Keep up the great work, everyone! Don’t forget to check your answers on the last post. Here’s the math du jour:
11. If a number is raised to the three-fifths power and multiplied by 3, and then the square root is taken, the result is 9. What is the number? (10 pts.)
12. At Half-and-Half High School, there are 408 ninth-graders who are involved in at least one of these activities: playing a musical instrument, playing a sport, or acting in the school drama productions. 164 students play a musical instrument, 208 play a sport, and 99 are in drama. 11 students are in all three activities. If a ninth-grader is selected at random from this group, what is the probability that he or she is involved in more than one activity? (10 pts.)
13. A dog named Polly is tethered by a 30-foot rope to a pole in the middle of a yard shaped like a regular hexagon. If she can just reach the midpoint of one the yard’s sides when she stretches the rope to its full length, what percentage of the yard can Polly reach? Express your answer as a decimal to the nearest tenth. (10 pts.)
14. Bonus. What is the remainder when 22014 is divided by 7? (20 pts.)
15. Bonus. Dartboards on the planet Zygote look slightly different than the ones on planet Earth, as shown here. The centers of the red circles are positioned halfway from the center to the edges of the board, and their radii are one-fourth of of the board’s radius and twice that of the green circles. What is the probability that when a Zygotean throws a dart at the board, it will hit on a region that is within the blue square but also within a red or green circle?