final pratice exam help please no calculator

Question

Answer 1

18).

The function f(x) = - 5/(x + 4)³.

f(x) = - 5(x + 4)^{- 3}.

Apply formula : (d/dx)(xⁿ) = nx^{n - 1}.

f '(x) = - 5[(- 3)(x + 4)^{- 3 - 1}]

f '(x) = 15(x + 4)^{- 4}

f '(x) = 15/(x + 4)⁴.

Solution : Option (b) is the correct choice.

Answer 2

17)

Given reduced echelon form of matrix using Gauss Jordan Elimination method is,

By using Gauss Jordan Elimination method,we got reduced row echelon form of matrix.

Number of variables n = 3

Rank of matrix A ( first 3 columns ) is R(A) = 2

Rank of echelon form  is R(AB) = 2

R(A) = R(AB) = 2 < n.

The system is consistent.

And system has infinitely many solutions.

Let z = z

y + 3z = 4  ⇒  y = 4 - 3z

x = 2

Solution : Option (c) is the correct choice.

Comments

Number of variables n = 3

Rank of matrix A ( first 3 columns ) is R(A) = 2

Rank of echelon form  is R(AB) = 2

R(A) = R(AB) = 2 < n.

 

I have no idea what those words mean. And the steps below confuses me. Is there another way to do this to get the answer without using the rule that was assigned?

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Number of variables means [x y z] therefore n = 3.

Rank of matrix A means the number of non-zero rows in the matrix.

The first two rows of the matrix are not zero.

As the last row in the matrix contains zeroes, then rank of the matrix is 2.

Rank of echelon form  is R(AB) = 2

Even here the first two rows of the matrix are not zero.

As the last row in the matrix contains zeroes, then rank of the echelon form of matrix is 2.

 

Conditions:

System of equations AX = B does not have solutions when rank of [A] < rank [A|B]

System of equations AX = B have unique solutions when rank of [A] = rank [A|B] = n

System of equations AX = B have infintely many solutions when rank of [A] = rank [A|B] < n

 

In this problem, R[A] = R[A|B] = 2 < n, the system has infinitely many solutions.

Answer 3

19).

A correlation coefficient, designated by r, is a number in the range -1 < r < 1, that indicates how well a regression equation truly represents data being examined.

• If r is close to 1 (or -1), the model is considered a "good fit". 
• If r is close to 0, the model is "not a good fit". 
• If r = ± 1, the model is a "perfect fit" with all data points lying on the line.
• If r = 0, there is no linear relationship between the two variables.

Considering that, r is close to positive 1.

From the above data, 0.98 is close to + 1.

Solution : Option (a) is the correct choice.

Comments

That is not the correct answer. The correct Answer is C. So how can i do this problem?

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The points of a certain set don' t lie close to a line.

Means that, the correlation coefficient is doesn ' t closer to + 1 and - 1.

From the given options, 0.02 is doesn ' t closer to + 1 and - 1.

So, the best possible value of the correlation coefficient is 0.02.

Solution : Option (c) is the correct choice.