Check all of the number that are potential rational root of f(x) = x4 – 2x3 5x2 – 7x 9

The correlation coefficients that indicate that an increase in one variable results in a decrease in the other;

B. r=-0.5776

C.r=0.2361

Correlation coefficient is a measure of how similar two datasets are acting.

When the correlation coefficient comes out as -1, it means that both the datasets are negatively oppositely correlated. One data increases, other data starts decreases in the opposite direction.

When the correlation coefficient comes out below 0, then values are negatively correlated. SO,

All of the given option are negatively correlated.

If the correlation coefficient comes out as 0, that means both the data sets are uncorrelated.

Therefore, the correlation coefficients that indicate that an increase in one variable results in a decrease in the other;

B. r=-0.5776

C.r=0.2361

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The value of (gof)(x) is [tex]3x^2[/tex] - 12x + 17

The first function is

g(x) = [tex]3x^2[/tex] + 5

The second function is

f(x) = x - 2

The function is the mathematical statement that shows the relationship between one variable and another variable. If one variable is independent variable and another variable is dependent variable. The function consist of the different variable, numbers and mathematical operators

Then the value of (gof)(x) is

g(f(x) = g(x-2)

Then,

g(x - 2) = 3 × [tex](x-2)^2[/tex] + 5

Expand the terms

g(x - 2) = 3 × ([tex]x^2[/tex] - 4x + 4) +5

g(x - 2) = [tex]3x^2[/tex] - 12x + 12 +5

Add the terms

g(x - 2) = [tex]3x^2[/tex] - 12x + 17

Hence, the value of (gof)(x) is [tex]3x^2[/tex] - 12x + 17

The complete question is

If g(x) = 3x^2+ 5

f(x) = x - 2

Find the value of (gof)(x)

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The two quantities x and y, are directly proportional. If x is doubled, then value of y will also be doubled.

If two quantities become directly proportional, it indicates that if one increases by a specific percentage, the other also increases by the same percentage.

For the given situation;

x and y are in the direct proportional relation.

Thus,

x ∝ y

Thus,

x = k y

k = proportionality constant.

Thus,

multiplying both side by 2

2 x = 2 k y

Y also becomes twice .

If x is multiplied by 4 then,

4 x = 4 k y

y also get 4 times.

Thus, if x is doubled, then value of y will also be doubled and if x get 4 timed y also become 4 times.

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a) Number of elements in the union of all three sets when the sets are pairwise disjoint is 300

b) Number of elements in the union of all three sets when there are 50 common elements in each pair of sets and no elements in all three sets  is 150

c) Number of elements in the union of all three sets when there are 50 common elements in each pair of sets and 25 elements in all three sets  is 175

d) Number of elements in the union of all three sets when the sets are equal is 100

What do you mean by relation and function?

(INPUT, OUTPUT) is a representation of an ordered pair.

The relationship between INPUT and OUTPUT is demonstrated by the relation. A function, on the other hand, is a relation that yields one OUTPUT for each given INPUT. Although all relations are functions, not all functions are relations. A function is a relationship that states that there should only be one output for each input, or we could refer to it as a particular category of relationship (a collection of ordered pairs) that adheres to a rule.

Given are three distinct sets, A1, A2, and A3, each with 100 members. The number of elements in the uninon set, A1 U A2 U A3, are as follows, according to the circumstances.

First off, if we remember the formula, it will be really simple to determine how many components make up the union set;

n(A1 U A2 U A3) = n( A1 ) + n( A2 ) + n( A3 ) - n( A1 ∩ A2 ) - n( A2 ∩ A3 ) - n( A1 ∩ A3 ) + n( A1 ∩ A2 ∩ A3 ),

a) This states that we dont have any common elemets in  any pair of these sets,

n( A1 ∩ A2 ) = 0, n( A2 ∩ A3 ) = 0 , n( A1 ∩ A3 )  = 0 and also  n( A1 ∩ A2 ∩ A3 ) = 0 and as given n( A1 ) = n( A2 ) = n( A3 ) = 100 .

Hence the no of elements in the union set A1 U A2 U A3 will be

n(A1 U A2 U A3)

= n( A1 ) + n( A2 ) + n( A3 ) - n( A1 ∩A2 ) - n( A2 ∩ A3 ) - n( A1 ∩ A3 ) + n( A1 ∩ A2 ∩ A3 )

= 100 + 100 + 100 - 0 - 0 - 0 + 0

= 300      

b)  We have

n( A1 ) = n( A2 ) = n( A3 ) = 100

n( A1 ∩ A2 ) = n( A2 ∩ A3 ) = n( A1 ∩ A3 ) = 50 and n( A1 ∩ A2 ∩ A3 ) = 0 .

