A fair die was rolled and the events A and B were recorded as follows: A = {1, 3, 5} and B = {2, 3, 4, 5}. Find P(A/B).
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Express sin 3θ in terms of sin θ
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Without using a mathematical table or calculator, evaluate:
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i) cos(165°)
ii) tan(A + B) given that A and B are acute angles having sin(A) = 7/25 and cos(B) = 5/13
The daily prophet obtained by Fruits Beverages Company in its business is given by the objective function f(x, y) = 250x + 350y − 2200 and the constraints:
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x + y ≥ 5.5
4x + 2y ≥ 16
x + 2.5y ≥ 9
i) Represent the linear programming problem graphically
ii) Determine the minimum and maximum profit of the company
Given the linear inequalities: 2y ≤ 4x, x ≤ 6, y ≥ 2, and 2x + 3y ≤ 30
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i) Draw the corresponding graph
ii) List the corner points of the feasible region
Given the system of linear equations below
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x + y + z = 7
x − y + 2z = 9
2x + y − z = 1
i) Write the system of equations in matrix form
ii) Find the determinant and the inverse of the matrix
iii) ...
Use the truth table to show that p ↔ q logically implies p → q
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Write the contrapositive of the inverse of p → q
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Use the laws of algebra to simplify
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i) [A ∩ (B ∩ C´)] ∪ C
ii) (X ∩ Y´) ∪ (X ∩ Y ) ∪ (Y ∩ X´)
Out of a group of 17 girl guides and 15 boy scouts, 22 play handball, 16 play basketball, 12 of the boy scouts play handball, 11 of the boy scouts play basketball, 10 of the boy scouts play both and 3 of the girls play neither of the two
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i) How many girls play both handball and basketball?
ii) How many in the group play handball only and basketball only