Find the local maximum and minimum values of f using both the First and Second Derivative Tests. (If an answer does not exist, enter DNE.) Х f(x) x2 + 9 local maximum value (3,6) 6) x _3, local minimum value x

If this property is violated, the observations are said to be: autocorrelated

What is Random Series?

The results of an experiment are functions of an integer argument, and the results are described by a random series: U1, U2.. (or, simply, sequences of random values - 1st value, 2nd value, etc).

The term "time series" and, occasionally, "random processes with discrete time" are frequently used to describe random series. The Markov chain exemplifies a crucial category of random series.

In this question, it's asked when the property of independence is violated.

If the consecutive observations are correlated or linearly related, then they are said to be autocorrelated. This denotes that there will be an association of the current time period with the successive and preceding time periods. Violation of the autocorrelation assumption yields inaccurate results.

Hence, The observations are said to be: autocorrelated in the random series.

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If no box has a card with the same letter as the box, then count the number of elements as 24 ways.

Given that,

Four randomly selected cards with the letters A, B, C, and D are placed in the corresponding boxes. There is exactly one card in each box.

We have to find If no box has a card with the same letter as the box, then count the number of elements.

We know that,

A permutation is a mathematical calculation that establishes the number of possible arrangements for a given set, taking into account the arrangement's order.

From the given information:

The permutation approach can be used to represent the four cards that are randomly placed in the four boxes and can be used to express the following:

=⁴P₄

Since no box contains a card that begins with the same letter as the box, it follows that

Card A can be inserted into a box four different ways,

Card B three different ways,

Card C two ways, and

Card D one way.

The four cards' permutation can then be calculated as follows:

⁴P₄=4!/0!=4×3×2×1/1=24.

Therefore, If no box has a card with the same letter as the box, then count the number of elements as 24 ways.

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The domain of the function is 24.The collection of all potential inputs for a function is known as its domain.

Explanation:

F(x)= 12x-5 and G(x) = 2x²+3

Find (G-F) (-2) ,    put x = 0 ,   2+3-12-5 = -12.

-12 * -2 = 24.

The domain of the function is 24.    

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The Mean absolute deviation and the mean are not same.

Given,

The mean;-

The average of a group of variables is referred to as the mean in mathematics and statistics. There are several methods for calculating the mean, including simple arithmetic means (adding the numbers together and dividing the result by the number of observations), geometric means, and harmonic means.

Mean absolute deviation;-

The average distance between each data point and the mean is known as the mean absolute deviation of a dataset. It offers us a sense of how variable a dataset contains.

Therefore,

The Mean absolute deviation and the mean are not same.

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The slope of the line is 2.

From the question, we have

the slope of the line that passes through two points is given by:

m = (y1 - y2) / (x1 - x2)

=(10-12)/(3-4)

=2

The slope of the line is 2.

Slope of a Line :

The ratio of the change in the y coordinate to the change in the x coordinate is known as a line's slope in mathematics.

Y and X, respectively, stand for the net change in the y-coordinate and the net change in the x-coordinate.

As a result, the formula for the change in y-coordinate with respect to the change in x-coordinate is m = change in y/change in x = y/x.

where the slope of a line is denoted by "m".

The graph of the equation y = mx + c has a slope of m, an intercept of m, and a y-intercept of c. In the slope-intercept version of the linear equation, m and c are real integer values.

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Because EFGH is a rhombus, the distance from E to F is the same distance from E to H. Since E is the same distance from F as it is from H, it must lie on the perpendicular bisector of FH. By the same reasoning, G must lie on the perpendicular bisector of FH. Therefore, line EG is the perpendicular bisector of segment FH. So, reflecting rhombus EFGH across line FH will take E to G and G to E (because E and G are on the line of reflection) and F to H and H to F (since FH is perpendicular to the line of reflection, and R and H are the same distance from the line of reflection, on opposite sides). Since the image of rhombus EFGH reflected across EG is rhombus EHGF (the same rhombus), line EG must be a line of symmetry from rhombus EFGH.

The direction of increase of the given objective functions is

(a) in the direction of x₁

(b) in the direction of x₂

(c) in the direction of x₂

In the question ,

three objective functions are given ,

we have to find the direction in which the given function increase ,

So ,

Part (a) ,

z = 4x₁ - x₂

According to the signs of the variables given ,

the function z will increase in the direction of x₁ , because x₁ has positive sign and it will decrease in the direction of x₂ as it has a negative sign .

Part(b) ,

z = -x₁ + 2x₂

According to the signs of the variables given ,

the function z will increase in the direction of x₂ , because x₂ has positive sign and it will decrease in the direction of x₁ as it has a negative sign .

Part(c) ,

z = -x₁ + 3x₂

According to the signs of the variables given ,

the function z will increase in the direction of x₂ , because x₂ has positive sign and it will decrease in the direction of x₁ as it has a negative sign .

