What's 11,000lb in tons​

Answer: Option C.

Step-by-step explanation:

Ok, first, a linear function is something of the shape of:

y = a*x + b.

And the graph of those functions is a line, as the name implies, so we can discard that option.

So this must be a non-linear function, you can see that is a function because each value of x has only one value of y related to it.

Second, in a Venn diagram you will see that the set of functions is contained into the set of relationships, this means that all the functions are relationships, but not all the relationships are functions, and we know that this is a non-linear function, so this also must be a relationship.

Then the correct option is C, nonlinear, and a relationship.

Answer:I have the same thing

Step-by-step explanation:

Answer:

1. First, we need to find the area of the rectangle, then subtract the non-shaded region from the total of the rectangle's area.

Area of rectangle formula;

A = LW

Where 'L' represents the length, and 'W' represents the width.

Plug in your values:

A = LW

A = 8(13)

A = 104, now that we've found the area of this total rectangle, we need to find the area of the triangle and subtract that from the area of the rectangle.

Formula for area of triangle;

A = BH x 1/2

Where 'B' represents the base, and 'H' represents the height and 1/2 is just 1/2.

But, if we look at this triangle we can see that we don't have the base.

So what we have to do is subtract the given side lengths beside it (which you add up) from the total width.

Given length beside unknown base: 4 and 4

So, (4 + 4) = 8, and the total width is 13.

So: 13 - 8 = 5, 5 is our base.

Now we plug these into our formula:

A = BH x 1/2

A = 5(6) x 1/2

A = 30 x 1/2

A = 30/2, which equals to 15.

Now we subtract the non shaded region(triangle) from the shaded region(total area of rectangle).

104 - 15 = 89 meters.

2. In this figure, we find the area of the whole triangle, not considering the small empty vertical-positioned rectangle to the bottom left corner.

Let's find the total base and total height.

As we can see, in the bottom triangle the height is 4, the other triangle has a height of 5. Combine these to get (4 + 5) = 9 is our total height of the whole triangle.

Now we find the base, 5 is the base of the bottom triangle and the other triangle has a base of 2, combine these to get: (5 + 2) = 7 is the total base of the whole triangle.

Now plug these into our formula of area of triangle;

A = BH x 1/2

A= 7(9) x 1/2

A = 63/2

A = 31.5, is the area of the whole triangle.

Now let's find the area of the empty rectangle to our bottom left corner.

Our length is 4, our width is 2.

A = LW

A = 4(2)

A = 8

Now subtract the empty rectangle's area from the total area of the triangle:-

31.5 - 8 = 23.5 inches.

3. We can see that in this figure, there is an empty semi circle(that has no area) apart of a square.

So to find the area of the unfinished square, we find the area of the semi circle and subtract it from the total area of the square.

Formula for area of a circle:

A = π\(r^{2}\)

Where 'π' represents pi aka (22/7 or 3.14), and 'r' represents the radius which is being squared.

But if we were to find the area of a semi circle, we would have to divide the whole formula of a regular circle by 2.

So, A = π\(r^{2}\)/2

Now, we plug in the values showing in the diagram into our equation.

Though, since we are given a diameter of 6, we need to find the radius which is 1/2(half) of the diameter.

SO,

1/2 x 6 = 3.

Now that we have our radius, we can finally plug this into our equation:-

A = π\(r^{2}\)/2

A = 3.14(3^2)/2

A = 3.14(9)/2

A = 28.26/2

A = 14.13, is our area of the semi circle.

Now we have to find the total area of the square, which we easily just multiply the two lengths.

6(length) x 6(width)

= 36, is the area of the total square.

Now we subtract the area of the semi circle from the area of the total square:

36 - 14.13 = 21.87 feet.

4. To find the area of this, we must split the figure into two shapes, a rectangle and a semi circle.

Using the formulas we applied to our past problems;

(Rectangle)

A = LW

A = 20(8)

A = 160, is the area of the rectangle

Now the semi circle (ignore the 12.56, because it's just the circumference):

We have to find the radius, (1/2 x diameter), so: (1/2 x 8) = 4 is our radius.

