exponential form, we need to use the properties of logarithms. The equation Y^x = 65 / 177 can be rewritten in logarithmic form as Log Y (65/177) = x. Using the property of logarithms, Log a^b = b Log a, we can rewrite the equation as Log (65/177) Y = x. This is the same as option C, Log 65/177 y = x.
Therefore, the correct answer is C. Log 65/177 y = x.
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Which inequality is true when the value of x is -3?
-x+6.5 < 1
-x+6.5 < -1
x + 6.5 < -1
-x+6.5 > 1
Answer:
-x + 6.5 > 1 Is true.
Step-by-step explanation:
The explaination is given in the Picture.
Cindy bought 7/8 yard of ribbon jacob bought 4/5 the length as cindy how much ribbon did jacob buy
If Cindy bought 7/8 yards of ribbon, then the length of Ribbon that Jacob bought is 7/10 yard.
The length of ribbon which Cindy bought is = 7/8 yard;
Jacob bought 4/5 the length as Cindy,
Which means that he bought, (4/5) × (7/8) yards of ribbon,
On multiplying these two fractions,
We get,
⇒ (4/5) × (7/8) = (4×7)/(5×8) = 28/40;
On simplifying this fraction, we divide both the numerator and denominator by their greatest common factor, which is 4,
We get,
⇒ 28/40 = 7/10,
Therefore, Jacob bought 7/10 yard of ribbon.
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Magnus needed to put 6 gallons 3quarts of gas into his boat on Monday and twice as much on Saturday if he had 19 gallon jug of gas available did he have enough gas for both days.
Therefore , the solution of the given problem of unitary method comes out to be he only had a 19 gallon jug of petroleum, which was insufficient for both days.
Describe the unitary method.To finish the job using the unitary method, multiply the subsets measures taken from this microsecond section by two. In a nutshell, when a wanted thing is present, the characterized by a variable group but also colour groups are both eliminated from the unit technique. For instance, 40 changeable-price pencils would cost Inr ($1.01). It's conceivable that one nation will have complete control over the strategy used to achieve this. Almost all living things have a unique trait.
Here,
Magnus had to fill up his skiff with 6 gallons and 3 quarts of gas on Monday. We can observe that 1 quart is equivalent to 0.25 gallons to express this in decimal form:
=> 6 gallons 3 quarts = 6 + 3/4 = 6.75 gallons
Magnus used 6.75 litres of fuel on Monday as a result.
He required twice as much petrol on Saturday as he did on Monday:
=> 13.5 gallons from
=> 2 (6.75" gallons).
So on Saturday, he consumed 13.5 litres of fuel.
Overall, he employed:
=> 6.75 gallons + 13.5 gallons = 20.25 gallons
He only had a 19 gallon jug of petroleum, which was insufficient for both days.
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the data is given for 62 students in certain class regarding their mathematics marks out of 100.take the classes 0-10,10-20..and prepare frequency distribution table and cumulative frequency table more than or equal to type 55,60,81,90,45,65,45,52,30,85,20,10,75,95,09,20,25,39,45,50,78,70,46,64,42,58,31,82,27,11,78,97,07,22,27,36,35,40,75,80,47,69,48,59,32,83,23,17,77,45,05,23,37,38,35,25,46,57,68,45,47,49.from the prepared table answer the following question 1.
The frequency and cumulative frequency distribution tables for the given data are below in the solution part.
What is the cumulative frequency of the data?Cumulative frequency is used to calculate the number of observations in a data collection that is above (or below) a specific value.
The data is provided for 62 students in a certain class in terms of their maths marks out of 100.
55, 60, 81, 90, 45, 65, 45, 52, 30, 85, 20, 10, 75, 95, 09, 20, 25, 39, 45, 50, 78, 70, 46, 64, 42, 58, 31, 82, 27, 11, 78, 97, 07, 22, 2 36, 35, 40, 75, 80, 47, 69, 48, 59, 32, 83, 23, 17, 77, 45, 05, 23, 37, 38, 35, 25, 46, 57, 68, 45, 47, 49.
The frequency distribution table for the given data is as follows:
Class Frequency
(Marks obtained) (No. of students)
0 - 10 4
10 - 20 3
20 - 30 8
30 - 40 9
40 - 50 13
50 - 60 6
60 - 70 5
70 - 80 6
80 - 90 5
90 - 100 3
N = 62
The cumulative frequency table more than or equal to the type for the given data is as follows:
Class Frequency Cumulative frequency
(Marks obtained) (No. of students)
0 - 10 4 62
10 - 20 3 58
20 - 30 8 55
30 - 40 9 47
40 - 50 13 38
50 - 60 6 25
60 - 70 5 19
70 - 80 6 14
80 - 90 5 8
90 - 100 3 3
N = 62
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