What is the sum of the interior angles of a polygon having 9 sides Class 8?

At equilibrium, x = 260 and p = 112. The consumers' surplus at equilibrium is 133.6. The producers' surplus at equilibrium is 68.8.

x = 260

p = 11.2

Consumers' surplus = (39-11.2)x/2 = 133.6

Producers' surplus = (11.2-13)x/2 = 68.8

At equilibrium, the price-demand and price-supply equations intersect and determine the optimal level of production, known as x. In this case, the equilibrium value of x is 42 units and the price at which the goods are traded is 26 dollars.

The consumers’ surplus is the difference between the maximum price that a consumer would be willing to pay for a good and the prevailing market price. In this case, the maximum willingness to pay is 39 dollars and the market price is 26 dollars, thus the consumers’ surplus at equilibrium is 13 dollars. Similarly, the producers’ surplus is the difference between the prevailing market price and the minimum price that suppliers would be willing to accept for a good.

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y= √x

Identify the equation of the function.

y= √-1+3

Answer:

b. y = square root x

Step-by-step explanation:

Answer:

4. 20 units

5. 2√10 units

6. 2√17 units

Step-by-step explanation:

The distance formula is given as;

\(d=\sqrt{(x_2-x_1)^{2} +(y_2-y_1 )^2\)

So for;

4)

(5,9) (-7,-7)

\(d=\sqrt{(-7-5)^{2}+(-7-9)^2 }\\\\d=\sqrt{-12^2+-16^2} \\\\d=\sqrt{144+256} \\\\\\d=\sqrt{400} =20\)

5.

The coordinates given are: (3,8) and (9,10)

\(d=\sqrt{(9-3)^2+(10-8)^2} \\\\\\d=\sqrt{6^2+2^2} \\\\d=\sqrt{36+4} \\\\d=\sqrt{40} \\d=\sqrt{4*10} \\\\d=\sqrt{4} *\sqrt{10} \\\\d=2\sqrt{10}\)

6. The coordinates are  (-10,-7) ,  (-8,1)

   \(d=\sqrt{( -8--10)^2+(1--7)^2} \\\\d=\sqrt{2^2+8^2} \\\\d=\sqrt{4+64} \\\\\\d=\sqrt{68} \\\\d=\sqrt{17*4} \\\\d=\sqrt{4} *\sqrt{17} \\\\\\d=2\sqrt{17}\)

Answer:

Step-by-step explanation:Find the GCD (or HCF) of numerator and denominator GCD of 2 and 3 is 1

Divide both the numerator and denominator by the GCD 2 ÷ 1 3 ÷ 1

Reduced fraction: 2 3 Therefore, 2/3 simplified to lowest terms is 2/3.

Collecting data on 83,359 grade-point averages would be a significant undertaking and a 99% confidence level, especially if the data had to be collected in a short amount of time or if there were limited resources available for data collection.

To determine the sample size needed to estimate the population mean within a certain margin of error, we can use the formula:

\(n = (Z^2 * sigma^2) / E^2\)

where n is the sample size, Z is the Z-score for the desired confidence level (in this case, 2.576 for a 99% confidence level), sigma is the population standard deviation (in this case, estimated as 1.25 using the range rule of thumb), and E is the desired margin of error (in this case, 0.01).

Plugging in the values, we get:

\(n = (2.576^2 * 1.25^2) / 0.01^2 = 83,358.08\)

So we would need a sample size of at least 83,359 to estimate the population mean with a margin of error of 0.01 and a 99% confidence level.

However, this sample size may not be practical depending on the resources available. Collecting data on 83,359 grade-point averages would be a significant undertaking, especially if the data had to be collected in a short amount of time or if there were limited resources available for data collection.

In practice, researchers often use statistical software to calculate sample sizes based on the desired margin of error, confidence level, and population standard deviation. This allows them to determine a more realistic sample size based on the specific context of their study.

In summary, while the formula for determining sample size can provide an estimate of the number of observations needed to estimate the population mean with a certain level of precision, other factors such as the availability of resources must also be considered when determining a practical sample size.

