A) All the first six terms in the pattern are,
⇒ 47, 39, 31, 23, 15, 7
Every number is 8 more than the next number.
B) The 30th term in this pattern is, - 185
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;
A pattern rule for a number pattern is represented by,
⇒ 55 - 8n, where n is the term number.
Now, All the first six terms in the pattern are,
Substitute n = 1;
⇒ 55 - 8n
⇒ 55 - 8 × 1
⇒ 55 - 8
⇒ 47
Substitute n = 2;
⇒ 55 - 8n
⇒ 55 - 8 × 2
⇒ 55 - 16
⇒ 39
Substitute n = 3;
⇒ 55 - 8n
⇒ 55 - 8 × 3
⇒ 55 - 24
⇒ 31
Substitute n = 4;
⇒ 55 - 8n
⇒ 55 - 8 × 4
⇒ 55 - 32
⇒ 23
Substitute n = 5;
⇒ 55 - 8n
⇒ 55 - 8 × 5
⇒ 55 - 40
⇒ 15
Substitute n = 6;
⇒ 55 - 8n
⇒ 55 - 8 × 6
⇒ 55 - 48
⇒ 7
B) The 30th term in this pattern is,
Substitute n = 30;
⇒ 55 - 8n
⇒ 55 - 8 × 30
⇒ 55 - 240
⇒ - 185
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Find the values of the six trigonometric functions of an angle in standard position if the given point lies on its terminal side
The point being used in the problem is (-1,5)
we need to use the concept of the right triangle formed by the angle and the point in the coordinate plane.
Let's call the angle in standard position θ. The point (-1, 5) lies on the terminal side of θ. We can use the Pythagorean Theorem to find the length of the adjacent side (x) and the opposite side (y) of the right triangle formed by θ and the point.
x = √((-1)^2 + 5^2) = √(1 + 25) = √26
y = 5
The values of the six trigonometric functions of θ can then be found as follows:
sin(θ) = y/r = 5/√26
cos(θ) = x/r = -1/√26
tan(θ) = y/x = 5/(-1) = -5
csc(θ) = 1/sin(θ) = √26/5
sec(θ) = 1/cos(θ) = -√26
cot(θ) = 1/tan(θ) = -1/5
where r is the distance from the origin to the point, which can be found using the distance formula:
r = √((-1)^2 + 5^2) = √26
So the values of the six trigonometric functions of the angle in standard position with a point of (-1, 5) on its terminal side are: sin(θ) = 5/√26, cos(θ) = -1/√26, tan(θ) = -5, csc(θ) = √26/5, sec(θ) = -√26, and cot(θ) = -1/5.
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Mia must solve the system of equations
3x+4y=8
x-4y=4
As a first step she produces the equation 4x=12 from the system above. What property of equality can be
used to justify this much simpler equation?
Answer:
x=3 and y=-¼
Step-by-step explanation:
3x + 4y=8-(x-4y=4)
4x and 4x out then left 4x=12 By simplified and x = 3
the _____ -colored section of the emergency response guidebook (erg) contains a list of chemicals organized by id number and includes only the product name and guide number.
The product name and guide number associated with each HMN listed in the Orange-colored section of the ERG.
The Orange-colored section of the Emergency Response Guidebook (ERG) contains a list of chemicals organized by ID number. This section includes only the product name and guide number associated with each chemical.The product name and guide number associated with each HMN listed in the Orange-colored section of the ERG.
The formula used to find the guide number associated with each chemical is as follows: Guide Number = Hazardous Material Number with the prefix code “40”, indicating the product is an oil.
By using the formula and prefix codes provided, it is possible to quickly identify the product name and guide number associated with each HMN (HMN) - 48,000. For example, if a chemical has an HMN of 48,200, then the associated guide number would be 200.
In addition to the formula, the ERG also provides a table of prefix codes that can be used to identify the type of product associated with each HMN. For example, if a product has a HMN of 48,310, then the associated guide number is 310 and the associated product will begin with the prefix code “40”, indicating the product is an oil.