Therefore , The direction of increase of the given objective functions is

(a) in the direction of x₁

(b) in the direction of x₂

(c) in the direction of x₂ .

The given question is incomplete , the complete question is

For each of the following, determine the direction in which the objective function increases:

(a) z = 4x₁ - x₂

(b) z = -x₁ + 2x₂

(c) z = -x₁ + 3x₂

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Exactly one unique triangle exists with the given side lengths, option B is correct.

Here, we are given that the three sides of triangle are- 12, 15 and 18.

According to the triangle inequality theorem- “The sum of the length of any two sides of a triangle should be greater than the third side”. Let us see if this holds in this case-

(12 + 15) > 18

(15 + 18) > 12

(12 + 18) > 15

Thus, we see that the triangle inequality theorem is satisfied. So there is only one triangle possible with the sides of given lengths.

Hence, exactly one unique triangle exists with the given side lengths, option B is correct.

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Your question was incomplete. Check for full content below-

How many triangles exist with the given side lengths?

12 in, 15 in, 18 in

A) No triangle exists with the given side lengths.

B) Exactly one unique triangle exists with the given side lengths.

C) More than one triangle exists with the given side lengths.

The value of the total distance between the two stations is 2520m

The train runs with the following acceleration:

v = u + at

12 = 0 + a(120)

a = 0.1 m/s2.

Distance covered by the train in first part:

S = 1/2at^2

S = 1/2×0.1×(120)^2

S = 720m

Distance covered in second part:

S = ut

S = 12×60 = 720m

Train deceleration is given by

v = u+ at

0 = 12+a (180)

a = -1/15

Distance covered by the train in last part:

S = ut- 1/2at^2

S = 12(180) - 1/2(1/15)(180)^2

S = 2160 - 1080

S = 1080m

Therefore,  The value of the total distance between the two stations is 720+720+1080 = 2520m.

The complete question is :A tram leaves a station and accelerates for 2 minutes until it reaches a speed of 12 meters per second. It continues at this speed for 1 minute. It then decelerates for 3 minutes until it stops at the next station .Calculate the distance, in meters, between the two stations.​

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Converted form of ratio 60:52 in form n:1 is 10/7 : 1.

How to write a ratio in n:1 form?

In order that a ratio is written in the form n:1 we must make the right hand side equal to one.

n can be expressed as a decimal or a fraction.

According to the given question:

Convert ratio 60:52 in n:1 form

So, divide both sides of ratio with 52 to get 1 on right side of ratio.

60/52 : 1

10/7 : 1

Hence 10/7 : 1 is the converted form.

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Answer:

[tex]3(4)^{23}[/tex]

Step-by-step explanation:

Let the first term be [tex]a[/tex] and the common ratio be [tex]r[/tex].

We know [tex]a=3[/tex] and [tex]ar=12[/tex], meaning [tex]r=4[/tex].

This means the 24th term is [tex]3(4)^{23}[/tex].

Answer:

The function crosses the Y axis (the up down axis) at -1

Step-by-step explanation:

The average rate of change of the function, f(x)=50(1.021)^x over the interval of x=7 to x=10 is calculated as: 1.24.

The average rate of change = f(b) - f(a) / b - a.

Given the following:

The function is: f(x) = 50(1.021)^x

Interval is: x = 7 to x = 10

Therefore:

a = 7

b = 10

f(a) = f(7) = 50(1.021)^7

f(a) = f(7) = 57.83

f(b) = f(10) = 50(1.021)^10

f(b) = f(10) = 61.55

Therefore:

Average rate of change = (61.55 - 57.83) / 10 - 7

= 1.24.

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The current required to produce metal at a rate of 5.00 g/min is 274A

The electrolyte ion equation is;

Ni²⁺ (aq)  +  2e⁻   →   Ni (s)

Faradays constant = 9.65 * 10⁴ C/mol

Molar mass of Nickel = 58.69 g/mol

Number of moles of nickel; n_ni = 5 g/min * 1 mol/58.69 g/mol = 0.0852 mol

n_e = 0.0852 mol * 2/1

n_e = 0.170 mol

I = nF/t

where;

t is in minutes

F is faradays' constant

Thus;

I = (0.17 * 9.65 * 10⁴)/(1 * 60)

I = 274 A

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Point C - Tolerance values above 0.2 may indicate multi collinearity in the data is correct.

Given that

It must be below 0.2, along with VIF above 10.

The remaining options are not correct.

A. If the average variance inflation factor is greater than 1 then the regression model might be biased.

B. Multi collinearity in the data is shown by a VIF (variance inflation factor) greater than 10.

D. The tolerance is 1 divided by the VIF (variance inflation factor).

Hence the answer is Point C - Tolerance values above 0.2 may indicate multi collinearity in the data is correct.

