what kind of autocorrelation is assumed in the classical linear regression model? what kind of autocorrelation is assumed in the classical linear regression model? positive autocorrelation negative autocorrelation no autocorrelation serial correlation g

The inequality that can be used to solve for x, the number of minutes it will take Amy to finish typing her paper is D. 38x + 1,450 > 4,000.

Inequalities are created through the connection of two expressions. It should be noted that the expressions in an inequality aren't always equal. Inequalities implies that the expressions are not equal. They are denoted by the symbols ≥ < > ≤.

Since Amy types at an average speed of 38 words per minute and has already typed 1,450 words of her final paper, which will be more than 4,000 words.

Let the number of minutes be x.

This will be:

1450 + 38(x) > 400

1450 + 38x > 4000

In conclusion, the correct option is D.

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The dimensions of the rectangle that will allow for the most economical fence to be built is 50 feet and 25 feet in length and width respectively.

Given in the question,

Area = 1250 ft²

The three sides cost $3 per foot, and the fourth side costs $9 per foot.

Let x and y be the length and width of the rectangle.

Because the area is 1250 ft², therefore

xy = 1250, or

y = 1250/x            

Case 1: Three sides are (x,y,x) and the 4-th side is y.

The cost is

C = 3(2x +y) + 9y

  = 6x + 12y

  = 6x + 12(1250/x)

  = 6x + 15000/x

For C to be minimum, C' = 0. That is

6 - 15000/x² = 0

x² = 15000/6

x =  50 ft, y = 1250/50 = 25 ft

C = 6(50) + 15000/(50²) = $600

Case 2: Three sides are (y,x,y) and the 4-th side is x.

The cost is

C = 3(x + 2y) + 9x

   = 12x + 6y

   = 12x + 6(1250/x)

   = 12x + 7500/x

For C to be minimum, C' = 0.

12 - 7500/x² = 0

x² = 7500/12 = 625

x = 25 ft, y = 50ft

C = 12(25) + 7500/25 = $600

Thus, the Dimensions will be 25 feet and 50 feet.

Question:

A fence is to be built to enclose a rectangular area of 1250 square feet. the fence along three sides is to be made of material that costs ​$3 per foot. the material for the fourth side costs ​$9 per foot. find the dimensions of the rectangle that will allow for the most economical fence to be built.

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By using the properties of parallelogram, it can be calculated that

[tex]\angle CFE = 30^{\circ}[/tex]

[tex]\angle[/tex]DEF = 70°

[tex]\angle AED = 110^{\circ}[/tex]

What is a parallelogram?

Parallelogram is a four sided two dimensional figure whose each pair of opposite sides are parallel.

Here, ABCD is a parallelogram

[tex]\angle CFE = 30^{\circ}[/tex] [Alternate angle]

[tex]140 = \angle CEF + \angle CFE[/tex] [ Exterior angle of a triangle is equal to the sum of two opposite interior angle]

[tex]\\\angle CEF = 140 - 30\\\angle CEF = 110^{\circ}[/tex]

[tex]\angle[/tex]DEF = 180 -  110 [ Angle on a straight line]

         = 70°

[tex]\angle AED = 110^{\circ}[/tex] [Vertically opposite angle]

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The circumference of circle of radius 70 cm is 440 [tex]cm^{2}[/tex].

According to the question,

We have the following information:

Radius of the circle = 70 cm

(Diameter is twice that of its radius..)

We know that the following formula is used to find the circumference of circle:

Circumference of circle = 2πr

(More to know: the formula to find the area of circle is π[tex]r^{2}[/tex].)

(More to know: there are two values of π. One is 3.14 and one is 22/7.)

Circumference of circle = 2*(22/7)*70

Circumference of circle = 440 [tex]cm^{2}[/tex]

Hence, the circumference of the circle of radius 70 cm is 440 [tex]cm^{2}[/tex].

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A) The equation is 22 + (d * 1/2) = 30

B) The plant that still have to grow 8 cm more

C) d = 16 days, d represents the number of days

Step-by-step explanation:

Given:

Initial height (basil plant at buying) = 22cm

Plant grows on everyday = 1/2cm

A) Given:

Total  height (to be grown) = 30 cm.

The equation is,

Initial height+ ( number of days * plant grows on everyday) =  Total height

22 + (d * 1/2) = 30  →  equation 1

B) The plant that still have to grow = Total height - Initial height

= 30 - 22

= 8 cm

C) Solving the value d using equation 1:

22 = 30 - (d * 1/2)

    44 = 60 - d 

      d = 16 days

Hence, A) The equation is 22 + (d * 1/2) = 30.

