The statement "If dy/dx is undefined for a given value of x, then the line tangent to the curve y = f(x) at that value does not exist" is false.
If the derivative dy/dx is undefined at a given value of x, it means that the slope of the tangent line is undefined at that point.
However, the tangent line can still exist.
For example, consider the curve y = |x| at x = 0.
The derivative dy/dx is undefined at x = 0 since the slope changes abruptly at that point. However, we can still draw a tangent line at x = 0, which is the y-axis itself.
Therefore, even if the derivative is undefined, it does not necessarily mean that the tangent line does not exist.
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The quastion is on graph theory, matching.
Let A and B each be sets of N labeled vertices, and consider bipartite graphs between A and B.
Consider taking |E| =aN, i.e., the total number of edges is proportional to the number of vertices. This is a relatively sparse number of edges, given the total number of edges that can exist between A and B.
6) Show that taking |E| = 3/N, the expected number of matchings goes to 0 as N › [infinity]. (5 points)
7) Show that taking |E| = 4.V, the expected number of matchings goes to infinity as N › [infinity]. (5 points)
The expected number of matchings goes to infinity as N › [infinity].
Matching in Graph Theory:A matching in Graph Theory is a set of edges of a graph where no two edges share a common vertex. In other words, a matching is a set of independent edges of a graph. A perfect matching in a Graph Theory is a matching of size equal to half the number of vertices in a graph.The expected number of matchings goes to 0 as N › [infinity]:The expected number of matchings goes to zero as N › [infinity] when |E| = 3/N. It is because 3/N is a relatively dense number of edges that are independent of the number of vertices that can exist between A and B. The expected number of matchings is thus very small in comparison to the total number of matchings possible as N › [infinity].The expected number of matchings goes to infinity as N › [infinity]:The expected number of matchings goes to infinity as N › [infinity] when |E| = 4.V. It is because 4.V is a relatively large number of edges that are independent of the number of vertices that can exist between A and B. The expected number of matchings is thus very large in comparison to the total number of matchings possible as N › [infinity]. Hence the expected number of matchings goes to infinity as N › [infinity].
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1. Lukas deposited $3000 into a
savings account that earns
3.7% interest compounded
annually. What is the total
value of the account after 5
years?
The width of a rectangular frame is 6 in. shorter than its length. The area of the frame is 216 in?
What is the frame's length?
Answer:
18 in
Step-by-step explanation:
len = y
width= y - 6
the area of rectangle is len x width
(Y) x (Y-6) = 216
Y^2 - 6Y = 216, Y^2 - 6y -216 = 0
y = (36 /2) or (-24 /2)
len couldn't be negative so 18
Can someone help me? Ill give brainliest :)
Fill in the blank.
Find the inverse Laplace transform of
a) F(s)= 10/s(s+2)(s+3)²
b) F(s)= s/s²+4s+5
c) F(s)=e^-3s s/(s-2)^2 +81
a) The solution to the given problem isL(F) = f(t) = 0 + (-(10 + 7C)/6)[tex]e^{-2t}[/tex]) + C[tex]e^{-3t}[/tex]+ D[tex]e^{-3t}[/tex]
b) The solution to the given problem isL(F) = [tex]e^{-2t}[/tex] [sin t + cos t](c)
c) The solution to the given problem is L(F) = 1/9 [[tex]e^{2t}[/tex] sin 9t - 3[tex]e^{2t}[/tex]) cos 9t]
(a)The inverse Laplace transform of F(s) = 10/s(s + 2)(s + 3)² can be found as follows:
L(F) = L{10/[s(s + 2)(s + 3)²]}
= 10 ∫∞₀[tex]e^{-st}[/tex]) /[s(s + 2)(s + 3)²] dt
L{F} = L⁻¹{10/[s(s + 2)(s + 3)²]}
By using partial fractions, we can simplify the equation and get it in a form that can be integrated easily.
