Vectors

Step 1: The probability that the student studied for at most 2 hours is given by: Step 2: Substitute the given values: Step 3: Substitute : Step 4: Compute the value: Thus, the probability that the student studied for at most 2 hours is 0.55.

Step 1: The effective annual rate for a given nominal rate compounded times per year is given by: where: - (10% nominal rate), - is the number of compounding periods per year.
Step 2: First, compute for semi-annual compounding ( ):
Step 3: Compute the value:
Step 4: Now, compute for quarterly compounding ( ):
Step 5: Compute the value:

Step 1: Plot the constraints on the graph:
Step 2: Identify the feasible region satisfying and the constraints.
Step 3: Compute at each vertex of the feasible region. The maximum is the solution.