Moustapha A.

Tutor since 2000 (Math/STAT) University level

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Linear Algebra

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Question:

Solve the following system of linear equations: $(x+y=5\\x-y=1$)

Moustapha A.

Answer:

add the first equation to the second equation to get $$x=3$$, then substitute back in the first equation to get $$y=2$$.

Discrete Math

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Question:

At a college, 546 students have taken a course in calculus, 178 have taken a course in discrete mathematics, and 165 have taken a course in both calculus and discrete mathematics. How many students have taken a course in either calculus or discrete mathematics?: *

Moustapha A.

Answer:

546+178-165= 559 students

Statistics

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Question:

If a random sample of size n=100 is drawn from a population having µ=9 and σ =5, determine the probability that the mean from the sample will be (i) At most 10 (ii) At least 8.5

Moustapha A.

Answer:

(i) p (mean ≤ 10) = p (z ≤ $$\frac{10-9}{5/\sqrt{100}}$$) = 0.9773 = 97.73% (ii) p (mean ≥ 8.5) = p (z ≥ $$\frac{8.5-9}{5/\sqrt{100}}$$) = 0.8413 = 84.13%

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