Math Mastery Exam 02

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What does the correlation measure?

The difference between the maximum and minimum values of a dataset

The average of the squares of the deviations from the mean

The strength and direction of the relationship between two variables (correct)

The middle value of a dataset when it is arranged in order

What is the value of g(6) if g(x) = |5x^2 – x^3|?

216 (correct)

36

-54

-36

If a unit integrator is cascaded to a control system and a unit ramp input is applied, what is the value of the steady-state error?

0.20

0.25 (correct)

0.15

0.10

What is the union of C and the intersection of A and B?

{1, 2, 4, 5, 9} Signup and view all the answers

What is the Laplace transform of F(t) = 3 + t?

3/s + 1/s^2 Signup and view all the answers

What is the value of cos 2z if cos z = 2?

7 Signup and view all the answers

What is the simplified form of i29 + i21 + i?

i51 Signup and view all the answers

How many even numbers are present in the union of sets A and B?

6 Signup and view all the answers

What is the range of f(z) = arg 1/(1 – z) for |z| = 1, z ≠ 1?

(-π/2, π/2) Signup and view all the answers

What is the function used for determining the similarity between a signal and its delayed version?

Cross-correlation function Signup and view all the answers

What is the centroid's location in the root locus diagram of the transfer function K(s+6)/(s+3)(s+5)?

-2 Signup and view all the answers

What is the inverse transform of the Laplace transform function L(s) = 20s/(s2 + 20s + 75)?

Ae-5tcos15t Signup and view all the answers

What is the probability of the homebuilder completing a house within a certain number of days?

At least 95% Signup and view all the answers

What is the Taylor series generated by the function f(x) = eˣ at x = 0?

A series with terms involving xⁿ/n! Signup and view all the answers

What is the directional derivative of U = 2x³y - 3y²z at P(1, 2, −1) in a direction toward Q(3, −1, 5)?

The dot product of the gradient of U at P and the unit vector in the direction of Q Signup and view all the answers

What is the value of the determinant of the matrix A = [(1,0,2),(2,-3,4),(-3,1,9)]?

-40 Signup and view all the answers

What is the value of (A + B)∙(B + C) for vectors A = 8i + 2j + 2k, B = 4i + 2j + 4k, and C = 6i + 8j + 10k?

264 Signup and view all the answers

What is the Maclaurin series for f(x) = 1/(1 – 2x)?

1 – 2x + 4x² - 8x³ Signup and view all the answers

What is the simplified expression for the square root of 8 – 15i?

± (3/sqrt 2 – 5i/sqrt 2) and ± (3/sqrt 2 + 5i/sqrt 2) Signup and view all the answers

What is the probability that at least one doctor is available when needed?

0.98 Signup and view all the answers

What is the rejection probability of a Null Hypothesis when it is true?

Level of Significance Signup and view all the answers

Under which condition does an initially relaxed system become unstable?

only if bounded input generates unbounded output Signup and view all the answers

What is the Laplace transform of the function f(t) = u(t – 1) + u(t – 2)?

(e^-s - e^-2s)/s Signup and view all the answers

What is the transfer function of a system with impulse response g (t) = e(-t)?

1/(s+1) Signup and view all the answers

What is not a possible combination of mean and standard deviation for a given population?

The mean is positive and the standard deviation is negative Signup and view all the answers

What is the coefficient of (x – 1)5 in the Taylor series for x ln(x) about x = 1?

-1/20 Signup and view all the answers

What must be true if every element from list M is larger than the corresponding element from list N?

The median of the elements in M is greater than the median of the elements in N Signup and view all the answers

What is the range of the temperatures in the first week of July in southern Iceland?

12°C Signup and view all the answers

What is the z-transform of the finite duration signal x(n) = {2,3,4,5,7,0,1}?

2 + 4z-1 + 5z-2 + 7z-3 + z-5 Signup and view all the answers

What is the relationship between the elements of list M and list N?

Every element from list M is larger than the corresponding element from list N Signup and view all the answers