Probability, Combinations and Permutations

A basket contains 4 black, 2 red, and 5 green marbles. A sample of three marbles is drawn. Find the probabilities that the sample contains the following: 2 black balls and 1 green ball

Applications

(1) At noon, ship A is 60 nautical miles due west of ship B. Ship A is sailing west at 19 knots and ship B is sailing north at 25 knots. How fast is the distance between the ships changing at 8 PM, in knots? (2) A street light is at the top of a 22 ft tall pole. A woman 12 ft tall walks away from the pole with a speed of 9 ft/sec along a straight path. How fast is the tip of her shadow moving when she is 39 ft from the base of the pole?

Linear Programming: Simplex Method - Nonstandard Problems

A couple has $40,000 to invest. As their financial consultant, you recommend they invest some money in treasury bills that yield 6%, some money in corporate bonds that yield 8%, and some money in junk bonds that yield 10%. A. Prepare a table showing some of the ways this couple can achieve $3,000 per year in income. B. Solve, showing all work.

Solving the production costs problem using Simplex Method

Post edited to correct typo (sorry, maybe part of my problem :( !) Cauchy Canners produces canned whole tomatoes and tomato sauce. This season, the company has available 3,000,000 kg of tomatoes for these two products. To meet the demands of customers, it must produce at least 80,000 kg of sauce and 800,000 kg of whole tomatoes. The cost per kg is $4 to produce canned whole tomatoes and $3.25 to produce tomato sauce. Labor agreements require that at least 110,000 person-hours be used. Each kilogram can of sauce requires 3 minutes for one worker and each kilogram can of whole tomatoes requires 6 minutes for one worker. How many kilograms of tomatoes should Cauchy use for each produc... click for more

Develop probability tree and Joint probability table

A school system consists of three districts, north, south, and central. The North contains 25% of the students, the south contains 40% and the central contains 35%. A mininum competency test was given to all students; 10% of the north dist. failed, 15% of the south district failed and 5% of the central failed. a. Develop a probability tree showing all marginal, conditional, and joint probabilities. b. Develop a joint probability table. c. What is the probability that a student selected at random failed the test? I'm not sure if I'm getting the correct answers for the conditional probabilty (North .25/.10=2.5 Central .40/.05=8 South .35/.15=2.3 ) and I can't complete the joint prob... click for more