L(F) = 10 ∫∞₀ {1/s - 2/(s + 2) + 3/(s + 3) - 2/(s + 3)² + 1/(s + 2)(s + 3)} [tex]e^{-st}[/tex]dt
L{F} = L⁻¹{1/s} - 2L⁻¹{1/(s + 2)} + 3L⁻¹{1/(s + 3)} - 2L⁻¹{d/ds[1/(s + 3)]} + L⁻¹{1/(s + 2)}
As the inverse Laplace transform of L{F} is given by L(F)
= L⁻¹{1/s} - 2L⁻¹{1/(s + 2)} + 3L⁻¹{1/(s + 3)} - 2L⁻¹{d/ds[1/(s + 3)]} + L⁻¹{1/(s + 2)}
Thus, the solution to the given problem isL(F) = f(t) = 0 + (-(10 + 7C)/6)[tex]e^{-2t}[/tex]) + C[tex]e^{-3t}[/tex]+ D[tex]e^{-3t}[/tex]
(b)
The inverse Laplace transform of F(s) = s/[s² + 4s + 5] can be found as follows:
L(F) = L{s/[s² + 4s + 5]}
= ∫∞₀ s e^(–st) / (s² + 4s + 5) dt
L{F} = L⁻¹{s/[s² + 4s + 5]}
By using partial fractions, we can simplify the equation and get it in a form that can be integrated easily. L(F) = ∫∞₀ [s/(s² + 4s + 5)] [tex]e^{-st}[/tex]) dt
L{F} = L⁻¹{s/(s² + 4s + 5)}
The solution to the given problem isL(F) = [tex]e^{-2t}[/tex] [sin t + cos t](c)
c) The inverse Laplace transform of F(s) = ([tex]e^{-3s}[/tex]) s/[(s - 2)² + 81] can be found as follows:
L(F) = L{([tex]e^{-3s}[/tex]) s/[(s - 2)² + 81]}= ∫∞₀ ([tex]e^{-st}[/tex]) s/[(s - 2)² + 81] dt
L{F} = L⁻¹{([tex]e^{-3s}[/tex])) s/[(s - 2)² + 81]}
So, The solution to the given problem is L(F) = 1/9 [([tex]e^{2t}[/tex]) sin 9t - 3([tex]e^{2t}[/tex]) cos 9t]
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pls help asap will give brainliest
Answer:
148 feet squared
Step-by-step explanation:
Hope it's correct!<D
A = 2 (wl+hl+hw) = 2 x (4x6+5x6+5x4) = 148
What is the expanded form of 1,693,222,527? A. 1,000,000,000 + 600,000,000 + 90,000,000 + 3,000,000 + 220,000 + 20,000 + 2,000 + 500 + 20 + 7 B. 1,000,000,000 + 600,000,000 + 90,000,000 + 3,000,000 + 200,000 + 20,000 + 2,000 + 500 + 20 + 7 C. 1,000,000,000 + 600,000,000 + 9,000,000 + 3,000,000 + 200,000 + 20,000 + 2,000 + 500 + 20 + 7 D. 1,000,000,000 + 600,000,000 + 90,000,000 + 3,000,000 + 200,000 + 20,000 + 2,000 + 200 + 50 + 7
Answer:
A.
Step-by-step explanation:
Answer:
A. 4,000,000 + 600,000 + 10,000 + 2,000 + 200 + 50 + 8 + 9
Step-by-step explanation:
Which of the following possibilities will form a triangle?
Question 4 options:
1)
Side = 15 cm, side = 6 cm, side = 8 cm
2)
Side = 15 cm, side = 6 cm, side = 9 cm
3)
Side = 16 cm, side = 9 cm, side = 6 cm
4)
Side = 16 cm, side = 9 cm, side = 8 cm
Answer:
Option 4
Step-by-step explanation:
The smaller sides must add up to be greater than the largest side so:
1) 6 + 8 < 15
1) No
2) 6 + 9 = 15
2) No
3) 9 + 6 < 16
3) No
4) 9 + 8 > 16
4) Yes
How would I find the arc of WTV
To find the arc of circle WTV, you need the arc length or central angle. Use formulas: Arc Length = (Arc Angle / 360) × (2πr) or Arc Length = (Central Angle / 360) × (2πr).
