Author: EEBaum
Date: 2009-04-10 06:26
The mathematician in me is disappointed in the lack of sufficient information to solve many of these problems. However, I then realized that at least some of them are solvable with either abstract methodologies or by defining possible ranges for unspecified numbers.
My analysis...
1. The term "mutual bonds" does not appear in Wikipedia, and therefore does not exist. If he invested in mutual funds, Wilson has just lost the $328,416.23 due to the housing crash, and will not ever retire. He will be fired shortly, largely because of the drastic effects that his near-suicidal depression has had on his playing.
2. Initially, the depreciation formula seems irrelevant to the problem. However, it is in fact the most relevant part indeed. One would initially assume that someone who plays in a symphony orchestra would retain enough skill to at least be able to play the instrument, without practicing at all, just with the time spent playing during rehearsals and concerts. So, one might say, he will never become unable to play, barring death or physical injury, as long as he keeps with the orchestra.
According to the numbers provided, though, if Jethro's inclination to practice was initially 100%, or 1, he should have lost said inclination entirely in 16 days. In fact, after day 131, assuming he somehow had rejuvenated to 100%, his inclination would reach 0 by the very next day. The only way to reconcile this discrepancy is to assume that the orchestra meets very seldom indeed. Seeing has he stopped practicing altogether after almost 8 years with the orchestra, it can only be assumed that Jethro is "in the orchestra" for only two days out of the year. Without practicing outside of that, it is highly unlikely that Jethro can play the instrument at all, having only touched it a total of 8 times in the past four years.
3. This problem is particularly misleading, as it seems to suggest a correlation between the frequency of Wilma's remarks and the makeup of the group's personnel. The only relevant factor of this problem is the one that is suspiciously absent: The frequency and duration of rehearsals. A constant can be determined for the frequency of a second violinist's disparaging remarks (in RPH, i.e. Remarks Per Hour), with tables of such contents available both as approximated sectional averages and exact values by seat placement, but this data is useless without an indication of total rehearsal time. Unsolvable, not enough information.
4. A tricky problem, leading the solver to do a whole lot of unnecessary calculations. At the lower end, any major "important" orchestra has at LEAST a 1/4 chance of having a piece by Mozart, Beethoven, or Brahms on each concert, regardless of how many pieces are programmed. Over 40 concerts, this alone provides a (1/4) + (3/4 * 1/4) + (3/4 * 3/4 * 1/4) etc. probability of seeing Mozart, Beethoven, or Brahms. Imagine flipping a pair of coins 40 times and never having tails show up on both coins. One could even argue for the laughable possibility of a lower probability of hearing these composers, at which point the equation would be altered to a lower probability. Regardless, however, these calculations are rendered moot by the simple fact that all three composers will have a multiple-of-ten birthday celebrated within the next ten years, or any ten years for that matter (the "ten years" figure being the key to this problem). The probability of Horace going to four concerts of a major important orchestra during one of THOSE years without seeing Mozart, Beethoven, or Brahms is 0.
5. The reverberation of the hall is insignificant, provided that Wilma is a section violist (not principal). Reverberation is irrelevant. If nobody has noticed yet, nobody will continue to notice. If, however, the new hall employs a Jumbo-tron, one may worry that an obsessive-compulsive violist in the audience may cause some troubles indeed for dear Betty. However, this can very easily be dismissed as a discrepancy due to the delay of sound propagation. Betty's incompetence will remain undetected.
6. Provided that the brass section is not averse to alcohol consumption for reasons religious or otherwise, Ralph is dead already, as is Harold. At a very conservative estimate, two kegs plus three cups (as well as just two kegs) per week of coffee is a fatal dose of caffeine. This, of course, assumes that Ralph does not drink decaf, in which case he would simply never leave the restroom. In either case, he will no longer be with the orchestra.
7. I apologize that I am unable to solve this problem. All relevant data has been provided, but until I can locate my Calculus textbook and refresh my memory on the mathematical interactions of different kinds of infinity, I'll have to leave it unsolved. While not exact, Chris has provided a reasonable approximation.
-Alex
www.mostlydifferent.com
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