B) The plant that still have to grow 8 cm more.

C) d = 16 days, d represents the number of days.

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Answer: Y=1

Step-by-step explanation:

Equation - y=mx+b

y2-y1

First point: )-4, 1)

second point: (2,1)

Finding the slope:

m=0

b = ?

1=0x+b

y=0x+1

so thats why its y=1

Answer:

Paco, Tim, Jenny, Maria

Step-by-step explanation:

The equivalent equation for the expression y = 3x-6 is none.

Equivalent equation:

If the two equations are said to be equivalent when they have the same solution set. Then it is called as Equivalent equation.

Given,

Here we have the expression y = 3x-6

Now, we need to find the equivalent equation.

In order to find the equivalent equation, we have to take some sample values for x,

The sample value of x as 1, 2, 3

Now, we have to apply these values on the given expression first,

Then we get,

x = 1 => y = 3(1) - 6 = -3

x = 2 => y = 3(2) - 6 = 0

x = 3 => y = 3(3) -6 = 9

Now, we have to apply these to the given equation and which has the same value of the given expression,

x = 1 => 3(1) - 2y = 6 = -2y = 6 - 3 => y = -3/2

x = 2 => 3(2) - 2y = 6 = -2y = 6 - 6 => y = 0

x = 3 => 3(3) - 2y = 6 = -2y = 6 - 9 => y = 3/2

This is not equal one.

Move on to the second one,

x = 1 => 2(1) + 3y = -6 => 3y = -6 - 2 => y = -8/3

x = 2 =>  2(2) + 3y = -6 = 3y = -6 - 4 => y = -10/3

x = 3 =>  2(3) + 3y = -6 = 3y = -6 - 6 => y = -4

This is not a equivalent one.

Move on to the third expression,

x = 1 => 3(1) - 2y = 12 = -2y = 12 - 3 => y = -9/2

x = 2 => 3(2) - 2y = 12 = -2y = 12 - 6 => y = -3

x = 3 => 3(3) - 2y = 12 = -2y = 12 - 9 => y = -3/2

This is not a equivalent one.

Finally we have to use the last one, then  we get,

x = 1 => 2(1) - 3y = 18 => -3y = 18 - 2 => y = -16/3

x = 2 =>  2(2) - 3y = 18 => -3y = 18 - 4 => y = -14/3

x = 3 =>  2(3) - 3y = 18 => -3y = 18 - 6 => y = -4

Therefore, none of them are the equivalent one.

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By using the diagram and the given angle measure we get that:

if, m∠1 = 143°

then, m∠2 = 37°

         m∠3 = 143°

         m∠4 = 37°

What is angles?

An angle is formed when two straight lines or rays meet at a common endpoint.

What is Properties of Congruence?

       For all angles A ,

        ∠A≅∠A .

       An angle is congruent to itself.

        For any angles A  and  B ,

        if ∠A≅∠B , then ∠B≅∠A .

         Order of congruence does not matter.

        For any angles A,B,  and  C ,

        if ∠A≅∠B and ∠B≅∠C , then ∠A≅∠C .

        If two angles are both congruent to a third angle, then the first two        angles are also congruent.

I assume that, this refers to two intersecting lines which form four angles.

         ∠1 + ∠2 = 180°

          143° + ∠2 = 180°

          ∠2 = 180° - 143°

          ∠2 = 37°.

         It means that,  ∠1 = ∠3 =143° (properties of congruency)

         and ∠2 = ∠4 =37° (properties of congruency).

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Function [tex]-3x^2+18x+3[/tex] has maximum value at x = 3 and its maximum value is 30.

How do you find the maximum and minimum value of the function?

Calculus can be used to find the critical point, or the x-value of the vertex, by taking the derivative of the function, or f'(x). To determine the critical point, we shall set the function's first derivative to zero and solve for x. This point's maximum or minimum value can be determined by taking the second derivative, or f"(x). The second derivative will have a minimal value if it is positive. The second derivative will be the highest value if it is negative.

Given function:

[tex]-3x^2+18x+3[/tex]

To find the maximum and minimum value of the function use second derivative test.

