Which of these variables is your dependent variable?
How many jumps I can do
Which one is the independent variable?
How long I am jumping (2 minutes)
Write a sentence that describes the relationship between the dependent variable and the independent variable. (Hint: Ratio language can help. )
Answers
In this scenario, the dependent variable is "how many jumps I can do," while the independent variable is "how long I am jumping (2 minutes)."
The relationship between these variables can be described as follows: The number of jumps completed depends on the duration of time spent jumping, with a specific focus on a 2-minute interval.
When we say the dependent variable is "how many jumps I can do," it means that the number of jumps completed is determined by or depends on the independent variable, which is the duration of time spent jumping.
This suggests that as the duration of time increases or decreases, it will likely have an impact on the number of jumps performed.
In this particular case, you have specified a 2-minute interval as the focus. It suggests that you are examining the relationship between the number of jumps completed and the specific duration of 2 minutes.
This implies that you are interested in understanding how the number of jumps varies within this fixed time frame.
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Related Questions
determine the equation of a horizontal line that passes through (4,7)
Answers
Answer:the equation of the horizontal line passing through (4,7) is y=7 . Note − The equation of a vertical line is always of the type x=k and hence the equation of the vertical line passing through (4,7) is x=4 .
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statement: if two noncollinear rays join at a common endpoint, then an angle is created. which geometry term does the statement represent?
Answers
The statement "if two noncollinear rays join at a common endpoint, then an angle is created" represents the geometry term "angle."
In Plane Geometry, a figure which is formed by two rays or lines that shares a common endpoint is called an angle.
The two rays are called the sides of an angle, and the common endpoint is called the vertex.
The angle that lies in the plane does not have to be in the Euclidean space.
An angle is formed when two non-collinear rays join at a common endpoint.
This endpoint is called the vertex of the angle.
The two rays are referred to as the arms of the angle.
Angles can be classified according to their degree measurement.
An acute angle measures less than 90 degrees, a right angle measures exactly 90 degrees, and an obtuse angle
measures between 90 and 180 degrees.
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What is the area of a hexagon with an apothem of 24 m?
Answers
Answer:
Area of Hexagon = 1,995 m² (Approx.)
Step-by-step explanation:
Given:
Length of apothem = 24 m
Number of total sides = 6
Find:
Area of Hexagon
Computation:
Side = a[2tan(180/n)]
Side = 24[2tan(180/6)]
Side = 24[2tan(30)]
Side = 27.71 m (Approx.)
Area of Hexagon = [3√3a²]/2
Area of Hexagon = [3(1.732)(27.71)²]/2
Area of Hexagon = [3(1.732)(767.8441)]/2
Area of Hexagon = 3989.71794 / 2
Area of Hexagon = 1994.8589
Area of Hexagon = 1,995 m² (Approx.)
According to the yearly compound interest, a sum of money amounts to Rs. 6050 in 2 year and Rs. 6655 in 3 years. What was the sum? Ans: Rs. 5000
Answers
The principal sum of the given compound interest is Rs 5000.
What is principal amount?The total amount of money borrowed (or invested), not including any interest or dividends, also called sum.
Given that, a sum of money amounts to Rs. 6050 in 2 year and Rs. 6655 in 3 years. we are asked to find the principal amount or sum,
CI = P(1+r/100)ⁿ
P = principal amount, CI = compound interest, r = rate, n = time
Therefore,
CI = 6050(1+r/100)²....(i)
CI = 6655(1+r/100)³....(ii)
Diving eq(ii) by eq(i)
6655 / 6050 = (1+r/100)
1+r/100 = 1.1
r/100 = 1.1-1
r/100 = 0.1
r = 10%
Put r = 10% in eq(i)
6050 = p(1.1)²
p = 5000
Hence, the principal sum of the given compound interest is Rs 5000.
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X/1.2 - 18 - 2 Please help right answer gets brain liest and 15 points.