A = π\(r^{2}\)/2

A = 3.14(4^2)/2

A = 3.14(16)/2

A = 50.24/2

A = 25.12, is the area of the semi circle.

Now we add the two areas,

160 + 25.12 = 185.12 feet.

5. We split this figure into two shapes, a rectangle and a triangle.

Using the formulas we applied earlier to our past problems.

(Rectangle)

A = LW

A = 14(12)

A = 168, is the area of the rectangle.

(Triangle)

A = BH x 1/2

A = 8(12) x 1/2

A = 96 x 1/2

A = 96/2

A = 48, is the area of the triangle.

Now we add these areas;

168 + 48 = 216 centimetres.

The inverse relation of the function f(x)=1/3x*2-3x+5 is f-1(x) = 9/2 + √(3x + 21/4)

The function is given as

f(x)=1/3x^2-3x+5

Start by rewriting the function in vertex form

f(x) = 1/3(x - 9/2)^2 -7/4

Rewrite the function as

y = 1/3(x - 9/2)^2 -7/4

Swap x and y

x = 1/3(y - 9/2)^2 -7/4

Add 7/4 to both sides

x + 7/4= 1/3(y - 9/2)^2

Multiply by 3

3x + 21/4= (y - 9/2)^2

Take the square roots

y - 9/2 = √(3x + 21/4)

This gives

y = 9/2 + √(3x + 21/4)

Hence, the inverse relation of the function f(x)=1/3x*2-3x+5 is f-1(x) = 9/2 + √(3x + 21/4)

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Step 1:

Similar triangles are triangles that have the same shape, but different sizes. The corresponding angles are congruent and the sides are in proportion. Corresponding angle are angles in two different triangles that are “relatively” in the same position.

Step 2

Angle A is congruent to angle D

Angle B is congruent to angle E

Angle C is congruent to angle F.

Final answer

The measure of the angle C = 63

The probability that a box of 40 light bulbs will last for 5 years is very low, due to the short mean lifetime of 2 months and the relatively high standard deviation of 0.25 months.

The mean lifetime of a particular type of light bulb is given as 2 months, and the standard deviation is given as 0.25 months. The mean lifetime represents the average time that the light bulbs will last, while the standard deviation represents how much the lifetimes of the bulbs vary from the mean.

To determine the probability that a box of 40 light bulbs will last for 5 years, we need to convert the given information into a format that we can work with. 5 years is equal to 60 months, and since we have 40 light bulbs, we can assume that the lifetimes of the bulbs are independent and identically distributed. This means that the probability of one bulb lasting for 60 months is the same as the probability of any other bulb lasting for 60 months.

Next, we need to calculate the standard deviation of the sample mean. The standard deviation of the sample mean represents how much the means of different samples of size 40 would vary from the population mean. The formula for the standard deviation of the sample mean is given by the following equation:

standard deviation of the sample mean = standard deviation of the population / square root of the sample size

In this case, the standard deviation of the population is given as 0.25 months, and the sample size is 40. Therefore, the standard deviation of the sample mean is:

0.25 / sqrt(40) = 0.0395

Now that we have the mean lifetime and the standard deviation of the sample mean, we can use the normal distribution to determine the probability that a box of 40 light bulbs will last for 5 years. We can assume that the lifetimes of the bulbs follow a normal distribution with a mean of 2 months and a standard deviation of 0.0395 months (which is the standard deviation of the sample mean).

To find the probability that a bulb will last for 60 months, we can use the following equation:

z = (x - μ) / σ

where z is the standard score, x is the value we want to find the probability for (60 months in this case), μ is the mean, and σ is the standard deviation.

Plugging in the values, we get:

z = (60 - 2) / 0.0395 = 1509.49

To find the probability corresponding to this standard score, we can use a standard normal distribution table or a calculator. The probability is extremely small (close to zero), which means that it is highly unlikely that all 40 light bulbs will last for 5 years.

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Answer:

Percentage of boy students is 45 per cent.

The total number of students is 480.

Step-by-step explanation:

To find the percentage of boy students, just subtract 55% (the percentage of girl students) from 100%, then you'll get 45%.

To find the total number of students, just use algebraic equation, rearrange it, and solve for x.

