1Given the price-supply points (7,500, 2.28) and (7,900, 2.37), calculate the slope 'm' for the price-supply equation p = mx + b.
2Solve for x in the equation: log5(x + 2) + log5(x) = log5(x + 12).
3Identify the formula for the Future Value (FV) of an ordinary annuity based on the course materials.
4In a Leontief Input-Output model, which equation represents the relationship between the Total Production (X), Technology Matrix (M), and Final Demand (D)?
5Find the radius of a circle where a central angle of 60 degrees intercepts an arc length of 15.7 cm. (Use pi ≈ 3.14)
6An employee attempts a test with a pass rate of 40% on the 1st trial. If they fail, the pass rate on the 2nd trial is 60%. What is the probability that the employee passes the test on either the first or the second attempt?
7Which of the following are valid elementary row operations used in Gauss-Jordan Elimination?
8Determine the vertex of the quadratic function f(x) = (x^2 / 2) + x - 4.
9In the context of the course bonus question, express tan(theta) in terms of 'a' given that theta = arcsec(a) for 0 ≤ theta < pi/2.
10Identify the constraints that would define a bounded feasible region in a linear programming problem based on the provided materials.