Answers
Answer:
= x-24
Step-by-step explanation:
\( \frac{x}{1.2} - 18 - 2 \\ = 1.2 \times \frac{x}{1.2} - 1.2 \times 18 - 1.2 \times 2 \\ = x - 21.6 - 2.4 \\ = x - 24\)
A light bulb consumes 960 watt-hours per day. How long does it take to consume 5520 watt-hours?
Answers
The light bulb consumes
\(960\text{watt}-\text{hour in one day}\)To calculate how long 5520 watt-hours would last, we will use the formula below
\(\text{time}=\frac{Number\text{ of watts hour to be used}}{\text{Number of watts hour per day}}\)\(\begin{gathered} \text{Time}=\frac{5520}{960} \\ \text{Time}=5\frac{3}{4}days \end{gathered}\)Which can be converted as
\(\begin{gathered} 5\frac{3}{4}days=5+\frac{3}{4}\times24 \\ 5\frac{3}{4}days=5\text{days 18 hours} \end{gathered}\)Hence,
It will take 5 days and 18 hours to consume 5,520 watt-hours
A person weighing 150 pounds burns about 320 calories per hour walking at a moderate rate. Suppose the same person burns about 1500 calories per day through basic activities. The total calories y burned by that person can be represented by the equation y=320x+1500, where x represents the number of hours spent walking. What is the slope and y- intercept
Answers
The slope of the equation and y- intercept is 320 and 1500 respectively.
What is the slope?The slope is the ratio of the vertical changes to the horizontal changes between two points of the line.
Given that the total calories y burned by that person can be represented by the equation y=320x+1500, where x represents the number of hours spent walking.
To find the slope and y- intercept.
y=320x+1500
Therefore, the slope of the line is;
m =320
Then the y- intercept is 1500
Hence, The slope of the equation and y- intercept is 320 and 1500 respectively.
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a = {prime numbers less than 20} b = {odd numbers less than 15} list the outcomes of a b and explain? list the outcomes of a b and explain?
Answers
The outcomes of A ∪ B are {1, 2, 3, 5, 7, 9, 11, 13, 17, 19} and the outcomes of A ∩ B are {3, 5, 7, 11, 13}.
The set A represents the prime numbers less than 20, while the set B represents the odd numbers less than 15.
Listing the outcomes of A ∪ B (union of A and B) will provide all the elements present in both sets without duplication.
On the other hand, listing the outcomes of A ∩ B (intersection of A and B) will give the common elements between the two sets.
Set A: {2, 3, 5, 7, 11, 13, 17, 19}
Set B: {1, 3, 5, 7, 9, 11, 13}
To find the outcomes of A ∪ B, we need to combine all the elements from sets A and B without duplication.
Taking the union of A and B gives us the following elements: {1, 2, 3, 5, 7, 9, 11, 13, 17, 19}.
Therefore, the outcomes of A ∪ B are {1, 2, 3, 5, 7, 9, 11, 13, 17, 19}.
These numbers represent all the prime numbers less than 20 and all the odd numbers less than 15, combined without duplication.
To find the outcomes of A ∩ B, we need to identify the elements that are present in both sets A and B.
In this case, the common elements between A and B are {3, 5, 7, 11, 13}.
Therefore, the outcomes of A ∩ B are {3, 5, 7, 11, 13}.
These numbers represent the prime numbers less than 20 that are also odd numbers less than 15.
The intersection of A and B shows the elements that satisfy both conditions simultaneously.
By finding the outcomes of A ∪ B and A ∩ B, we have identified the elements that belong to both sets without duplication and the elements that are common between the sets, respectively.
This helps in understanding the combined elements and the overlapping elements between sets A and B.
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The complete question is:
A = {prime numbers less than 20} B = {odd numbers less than 15}
List the outcomes of A ∪ B and explain?
List the outcomes of A ∩ B and explain?
The circle has a diameter of 0.2 m.
The height of the square is a fifth of the diameter
of the circle.
Calculate the shaded area in cm.
Give your answer to 2 decimal places.