By using the formula and prefix codes provided, it is possible to quickly identify the product name and guide number associated with each HMN listed in the Orange-colored section of the ERG.
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if a chi-square test for equality of proportions has 6 populations, then degrees of freedom must be used
The chi-square test for equality of proportions with 6 populations will have 5 degrees of freedom, which allows for more independent observations and more reliable results.
The degrees of freedom for a chi-square test for equality of proportions are calculated using the following formula: df = (r-1)(c-1). In this formula, r represents the number of populations and c represents the number of categories. In the case of 6 populations, the degrees of freedom would be calculated as df = (6-1)(1-1) = 5. This means that the chi-square test for equality of proportions with 6 populations will have 5 degrees of freedom. This is necessary because the chi-square test measures the difference between the expected and observed frequencies of a given variable, and degrees of freedom are used to determine the number of independent observations that can be made. The higher the number of degrees of freedom, the more independent observations that can be made, and thus the more reliable the results of the chi-square test are.
Therefore, the chi-square test for equality of proportions with 6 populations will have 5 degrees of freedom, which allows for more independent observations and more reliable results.
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if the correlation between two variables is close to 1.0, we cannot conclude that the explanatory variable causes changes in the response variable when the study is .
if the correlation between two variables is close to 1.0, we cannot conclude that the explanatory variable causes changes in the response variable when the study is observational.
Two variables are said to be causally related in statistics if the occurrence of one variable influences or modifies the other variable. In this case, one variable is the cause and the other is the effect.
We are unable to draw the conclusion that changes in one variable are responsible for changes in the other.An outcome of a study is measured by a response variable. A response variable changes are explained by or affected by an explanatory variable. You will often find explanatory variables called independent variables and response variables called dependent variables.
If their values change so that as the value of one variable increases or decreases so does the value of the other variable (although it may be in the opposite direction).So, we cannot conclude that the explanatory variable causes changes in the response variable when the study is observational.
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along which of these segments of the supply curve is supply least elastic? question 23 options: gh cd ac ab
The correct answer is option 4. The segment of the supply curve that is supplied least elastic is ab.
The supply curve is the graph of the relationship between the price of a good and the quantity supplied. The degree of elasticity of supply is determined by how much the quantity supplied changes in response to a change in price. If the supply curve is more elastic, it means that the quantity supplied changes more in response to a change in price, while if it is less elastic, it means that the quantity supplied changes less in response to a change in price.
The segment along which the supply is least elastic is indicated by the flatter portion of the curve, where a change in price results in a smaller change in quantity supplied. In this case, segment ab has the least elastic supply.
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Complete Question:
along which of these segments of the supply curve is supply least elastic?
gh cd ac aby-6≤-3(x+4) in slope intercept form WITH STEPS!!!
The slope intercept form of the inequality is y ≤ -3x - 6.
What is Slope?Slope of a line is the ratio of the change in y coordinates to the change in the x coordinates of two points given.
Slope intercept form of a linear equation is of the form y = mx + c.
m : slope and c : y intercept
In the case of inequalities, symbol change from equality sign to inequality sign.
Given linear inequality is,
y - 6 ≤ -3(x + 4)
y - 6 ≤ -3x - 12
y ≤ -3x - 12 + 6
y ≤ -3x - 6
Hence the slope intercept form of the inequality is y ≤ -3x - 6.
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PLEASE HELP 50 points
The situation that could not be represented by the algebraic expression b + 5 is given as follows:
If there are b ounces of water in a bottle, b + 5 could represent the amount of water after you drink 5 bottles.
How to interpret the algebraic expression?The algebraic expression for this problem is defined as follows:
b + 5.
Meaning that an unknown amount b is increased by a value of 5.
For the answer of this problem, the correct expression would be of b - 5 instead of b + 5, hence it is the option that could not be represented by the algebraic expression b + 5.