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In given word problem , number of total pages in the book is 168.

What is word problem?

      Word problems in mathematics that concentrate on addition, subtraction, multiplication, and division, among other more precise operations A math word problem is a question that is written as one or more sentences and asks students to use their mathematical understanding to solve an issue from "real world." In order for kids to understand the word problem, they must be familiar with the terminology that goes along with the mathematical symbols that they are used to.

Here Eden and Kember are reading the same book.

Here Eden reads 1/6 pages of the book. And Kimber reads,

=> 1/6(total pages)+32 which is 60.

=> 1/6(x)+32=60

=>1/6(x)=60-32=28

=> x = 28*6

=> x = 168.

Therefore total number of page in the book is 168.

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f(x) was transformed to make g(x) by B) Horizontal or vertical stretch.

The transformation of a function may involve any change.

Usually, these can be shift horizontally (by transforming inputs) or vertically (by transforming output), stretching (multiplying outputs or inputs) etc.

Given that the function g(x) is a transformation of the parent function f(x).

To Decide how f(x) was transformed to make g(x).

The reflection of the point (x,y) across the line y = 1/2 x is the point (y, x).

By the given tables we can see that;

g(x) = 1/2 f (x)

Therefore, f(x) was transformed to make g(x) by B) Horizontal or vertical stretch.

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The anagrams that can be created from the word accommodate is N=4989600.

An anagram is a word or phrase made by rearranging the letters of another word or phrase, often using all of the original letters exactly once.

The original word or phrase is known as the anagram's subject. An anagram is any word or phrase that exactly duplicates the letters in a different order. An "anagrammatist" is someone who makes anagrams, and the purpose of a serious or expert anagrammatist is to make anagrams that reflect or remark on their subject.

Given word is

'accommodate'

Total number of letters= 11

Number of a = 2

c=2

m=2

0=2

The rest are one each.

Therefore, the number of possible arrangements can be written as;

N = 11!/(2!2!2!2!)

N = 39916800/8

N=4989600

Therefore, the anagrams that can be created from the word accommodate is N=4989600.

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This equation [tex]\frac{3}{m + 3}[/tex] - [tex]\frac{m}{3 - m}[/tex] = [tex]\frac{m^{2 } + 9}{m - 9}[/tex] has no solution.

Since we have given that

[tex]\frac{3}{m + 3}[/tex] - [tex]\frac{m}{3 - m}[/tex] = [tex]\frac{m^{2 } + 9}{m - 9}[/tex]

We need to find the solution of the above equation:

Since is a rational equation so, we will check for its extraneous solution.

[tex]\frac{3}{m + 3}[/tex] - [tex]\frac{m}{3 - m}[/tex] = [tex]\frac{m^{2 } + 9}{m - 9}[/tex]

[tex]\frac{3}{m + 3}[/tex] +  [tex]\frac{m}{3 - m}[/tex]  =  [tex]\frac{m^{2 } + 9}{m - 9}[/tex]  

[tex]\frac{3(m + 3) + m(m +3)}{m^{2} - 9}[/tex] =   [tex]\frac{m^{2 } + 9}{m - 9}[/tex]

[tex]\frac{3m - 9 + m^{2} +3m }{m^{2}-9 }[/tex] =  [tex]\frac{m^{2 } + 9}{m - 9}[/tex]

[tex]\frac{m^{2} -9+6m}{m^{2} -9}[/tex] =  [tex]\frac{m^{2 } + 9}{m - 9}[/tex]

[tex]m^{2} +6m -9 = m^{2} + 9[/tex]

[tex]6m = 18[/tex]

[tex]m = \frac{18}{6} = 3[/tex]

Hence, the extraneous solution in case of rational equation is 3 , when we put m = 3, it becomes undefined so, it has no solution.

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The equation of a line that passes through points (a,b) and (c,d) is (c-a)y = (d-b)x+b(c-a)-a(d-b).

A line's equation is an algebraic way of expressing the collection of points that make up a line in a coordinate system.

The many points that collectively make up a line on the coordinate axis are represented as a group of variables (x, y) to create an algebraic equation, also known as an equation of a line.

Let the two points are (a,b) and (c, d)

To find the equation of line,

Use formula y- y₁ = (y₂-y₁/x₂-x₁) (x-x₁)

The equation of line,

y-b = (d-b/c-a)(x-a)

(c-a)(y-b) = (d-b)(x-a)

(c-a)y = (d-b)x+b(c-a)-a(d-b)

The required equation of the line is (c-a)y = (d-b)x+b(c-a)-a(d-b).

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The triangle with angles 44 degrees, 54 degrees, and 82 degrees will be a scalene triangle.

We are given the following:

The measures, in degrees, of the three angles of a triangle are x, x + 10, and 2x - 6.