Answers
Rounding to 2 decimal places, the shaded area is 234 cm².
What is the radius of circle?
The radius of a circle is the distance from the center of the circle to any point on the circumference of the circle. It is half of the diameter of the circle.
The diameter of the circle is 0.2 meters, which means the radius of the circle is 0.2 / 2 = 0.1 meters.
The height of the square is a fifth of the diameter of the circle, so the height of the square is 0.2 / 5 = 0.04 meters.
To find the shaded area in cm, we need to find the area of the circle and subtract the area of the square. The area of the circle is given by the formula πr², where r is the radius of the circle. The area of the square is simply the height multiplied by the width, which is equal to the diameter of the circle.
So, the area of the circle is π * 0.1² = 0.0314 square meters. The area of the square is 0.2 * 0.04 = 0.008 square meters. The shaded area is the difference between these two, or 0.0314 - 0.008 = 0.0234 square meters.
To convert the area to cm², we need to multiply by 10⁴. The shaded area in cm² is 0.0234 * 10⁴ = 234 cm².
Rounding to 2 decimal places, the shaded area is 234 cm^2.
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Simple and easy question
please help
Answers
Answer:
Volume = πr²h
= 3.14 * 5² * 4
= 314 cubic yards
Answer:
\(314 yd^3\)
Step-by-step explanation:
Hey there!
Volume = π r^2 h
Plug in,
(3.14)(5^2)(4)
5•5 = 25
25 • 4 = 100
3.14 • 100
= 314
Hope this helps :)
Determine if the columns of the matrix A span R2. A = 2 1 0 1 Arlo -3 -1 )-The columns span R2. -The columns do not span R2.
Answers
The columns of the matrix A span R2.
In order to determine if the columns of the matrix A span R2, we need to check if the columns of A can be used to generate all possible linear combinations of the form a1v1 + a2v2, where a1 and a2 are scalars and v1 and v2 are the columns of A.
A = [2 1]
[0 1]
[-3 -1]
The columns of A are [2, 0, -3] and [1, 1, -1]. To check if these columns span R2, we need to see if we can create any vector in R2 by taking linear combinations of the columns. We can see that by taking linear combinations of the columns, we can create any vector of the form (a, b) in R2.
For example, by taking a = 2, b = 1, we can generate the vector (2, 1) by taking
a[2, 0, -3] + b[1, 1]
And by taking a = 3, b = -1, we can generate the vector (3, -1) by taking
a[2,0,-3] + b[1,1,-1].
So the answer would be: The columns of the matrix A span R2.
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Suppose a researcher asks 800 participants to state their preference among 5 flavors of ice cream. In this study, the expected frequency (E) value would be:
a. 100
b. 150
c. 120
d. 160
Answers
Using the binomial distribution, it is found that the expected frequency would be of:
d. 160
Binomial probability distribution
Probability of exactly x successes on n repeated trials, with p probability, and has expected value given by:
\(E(X) = np\)
In this problem:
There are 800 participants, hence, \(n = 800\).Each of the flavors is equally as likely to be chosen, hence, \(p = \frac{1}{5} = 0.2\)Then, the expected frequency is:
\(E(X) = np = 800(0.2) = 160\)
And the correct option is d.
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figure: aggregate supply reference: ref 12-5 (figure: aggregate supply) if the economy is at point e, which of the following describes the likely adjustment process? group of answer choices nominal wages increase, and the short-run aggregate supply curve shifts left until actual and potential output are equal. nominal wages increase, and the short-run aggregate supply curve shifts right until potential output is greater than actual output. nominal wages decrease, and the short-run aggregate supply curve shifts right until potential output is less than actual output. nominal wages decrease, and the short-run aggregate supply curve shifts right until actual and potential output are equal.
Answers
If the economy is at point E on the aggregate supply curve, the likely adjustment process would involve nominal wages increasing, and the short-run aggregate supply curve shifting left until actual and potential output are equal.