Hence the no of elements in the union set A1 U A2 U A3 will be

n(A1 U A2 U A3)

= n( A1 ) + n( A2 ) + n( A3 ) - n( A1 ∩ A2 ) - n( A2 ∩ A3 ) - n( A1 ∩ A3 ) + n( A1 ∩ A2 ∩ A3 )

= 100 + 100 + 100 - 50 - 50 - 50 + 0

= 150      

c) We have

n( A1 ) = n( A2 ) = n( A3 ) = 100

n( A1 ∩ A2 ) = n( A2 ∩ A3 ) = n( A1 ∩ A3 ) = 50 and

n( A1 ∩ A2 ∩ A3 ) = 25 .

Hence the no of elements in the union set A1 U A2 U A3 will be

n(A1 U A2 U A3)

= n( A1 ) + n( A2 ) + n( A3 ) - n( A1 ∩ A2 ) - n( A2 ∩ A3 ) - n( A1 ∩ A3 ) + n( A1 ∩ A2 ∩ A3 )

= 100 + 100 + 100 - 50 - 50 - 50 + 25

= 175      

d) This states that all the common elemets are present in the three sets, so

n( A1 ) = n( A2 ) = n( A3 ) = 100 as well as n( A1∩ A2 ) = n( A2 ∩ A3 ) = n( A1 ∩ A3 ) = n( A1 ∩ A2 ∩ A3 ) = 100

Hence the no of elements in the unino set A1 U A2 U A3 will be

n(A1 U A2 U A3)

= n( A1 ) + n( A2 ) + n( A3 ) - n( A1 ∩ A2 ) - n( A2 ∩ A3 ) - n( A1 ∩ A3 ) + n( A1 ∩ A2 ∩ A3 )

= 100 + 100 + 100 - 100 - 100 - 100 + 100

= 100    

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The correct option is,

There is no relationship between attending training and the preferred source of auto parts.

What is Null Hypothesis?

The null hypothesis in inferential statistics is that two possibilities are equal. The underlying assumption is that the observed difference is just the result of chance. It is feasible to estimate the probability that the null hypothesis is correct using statistical testing.

Null hypothesis always states that there is no significant difference between given observations. This also means that there is no such relationship between the two sets. That is, there is no effect of value in one set increases on value of another set will increase or decrease.

Hence the Null Hypothesis for given statement , "the relationship between attending training and preferred source of ordering parts " is :

H0 : There is no relationship between attending training and the preferred source of auto parts.

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Two positive numbers that satisfy x=21 and y=7

XY = 147

x +3y = x + 3(147/x) = (x²+ 441)/x = f(x)

0= f'(x) = (x ( 2x) - x² - 441)/x²

         = 2x² - x² -441)/x²

         = (x² - 441)/x²

So then x² - 441 = 0

             x = 21 , as x>0

x=21 and y=7,

the max sum is 21 +3(7) = 42

Related to best a regular and a primary-order (linear) time period, in which m is the slope and b is the y-intercept. every so often, the above is referred to as a "linear equation of variables," where y and x are the variables. a linear feature is defined as a feature that has both one or two variables without exponents. it is a function that graphs to the direct line.

A linear equation in two variables is of the shape Ax + by way of + C = zero, in which A and B are the coefficients, C is a consistent term, and x and y are the two variables. Linear functions are those whose graph is an instant line. A linear feature has the subsequent shape. y = f(x) = a + bx. A linear characteristic has one impartial variable and one based variable. The independent variable is x and the base variable is y.

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The sample space is all the cards in the deck if an experiment involves choosing one card from a deck of playing cards.

Given statement,

If an experiment is selecting a card from a deck of cards, then the sample space is,

For the given case,

The sample space in this case is " all the cards in the deck "

Therefore, If an experiment is selecting a card from a deck of cards, then the sample space is all the cards in the deck.

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Total number of games for 9 teams so that each team will play 12 games in the baseball league will be 432

Total number of teams in the baseball league is 9

Total number of games that each team will play is 12

Since, each team will have option of 8 teams to play with since no team can play with itself

Therefore, number of games that each team will play after playing 12 games will be 8 x 12 = 96

Since there are 9 teams, therefore total number of games that two teams will play = 96 x 9 = 864

Now, as it takes two teams to play a game therefore the required number of games for the 9 teams = 864/2 = 432

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Sampling variation will have more impact on confidence interval, but is not accounted for by the margin of error.