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||
2. Complete the steps for factoring 2x3 - 36x² + 162x by writing words, numbers,
or expressions in the blanks.
2x336x2 + 162x=
(x2-18x+81)
_2x [x²-2(____)x+ (__________)²]
=
11
(x-.
_)(x-____
_2=(x-_9_) ²
Factor out
Rewrite the trinomial.
Use the
pattern.
Simplify.
The solution is given below.
What is equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign. In its simplest form in algebra, the definition of an equation is a mathematical statement that shows that two mathematical expressions are equal. For instance, 3x + 5 = 14 is an equation, in which 3x + 5 and 14 are two expressions separated by an 'equal' sign.
here, we have,
2x3 - 36x² + 162x
=2x *(x^2-18x+81) Factor out- 2x
= 2x [x²-2(9)x+ (9)²] Rewrite the trinomial.
=2x*(x-9)(x-9)
= 2x*(x-9) ² Simplify.
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Please help me answer this :)
extra points
The domain of the function y =x²-4 has no values and the range is -2≤x≥2. And the graph is a function of x
What is domain and range?The domain of a function is the set of values that we are allowed to plug into our function. This set is the x values in a function such as f(x). The range of a function is the set of values that the function assumes. This set is the values that the function shoots out after we plug an x value in.
The equation of the graph is y = x²-4. since the root of the equation is x = -2 and +2
(x+2)(x-2) = x²+2x-2x-4
= x²-4
therefore the equation y = x²-4 has no domain and the range of value of x -2>x≤2.
The graph is a function of x
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Michael has $16 and wants to buy a mixture of cupcakes and fudge to feed at least 4 siblings. Each cupcake costs $4, and each piece of fudge costs $2.
This system of equations models the scenario:
4x + 2y ≤ 16
x + y ≥ 4
Part A: Describe the graph of the system, including shading and the types of lines graphed. Provide a description of the solution set. (4 points)
Part B: Is the point (2, 3) included in the solution area for the system? Justify your answer mathematically. (3 points)
Part C: Choose a different point in the solution set and interpret what it means in terms of the real-world context. (3 points)
Note that the solution of the given inequalities [4x+2y ≤ 16 and x+y>4.] is (4, 0).
What is inequality in Math?Inequalities are mathematical expressions in which neither side is equal. Unlike equations, we compare two values in inequality. In between, the equal sign is substituted by a less than (or less than or equal to), larger than (or greater than or equal to), or not equal to sign.
Part A: The solution of the inequalities is (4, 0)
Part B: In figure attached, we can see that the point (2, 3) included in the solution area for the system.
Therefore, the solution of the given inequalities is (4, 0).
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Evaluate - 3.28 - (-4.4) + (-p) where p = 9.7.
Answer:
-8.58
Step-by-step explanation:
-3.28+4.4-9.7=-8.58
diagonalize the matrix by finding the eigenvalues of a listed in increasing order, the corresponding eigenvectors, a diagonal matrix d, and a matrix s such that .
The diagonal matrix D has the eigenvalues 7, 2, and 3 along the diagonal.
To diagonalize matrix A, we first need to find the eigenvalues and eigenvectors.
The eigenvalues can be found by solving the characteristic equation det(A - λI) = 0, where I is the identity matrix and λ is the eigenvalue.
For the given matrix A, the characteristic equation is:
[tex]\begin{vmatrix}4 - \lambda & 1 & 2 \1 & 4 - \lambda & 2 \1 & 1 & 5 - \lambda\end{vmatrix} = 0[/tex]
Expanding the determinant and solving for λ, we find the eigenvalues are λ = 7, 2, and 3.
Now, we find the corresponding eigenvectors by solving the equation Av = λv for each eigenvalue. For each eigenvalue, we can write the equation as (A - λI)v = 0 and solve for v.