To find the arc of a circle, WTV, you would need to know either the length of the arc or the measure of the central angle subtended by the arc. If you have the length of the arc, you can use the formula:
Arc Length = (Arc Angle / 360 degrees) × (2πr),
where r is the radius of the circle. Rearranging the formula, you can solve for the Arc Angle:
Arc Angle = (Arc Length / (2πr)) × 360 degrees.
If you know the measure of the central angle, you can calculate the arc length using a similar formula:
Arc Length = (Central Angle / 360 degrees) × (2πr).
To find the radius, you would need additional information such as the diameter or circumference of the circle. Once you have the radius, you can substitute the values into the appropriate formula to find either the arc length or the central angle of the circle.
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Katie is making bread.
She’s needs 6/3 cups of flour to make one whole loaf of bread.
She has 2/3 cup of flour.
Katie can make less than one whole loaf of bread or more than or exactly one loaf
Danny is in a 90 m high watchtower. Lily and Bryan are out searching for clues in regards to a route taken by an escaped prisoner. Lily radios to Danny that she has found some evidence and estimates that she is 350 m from the base of the watchtower. Danny radios this information to Bryan, who estimates that from his location, the angle of elevation to the top of the watchtower is 20°. Danny estimates that the angle from Bryan to the base of the watchtower to Lily is 85°.
a) To the nearest meter, how far is Bryan from the base of the watchtower?
b) To the nearest meter, how apart are Bryan and Lily?
a) Bryan is 1,168 meters away from the base of the watchtower
b) The nearest meter, Bryan and Lily are 315
a) To the nearest meter, Bryan is 1,168 meters away from the base of the watchtower.
Let AB be the watchtower. From B, the angle of elevation to the top of the tower is 20°.
We have to find BC.
BC/AB = tan 20°
BC = AB tan 20°
BC = 90 tan 20°
BC = 32.3
Therefore, BC = 32 meters
Now we have to find AC. AC is the distance between the foot of the watchtower and Bryan's position.
To do that, let BD = h be the height of the tower and AD = x be the distance between A and D.
From the information given, we know that tan 85° = h/x.
Rearranging the formula, x = h/tan 85°
x = 90/tan 85°
x = 418.55 meters
Therefore, AC = x + BC
AC = 418.55 + 32.3
AC = 450.85 meters
So, to the nearest meter, Bryan is 1,168 meters away from the base of the watchtower.
b) To the nearest meter, Bryan and Lily are 315 meters apart.
Let E be the position of Lily and AD be the distance from the foot of the watchtower to the position of Bryan. We have already found that AD = 418.55 meters.
Bryan and Lily are along the same horizontal line.
So, BE is the distance between them. We have to find BE.
From triangle AEB, tan 20° = h/AE.
Rearranging the formula, AE = h/tan 20°
AE = 90/tan 20°
AE = 267.9 meters
From triangle DEC, tan 85° = h/DE.
Rearranging the formula, DE = h/tan 85°
DE = 90/tan 85°
DE = 3,442.97 meters
Therefore, EC = DE - DC = 3,442.97 - 350 = 3,092.97 meters
Now, BE = AC - EC
BE = 450.85 - 3,092.97
BE = -2,642.12 meters (negative value means Bryan is to the left of Lily)So, to the nearest meter,
Bryan and Lily are 315 meters apart. Answer: (a) 1168m and (b) 315m
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Is Game of Thrones based on history or hollywood?
Answer:
It is based on history
Step-by-step explanation:
Answer: the answer is based on history
Step-by-step explanation:
help what is The expression 4x gives the perimeter of a square with a side length of x units. What is the perimeter of a square with a side length of 5/7 units?
Answer:
2 6/7 units
Step-by-step explanation:
You substitute 5/7 in for x
4(5/7) = 20/7 = 2 6/7 units
You can also add 5/7 + 5/7 + 5/7 + 5/7 to check your work
I'm begging you please please help please please ASAP please please help please please ASAP please please help please please ASAP please please help please please ASAP
Answer:
15
Step-by-step explanation:
the height of the person is y = 6 and the distance from the ladder is also 6 = x. To find the angle formed by the ladder we use [tex]arctan(\frac{y}{x})[/tex] which in this case is
[tex]arctan\frac{6}{6} = arctan(1)\\= 45 degrees[/tex]
now we know that the person is 9 feet away from wall and 6 feet away from the ladder so the total x distance is 9+6 = 15 = x
to find y we use tan(45) = [tex]\frac{y}{x}[/tex]
multiply both sides by x = 15 and simplify to get y = 15
The domain of the function f(x) = 8 - 5x is restricted to the positive integers. Which values are elements of the
range?