The workings are shown in the picture attached. Hope this helps!

Answer:

total of students is 480

Step-by-step explanation

let t = total of students.

if 55% of the students in school are girls.

then 45% of the students in the school are boys.

if there are 216 boys in school.

\(45\% \times t = 216 \\ t = \frac{216}{45\%} \\ t = \frac{216}{ \frac{45}{100} } \\ t = \frac{216 \times 100}{45} \\ t = 480\)

Step-by-step explanation:

To determine the future value for the 401(k), we need to determine the amount contributed annually. It is stated that the amount the employee contributes to the fund is 9% of $45,624. $45,624(0.09) = $4,106.16 The employer contributes a maximum of 3% of the employee contribution. Therefore: $45,624(0.03) = $1368.72.  Therefore, the total annual contribution is $5,474.88, giving a future value of $196,302.40. For the Roth IRA, the monthly contributions are $352.45 giving a future value of $152,636.09. Therefore, the 401(k) has a greater future value by $43,666.31.

The radical equation that has an extraneous solution is 5✓x + 10 - 15 = 30

Based on the information given, the radical equation that has an extraneous solution is 5✓x + 10 - 15 = 30.

This will be:

5✓x + 10 - 15 = 30

Collect like terms

5✓x = 30 - 10 + 15

5✓x = 35

✓x = 35/5

✓x = 7

x = 7² = 49

The equation that does not have an extraneous solution will be ✓x + 1 + 7 = 4. Here, ✓x = -4 and has no solution.

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Answer:

x+12

Step-by-step explanation:

7x+13=97

   -13   -13

7x=84

/7   /7

x=12

To sketch the region in the plane consisting of points whose polar coordinates satisfy the conditions \(1 < r \leq 2\) and \(\frac{3}{4} \leq \theta \leq \frac{5}{4}\), we can visualize the region as follows:

1. Start by drawing a circle with radius 1. This represents the condition \(r > 1\).

2. Inside the circle, draw another circle with radius 2. This represents the condition \(r \leq 2\).

3. Now, mark the angle \(\theta = \frac{3}{4}\) on the circle with radius 1, and mark the angle \(\theta = \frac{5}{4}\) on the circle with radius 2.

4. Shade the region between the two angles \(\frac{3}{4}\) and \(\frac{5}{4}\) on both circles.

The resulting sketch should show a shaded annular region between the two circles, with angles \(\frac{3}{4}\) and \(\frac{5}{4}\) marked on the respective circles. This annular region represents the set of points whose polar coordinates satisfy the given conditions.

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This statement is true, as the test statistic represents the number of standard deviations between the observed sample proportion and the claimed value (po) under the null hypothesis.

- The large value of the test statistic means that our observed data are not surprising when the null hypothesis is true. This statement is false. A large test statistic implies that the observed data is surprising when the null hypothesis is true, which means there is evidence against the null hypothesis.
- The researcher should fail to reject the null hypothesis. This statement is false. A large test statistic suggests evidence against the null hypothesis, so the researcher should reject the null hypothesis in favor of the alternative hypothesis.

- When the null hypothesis is true, the test statistic comes from a standard normal distribution. This statement is true, as the test statistic follows a standard normal distribution when the null hypothesis is true.
- There is a 4.318% chance that the alternative hypothesis is true. This statement is false. The test statistic does not directly provide the probability of the alternative hypothesis being true. Instead, we can use the test statistic to calculate the p-value, which represents the probability of obtaining a test statistic as extreme as the observed one, assuming the null hypothesis is true.

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Answer:

o,m would be 20

Step-by-step explanation:

because the other side is 20 and you just put 10 on the other side

Answer:

See below

Step-by-step explanation:

OM   triangle OCB is isosceles rt triangle with hyp = 10

    Pythagorean theorem

            10^2  = S^2 + S^2     Shows s = sqrt (50)

                then triangle COM

                    pythagorean theorem again

                        5^2 + OM^2 = (sqrt(50))^2

                         25 +  OM^2 = 50

                                   OM^2 = 25

                           OM = 5 cm

Funny....here is an easier way    OM is 1/2 way across the square with side length of 10     so it is = to 5 cm

  ~D'Oh !