For example, for λ = 7, we have:
[tex]\begin{bmatrix}-3 & 1 & 2 \1 & -3 & 2 \1 & 1 & -2\end{bmatrix}\begin{bmatrix}v_1 \v_2 \v_3\end{bmatrix} = \mathbf{0}[/tex]
where the matrix on the left is (A - 7I) and the vector on the right is v.
Solving for v, we find that the eigenvector corresponding to λ = 7 is v = (1, 1, -2).
The diagonal matrix D can be written as:
[tex]\begin{bmatrix}7 & 0 & 0 \0 & 2 & 0 \0 & 0 & 3\end{bmatrix}[/tex]
So, the diagonal matrix D has the eigenvalues 7, 2, and 3 along the diagonal.
The diagonalization of a matrix A is given by [tex]A = SD^{-1} S[/tex], where D is a diagonal matrix with the eigenvalues along the diagonal, and S is the matrix of eigenvectors with the columns being the corresponding eigenvectors. [tex]S^ {-1}[/tex] is the inverse of S.
Did you mean Diagonalize the matrix [tex]A = \left[\begin{array}{ccc}4&1&2\\1&4&2\\1&1&5\end{array}\right][/tex] by finding the eigenvalues of A listed in increasing order, the corresponding eigenvectors, a diagonal matrix D, and a matrix S such that [tex]A = SD^{-1} S[/tex].
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LarApCalc10 2.3.022. Find the marginal cost for producing x units. (The cost is measured in dollars.) C = 300(6 + 4x) dollars per unit Need Help? Read It Watch It Talk to a Tutor
The marginal cost of producing x units is equal to 300 multiplied by the sum of 6 and 4x dollars per unit.
The marginal cost for producing x units is calculated by taking the derivative of the cost equation with respect to x. The cost equation is C = 300(6 + 4x). Differentiating with respect to x, the marginal cost is found to be the derivative of the cost equation, which is equal to 300 multiplied by the derivative of the equation, 6 + 4x. The derivative of 6 + 4x is 4, so the marginal cost is 300 multiplied by 4, or 1200 dollars per unit. Therefore, the marginal cost for producing x units is 1200 dollars per unit.
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Oliver borrowed $2,000 to purchase a riding lawn mower for his lawn care business. The bank offered him an interest rate of 13% for 9 months. Calculate the simple interest using I = prt.
$195
$260
$1,500
$2,340
Answer:
The correct answer option is $195
Step-by-step explanation:
2000 * 13% / 9 months * 9 months
2000 * 0.13 / 9 * 9 = 2000 * 0.014444 * 9 = 195
Real easy simple question please help!
The points of the plane do not correspond to a function because they do not have any constant relationship between them.
What is a function?A function is a mathematical term that refers to a quantity being a function of another if the value of the first depends on the value of the second. For example, the area A of a circle is a function of its radius r.
According to the above, if the points of the plane were a function, they would all have a location relationship, for example, they would mark a constant line or a parabola.
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3/8 + 4/5 please help me
[tex]\cfrac{3}{8}+\cfrac{4}{5}\implies \cfrac{(5)3~~ + ~~(8)4}{\underset{\textit{using this LCD}}{40}}\implies \cfrac{15+32}{40}\implies \cfrac{47}{40}\implies 1\frac{7}{40}[/tex]
Answer:
47/40
Step-by-step explanation:
[tex](\frac{3}{8}\cdot\frac{5}{5})+(\frac{4}{5}\cdot\frac{8}{8})=\frac{15}{40}+\frac{32}{40}=\frac{47}{40}[/tex]
Counting numbers containing 2s first four value of this set
The first four value of this set of 2s will be 2, 4, 6 and 8.
What are counting numbers?The set of numbers we use to learn how to count are called counting numbers. They are also known as natural numbers, maybe because they are the first numbers we naturally learn and hence feel natural to us. They are also sometimes referred to as positive integers.
Numbers that we can use to count things are called counting numbers, for example 1, 2, 3, and so on. They are also called natural numbers.