-2
3
8
13
18
23
Answer:
23
Step-by-step explanation:
please mark me as brainliest
3. Find the values of x, y, and z. *
125°
Answer:
Your question is Incomplete....
A glass company is repairing a window in the shape of an equilateral triangle. If the length of one side of the triangle is 17 inches and the company charges $12 per square inch, the cost of the replacement window will be $___.
Answer:
the cost of the replacement window will be $1501.44.
Step-by-step explanation:
area of an equilateral triangle:
[tex]A = \frac{\sqrt{3}}{4} a^{2}[/tex]
A = (√3)/4 * (17)^2
A = 125.12 in^2
125.12 * 12 = $1501.44
Can you help me please thank you
Write a survey question for which you would expect to collect numerical data.
Answer:
How many siblings do you have?
In the data set #2 {75,80,85,75,85}, what is the mean?
Answer:
80
Step-by-step explanation:
if a, b, and c are n n invertible matrices, does the equation c 1 .a c x /b 1 d i n have a solution, x? if so, find it.
The equation c₁ · a · c · x / b₁ · d · iₙ can have a solution for x if and only if the matrices a, b, and c are compatible and satisfy certain conditions.
Further information about the matrices and their properties is required to determine the specific solution.
To determine if the equation c₁ · a · c · x / b₁ · d · iₙ has a solution, we need to consider the compatibility and properties of the matrices involved.
Let's break down the equation:
c₁: The first column of matrix c.
a: Matrix a.
c: Matrix c.
x: The solution vector.
b₁: The first row of matrix b.
d: Matrix d.
iₙ: The identity matrix of size n.
For the equation to have a solution, the matrices a, b, and c need to be compatible, meaning their dimensions align appropriately for matrix multiplication. Specifically, the number of columns in matrix a should match the number of rows in matrix c.
Additionally, certain conditions or properties of the matrices may be required to ensure a solution exists. Without additional information about the specific matrices a, b, c, and d, it is not possible to determine the solution for x.
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Urgent!!!!
Sean bought three pairs of the same socks and a shoe polish for $1450. If the
polish cost $340, how much is the cost of one pair of soc
Show how you got your answer (4marks)
Answer:
One pair of socks is $370.
Step-by-step explanation:
Sean bought three pairs of the same socks and a shoe polish for $1450. If the
polish cost $340, how much is the cost of one pair of socks.
6x - 340 = 1450
6x = 1450 -340
6x = 1110
2x = 1110 / 3
2x = 370
An efficiency study of the morning shift at a certain factory indicates that an average worker who arrives on the job at 9:00 A.M. will have assembled f(x)=−x3+12x2+15x units x hours later. a) Derive a formula for the rate at which the worker will be assembling units after x hours. r(x)=_______. b) At what rate will the worker be assembling units at 10:00 A.M.? The worker will be assembling ______ units per hour. c) How many units will the worker actually assemble between 10:00 A.M. and 11:00 A.M. ? The worker will assemble _________ units.
A)the required formula is r(x) = -3x² + 24x + 15.B)the worker will be assembling 36 units per hour at 10:00 A.M.C)the worker will assemble 70 units between 10:00 A.M. and 11:00 A.M.
a) Derive a formula for the rate at which the worker will be assembling units after x hours. The worker assembles f(x)= −x³ + 12x² + 15x units in x hours.
To determine the formula for the rate at which the worker will be assembling units after x hours, we can differentiate the given function with respect to time t.
We can write this function as:f(x) = -x³ + 12x² + 15xf'(x) = -3x² + 24x + 15
On differentiating the given function, we get the rate at which the worker will be assembling units after x hours is:r(x) = -3x² + 24x + 15
Therefore, the required formula is r(x) = -3x² + 24x + 15.
b)The worker arrives at 9:00 A.M. and we want to determine the rate at which the worker will be assembling units at 10:00 A.M, which means the worker will be assembling units after 1 hour.