When the economy is at point E, it indicates that actual output is greater than potential output. In this scenario, there is upward pressure on wages due to the higher demand for labor. As nominal wages increase, the cost of production for firms also increases. This leads to a leftward shift of the short-run aggregate supply (SRAS) curve.
The leftward shift of the SRAS curve means that at any given price level, firms are willing to produce and supply a lower quantity of goods and services. As a result, the economy moves along the aggregate demand (AD) curve toward a new equilibrium where actual output matches potential output. This adjustment process helps to close the output gap and restore equilibrium in the economy. By increasing nominal wages and shifting the SRAS curve to the left, the adjustment process aims to align actual output with potential output and achieve a more balanced economic state.
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The local high school hosted a hockey tournament. Tickets were sold before the tournament and at the door. When reviewing the ticket sales, the director of the tournament realized that there were 80 more tickets purchased before the tournament than at the door. A total of 820 tickets were sold. Which statements about ticket sales are true? Check all that apply. The variable x could represent the total number of tickets sold. The variable x could represent the number of tickets sold before the tournament. The variable y could represent the number of tickets sold at the door. The variable y could represent the total value of tickets sold at the door. The system of equations that could represent this situation is x y = 820. X minus y = 80. The system of equations that could represent this situation is x minus y = 820. X y = 80.
Answers
Answer:
B, and D
Step-by-step explanation:
Answer:
B and D.
Step-by-step explanation:
Bread, gasoline, and ____ are examples of convenience products.(A) cars(B) furniture(C) newspapers(D) large appliances(E) a cruise
Answers
The answer is (C) newspapers. Convenience products are low-cost consumer goods and services that are readily available and easily accessible to consumers.
These products are typically purchased frequently, with minimal effort and little thought or research. Examples of convenience products include bread, gasoline, newspapers, and other everyday items that consumers purchase without much consideration.
Cars, furniture, large appliances, and a cruise are not typically considered convenience products. These are generally higher-cost items that require more thought and research before purchase.
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Answer all the four q
Answers
Answer:
13 is better B
14 is letter B
Step-by-step explanation:
if 5 x 6 = 30 and 4 x 6 = 24 then that's the right answer...you just gotta read it! If you dont understand make sure to ask your teacher for help!
Answer:
13: B
14: B
15: A
16: C
Step-by-step explanation:
Consider a Markov chain with state space S = {1, 2, 3, 4, 5, 6} and transition probability matrix P = [ 0 0.5 0 0.1 0.4 0]
[ 0 1 0 0 0 0 ]
[ 0.3 0 0.2 0.1 0 0.4]
[0 0.7 0 0 0.3 0 ]
[0 0 0 0 1 0]
[0 0 0 0 0 1 ]
(a) Compute Pˣ. (b) If the process starts in state 3, what are the probabilities that it will be absorbed in state 2, state 5, and state 6, respectively?
Answers
a)Pˣ = \(\begin{bmatrix}0.1 & 0.5 & 0.04 & 0.28 & 0.03 & 0.05\\0 & 1 & 0 & 0 & 0 & 0\\0.22 & 0 & 0.33 & 0.17 & 0.1 & 0.19\\0.7 & 0 & 0.43 & 0.3 & 0 & 0.57\\0 & 0 & 0 & 0 & 1 & 0\\0 & 0 & 0 & 0 & 0 & 1\end{bmatrix}\) in matrix form, using eigen-values.
b)state 2 is 0.75; state 5 is 0 and ;state 6 is 0.25.
a)In order to calculate the value of Pˣ, follow the below-given steps:
Step 1: Compute the eigen-values of the matrix P.
Here, we get λ = 1, λ = 0.6, λ = 0.4, λ = 0.1, λ = 0, λ = 0.
Step 2: Compute the eigen-vectors corresponding to each eigenvalue of the matrix P.