Angle VMO :     VO = 12    OM = 5      ARCTAN (12/5) = 67.4°

Angle  VBM:       VM =  12/sin67.4 = 13 cm     then ARCTAN 13/5 = 69°

According to the solving the area of the square is 68.0625.

As is common knowledge, a square is a four-sided, two-dimensional figure. It is also referred to as a quadrilateral. The total quantity of unit squares forming a square is referred to as the square's area. In other words, it is described as the area that the square takes up.

The box formed after cutting the square from each corner will have the dimensions as,

length = 104 - 2x, width = 39 - 2x, height = x.

∴ volume of the box = length × width × height

∴ v = (104 - 2x)(39 - 2x)(x) -----(i)

∴ v = (104 - 2x) (39x - 2\(x^{2}\))

∴ v = 104(39x - 2\(x^{2}\)) -2x(39x - 2\(x^{2}\))

∴ v = 4056x - 208\(x^{2}\) - 78\(x^{2}\) + 4\(x^{3}\)

∴ v = 4\(x^{3}\) - 286\(x^{2}\)  + 4056x

let f(x) =  4\(x^{3}\) - 286\(x^{2}\)  + 4056x  -----(ii)

To, find x for which f(x) is maximum,

⇒we should apply second derivative test ,

According to this test, first we should find critical points at which f'(x) = 0.

then if f''(x) < 0 for that critical point then f(x) is maximum at that critical point.

∴ let us consider, f'(x) = 0.

now, f(x) =  4\(x^{3}\) - 286\(x^{2}\)  + 4056x

⇒ f'(x) = 12\(x^{2}\) - 572x + 4056.  -----(iii)

⇒ f'(x) = 4(3\(x^{2}\) - 143x + 1014)

⇒ f'(x) = 0.

⇒  f'(x) = 4(3\(x^{2}\) - 143x + 1014) = 0

⇒ x = (-b ± \(\sqrt{b^{2} - 4ac }\))/2a    ; where a = 3, b = -143, c = 1014.

∴ x = (-(-143) ± \(\sqrt{(-143)^{2} -4(3)(1014)}\))/2×3

∴ x = (143 ± \(\sqrt{8281}\))/6.

∴ x = \(\frac{143 + 91}{6}\)  , x = \(\frac{143 - 91}{6}\)

⇒ x = 39, 8.25

the square of length 8.25 inch should be cut from each side to det contained with the maximum volume.

Area of the square is = \(x^{2}\) = \(8.25^{2}\)

∴ Area = 68.0625

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Answer: 0.2737

Step-by-step explanation:

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Answer:

g(f(x)) = 8x² - 28x + 34

Step-by-step explanation:

f(x) = 2x² - 7x + 6

g(x) = 4x + 10

g(f(x)) = y

y = 4 ( 2x² - 7x + 6 ) + 10 = 8x² - 28x + 34

g(f(x)) = 8x² - 28x + 34

Answer:

f(X)=2x^2-7x+6

g(X)=4x+10

Step-by-step explanation:

now according to question, g(f(X))=g{f(X)}

=g(2x^2-7x+6)

=4(2x^2-7x+6)+10

= 8x^2-14x+24+10

=8x^2-14x+34

Using limits, the end behavior of the functions are given as follows:

a. Rises to the left and falls to the right.

b. Rises to the left and rises to the right.

c. Falls to the left and rises to the right.

The end behavior of a function f(x) is given by the limit of f(x) as x goes to infinity.

In item a, we have that, respectively, to the left and to the right.

\(\lim_{x \rightarrow -\infty} f(x) = \lim_{x \rightarrow -\infty} -5x^3 = -5(-\infty)^3 = \infty\)

\(\lim_{x \rightarrow \infty} f(x) = \lim_{x \rightarrow \infty} -5x^3 = -5(\infty)^3 = -\infty\)

Hence it rises to the left and falls to the right.

In item b, we have that, respectively, to the left and to the right.

\(\lim_{x \rightarrow -\infty} f(x) = \lim_{x \rightarrow -\infty} 3x^6 = 3(-\infty)^6 = \infty\)

\(\lim_{x \rightarrow \infty} f(x) = \lim_{x \rightarrow \infty} 3x^6 = 3(\infty)^6 = \infty\)

Rises to the left and rises to the right.

