Responses have dwindled each week since these questions do not count for Black and Gold points, but there are a few dedicated students that still have been waiting for the problems of the week. Instead, there will be a set of problems for the month of April and the month of May. The prize list is still up for grabs for 4th quarter. Good luck!
Problems of the Month
1. If b is positive, what is the value of b in the geometric sequence 9, a, 4, b? Express your answer as a common fraction. A geometric sequence is found by multiplying by a common factor. For example, in the sequence 1, 2, 4, 8... the common factor is 2. Find the common factor, and then use it to solve.
2. Noel earns $25 each week mowing lawns. Each week he spends two-fifths of his earnings on himself and has the rest of his earnings placed directly into a savings account. Every third week he withdraws $20 from his savings account to take his girlfriend to the movies. If he continues this same spending pattern, how many weeks will it take Noel to first exceed $125 in his savings account? Express your answer as a whole number.
3. Two complementary angles A and B have measures in the ratio of 13 to 17. What is the ratio of the measure of the supplement of angle A to the supplement of angle B? Express your answer as a common fraction.
4. Amy and Belinda each roll a sheet of 6-inch by 8-inch paper to form a cylindrical tube. Amy tapes the two 8-inch sides together without overlap. Belinda tapes the two 6-inch sides together without overlap. What is the difference of the volumes of the two tubes?
5. The scale of a certain map is 0.8 inch = 16 miles. A square park is represented on this map by a square with side length 0.625 inch. What is the actual area of this park? Express your answer as a decimal to the nearest hundredth.
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