Math Is Fun Forum

Two days ago, Sam was fifteen. On the next year, he will be 18. What is his B'day and today's date?

Thanks in advance.

Please help me with these problems...

4.  Ternary Huffman. Trimedia Disks Inc. has developed “ternary” hard disks. Each cell on a disk can now store values 0, 1, or 2 (instead of just 0 or 1). To take advantage of this new technology, provide a modified Huffman algorithm for compressing sequences of characters from an alphabet of size n, where the characters occur with known frequencies f1, f2, . . . , fn. Your algorithm should encode each character with a variable-length codeword over the values 0, 1, 2 such that no codeword is a prefix of another codeword and so as to obtain the maximum possible compression. Prove that your algorithm is correct.

5.  The basic intuition behind Huffman's algorithm, that frequent blocks should have short encodings and infrequent blocks should have long encodings, is also at work in English, where typical words like I, you, is, and, to, from, and so on are short, and rarely used words like velociraptor are longer.

However, words like fire!, help!, and run! are short not because they are frequent, but perhaps because time is precious in situations where they are used.

To make things theoretical, suppose we have a file composed of m different words, with frequencies
f1, . . . , fm. Suppose also that for the ith word, the cost per bit of encoding is Ci. Thus, if we find a prefix-free code where the ith word has a codeword of length li, then the total cost of the encoding will
be (summation) i  fi  Ci  li.

Show how to modify Huffman's algorithm to find the prefix-free encoding of minimum total cost.

6.  A server has n customers waiting to be served. The service time required by each customer is known in advance: it is ti minutes for customer i. So if, for example, the customers are served in order of increasing i, then the ith customer has to wait  (summation)( j = 1 to i) tj minutes.

We wish to minimize the total waiting time

                T = (summation((i = 1 to n) (time spent waiting by customer i)

Give an efficient algorithm for computing the optimal order in which to process the customers.

This is urgent.
Thanks in advance!

18 people are randomly selected with a mean score of 550 and a std. dev. of 140. Find the 95% confidence interval for the population variance and std.

can you tell me how i find point estimates for population variance and standard deviation?

Thanks in advance.

Show that    lim          Sinx = 0
              x--> infinity

and              lim          Cosx = 0
              x--> infinity

Man pushes a sled horiz to move up a hill.  Weight of girl plus sled is 35kg.  The anlge is 15 deg.  The height is 3.6m.If the sled movves up hill with constant veloxity how much work done by father?

Thanks in Advance!

a time t=0, a tank contains 4 lbs if salt dissolved in 100 gallons of water. Suppose brine, containing 2 lbs of salt per gallon, enters the tank at a rate of 5 gallons per minute. The mixed solution is allowed to drained from the bottowm of the tank at 5 gallons per minute. find the amount of salt in the tank after 10 minutes

I need the solution and similar kind of problems please

Find the inverse function.

f(x) = x^3+2x-1

Please help me.

Thanks in advance!

a, b, c are three integers satisfying the following properties:
1. 0 < a < b < c < 10000
2. a, b, c are all perfect squares.
3. a, b, c are in Geometric Progression.
What is the maximum possible value of a ?

Median salaries for two companies are $35,000 and $40,000. What additional info would be helpful to have before deciding which company you would like to work for?

Thanks in Advance!!!

Father is aged three times more than his son Rohit. After 8 years, he would be 2 and half times of Rohit's age. After further 8 years how many times would be Rohit's age.

I have a doubt in the first statement.

F = 3 R. Is this right?