In item c, we have that, respectively, to the left and to the right.

\(\lim_{x \rightarrow -\infty} f(x) = \lim_{x \rightarrow -\infty} 20x^3 = 20(-\infty)^3 = -\infty\)

\(\lim_{x \rightarrow \infty} f(x) = \lim_{x \rightarrow \infty} 20x^3 = 20(\infty)^3 = \infty\)

Falls to the left and rises to the right.

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First, we have to identify the right triangle formed

As you can observe, segment AB is divided into two equal parts. We can find one part of AB using the Pythagorean's Theorem

Where c = 15 and b = 12. Let's find a

Then, we know that AB = 2a, so

Answer: The value of G = 4.5

Step-by-step explanation:

As per given,

\(G\propto \dfrac{j^2}{m}\)

When we replace proportional sign with an equal to sign, we get

\(G=k\dfrac{j^2}{m}\), where k = constant

If G=0.05 when j = 0.4 and m=1.6, then

\(0.05=k\dfrac{0.4^2}{1.6}\\\\ 0.05=k(0.1)\\\\ k=0.5\)

Now,

\(G=0.5\dfrac{j^2}{m}\\\\\Rightarrow\ G=0.5\dfrac{6^2}{4}\\\\\Rightarrow\ G=4.5\)

hence, when j =6 and m=4, the value of G = 4.5

The proportion of those surveyed who chose basketball as their favorite sport is 34.149 (option a)

Let's denote the proportion of adults who chose basketball as their favorite sport as P(Basketball). To calculate P(Basketball), we need to divide the total number of adults who chose basketball by the total number of surveyed adults. Mathematically, it can be represented as:

P(Basketball) = (Number of adults who chose basketball) / (Total number of surveyed adults)

To calculate the number of adults who chose basketball, we sum up the values from the age range categories:

Number of adults who chose basketball = Number of adults (18-30) who chose basketball + Number of adults (31-50) who chose basketball + Number of adults (51 and above) who chose basketball

Looking at the table, we find that the number of adults (18-30) who chose basketball is 15, the number of adults (31-50) who chose basketball is 8, and the number of adults (51 and above) who chose basketball is 11. Adding these values together, we get:

Number of adults who chose basketball = 15 + 8 + 11 = 34

Now, let's calculate the total number of surveyed adults. We can sum up the values from the age range categories:

Total number of surveyed adults = Total number of adults (18-30) + Total number of adults (31-50) + Total number of adults (51 and above)

From the table, we find that the total number of adults (18-30) is 49, the total number of adults (31-50) is 48, and the total number of adults (51 and above) is 52. Adding these values together, we get:

Total number of surveyed adults = 49 + 48 + 52 = 149

Now, we have the values we need to calculate the proportion:

P(Basketball) = (Number of adults who chose basketball) / (Total number of surveyed adults)

= 34 / 149

Hence the correct option is (a).

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Answer:

a = 281.25 mg after two hours

Step-by-step explanation:

Here, we want to get the amount of aspirin that will be present after two hours

what we simply do here is to substitute 2 for t

Thus, we have it that;

a = 500(3/4)^2

a = 500•(0.75)^2

a = 281.25 mg

The distance between pair of parallel lines with the  following equation

y=2x+3 y=2x-7 \(2{\sqrt 5}\) units

​

Parallel lines are any two or more lines that lie in the same plane but never cross one another. Both have the same slope and are equally distant from one another. No matter how far we extend a parallel line, it will always remain straight.

The fundamental characteristics listed below make it simple to recognize parallel lines.

The slope of a line which is perpendicular to both the lines will be \(-\frac{1}{2}\).

Check what are the y-intercept of any one of the two lines & write the equation of the perpendicular line through it.

The y-intercept of line y = 2x-7 is (0, -7).

So, the equation of any line with slope \(-\frac{1}{2}\) and a y-intercept of −7 is

y = \(-\frac{1}{2}x-7\)

The perpendicular intersects or meets the line y = 2x -7 at (0,-7).