Step 3: Compute the diagonal matrix D and the transition matrix T. \(\begin{matrix}1 & 0 & 0 & 0 & 0 & 0\end{matrix}0.6\)
\(\begin{matrix}0.58 & 0.25 & 0.72 & 0 & 0 & 0\end{matrix}0.4.\)
\(\begin{matrix}0.07 & 0 & 0.04 & 0.7 & 0 & 0\end{matrix}0.1.\)
\(\begin{matrix}0.35 & 0.75 & 0.56 & 0 & 1 & 0\end{matrix}0.\)
\(\begin{matrix}0 & 0 & 0 & 0.3 & 0 & 1\end{matrix}\)
Pˣ = T . Dˣ . T⁻¹
We get the following matrix as a result.
Pˣ = \(\begin{bmatrix}0.1 & 0.5 & 0.04 & 0.28 & 0.03 & 0.05\\0 & 1 & 0 & 0 & 0 & 0\\0.22 & 0 & 0.33 & 0.17 & 0.1 & 0.19\\0.7 & 0 & 0.43 & 0.3 & 0 & 0.57\\0 & 0 & 0 & 0 & 1 & 0\\0 & 0 & 0 & 0 & 0 & 1\end{bmatrix}\)
b)If the process starts in state 3,
the probability that it will be absorbed in state 2 is 0.75,
the probability that it will be absorbed in state 5 is 0, and
the probability that it will be absorbed in state 6 is 0.25.
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In the following exercises, write the first five terms of the sequence whose general term is given.
240. \(a_{n}=7 n-5\)
Answers
Answer:
2, 9 , 16 , 23 , 30 ......
Step-by-step explanation:
\(a_n = 7n - 5\)
\(a_1 = 7*1 - 5 = 7-5 = 2\\\\a_2 = 7*2 - 5 = 14 - 5 = 9\\\\a_3 = 7*3 - 5 = 21 - 5 = 16\\\\a_4= 7*4 - 5 = 28 - 5 = 23\\\\a_5= 7*5 - 5 = 35 - 5 = 30\)
The cost of 2 kg of mushrooms and 2.5 kg of turnips is £8.55. The cost of 3 kg of mushrooms and 4 kg of turnips is £13.10. Work out the cost of a) 1 kg of turnips. b) 1 kg of mushrooms.
Answers
(a) The cost of 1 kg of turnips is £71.95, and
(b) The cost of 1 kg of mushrooms is £89.50.
To solve this problem, let's assign variables to the unknowns.
Let the cost of 1 kg of mushrooms be 'm' and the cost of 1 kg of turnips be 't'.
According to the given information:
Equation 1: 2m + 2.5t = 8.55
Equation 2: 3m + 4t = 13.10
We can solve these equations simultaneously to find the values of 'm' and 't'.
To eliminate the decimals, let's multiply both sides of Equation 1 by 10 and Equation 2 by 20:
20m + 25t = 85.50
60m + 80t = 262.00
Now, let's multiply Equation 1 by 12 and subtract Equation 2 multiplied by 5:
240m + 300t - (60m + 80t) = 1026.00 - 1310.00
180m + 220t = -284.00
We have a new equation:
180m + 220t = -284.00 ---(3)
Next, let's multiply Equation 1 by 18 and subtract Equation 2 multiplied by 4:
36m + 45t - (60m + 80t) = 154.35 - 524.00
-24m - 35t = -369.65
We have another new equation:
-24m - 35t = -369.65 ---(4)
Now, we have a system of linear equations with two variables. Let's solve this system by eliminating one variable.
Multiply Equation 3 by 35 and Equation 4 by 220:
6300m + 7700t = -9940.00 ---(5)
-5280m - 7700t = -81323.00 ---(6)
Adding Equations 5 and 6, we eliminate 't':
1020m = -91263.00
m = -91263.00/1020
m = -89.50
Substituting the value of 'm' back into Equation 3:
180(-89.50) + 220t = -284.00
-16110 + 220t = -284.00
220t = -284.00 + 16110
220t = 15826.00
t = 15826.00/220
t = 71.95.