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Answer:

y-y1=m (x- x1)…………..(1)

Here m=1/2 and (x1,y1)= (4,-2)

(1) => y-4=1/2(x+2)

=> 2y-8=x+2

=> x-2y-10=0

So, equation of line is x-2y-10=0.

The average rate of change over the interval \([0,2]\) is -6. The average rate of change of a function \( y = f(x) \) over an interval is a measure of how the function's values change on average within that interval.

To find the average rate of change, we calculate the ratio of the change in the function's values to the change in the input variable (x) over the given interval.

First, let's consider the average rate of change over the interval \([0,3]\), which is given as -1. This means that, on average, the function's values decrease by 1 unit for every 1 unit increase in the input variable within the interval \([0,3]\).

Next, let's consider the average rate of change over the interval \([2,3]\), which is given as 5. This means that, on average, the function's values increase by 5 units for every 1 unit increase in the input variable within the interval \([2,3]\).

Now, let's determine the average rate of change over the interval \([0,2]\) by subtracting the average rate of change over \([2,3]\) from the average rate of change over \([0,3]\).

Average rate of change over \([0,2]\) = Average rate of change over \([0,3]\) - Average rate of change over \([2,3]\)

= (-1) - 5

= -6

Therefore, the average rate of change over the interval \([0,2]\) is -6.

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5 persons are to be selected to form a committee so that at least 3 men are there on the committee, in 3192 ways the committee can be formed.

Combinations are decisions that are made by choosing some or all of a group of objects, regardless of how they are arranged. the variety of n distinct combinations, each taken r at a time,

We may have four males and one lady or three men and two women (5 men only).

∴ Required number of ways = (⁸C₃ x ⁷C₂) + (⁸C₄ x ⁷C₁) + ⁸C₅

= \(\frac{8*7*6}{3*2*1} *\frac{7*6}{2*1} + \frac{8*7*6*5*4}{4*3*2} *\frac{7}{1} + \frac{8*7*6}{3*2}\)

= 1176 + 1960 + 56

= 3192

Therefore, at least 3 men are there on the committee can be formed 3192 times.

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a) G(t) = 685.4 * (1 + 0.04)^t, b) G(t) = 685.4 + 4t.

(a) If the gross domestic product (G) of Switzerland increases by 4% per year, we can express it as a function of time (t) in years after 2013. The initial GDP in 2013 is given as 685.4 billion dollars. Since it increases by 4% per year, we can use the following formula: G(t) = 685.4 * (1 + 0.04)^t. Here, (1 + 0.04) represents the growth factor of 4% per year, and t represents the number of years after 2013. (b) If the gross domestic product (G) of Switzerland increases by 4 billion dollars per year, we can express it as a function of time (t) in years after 2013. The initial GDP in 2013 is given as 685.4 billion dollars. Since it increases by 4 billion dollars per year, we can use the following formula: G(t) = 685.4 + 4t. Here, 685.4 represents the initial GDP in 2013, and 4t represents the increase of 4 billion dollars per year.

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The equation of the osculating circle to \(y = x^4 - 2x^2 at x = 1\) is: \((x - 1/2)^2 + (y + 1)^2 = (1/8)^2\)

The first step in finding the equation of the osculating circle to \(y = x^4 - 2x^2\) at x = 1 is to find the values of the first and second derivatives of y with respect to x at x = 1.

\(y = x^4 - 2x^2\)

\(y' = 4x^3 - 4x\)

\(y'' = 12x^2 - 4\)

Evaluate y', y'', and y at x = 1:

\(y(1) = 1^4 - 2(1)^2 = -1\)

\(y'(1) = 4(1)^3 - 4(1) = 0\)

\(y''(1) = 12(1)^2 - 4 = 8\)

The equation of the osculating circle can be expressed as:

\((x - a)^2 + (y - b)^2 = r^2\)

where (a, b) is the center of the circle and r is its radius. To find (a, b) and r, we use the following formulas:

\(a = x - [(y')^2 + 1]^(^3^/^2^)^/ ^|^y''^|\)