We can use the formula:r(x) = -3x² + 24x + 15
To find the answer:r(1) = -3(1)² + 24(1) + 15r(1) = -3 + 24 + 15r(1) = 36 units per hour
Therefore, the worker will be assembling 36 units per hour at 10:00 A.M.
c)To find the number of units assembled by the worker between 10:00 A.M. and 11:00 A.M., we need to integrate the function r(x) = -3x² + 24x + 15 with limits 1 and 2.
We can use the formula:Integral of r(x)dx = f(x)
Using the formula, we get:f(2) - f(1) = Integral of r(x)dx between 1 and 2f(x) = -x³ + 12x² + 15x
Substituting the limits, we get:
f(2) - f(1) = [-2³ + 12(2²) + 15(2)] - [-1³ + 12(1²) + 15(1)]f(2) - f(1) = [−8 + 48 + 30] - [−1 + 12 + 15]f(2) - f(1) = 70
Therefore, the worker will assemble 70 units between 10:00 A.M. and 11:00 A.M.
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T
3/6
35. A soccer ball has a diameter of 9 inches. What is the volume to the nearest tenth? (TEKS
8.7A-R)
A 381.7 in
A
B
С
D
E
B 190.9 in
C 268.1 in
D 321.6 In
Answer:
I NEED HELP ON THE SAME QUESTION
Step-by-step explanation:
NO ONE INDERSTANDS JT FOR SOME REASON AND NEITHER DO I
Write a cosine function that has a midline of y=5, an amplitude of 3 and a period of 4/π
The equation for the cosine function is given as;cos(x) = 3 cos(π/2 x) + 5
A cosine function is defined as follows;cos(x) = a cos(b(x - h)) + kwhere a is the amplitude, period is 2π/b, and k is the midline. The amplitude, period, and midline of a cosine function can be used to find its equation.In this case,
we have a cosine function that has a midline of y=5, an amplitude of 3 and a period of 4/π. Thus, the amplitude of the function is given as 3, the midline is given as 5, and the period is 4/π.
The amplitude is the vertical distance from the midline to the highest point on the curve and also to the lowest point on the curve. The period is the distance over which the cosine function completes one full oscillation, or cycle.
In this case, we have a period of 4/π, so we can find b by the formula b = 2π/period = 2π/(4/π) = π/2.To find the phase shift, h, we use the formula h = x₀ - (π/b), where x₀ is the x-coordinate of the maximum or minimum value of the cosine function.
Since the midline is y=5, the maximum value of the cosine function occurs when y=8 and the minimum value occurs when y=2. The maximum and minimum values occur when cos(b(x - h)) = 1 and cos(b(x - h)) = -1, respectively.
Therefore, we have;8 = 5 + 3, cos(b(x - h)) = 1when x - h = 0, so x₀ = h2 = 5 - 3, cos(b(x - h)) = -1when x - h = π/b
Thus, h = 0 for the maximum value, and h = π/2 for the minimum value. We choose the value of h that corresponds to the maximum value of the cosine function, so h = 0.
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A population of values has a normal distribution with u = 42.3 and o = 44.6. You intend to draw a random sample of size n = 20. Find the probability that a single randomly selected value is greater than 19.4. P(X> 19.4) = Find the probability that a sample of size n = 20 is randomly selected with a mean greater than 19.4. P(M> 19.4) =
Previous question
(a) The probability that a single randomly selected value is greater than 19.4. P(X> 19.4) = 0.6965.
(b) The probability that a sample of size n = 20 is randomly selected with a mean greater than 19.4. P(M> 19.4) = 0.9883.
To solve these probability questions, we can utilize the properties of the standard normal distribution since we know the mean and standard deviation of the population.
(a) Find the probability that a single randomly selected value is greater than 19.4.
To calculate this probability, we need to standardize the value 19.4 using the formula: z = (x - μ) / σ, where x is the value, μ is the mean, and σ is the standard deviation.
z = (19.4 - 42.3) / 44.6 = -22.9 / 44.6 ≈ -0.51498
Using the standard normal distribution table or a calculator, we can find the corresponding probability for z > -0.51498, which is approximately 0.6965.