In this case, we are couting on 2s. The first four numbers will be:
= 2 × 1 = 2
= 2 × 2 = 4
= 2 × 3 = 6
= 2 × 4 = 8
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Mhanifa Please help
Identify the error in this outline.
error in capitalization
error in indentation
error in parallel structure
error in punctuation
error in division of points
Answer:
Step-by-step explanation:
Error in the division of points is the error in this outline. Thus option (E) is correct. Each heading's first word needs to be capitalized. Any proper nouns contained within each header must be capitalized. period.
What is a division
Multiplication is the opposite of division. If 3 groups of 4 add up to 12, then 12 divided into 3 groups of equal size results in 4 in each group. Creating equal groups or determining how many people are in each group after a fair distribution is the basic objective of division.
One of the four fundamental arithmetic operations, or how numbers are combined to create new numbers, is division. The other operations are multiplication, addition, and subtraction.
In order to emphasize related ideas in a sentence, parallelism is the use of comparable words, clauses, phrases, sentence structure, or other grammatical characteristics. It makes the statement succinct, understandable, and simple to read. Particularly in series, pairs, and items in an outline or list, parallel structuring is crucial.
Therefore, Thus option (E) is correct.
item is regularly priced at $80. Maya bought it on sale for 65% off the regular price. How much did Maya pay?
Answer:
52$
Step-by-step explanation:
Well, because we know our price was originally 80 dollars and maya bought it 65% off, we know that our answer is 65% of 80. 65% can be rewritten as .65, and we can now write our new equation as 80 x .65 = Mayas new price. Using a calculator we can find out that the answer is 52$
Please see picture thanks
Using compound interest, The future value of this investment at the end of year 1 is $16321.6.
Compound interest is defined.Compound interest is the type of interest that is calculated using both the principal and the interest that has accumulated over the preceding period. In contrast to simple interest, compound interest does not factor in the principal when calculating the interest for a subsequent period.
Every six months, or every semi-annually, the compound interest is added up.
Thus,
Rate = 4% / 2 = 2% =0.02
P = $16,000
n = 2
The compound interest is given by:
[tex]A = P (1 + \frac{r}{n})^n[/tex]
[tex]A = 16000(1 + \frac{0.02}{2})^2[/tex]
A = 16321.6
Hence, the future value of this investment at the end of year 1 is $16321.6.
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CAN SOMEONE HELP WITH THIS QUESTION?✨
The percentage error in the density of metal will be 3.4%.
What is the percentage?The percentage is defined as representing any number with respect to 100. It is denoted by the sign %. The percentage stands for "out of 100." Imagine any measurement or object being divided into 100 equal bits.
Given that the density of the metal in the handbook is 4.018 g/mL and the measured value of the density is 4.16 g/mL.
The percentage error will be calculated as:-
Percentage = [ ( 4.16 - 4.018 ) / 4.16 ] x 100
Percentage = 0.034x 100
Percentage = 3.4%
Hence, the percentage error will be 3.4% for the densities.
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write the algorithm for the following tasks. to calculate the sum of 9 and 4.
The algorithm to calculate the sum of 9 and 4. is:
Input 9Add 4 to 9Prnt the result 13How to determine the algorithmFrom the question, we have the following parameters that can be used in our computation:
algorithm to calculate the sum of 9 and 4
This implies that we write the steps to calculate the sum of 9 and 4
So, the steps are
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43. MODELING - Tornados The typical number of tornados in the United States in May is 11 more than 14 times the typical number of tornados in December. The sum of the typical number of tornados in December and in May is 341. Determine the typical number of tornados in the month of December anf also in the month of May.
The number of tornadoes in December and in May are : 22 and 341
How to solve for the tornadoesLet x be the typical number of tornadoes in December.
The typical number of tornados in May is 11 + 14x.
The sum of the typical number of tornados in December and in May is x + (11 + 14x) = 341.