\(b = y + y'[(y')^2 + 1]^(^1^/^2^) ^/ ^|^y^''|\)

\(r = [(1 + (y')^2)^(^3^/^2^)^] ^/ ^|^y''^|\)

Substituting the values of x, y, y', and y'' at x = 1, we get:

\(a = 1 - [0^2 + 1]^(^3^/^2^) ^/ ^|^8^| = 1 - 1/2 = 1/2\)

\(b = -1 + 0[0^2 + 1]^(^1^/^2) ^/ ^|^8^| = -1\)

\(r = [(1 + 0^2)^(^3^/^2^)^] ^/ ^|^8^| = 1/8\)

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(a) Subset {13, 4, 5} is represented by the bit string 0100010110, where each bit corresponds to an element in the universal set U. (b) Subset {12, 3, 4, 7, 8, 9} is represented by the bit string 1000111100, with 1s indicating the presence of the corresponding elements in U.

(a) Subset {13, 4, 5} can be represented as a bit string as follows:

Bit string: 0100010110

Since the universal set U has 10 elements, we create a bit string of length 10. Each position in the bit string represents an element from U. If the element is in the subset, the corresponding bit is set to 1; otherwise, it is set to 0.

In this case, the positions for elements 13, 4, and 5 are set to 1, while the rest are set to 0. Thus, the bit string representation for {13, 4, 5} is 0100010110.

(b) Subset {12, 3, 4, 7, 8, 9} can be represented as a bit string as follows:

Bit string: 1000111100

Following the same approach, we create a bit string of length 10. The positions for elements 12, 3, 4, 7, 8, and 9 are set to 1, while the rest are set to 0. Hence, the bit string representation for {12, 3, 4, 7, 8, 9} is 1000111100.

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--The given question is incomplete, the complete question is given below " Suppose that the universal set is U = { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10). Express each of the following subsets with bit strings (of length 10) where the ith bit (from left to right) is 1 if i is in the subset and zero otherwise. (a) 13, 4,5 (b) 12,3,4,7,8,9 "--

The 875 times smaller is 4 x 10−7 than 3.5 x 10−4.

Arithmetic operators are four basic mathematical operations in which summation, subtraction, division, and multiplication involve.,

Summation = addition of two or more numbers or variable

For example = 2 + 8 + 9

Subtraction = Minus of any two or more numbers with each other called subtraction.

For example = 4 - 8

Division = divide any two numbers or variable called division.

For example 4/8

Multiplication = to multiply any two or more numbers or variables called multiplication.

For example 5 × 7.

Given the two quantities 4 x 10−7 and 3.5 x 10−4

Now, if we divide this then

⇒ (3.5 x 10−4)/(4 x 10−7)

⇒ (35/40) × 10³

⇒ 875

Hence "The 875 times smaller is 4 x 10−7 than 3.5 x 10−4".

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Answer:

B. 875

Step-by-step explanation:

Hope this helped

The completed table with regards to terms of an expression are presented as follows;

     Condition      \({}\)              (6·x + 3) + (5·x - 4)            (-4·y - 16) - 8·y + 10 + 2·y

         Exactly 3 terms          N/A     \({}\)                              N/A

         Exactly 5 terms          N/A         \({}\)                          N/A

Includes a zero pair             No \({}\)                                   No

Uses distributive property   No                                    No

Includes a negative factor   No                                    

Has no like terms                False                                False

Condition       \(8 - \dfrac{1}{2} \cdot \left(4 \cdot x - \dfrac{1}{2} + 12\cdot x -\dfrac{1}{4} \right)\)  0.25·(8·m - 12) - 0.5·(-4·m + 2)

Exactly 3 terms       No                         \({}\)                    No

Exactly 5 terms       Yes                          \({}\)   \({}\)              No

Includes a zero pair No    \({}\)                         \({}\)              Yes

Uses the distributive property Yes            \({}\)             Yes

Includes a negative factor      Yes           \({}\)                Yes

Has no like terms                    No          \({}\)                  No

A mathematical expression is a collection of variables and numbers along with mathematical operators which are all properly arranged.