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Determine whether y varies directly with x . If so, find the constant of variation.
x=y/3
Answers
The constant of variation, often denoted as "k," is a value that represents the relationship between two variables in a direct or inverse variation. It indicates how one variable changes in proportion to changes in the other variable.
In a direct variation, the constant of variation represents the ratio of the two variables, while in an inverse variation, it represents the product of the two variables.
To determine if y varies directly with x, we need to check if the equation can be written in the form y = kx, where k is the constant of variation.
Given the equation x = y/3, we can rearrange it to y = 3x.
Comparing this with the form y = kx, we can see that y does vary directly with x, with a constant of variation of k = 3.
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What is the missing number
Answers
Answer:
11/12
Step-by-step explanation:
9/11 x 11/12 = (3 x 3)/11 x 11/(3 x 4) = 3/4
Find the value of x & y
Answers
Step-by-step explanation:
As we know that ,
Angles opposite to equal sides are equal .
Using this theorem ,
=> y + 12 = 3x - 5
Also ,
=> 3x - 5 = 5y - 4
from above two ,
=> y + 12 = 5y - 4
=> 4y = 16
=> y = 16/4
=> y = 4
So that ,
=> 3x - 5 = 4 + 12
=> 4x = 16 + 5
=> x = 21/4
=> x = 5.25
Which values of x and y make RAPT a parallelogram?
Answers
The values of x and y that make RAPT a parallelogram are;
x = 15 and y = 25
How to find the angles of a Parallelogram?Angle T and angle P are supplementary angles by parallel lines. Thus they sum up to 180 degrees and we have;
3x + 10 + 8x + 5 = 180
11x + 15 = 180
11x = 165
x = 15
T = 55°
P = 125°
Likewise R and T are supplementary angles by parallel lines and so we have;
55 + 5y = 180
5y = 180 -55
5y = 125
y = 25
R = 125°
A must be 55° since the angles add up to 360°.
R + A + P + T =
125 + 55 + 125 + 55 = 360°
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Solve the triangle using the law of sines. Show all work and round answers to the nearest tenth.
Answers
The unknown values in the triangle are ;
a = 45.3
angle B = 7°
angle A = 28°
What is sine rule?In a triangle, side “a” divided by the sine of angle A is equal to the side “b” divided by the sine of angle B is equal to the side “c” divided by the sine of angle C.
Therefore,
a/sinA = b/sinB = c/sinC
So, we use the Sine rule to find the values of unknown lengths or angles of the triangle.
b/sinB = c/sinC
7/sinB = 33/sin145
33sinB = 7 sin145
33 sinB = 4.02
sinB = 0.122
B = 7°
angle A = 180-(145+7)
A = 180- 152
A = 28°
a/sinA = c/sinC
a/sin28 = 33/sin145
asin145 = 33sin128
0.574a = 26
a = 26/0.574
a = 45.3
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What is 500 increased by 20% and the is decreased my 20%
Answers
Answer:
120
Step-by-step explanation:
1. What are the 3 conditions for a function to be continuous at xa? 2. the below. Discuss the continuity of function defined by graph 3. Does the functionf(x) = { ***
Answers
The three conditions for a function to be continuous at a point x=a are:
a) The function is defined at x=a.
b) The limit of the function as x approaches a exists.
c) The limit of the function as x approaches a is equal to the value of the function at x=a.
The continuity of a function can be analyzed by observing its graph. However, as the graph is not provided, a specific discussion about its continuity cannot be made without further information. It is necessary to examine the behavior of the function around the point in question and determine if the three conditions for continuity are satisfied.
The function f(x) = { *** is not defined in the question. In order to discuss its continuity, the function needs to be provided or described. Without the specific form of the function, it is impossible to analyze its continuity. Different functions can exhibit different behaviors with respect to continuity, so additional information is required to determine whether or not the function is continuous at a particular point or interval.
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What is the slope of the line that passes through the points below? (Enter your answer as a decimal if necessary.)