What is Sampling variation?

What factors lead to sampling variation?

Sample Sizes and Variability

What does the sample variation reveal?

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The taxi company charged a pick-up fee of $3. 80 plus $2. 25 per mile. So, the number of miles in the taxi ride with the total fare $33. 05 is 13 miles.

Write and solve an equation

Supppse, the number of miles = x

Total fare = a pick-up fee + fare per mile × the number of miles

Total fare = 3.80 + 2.25 x

Determine the number of miles

Total fare = 3.80 + 2.25 x

33.05 = 3.80 + 2.25 x

2.25 x = 33.05 - 3.80

2.25 x = 29.25

        x = 29.25/2.25

        x = 13

The number of miles in the taxi ride is 13 miles.

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Answer:

146304 marbles

Step-by-step explanation:

We do not need to worry about the color part, at least right now

One box contains 576 marbles

To find how many are in 2 boxes we would do 576 * 2

To find 254, we would do 576 * 254

Now, I would suggest using lattice multiplication here. If you do not know how to do that, long multiplication works fine.

I can't show that here, but I can show the answer:

576 * 254 = 146304

So, there are 146304 marbles is 254 boxes

The maximum absolute values of the shear and bending moment is 2P and 3Pₐ respectively.

(a) Diagram is shown in image.

From A to B:

+∑Fy = 0: V = -P

+∑M₁ = 0: M = -P

From B to C:

+∑Fy = 0:

-P-P-V = 0

⇒ V = -2P

+∑M₂ = 0:

Pₓ+P(x - a)+M =0

⇒

M = -2Pₓ + Pₐ

(b) The maximum bending moment occurs in a beam, when the shear force at the section is zero or changes the sign because at point of contra fixture the bending moment is zero.

Therefore

|V|max = 2P

|M|max = 3Pₐ

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If the required return is 10 percent then the profitability index for project 1 is 1.140 and project 2 is 1.284. If the company applies the profitability index decision rule, then project 2 should the firm accept.

In the given question, the michner corporation is trying to choose between the following two mutually exclusive design projects.

A1. Profitability index

Profitability index = present value of cash flow/initial investment

Project 1

Present value of future cash flows = 37600/(1+0.1)³

Present value of future cash flows = 93,505.634

Initial investment = 82,000

Now substitute values in formula

Profitability index = 93,505.634/82,000

Profitability index = 1.140.

Project 2

Present value of future cash flows = 11,200/(1+0.1)³

Present value of future cash flows = 27,852.742

Initial investment = 21,700

Now substitute values in formula

Profitability index = 27,852.742/21,700

Profitability index = 1.284

A2. Multiple choice.

The project with higher probability index should be accepted, therefore Project 2 should be accepted.

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No. Linear functions and quadratic functions are not the same.

Given,

A straight line on the coordinate plane is represented by a linear function. As an illustration, the equation y = 3x – 2 depicts a linear function because it is a straight line in the coordinate plane. This function can be expressed as f(x) = 3x - 2 since y can be replaced with f(x).

A polynomial function of degree 2 known as a quadratic function is expressed in the generic form f(x)=ax2+bx+c. Where a0, real numbers a, b, and c are used. The graph of the quadratic function f(x)=x2 that squares an input value is shown below.

When we graph a linear function, we get a straight line, however with a quadratic function, we get a parabola. In contrast to the slope of a linear polynomial, the slope of a quadratic polynomial is dynamic.

That is,

Linear functions and quadratic functions are not the same.

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Using tangent line approximation formula,

the tangent line approximation at x= 29.2 is

L(x) = 2x - 1 or L(29.2) = 57.4

Given a function f differentiable at tangent

x=a, we can find that the slope of the tangent of y=f(x) at (a,f(a)) can be found by writing . ). The resulting tangent line through (a,f(a)) and the gradient m=f'(a) is the point-gradient given by

y−f(a)=f'(a)(x−a) has an equation of the form This can also be expressed as y=f'(a)(x−a)+f(a).

Replacing the variable y by the expression L(x) yields

points (a, f( a)) called L(x)=f′(a)(x−a)+f(a). , L(x) is just the new name for the tangent, and

f(x)≈L(x) for x near a.

