Math Mastery Exam 02
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Questions and Answers

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?

<p>{1, 2, 4, 5, 9} (D)</p> Signup and view all the answers

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

<p>3/s + 1/s^2 (A)</p> Signup and view all the answers

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

<p>7 (D)</p> Signup and view all the answers

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

<p>i51 (B)</p> Signup and view all the answers

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

<p>6 (A)</p> Signup and view all the answers

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

<p>(-π/2, π/2) (A)</p> Signup and view all the answers

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

<p>Cross-correlation function (A)</p> 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)?

<p>-2 (A)</p> Signup and view all the answers

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

<p>Ae-5tcos15t (C)</p> Signup and view all the answers

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

<p>At least 95% (C)</p> Signup and view all the answers

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

<p>A series with terms involving xⁿ/n! (B)</p> 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)?

<p>The dot product of the gradient of U at P and the unit vector in the direction of Q (D)</p> 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)]?

<p>-40 (A)</p> 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?

<p>264 (B)</p> Signup and view all the answers

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

<p>1 – 2x + 4x² - 8x³ (B)</p> Signup and view all the answers

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

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

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

<p>0.98 (C)</p> Signup and view all the answers

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

<p>Level of Significance (B)</p> Signup and view all the answers

Under which condition does an initially relaxed system become unstable?

<p>only if bounded input generates unbounded output (C)</p> Signup and view all the answers

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

<p>(e^-s - e^-2s)/s (B)</p> Signup and view all the answers

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

<p>1/(s+1) (A)</p> Signup and view all the answers

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

<p>The mean is positive and the standard deviation is negative (C)</p> 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?

<p>-1/20 (C)</p> 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?

<p>The median of the elements in M is greater than the median of the elements in N (D)</p> Signup and view all the answers

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

<p>12°C (C)</p> 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}?

<p>2 + 4z-1 + 5z-2 + 7z-3 + z-5 (B)</p> Signup and view all the answers

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

<p>Every element from list M is larger than the corresponding element from list N (C)</p> Signup and view all the answers

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