Quantitative Methods

1. Administrators at a university will charge students $200 to attend a seminar. It costs $3000 to reserve a room, hire an instructor, and bring in the equipment. Assume it costs $35 per student for the administrators to provide the course materials. How many students (whole numbers) would have to register for the seminar for the university to break even? 2. Jim is considering pursuing an MS in Information Systems degree. He has applied to two different universities. The acceptance rate for applicants with similar qualifications is 30% for University X and 55% for University Y. What is the probability that Jim will be accepted at both universities? 3. Employees of a local comp... click for more

A block suspended above the ground by a light rope wrapped around a pulley wheel, is released allowing it to rotate freely, letting the block fall to the ground. To determine the rotational speed, speed, time to reach the ground.

A 2 Kg block is suspended 5 m above the ground by a light rope wrapped around a 3 kg solid pulley wheel, as shown in figure. The pulley wheel, which was initially at rest, is then released allowing it to rotate freely, letting the block fall to the ground. Ignoring friction effects the rope mass: (a) Briefly state where, and in what forms, energy is stored in this system: (Note – numerical calculations are not required here, just clear comments about the forms and locations of energy storage. State any assumptions you make) (1) Before the pulley wheel is released. (2) Just before block hits ground. (b) What is the rotational speed of the pulley wheel (in revolutions per sec... click for more

Unbounded Self Adjoint Operator.

Let H be the unbounded self-adjoint operator defined by -d^2/dx^2 (the negative of the second derivative with respect to x) on: D(H) ={f element of L^2 | Integral( |s^2 F f(s)|^2 )ds element of L^2} Where "F" denotes the Fourier Transform. Question: For the state vector h(x) = 1/sqrt(2) if x is in [0,2] 0 if x is not in [0,2] What is the probability that the observable H will be measured in the interval [1/2,1] ?

Problems on Business Math including Forecasting, Exponential smoothing, decision analysis, Normal distribution are included in this posting.

1. A food distributor carries 64 varieties of salad dressing. Appleton Markets stocks 48 of these flavors. Beacon Stores carries 32 of them. The probability that a flavor will be carried by Appleton or Beacon is 15/16. Find the probability a flavor is carried by both Appleton and Beacon. 2. The time it takes to travel from home to the office is normally distributed with  = 25 minutes and  = 5 minutes. a. What is the probability the trip takes more than 20 minutes? b. What is the probability the trip takes less than 15 minutes? c. What is the probability the trip takes between 30 and 35 minutes? d. What is the probability the trip takes more than 40 minutes? ... click for more

PERT/CPM - Markov Process.

PERT/CPM - Markov Process. See attached file for full problem description.