For example, suppose the function y=f(x) is known to have a tangent approximation at the point (1, 3) given by L(x)=3−2(x−1), but the function Other things about f.

we have given that,

f(x) = 2x - 1

x= 29.0 near to 29.2

f(29.0) = 58 - 1 = 57

f'(x) = 2

so, the point is (29.0, 57) and slope of tangent is 2 .

tangent line , 57 = 2(29) + b

=> b = -1

then equation is 2x - 1 = y

we to calculate tangent line approximation give as an approximation for at x = 29.2

tangent line approximation,

y = 2 (29.2) - 1 = 57.4

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Complete question:

suppose and f (x) = 2x - 1 , what does the tangent line approximation give as an approximation for x= 29.2??

Answer:

8.06 m

Step-by-step explanation:

Assuming the tree forms a right angle with the ground, the distance from the student to the tree represents the hypotenuse of a right triangle.

The hypotenuse can be found using the Pythagorean Theorem.

[tex]a^2+b^2=c^2\\a=8m\\b=1m\\c^2=(8m)^2+(1m)^2\\c^2=65m^2\\c=\sqrt65m^2\\c=8.06m[/tex]

Answer:

R = 1

Step-by-step explanation:

R = y/x

Substitute the x and y values, for example, the first row

5.8/5.8 = 1

Therefore the answer is 1

The distance from Amelia to the top of the tower is 100 feet.

Trigonometric Identities are equality statements that hold true for all values of the variables in the equation and that use trigonometry functions. There are numerous distinctive trigonometric identities that relate a triangle's side length and angle. Trigonometry is the study of angles and the angular relationships between planar and three-dimensional shapes. The cosecant, cosine, cotangent, secant, sine, and tangent are among the trigonometric functions (also known as the circle functions) that make up trigonometry.

Given,

Considering the query;

The tower has a 50-foot height.

Amelia's position and the top of the tower form a 30° angle.

Trigonometric identities, therefore;

Thus,

x = 50/sin30°

sin 30° = 50/x.

x = 50/0.5

x = 100 ft.

The distance from Amelia to the top of the tower is 100 feet.

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Sadie didn't simplify the expression properly and made mistakes during the simplification. The correct answer after simplification will be [tex]3a^{3} b\sqrt{6ab }[/tex]

Whenever we are about to simplify an expression, we should do it till the most simplified answer we got and follows the maths rules properly.
Sadie simplified the expression [tex]\sqrt{54a^{7}b^{3} }[/tex].

He first made an error during the simplification step at
[tex]\sqrt{3^3 \cdot 6 \cdot a^2 \cdot a^5 \cdot b^2 \cdot b}[/tex] where it should be [tex]3^{2}[/tex] not [tex]3^{3}[/tex].
Secondly, he came to the answer [tex]3a b \sqrt{6 a^5 b}[/tex] but we can simplify it more by simplifying [tex]a^{5}[/tex].

We can find the correct answer by simplifying the expression [tex]\sqrt{54a^{7}b^{3} }[/tex] by the following:

[tex]\sqrt{54a^{7}b^{3} }[/tex] = [tex]\sqrt{3^2 \cdot 6 \cdot a^2 \cdot a^5 \cdot b^2 \cdot b}[/tex]

=  [tex]3 \cdot a \cdot|b| \sqrt{6 \cdot a^5 \cdot b}[/tex]

= [tex]3 a b \sqrt{6.a^4.a.b}$[/tex]
= [tex]3.a.b.a^{2} \sqrt{6ab}[/tex]
[tex]= 3a^{3}b\sqrt{6ab}[/tex]

So the most simplified answer to the expression  [tex]\sqrt{54a^{7}b^{3} }[/tex]  is  [tex]3a^{3}b\sqrt{6ab}[/tex].

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Your question is incomplete, but most probably your full question is:

Sadie simplified the expression [tex]\sqrt{54 a^7 b^3}[/tex], , where [tex]$a \geq 0$[/tex] as shown:

[tex]\sqrt{54 a^7 b^3}=\sqrt{3^3 \cdot 6 \cdot a^2 \cdot a^5 \cdot b^2 \cdot b}=3 a b \sqrt{6 a^5 b}[/tex]

Describe the error Sadie made, and explain how to find the correct answer.