Now, to find the point of intersection of the perpendicular & the other line, solve the two equations.

Solve for x:

                    2x + 3 =    \(-\frac{1}{2}x-7\)

                          \(\frac{5}{2} x\) = -10                                        (combine them like terms)

                            x = -4                                         (multiply each side by 2\5)              

Find y:

               y = \(-\frac{1}{2}.(-4)-7\)

                  = -5

so, the point is (-4,-5).

Now using the Distance Formula, find the distance between the points (-4,-5) and (0,−7).

​

\({\displaystyle d={\sqrt {\left(x_{2}-x_{1}\right)^{2}+\left(y_{2}-y_{1}\right)^{2}}}\)

  \(={\sqrt {\left(0-(-4\right)^{2}+\left(-7-(-5\right))^{2}}}\)

  \(={\sqrt {4^2 +(-2)^2}}\)

  \(=2{\sqrt 5}\)

​

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​

Answer:

Add an "x" between "ninety" and "eight". Ninety x Eight = 720.

90 x 8 = 720

let's assume the temperature on 5th day be x

We know that :

\( \boxed{mean = \frac{sum \: \: of \: all \: \: observations}{number \: \: of \: \: observations} }\)

So,

\( \hookrightarrow \: 0 = \dfrac{ - 2 + ( - 2) + ( - 2) + ( - 2) + x}{5} \)

\( \hookrightarrow \: 0 \times 5= - 2 - 2 - 2 - 2 + x\)

\( \hookrightarrow \: 0 = - 8 + x\)

\( \hookrightarrow \: x = 8\)

Therefore, temperature on the fifth day was x = 8

Excel displays the error message "#DIV/0!" in cells to indicate a divide-by-zero error. This occurs when a formula attempts to divide a value by zero, which is mathematically undefined. To resolve this error, you can check the input values and formulas in your spreadsheet to ensure they are valid and avoid division by zero.

In Excel, when a formula attempts to divide a value by zero, the software will display the error message "#DIV/0!" in the affected cells. This is a helpful indication to the user that the calculation has failed and that the formula needs to be adjusted. It is important to note that this error message can impact other calculations in the spreadsheet, so it is important to resolve it as soon as possible to prevent inaccuracies in the data. Excel provides several ways to handle divide-by-zero errors, such as using the IFERROR function or adjusting the formula to include an IF statement to avoid errors.
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The length of Raj's piece of string is 12x units.

To determine the length of Raj's piece of string, we need to find Kiki's third-longest piece.

Looking at the line plot or list of lengths provided, we can identify the third-longest length of Kiki's pieces.

Let's assume Kiki's third-longest piece has a length of x units.

According to the problem, Raj's piece of string is 12 times as long as Kiki's third-longest piece.

Therefore, the length of Raj's piece of string would be 12 × x units.

We can only express it as 12x units, where x represents the length of Kiki's third-longest piece.

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Answer:

140 db

Step-by-step explanation:

I have succesfully finished tihs

The value is closest to the sound level of the vocalizations of a blue whale is 140dB.

We have given that,

Intensity(I)= 106.8 watts/meter^2

The intensity of sound hair by the human ear is,

\(I_0=1\times10^{-12}\)

Sound intensity is defined as the power carried by sound waves per unit area in a direction perpendicular to that area.

We have to find which value is closest to the sound level, in decibels, of the vocalizations of a blue whale

So we have given the formula

\(B=10 log(\frac{I}{I_0} )\)

So use the given value we get

\(B=10 log(\frac{106.8}{1\times 10^{-12}} )\)

B= 140.28 dB≈140 dB

Therefore the value is closest to the sound level of the vocalizations of a blue whale is 140dB.

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

Multicollinearity in a multivariate regression model refers to the correlations between two or more independent variables. Multicollinearity can lead to skewed or false results when a researcher or analyst attempts to determine how effectively each independent variable can be used to predict or understand the dependent variable in a specific statistical model.

It is the term which is generally used to describe the situation in which two or more explanatory variables in a multiple regression model have strong linear correlations with one another but not with the dependent variable. Many times, the creation of new dependent variables that are reliant on other variables can also result in multicollinearity.

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