On differentiating the above function we get,

-6x + 18

Now, find critical point

-6x + 18 = 0

-6x = - 18

x = - 18/-6 = 3

x = 3

Here, x = 3 is the critical point. Now again differentiate the above function we get,

-6

As , [tex]f^{''}(x)[/tex] < 0 , therefore x = 3 will given a maximum value of function and maximum value is

f(3) = [tex]-3(3)^2+18x+3 = -3(9) + 18(3) + 3 = -27 + 54 + 3 = 27 + 3 = 30[/tex]

Hence , function [tex]-3x^2+18x+3[/tex] has maximum value at x = 3 and its maximum value is 30.

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4, 7/4, -1/2, -11/4, is Arithmetic progression.

What is Arithmetic progression ?

An arithmetic progression or arithmetic sequence ( AP ) is a sequence of numbers such that the difference between the consecutive terms is constant.

Here the series is given

4, 7/4, -1/2, -11/4,.....

In series, take 1st and 2nd terms to know common difference.

the common difference is = 7/4 - 4

                                              = (7 - 16) / 4 = -9/4

Now, take 3rd and 2nd term

common difference = -1/2 - 7/4

                                 = (-2 - 7) / 4 = - 9/4

so, we get the common difference is -9/4.

By that we can clearly say that given sequence of series is a Arithmetic sequence.

Hence, 4, 7/4, -1/2, -11/4, is Arithmetic progression

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Using a system of equations, it is found that:

Leah takes 3 minutes to run a lap and 6 minutes to walk a lap.

The variables of the system of equations are presented as follows:

She requires 84 minutes to do 8 laps running and 10 laps walking, hence the first equation is:

8x + 10y = 84.

She requires 66 minutes to do 2 laps running and 10 laps walking, hence the second equation is:

2x + 10y = 66.

Simplifying by 2, we have that:

x + 5y = 33.

x = 33 - 5y.

Replacing in the first equation, we can find the time it takes to walk a lap, as follows:

8(33 - 5y) + 10y = 84.

264 - 40y + 10y = 84

30y = 180

y = 180/30

y = 6 minutes.

Then the time it takes to run a lap is obtained as follows:

x = 33 - 5y = 33 - 5(6) = 33 - 30 = 3 minutes.

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There is no vertex in the graph and the transformations from are

By definition, a graph that has a vertex would have an obvious maximum or minimum point on it

In this case, there is no point that can be regarded as the minimum or the maximum in this graph

This means that the graph has no maximum or minimum; in other words, there is no vertex

The parent function of the above graph is a cubic function

A cubic function passes through the origin

However in this graph, we can see that the graph is 4 units to the left of the origin and 2 units below the origin

This means that the transformation is (x - 4, y - 2)

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21/8 must be added to the terms to give the result as 6. The answer will be in a fraction.

What is a fraction?

In general, any number of equal pieces is represented by a fraction, which is a portion of the entire. In ordinary English, a fraction refers to the number of parts of a specific size.

Main Body:

Let the term to be added be x.

3+3/8+x =6

on solving this we will get the value of  x= 21/8

Hence the answer of this question is 21/8.

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The probability that there are no counts in a 30 second interval is 0.284

What is probability ?

Probability refers to potential.This branch of mathematics deals with the occurrence of a random event. The value's range is 0 to 1. Before we can determine the probability that a particular event will occur, we must first know the total number of outcomes.

Given that,

Assume that a Geiger counter records counts using a poisson process, with an average rate of 2 counts per minute.

0.284

P(X < 10 Seconds)  = P(X<1/6 minutes) = F(1/6) = 1-e-2*1/6 = 1-e-1/3 = 0.284

Therefore, the  probability that there will be no counts in a 30-second period is 0.284.

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Table C is the only table that represents a function

A function is a relationship between inputs where each input is related to exactly one output. Every function has a domain and codomain or range. A function is generally denoted by f(x) where x is the input

Based on the definition of function as seen above. Let's check the tables:

Table A has two inputs with the same value (4)  but with different outputs. So  Table A is not a function

Table B also has two inputs with the same value (9)  but with different outputs. Thus, Table B does not represent a function

In Table C  each input has exactly one output. Table C represents a function

Table D also has two inputs with the same value (8)  but with different outputs. So Table D does not represent a function

Therefore, Table C represents a function

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81 percentile of the given test is 482

The square root of the means of the squared deviations from the arithmetic mean is known as the standard deviation. Standard deviation is used in finance to quantify the risks associated with an investment instrument.

Given that the Marble Academy of Whoville conducts an annual test for all high school juniors one year, the scores on the test were approximately normally distributed with a mean of 420 and a standard deviation of 70

Here mean μ = 420 and Standard deviation σ = 70

We have find 81 percentile of this test = ?

