Finding the Area of a Circle using the Unit Circle

Please see the attached file for the fully formatted problems. Given square is 11*11, unit square is 1*1 without using any algebraic equation by using scissors or folding it, we can find the area of 11*11 square in terms of unit square. With a similar idea we can do triangles (Main triangle and unit triangle). ...continues

Serial Problem

At Very Long Hotel in Florida, there are n rooms located along a very long corridor and numbered consecutively from 1 to n. One night after a party, n people, who have been likewise numbered from 1 to n, arrived at this hotel and proceeded as follows: Guest 1 opened all the doors. Then Guest 2 closed every second door beginnin ...continues

Coconut Problem

An island is inhabited by five men and a pet monkey. One afternoon the men gathered a large pile of coconuts which they proposed to divide equally among themselves the next morning. During the night one of the men awoke and decided to help himself to his share of the nuts. In dividing them into five equal parts he found that the ...continues

Probability : Combinations

Mr james just won 6 tickets for each of 2 consecutive Giants home football games. For the first game, Mrs James will not be able to attend so he has 5 extra tickets. He will invite 5 of his 9 closest friends from work to go with him. Mr. and Mrs. James will both attend the second game. They have 4 extra tickets and are consideri ...continues

Probability : Counting Principle

A social security number has 9 digits. How many different S.S numbers are possible if: a. repetition of digits is permitted b. repetition of digits is not permitted c. the first digit cannot be a 0 and repetition is not permitted I need the layout (counting principle) ex. 9 8 7 - 6 5 - 2 1 4 3 - - - - - - - - ...continues

Probability

In her wallet, Susan has 12 bills. 6 are $1 bills, 2 are $5 bills, 3 are $10 bills, and 1 is a $20 bill. She passes a volunteer seeking donations for the American Red Cross and decides to select 1 bill at random. Determine: a. probability she selects $ 5 bill (my ans: 1/5) b. probability she does not select a $5 bill (my ans ...continues

Probability

Each of the numbers 1 through 10 inclusive has been written on a separate piece of paper. The 10 pieces of paper have been placed in a hat. If one piece of paper is selected at random, with replacement, find the probability that the number selected is: a. greater than 3 b. even c. odd or greater than 3 d. odd or less than ...continues

Mathematical Induction

Prove that the Fibonacci sequence can be obtained by the recurrence relationship. See attached file for full problem description.

Proof of function integrable over [a,b]

Let f: [a,b] mapped onto Reals be a nonnegative function that is integrable over [a,b]. Then the integral from a to b of f = 0 if and only if greatest lower bound of f (I) = 0 for each open interval I in [a,b].

Real Anaylsis

Let f: [a,b] be mapped onto the Reals be a function that is integrable over [a,b] and let g: [a,b] be mapped onto the Reals be a function that agrees with f except at finitely many points. Is g integrable over [a,b]? Why or why not?