A line passes through (0, 2) and has a slope of 13. What is the equation of the line in slope-intercept form?

y = 1/3x + 2 (y equals 1 third x plus 2)

y = 1/3x − 2 (y equals 1 third x minus 2)

y = −1/3x + 2 (y equals negative 1 third x plus 2)

y-intercept is : (0 , 2)

slope = 13 or 13/1 (this is positive so slope will be positive)

slope = rise/run = y/x

Answer:

undefined slope

Step-by-step explanation:

a vertical line parallel to the y- axis has an undefined slope

Answer:26%

Step-by-step explanation:

(-14, -5) is the image point of (-9, -5) after the transformation T(-5,0)

Transformation is defined as the change in the position of a point, a line or a geometric figure

Given:  point (-9, -5) with transformation T (-5,0)

This implies there is a change in the position of the original point by (-5, 0). Thus, the image point can be determined as follows:

image point = (-9, -5) + (-5,0)

                    = (-9+(-5), -5+0)

                    = (-14, -5)

Therefore, the image point is (-14, -5)

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The rule in function notation for the courier company charge on delivery is

C = 15 + 1.6x

Independent variables  are the ones that you include in the model to explain or predict changes in the dependent variable.

The dependent variable is what you want to use the model to explain or predict. The values of this variable depend on other variables. It is the outcome that you’re studying. It’s also known as the response variable, outcome variable, and left-hand variable.

Given in the question,

A courier company charges $15 plus $1.60 per pound to deliver packages

Here , the dependent variable is cost of delivery because it is depending on how much a packages is weighting

The independent variable here is the weight of package because it doesn't depend on anything.

Let the cost of delivery be C and weight of package be x

The function for the charge will be :

C = 15 + 1.6x

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The y-intercept of f(x) = 3(1/2)x is less than the y-intercept of the graphed function.

The y-intercept of function, y = mx + b, is the value of b, which is the point on the graph where the line intersects the y-axis.

Given the function, f(x) = 3(1/2)x, the y-intercept is 0 because if we examine the equation given in slope-intercept form as y = mx + b, there is no value of b, or rather, the value of b is equal to 0.

In the given graph above, the line of the function intercepts the y-axis at 4. This implies that the y-intercept of the function on the graph is 4.

Therefore, f(x) = 3(1/2)x has a y-intercept that is less than that of the function in the given graph.

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The probability that the X is between 72 and 84 is 0.340 , the correct option is (d) .

In the question ,

it is given that ,

The random variable X is said to be normally distributed  ,

the mean is given as , μ = 70 , and

standard deviation of normal distribution is  (σ) = 10

probability that X is between 72 and 84 is written as P(72 < X < 84)

= P((72 - 70)/10 [tex]<[/tex] Z [tex]<[/tex] (84 - 70)/10)

= P(0.2 < Z < 1.4)

= P(0 [tex]<[/tex] Z [tex]<[/tex] 1.4) – P(0 [tex]<[/tex] Z [tex]<[/tex] 0.2)

From the z table , we get the values as

= 0.4192 – 0.0793

= 0.3399

≈ 0.340

Therefore , The probability that the X is between 72 and 84 is 0.340 , the correct option is (d) .

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The correct statements for least square estimates is the 3rd and 4th statements.

Least square estimates is method to predicted the observed Y value with minimized the sum of squared errors when using the fitted line.

The first and second statements is about simple linear regression. Simple linear regression is refers to linear line as parameter for fitting a model.

All statements are correct, but since the question asks for which statement is correct for least squares estimation, only the third and fourth statements are correct.

Thus, the 3rd and 4th statements is correct for least square estimates.

Your question is incomplete, but most probably your full question was (image attached)

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The best description of the graph of the proportional relationship is: D.  A line from (0, 0) going through (43, 36.55) where the x-axis is labeled Weight (in pounds) while the y-axis is labeled Cost (in dollars).

The graph that represents a proportional relationship is a straight line graph that passes through the origin (0, 0) and has a constant of proportionality, k, which is y/x.

Thus, given that the relationship between total cost for laundry service (y) is proportional to the weight of laundry (x), it means that the graph that will pass represent this would have the following features:

Therefore, the best description in words is: option D (last option).

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Answer:

Its A i did the practice exam test

Step-by-step explanation:

the guy above was wrong and didn't even make sense so here you go ;)

The total cost of 44 people in the class party will be $631

The total cost in dollars of a class party is 59 + 13n

Where n = number of people attending in the class party

Let F(n) be the function representing the total cost in dollars of a class party

Such as, F(n) = 59 + 13n

As per the question, the total cost of attending the 44 people will be:

For 44 people we have n = 44

As we had, F(n) = 59 + 13n

Here, F(n) will be treated as a function in which n will be its domain while F(n) will give the output as a range.

F(44) = 59 + 13(44)

     = 59 + 572

    = 631

Total cost will be $631

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