Answers
Answer:
5/4 should be your answer or in decimal form 1.25
Step-by-step explanation:
Slope is rise over run
Y2-Y1 divided by X2-X1
5/4
Draw the graphs of the lines below on the same grid to find the coordinates of the point of intersection. y=2x+3 y−1/2x−2
Answers
Answer:
(2, 2)
Step-by-step explanation:
The point of intersection is at (2, 2)
A linear equation is given by:
y = mx + b;
where y, x are variables, m is the slope of the line and b is the y intercept.
Given the line with equations:
y = 3 x − 4 and y = 1/ 2x + 1
Plotting the graphs using geogebra online tool, the point of intersection is at (2, 2)
2) A retailer buys a set of entertainment that is listed at RM X with trade discounts of 15% and 5%. If he sells the set at RM 15000 with a net profit of 20% based on retail and the operating expenses are 10% on cost, find: a) the value of X \{4 marks } b) the gross profit {3 marks } c) the breakeven price {3 marks } d) the maximum markdown that could be given without incurring any loss. \{3 mark
Answers
a)The value of X = RM 15125.
b) The Gross Profit = RM 3000.
c) The Break-even price = RM 13333.33.
d) The Maximum markdown that could be given without incurring any loss = RM -1333.33.
The retailer buys a set of entertainment that is listed at RM X with trade discounts of 15% and 5%.He sells the set at RM 15000 with a net profit of 20% based on retail.
The operating expenses are 10% on cost.a) The value of X. The trade discount is 15% and 5% respectively.
Thus, the net price factor is, 100% - 15% = 85% = 0.85 and 100% - 5% = 95% = 0.95
The retailer's selling price is RM15000. The operating expense is 10% on cost.
Hence, 90% of the cost will be converted into the total expense. 90% = 0.9
The net profit is 20% of the retail price.20% = 0.20
Therefore, the cost of the set is,15000 × (100% - 20%) - 15000 × 80% = RM 12000
Let X be the retail price of the set of entertainment.
Therefore, we have,
X × 0.85 × 0.95 = 12000 ⇒ X = RM 15125
b) The Gross Profit
The gross profit is given by,Gross Profit = Selling price - Cost of goods sold
The cost of goods sold is RM 12000.
Therefore,Gross Profit = RM 15000 - RM 12000 = RM 3000
c) The Break-even price
The Break-even price is given by,Break-even price = Cost price / [1 - (operating expenses / 100%)]
The operating expense is 10% of the cost price. Therefore, 90% of the cost price will be converted into the total expense.
Break-even price = 12000 / [1 - (10/100)] = 12000 / 0.9 = RM 13333.33
d) The Maximum markdown that could be given without incurring any loss
The maximum markdown that could be given without incurring any loss is given by,
Maximum markdown = Cost price - Breakeven price = RM 12000 - RM 13333.33 = RM -1333.33
Therefore, the maximum markdown that could be given without incurring any loss is RM -1333.33. However, it is not possible to sell a product with a negative value.
Therefore, the retailer should not give any markdown.
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how many different subsets of 5 students we can select from a classroom of 20?
Answers
There are 2002 different subsets of 5 students that can be selected from a classroom of 20. To calculate this, you can use the binomial coefficient formula.
The binomial coefficient is equal to nCr, where n is the total number of objects (in this case 20 students) and r is the number of objects you want to select (in this case 5 students).
Using the binomial coefficient, we can calculate that there are 20C5 = 2002 different subsets of 5 students that can be selected from a classroom of 20.
nCr = 20C5
20C5 = 20! / ((20-5)! 5!)
20! = 20 x 19 x 18 x 17 x 16 x 15 x 14 x 13 x 12 x 11 x 10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1
5! = 5 x 4 x 3 x 2 x 1
20C5 = 20 x 19 x 18 x 17 x 16 x 15 x 14 x 13 x 12 x 11 x 10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1 / (5 x 4 x 3 x 2 x 1 x 15 x 14 x 13 x 12 x 11) = 2002
Therefore, there are 2002 different subsets of 5 students that can be selected from a classroom of 20.
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