Combining like terms, we get 15x + 11 = 341.
Subtracting 11 from both sides, we get 15x = 330.
Dividing both sides by 15, we get x = 22.
So the typical number of tornados in December is 22, and the typical number of tornadoes in May is 11 + 14x = 11 + 14 * 22 = 341.
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Help me pls I don’t know what I’m doing
The right answer is D, which is the domain (-2 x 4) and range (-3 y 0).
What is meant by the terms "domain" and "range"?The range of values that can be plugged into a function is its domain.
The x values for such a function as f are contained in this set (x).
The collection of values that a function can accept is known as the range of the function.
After we enter an x value, the function returns this set of values.
Regarding the posed query;
The function's graph is provided;
It is evident from the graph that the curve's x-axis starting and ending points are -2 and 4, respectively.
As a result, the function's range, taking into account both, is between -2 and 4.
Domain [-2 x 4].
For the y values, which make up the function's range.
On the negative y-axis, the curve begins at -3 and ends at zero.
As a result, the function's range will encompass both -3 and 0 in total.
Range -3 y 0 range. Thus, option D provides the domain and the range.
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What is the probability of landing on a 5 when rolling a six-sided number cube?
Answer: 1/6
Step-by-step explanation: there are 6 sides, so we know the answer will be something/6. There is only one 5 on this 6-sided cube which is why the probability of rolling it would be 1/6
find an equation of the tangent to the curve at the point corresponding to the given value of the parameter.
The equation of the tangent at (2,7) is y = 4x - 1.y = x^2 + 3; t = 2
Given: y = x^2 + 3 and t = 2
We need to find the equation of the tangent at (2,7).
First, we find the slope of the tangent line by taking the derivative of the function:
y' = 2x
At x = 2, the slope is 2*2 = 4.
Now, we can use the point-slope form of the equation of a line to find the equation of the tangent line:
y - y1 = m(x - x1)
y - 7 = 4(x - 2)
Simplifying:
y = 4x - 1
Therefore, the equation of the tangent at (2,7) is y = 4x - 1.
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What kind of angle is this
This triangle is similar by the rule of (d)SAS.
What is similar shape?When applying a scale factor, similar shapes are enlarged versions of one another. All of the corresponding angles and lengths in related shapes are equal and in the same ratio.
We divide the length of the enlarged shape by the length of the original shape to calculate the length scale factor.
In this given diagram, there are two triangle ΔRST and ΔRUV
where, RS/SU = RT/RV
and ∠SRT = ∠URV
So ΔRST ~ ΔRUV by the rule of SAS
So that option (d) is correct answer.
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2 3/8 x 5 3/4
Preform the indicated operation
The solution to the given fraction 2 3/8 x 5 3/4 is 13 21/32
How to solve fractions?A fraction is a number which has a numerator and a denominator. A numerator is the top or upper value while a denominator is the bottom or lower value.
2 3/8 x 5 3/4
= 19/8 × 23/4
Multiply numerator and denominator respectively
= (19 × 23) / (8 × 4)
= 437 / 32
= 13 21/32
Therefore, 13 21/32 is the solution to the fraction.
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to draw accurate conclusions about change in an experiment, which of the following is required? a. experimental control b. correlation c. causation d. single case study
Option A and C, To draw accurate conclusions about change in an experiment, both experimental control and causation are required.
Experimental control means that the experiment is designed and conducted in a way that allows for a clear determination of the effect of the independent variable on the dependent variable, by controlling for extraneous variables and minimizing the effects of confounding variables.
Causation means that a relationship exists between the independent variable and the dependent variable, such that a change in the independent variable directly and consistently results in a change in the dependent variable.
Correlation refers to the statistical relationship between two variables, but does not necessarily imply causation. A single case study provides information about a specific individual or situation, but may not be generalizable to a larger population.
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To draw accurate conclusions about change in an experiment, which of the following is required?
a. experimental control
b. correlation
c. causation
d. single case study