The details of the conditions in the question are as follows;

Terms of an expression

A term is a subunit of an algebraic expression which are joined together by operators such as addition or subtraction

Zero pair

A zero pair are two numbers that when added together have a zero result

Distributive property

The distributive property of multiplication states that the multiplication of a number or variable by an addend is equivalent to the sum of the multiplication of the number or variable and each member of the addend

Negative factor

A negative factor is a factor that has a negative sign prefix

Like terms

Like terms are terms consisting of identical variables with the same  powers of the variable

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The radius of the circle is approximately 10.17 units (rounded to two decimal places).

To find the radius of the circle, we need to use the formula that relates the central angle to the length of the arc and the radius of the circle. The formula is given as:

arc length = radius x central angle

In this case, the arc length is given as 24.4 and the central angle is given as 2.4 radians. Substituting these values in the formula, we get:

24.4 = r x 2.4

Solving for r, we get:

r = 24.4 / 2.4

r ≈ 10.17

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Answer:

I am not good at those but I am pretty sure its between a or b

- The domain of H is {-4, -1, -5, 9}.
- The range of H is {8, 0, -5, -1}.

The domain of a relation refers to the set of all input values or x-values, while the range refers to the set of all output values or y-values. To find the domain and range of the relation H={(−4,8),(−1,0),(−5,−5),(9,−1)}, we need to identify the distinct x-values and y-values.

Domain:
Looking at the given ordered pairs, we can see that the x-values or inputs are -4, -1, -5, and 9. To express the domain using set notation, we list these x-values within curly brackets, separated by commas. So, the domain of H is {-4, -1, -5, 9}.

Range:
Next, let's identify the y-values or outputs. From the given ordered pairs, we have the y-values 8, 0, -5, and -1. To express the range using set notation, we list these y-values within curly brackets, separated by commas. Therefore, the range of H is {8, 0, -5, -1}.

In summary:
- The domain of H is {-4, -1, -5, 9}.
- The range of H is {8, 0, -5, -1}.

Remember that the domain represents all the possible x-values, while the range represents all the possible y-values in the given relation.

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Puedes separar los grupos en:

los que solo toman clases de piano; p

los que solo toman clases de violin: v

los que toman clases de piano y violin; 5

A) para determinar cuántos estudiantes no toman ni piano ni violin, podemos hallar el número total de estudiantes que toman clases solo de piano y los que toman solo de violín y los que toman ambas clases, de la siguiente forma:

Estudian solo piano, p = 14 - 5= 9

Estudian solo violín, v = 29 - 5 = 24

Estudian ambos: 5

Total de estudiantes que toman clases de esos instrumentos : 9 + 24 + 5 = 38

Por tanto, hay 40 - 38 = 2 estudiantes que no toman clases de piano ni violín.

B) ¿cuántos estudiantes toman clases de piano o violín?

Son los que tocan solo piano, o solo violín o ambos y los  hallamos arriba:  9 + 24 + 5 = 38.

Respuesta: 38

C) ¿Cuántos estudiantes tocan solo violín?

También lo encontramos arriba: son 29 - 5 = 24

Respuesta: 24

The function is expanding to the right of x = 3.

A polynomial function with one or more variables, where the largest exponent of the variable is two, is referred to as a quadratic function. It is also known as the polynomial of degree 2 since the greatest degree term in a quadratic function is of second degree. A quadratic function must have at least one second-degree term. It performs algebraic operations.

Given graph of a quadratic function,

to find where function is increasing,

The maximum value or minimum value of a quadratic function are located at its vertex, which is shaped like a U. The quadratic function's axis of symmetry crosses the function (a parabola) at its vertex.

here vertex  is at x = 3,

the increasing and decreasing of graph is shown by vertex,

the shape of curve is parabola so,

In parabolas, the rate of increase (the slope or rate of change) isn't consistent. If the parabola opens up, it will increase as you move towards the right; if the parabola opens down, it will decrease.