The z score corresponding to the area 0.81 is

Z = 0.88  By standard normal table

X = μ + z σ

X = 420 + 0.88 x 70

= 420 + 62

= 482

Therefore 81 percentile of this test is 482

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The mean of the distribution of sample means is 100.

Considering the values provided in the question,

Population mean = 100

We know that,

The sample mean is a reliable indicator of the population mean.

That is, E( sample mean)=Mean(sample mean)= population mean

Here population mean is 100, therefore mean of distribution of sample means is also 100.

The total of all the values in a sample is known as the Sample Mean. It is a statistical metric used to examine different variables throughout time. It is calculated by statisticians and researchers by dividing the total sum of all data fragment values by the total number of data sets.

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In 2267 year, this population would be 400000.

From the question, we have

population is growing as  Pn = 200*(1.03)n

substituting the value, we get

400000 = 200*(1.03)n

2000 = 1.03n

ln(2000) = n*ln(1.03)

n = ln(20000) / ln(1.03)

n = 257.15

2010 + 257.15 = 2267 year , this population would be 400000.

Multiplication:

Mathematicians use multiplication to calculate the product of two or more numbers. It is a fundamental operation in mathematics that is frequently utilized in everyday life. When we need to combine groups of similar sizes, we utilize multiplication. The fundamental concept of repeatedly adding the same number is represented by the process of multiplication. The results of multiplying two or more numbers are known as the product of those numbers, and the factors that are multiplied are referred to as the factors. Repeated addition of the same number is made easier by multiplying the numbers.

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Answer:

Step-by-step explanation:

The solution of linear system of equations is the point of intersection of the lines.

Closer view of the graph gives us the point ( - 2, 6 ). See the attached.

Add vertical and horizontal lines from the point of intersection and take the closest values to the integer numbers on the x-axis and the y-axis. The numbers are -2 on the x-axis and 6 on the y-axis, therefore the answer is (- 2, 6).

The matching choice is B.

Answer:

5

Step-by-step explanation:

The graph shows the absolute value function.

y = |x - 3| + 5

First, we can see that the shape of the graph is a "V", so we have an absolute value function.

We can see that the slope is 1 (for each horizontal square that the line moves, it also moves one vertically) , so our function will be of the form

y = |x - a| + b

Notice that the above function has a vertex at (a, b)

And the graphed one ahs a vertex at (3, 5), with that we can conclude that the graphed function is:

y = |x - 3| + 5

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Answer:

it should be the first one, if not it’s the third

Step-by-step explanation:

Consuelo deposited an amount of money in a savings account that earned 6. 3% simple interest. After 20 years , she had earned $5’922 in interest then the initial deposit was $4700

Use the simple interest formula

I = P r t

where I = simple interest

P = principal

r= rate of interest

t= number of years

5922=Px6.3%x20

5922=Px1.26

P=5922/1.26

P=4700

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The slope of line 1 and line 2 are equal. Then the lines are parallel to each other.

A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.

The slope of the parallel lines will be equal.

The equations are given below.

5x − 3y = 2             ...1

5x − 3y = 8            ...2

The slope of line 1 is given as,

5x − 3y = 2

y = (5/3)x − 2/3

The slope of line 1 is 5/3.

The slope of line 2 is given as,

5x − 3y = 8

y = (5/3)x − 8/3

The slope of line 2 is 5/3.

The slope of line 1 and line 2 are equal. Then the lines are parallel to each other.

The graph is given below.

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The correct description of the graph of the inequality x - 3 ≥ 5, is: D. Closed circle on 8, shading to the right.

An inequality statement compares two unequal quantities. When plotting the graph of an inequality, if the inequality sign involve is "< or >", an open circle is used to mark the value of the variable on the number line, while a closed circle is used when the inequality sign involved is, "≤ or ≥".

Given the inequality, x - 3 ≥ 5, solve for x:

x - 3 ≥ 5

Add 3 to both sides

x - 3 + 3 ≥ 5 + 3 [addition property]

x ≥ 8

This means the possible values of x are greater than or equal to 8. The graph of the inequality would have a closed circle at 8, with the line shaded to the right on the number line.

The correct description is: D. Closed circle on 8, shading to the right.

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Answer:

-2

Step-by-step explanation:

Answer:

x=-2

Step-by-step explanation:

distribute

-7x-14-x=2

-8x-14=2

    +14. +14

-8x=16

/-8. /-8

x=-2

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