Therefore, P(X > 19.4) ≈ 0.6965.
(b) Find the probability that a sample of size n = 20 is randomly selected with a mean greater than 19.4.
For this question, we need to consider the sampling distribution of the sample mean. The mean of the sampling distribution is equal to the population mean (μ = 42.3), and the standard deviation of the sampling distribution, also known as the standard error, is equal to σ / √n, where σ is the population standard deviation and n is the sample size.
Standard error = 44.6 / √20 ≈ 9.9766
To find the probability that the sample mean is greater than 19.4, we need to standardize the sample mean using the formula: z = (x - μ) / (σ / √n), where x is the value (19.4 in this case), μ is the mean, σ is the standard deviation, and n is the sample size.
z = (19.4 - 42.3) / (44.6 / √20) ≈ -22.9 / 9.9766 ≈ -2.2972
Using the standard normal distribution table or a calculator, we can find the corresponding probability for z > -2.2972, which is approximately 0.9883.
Therefore, P(M > 19.4) ≈ 0.9883.
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what are the zeros of the polynomial function? f(x)=x2 9x−70 enter your answers in the boxes.
The zeros of the polynomial function f(x) = x^2 - 9x - 70 can be found by factoring or using the quadratic formula. The zeros are -5 and 14.
To find the zeros of the polynomial function f(x) = x^2 - 9x - 70, we can factor the expression or use the quadratic formula. Let's factor the expression:
f(x) = x^2 - 9x - 70
= (x - 14)(x + 5)
Setting each factor equal to zero, we get:
x - 14 = 0 --> x = 14
x + 5 = 0 --> x = -5
Therefore, the zeros of the polynomial function are x = -5 and x = 14. These values represent the x-coordinates where the function intersects the x-axis, indicating the points where the function equals zero.
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Find the length of the third side if necessary write in simplest radical form
Answer:
hi
Step-by-step explanation:
a cone and a cylinder have equal radii,r, and equal altitudes, h. If the slant height is l, then what is the ratio of the lateral area of the cone to the cylinder?
The ratio of the lateral area of the cone to the cylinder will be √(h²+r²)/2h.
What are a cone and a cylinder?The solid formed by two congruent closed curves in parallel planes along with the surface created by line segments connecting the corresponding points of the two curves is known as a cylinder.
A cylinder with a circular base is known as a circular cylinder. Based on the form of its base, a cone is given a name.
It is given that a cone and a cylinder have equal radii,r, and equal altitudes, h. The ratio of the lateral surface area of the cone to the cylinder will be calculated as below:-
The lateral area of the cone = πr√(h²+r²)
The lateral area of the cylinder = 2πrh
The ratio will be calculated as:-
R = πr√(h²+r²) / 2πrh
R = √(h²+r²) / 2h
Therefore, the ratio of the lateral area of the cone to the cylinder will be √(h²+r²)/2h.
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1st statement: In an experimental study we can examine the association between the independent and dependent variable 2nd statement: In an experimental study we can examine the temporal relationship between the independent and dependent variable O Both statements are true 1st statement is false, while the 2nd statement is true o 1st statement is true, while the 2nd statement is false O Both statements are false
The correct option to the statements "1st statement: In an experimental study we can examine the association between the independent and dependent variable, and 2nd statement: In an experimental study we can examine the temporal relationship between the independent and dependent variable" is: a. Both statements are true.
An experimental study can be used to determine the relationship between two variables. It is also used to determine whether there is a cause-and-effect connection between two variables.
In an experimental study, two groups are compared. One group receives the independent variable, and the other group receives the dependent variable.
In an experimental study, the following two statements are true:
In an experimental study, we can examine the association between the independent and dependent variable. It is the correlation or connection between the two variables we are interested in exploring
In an experimental study, we can examine the temporal relationship between the independent and dependent variable. It refers to the timing or sequence of events that occurs between the two variables in question.
The study must include a time element that describes the order in which the dependent and independent variables were introduced to the subjects.
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