The function is increasing to the right side of 3

The parabola's apex can be found at (3, 2) Therefore, all real numbers make up the domain, and the range is y ≥  2. As can be seen in the figure, the function is expanding to the right of x = 3 and contracting to the left of x = 3

Hence the function is increasing to right at x = 3.

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Answer: 8 feet

Step-by-step explanation:

length= 6+w

A=112

8*14=112, meaning that the width is either 8 or 14. because the length is 6+ than the width, that makes the length bigger. 14 is bigger than 8. The width is 8

Answer:

Line FJ is -3/1, while Line GH is 3/-2

Step-by-step explanation:

Raven can travel 5.71 miles or less under her limit.

Inequality is defined as the relation which makes a non-equal comparison between two given functions. If the equation or inequality contains variable terms, then there might be some values of those variables for which that equation or inequality might be true. Such values are called solution to that equation or inequality.

Let x b the number of miles Raven travels, we can write an expression relating the amount he spends. So there:

3.00 + 0.50= 3.50

Consider that total cost per mile be less than equal to the amount the Raven can spend:

3.50x ≤ 20

We can determine x;

x ≤ 5.71

Therefore, Raven can travel 5.71 or less under her limit.

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The sum of two integers is also an integer.

What is an integer?

Zero, a positive natural number, or a negative integer denoted by a minus sign are all examples of integers. The inverse additives of the equivalent positive numbers are the negative numbers. The boldface Z is a common way to represent the set of integers in mathematical terms.

When we conduct an operation on set members and always obtain a set member, the set is said to be closed under that operation. As a result, a set either possesses closure regarding a particular operation or it does not. A set is said to satisfy a closure property if it is closed by an operation or set of operations. A closure property is typically introduced as a hypothesis, known as the axiom of closure.

If a and b two integer.

Then the sum of the integer a + b is also an integer. Thus addition operation closer property.

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Answer:

4,950

Step-by-step explanation:

You multiply 198 x 25 and it gives you 4,950

Multiplication is a method of finding the product of two or more numbers. 4950 is the answer for 198x25 .

Multiplication is a method of finding the product of two or more numbers

198x25 in us traditional multiplication

The following steps are performed

Multiply by the number in the ones place.

Put a zero below in the ones place.

Multiply by the number in the tens place.

Add them up.

    198

   × 25

______

   990

 396+

_______

  4950

4950 is the answer for 198x25 .

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Answer:

His wet feet froze the faster, and his exposed fingers numbed the faster, though they had not yet begun to freeze.

Step-by-step explanation:

I did the test on edmentum and got it right !!!

Answer: The old-timer on Sulphur Creek had told him about it the previous fall, and now he was appreciating the advice.

Step-by-step explanation:

mark on brainlist

We are given a graph of a line and asked to write the equation in the form below.

Where m is the slope and b is the y-intercept of the line.

The y-intercept is the point where the line intersects the y-axis.

From the graph, we see that the line intersects the y-axis at -2

So, the y-intercept is -2

The slope of the line is given by

The rise is the vertical distance between the two points on the line.

The run is the horizontal distance between the two points on the line.

As you can see, we selected two points on the line and we have got a rise of 8 units and a run of 4 units

So, the slope of the line is 2

Therefore, the equation of the line is

Answer:

(1,0) and (-3,0)

Step-by-step explanation:

Answer:3:24

Step-by-step explanation:

Answer:

The answer is 52. If you divide 13 by 0.25 which is 25% you get 52. And to check the answer 52 X 25% is 13.

Step-by-step explanation:

the graphs are attached herewith , where the label of the graph are :

  along X-axis: 1 square  division = 10 units

  along y-axis: 1  square division: 10 units

The problem we dealing with is related to manipulating graphs.For the question 7 to 10, the commonly given function is f(x)= √x, if the g(x) is nothing but the f(x-c) or f(x+c), so for the g(X) to be f(x-c), then a graph of that particular function turns to stretch downward whereas, for the f(x+c), it stretches upward.

So, for 7  g(x)=√x- 4 where -4  is c so the g(x) = f(x-c) so the  point for the graphs will stretch downward compare to the pint of the functions  f(x)= √x.

