Algebra : Word Problem - Remainders

A large purse is full of coins. If you count them by 13's, 23's, or 31's, there will be one left over. If you count them by 73's there will be none left over. How many coins are there in the purse? Please be detailed in your response.

Algebra : Remainders

What is the remainder when the product of one hundred 5's is divided by 7? Please be detailed in your response.

Miner and Bickford's Fuse : How to get a Fuse of Specific Length

You are a miner and you have three pieces of Bickford's fuse of equal length. You need only 3/4 of one of them. You have no ruler or other measurement device with you. You cannot also bend the fuses as they are old and can be broken at any point while being bent. You only can ignite them from any end and extinguish at any moment ...continues

Simple trigonometric proof, with a twist.

Prove: sin(2arcsin(x))=2x*sqrt(1-x^2)

Patterns leading to Solutions

The following problem shows how working out examples and looking for patterns can lead to a general solution. A kindly prison warden decided to free his 25 prisoners for good behavior. The prisoners were locked in separate cells, numbered 1 through 25. Each cell had a lock that opened when the key was turned once and locke ...continues

Probability: Continuous Random Variables

1.) Suppose we are producing copper wire and putting the wire on spools. Each spool contains 100 feet of wire. Defects such as nicks in the wire can occur at random locations. What would be a reasonble distribution for each of the following: (a) the number of spools produced until a spool is produced that contains one or more de ...continues

Probability

1) Let X be a discrete random variable with probability mass function Pr{X=k}= c/(1+(k^2)) for k= -2,-1, 0, 1, 2. a) determine Pr{x <= 0} (b) Determine the mean of X (c) Determine all medians of X (d) Compute Pr{X=2 | X >= 0} (e) Determine the cumulative distribution function

Tangent to a curve: Condition

Find the condition that the curve y = mx + c to be a tangent to the parabola y^2 = 4 ax and also determine the point of contact.

How to get a million by spelling a word whose letters' product=1000000

If we assign number values to letters in the following way: A = 26, B = 25, C = 24 and so on until Y = 2 and Z =1, spell a word such that the product of its letters is as close to a million as possible. Explain how you went about solving this problem.

Getting three thousand bananas across a one thousand mile desert

You have three thousand bananas that you have to get to a destination 1000 miles away. You can only carry 1000 bananas at a time. You also must eat 1 banana per mile for energy. Assuming you design your trip as efficiently as possible, how many bananas will you have left when you arrive at the destination? (apparently someon ...continues