We know from the triangle angle sum property that the sum of its internal angles is 180 degrees.

Let us find the given angles;

x + x + 10 + 2x - 6 = 180 degrees

4x + 4 = 180 degrees

4x = 180 - 4 degrees

x = 176 / 4 degrees

x = 44 degrees

So,

Angles will be;

x = 44 degrees

x + 10 = 44 + 10 = 54 degrees

2x - 6 = 2 * 44 - 6 = 88 - 6 = 82 degrees

All the angles are different.

Thus, the triangle with angles 44 degrees, 54 degrees, and 82 degrees will be a scalene triangle.

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The full Python code is included below as an image, and it sets the base and height of triangles 1 and 2, then calculates the bigger area.

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After doing a hypothesis test the conclusion is reject [tex]H_0[/tex] .

Given:

tom is a big green bay packers and aaron rodgers fan. he claims that aaron rodger's average number of touchdowns per game is 2.45. dave (a hardcore bears fan) believes that tom might be inflating rodgers's statistics. from his debut until november 18, 2019, aaron rodgers has played 175 games! dave does not want to look at all of them. he randomly selects 52 games that rodgers played and finds the sample average number of touchdowns to be 1.942 with a standard deviation of 1.42.

here n = 52

σ = 1.42

x = 1.942

μ = 2.45

z = x - μ / σ/√n

= 1.942 - 2.45 / 1.42/√52

= -2.58

p value = 0.0049

[tex]H_0:mean = 2.45[/tex]

[tex]H_a:mean < 2.45[/tex]

Rejection rule:Reject [tex]H_0[/tex] if p value < 0.05

Conclusion Reject [tex]H_0[/tex]

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She needs to get her interest rate at will 5.592 %/year.

What is Compound interest?

Compound interest is the addition of interest to the principal sum of a loan or deposit or interest on interest plus interest.

[tex]A = P(1 + \frac{r}{n})^{nt}[/tex]

Where,

A = final amount

P = initial principal balance

r = interest rate

n = number of times interest is applied per time period

t = number of time periods elapsed

Solving for rate r as a decimal

r = n[(A/P)1/nt - 1]

r = 12 × [(2,500.00/2,000.00)1/(12)(4) - 1]

r = 0.0559158

Then convert r to R as a percentage

R = r * 100

R = 0.0559158 * 100

R = 5.592%/year

Hence, she needs to get her interest rate at will 5.592 %/year.

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There are 5 1's in the given identity matrix of order 5.

Given, an identity matrix of order 5

we have to find the number of 1 in the given matrix

So, as the matrix is an identity matrix and the order of the matrix is 5

in an identity matrix, the entry is 1 when

i = j i.e. on the diagonal elements.

As, the order of the matrix is 5 then, the number of 1's in the matrix are 5.

Hence, there are 5 1's in the given identity matrix of order 5.

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The expression that represents the total amount that can be raised from selling 50 tickets is -2t + 250 and the total amount that can be raised is $194.

What is total revenue?

Total revenue is the amount of money earned by a company from the sale of its goods and services. In other words, businesses use this metric to determine how well their core revenue-generating operations are performing. Total revenue is directly related to marginal revenue.

Number of tickets that will be sold = 50

Number of student tickets that will be sold = t

Number of adult tickets that will be sold = 50 - t

The total amount of money that can be raised from selling 50 tickets is the sum of the total amount raised from selling student tickets and adult tickets.

Total revenue = total amount raised from selling students tickets + total amount raised from selling adults tickets

Total revenue = [3 x t] + [(50 -t) x $5]

Total revenue = $3t + $250 - 5t

Total revenue = -2t + 250

Total revenue = -2(28) + 250

Total revenue = -56 + 250 = $194

Hence, the expression that represents the total amount that can be raised from selling 50 tickets is -2t + 250, and the total amount that can be raised is $194.

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Answer:

12.45, 0.25, -0.85, -12

Step-by-step explanation:

The larger the negative the lesser the value, opposite for positive numbers

The total unit of fuel used per mile f (N)= 12+ 2.2N

A linear function has the following form

y = f (x) = a + bx

A linear function has one independent variable and one dependent variable. The independent variable is x and the dependent variable is y.

The graph of a linear function is a straight line.

The train uses 12 unit of fuel per mile and an additional 2.2 unit of fuel per mile for each railcar on the train.

Therefore the unit of fuel used per mile by N railcars is 2.2N

The total number of unit of fuel used per mile = 12+2.2N

therefore f(N)= 12+2.2N

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A function containing a variable base raised to a fixed power   is considered to be a power function.

when a function has a constant base raised to a variable power. This can be called an exponential function, not a power function A power function may be a function with a single term that is the product of a real number, a coefficient, and a variable raised to a fixed real number. It is in the form of f(x)=kx^p, where k and p are the real numbers whereas k is the coefficient.

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