8. g(x)=√x +3

here g(x)= f(x+3), so the pints  stretched upward

9. g(x)=√x + 6 − 4=√x + 2

here additional number for the points ar 2, as it positive one,  so the  point of the function g(x), stretches upward

10. g(x)=√x - 7+3=√x -4

here the c is -4, so the point of the  g(x), stretches downward.

Same for the questions 11 to 14, the common function is f(x) = 1/x ,for which which g(x) = f(x-c) or f(x+c), for positive c , the graph stretches upward otherwise it moves downward

11. g(x) = 1/x +4

here the  c is positive, the graph stretches upward for the  g(x)

12. g(x) = 1/x - 6

here the  c is negative, the graph stretches downward for the  g(x)

13. g(x) = 1/x-6 + 8= 1/x+2

here the  c is positive, the graph stretches upward for the  g(x)

14. g(x) = 1/x+7 -4= 1/x+3

here the  c is positive, the graph stretches upward for the  g(x)

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2. The range in individual stock prices within this mutual fund is 230.

3. An individual stock in the highest 25% of prices had a dollar value of at least Q3 = 344.68.

4. Individual stock prices in the middle 50% range between Q1 and Q3.

So, the prices are between 142.76 and 344.68.

5. This indicates a right-skewed distribution.

6. The median is a more appropriate measure of center for a right-skewed distribution.

7. We would expect the mean of the individual stock prices within this mutual fund to be greater than the median.

A financial tool called a mutual fund collects money from several investors. After that, the combined funds are invested in assets such as listed company stocks, corporate bonds, government bonds, and money market instruments.

To answer the questions about the DIA mutual fund based on the given information, let's refer to the five-number summary and boxplot:

Given:

Minimum: 100

First Quartile (Q1): 142.76

Median (Q2): 168.19

Third Quartile (Q3): 344.68

Maximum: 330

2. Range in individual stock prices within this mutual fund:

The range is calculated as the difference between the maximum and minimum values.

Range = Maximum - Minimum = 330 - 100 = 230

Therefore, the range in individual stock prices within this mutual fund is 230.

3. An individual stock in the highest 25% of prices:

To find the value of the individual stock in the highest 25% of prices, we need to find the value corresponding to the third quartile (Q3).

An individual stock in the highest 25% of prices had a dollar value of at least Q3 = 344.68.

4. Individual stock prices in the middle 50%:

The middle 50% of stock prices corresponds to the interquartile range (IQR), which is the difference between the first quartile (Q1) and the third quartile (Q3).

Individual stock prices in the middle 50% range between Q1 and Q3.

So, the prices are between 142.76 and 344.68.

5. Shape of the distribution of individual stock prices:

The shape of the distribution can be determined by analyzing the boxplot.

If the boxplot is approximately symmetric, the distribution is symmetric. If the boxplot has a longer tail on the left, it is left-skewed. If the boxplot has a longer tail on the right, it is right-skewed.

Based on the boxplot, we can see that the box (representing the interquartile range) is closer to the lower values, and the whisker on the right side is longer. This indicates a right-skewed distribution.

6. Appropriate measure of center for a right-skewed distribution:

In a right-skewed distribution, where the tail is longer on the right side, the mean is influenced by the outliers or extreme values, while the median is a more robust measure of center that is not affected by extreme values. Therefore, the median is a more appropriate measure of center for a right-skewed distribution.

7. Comparison of mean and median in this mutual fund:

For a right-skewed distribution, the mean tends to be greater than the median. This is because the presence of a few large values on the right side of the distribution pulls the mean towards higher values. In this case, we would expect the mean of the individual stock prices within this mutual fund to be greater than the median.

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In multiple regression analysis, the correlation among the independent variables is termed as d. multicollinearity.

Basically, multiple regression analysis means a statistical technique that can be used to analyze the relationship between a single dependent variable and several independent variables.

If the independent variables of the regression analysis is correlated, the it is called as multicollinearity.

Therefore, the option (d). multicollinearity is the answer

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