The birthday paradox says that the probability that two people in a room will have the same birthday is more than half as long as the number of people in the room (n), is more than 23. This property is not really a para- dox, but many people find it surprising. Design a C++ program that can test this paradox by a series of experiments on randomly generated birth- days, which test this paradox for n = 5, 10, 15, 20,...,100. You should run at least 10 experiments for each value of n and it should output, for each n, the number of experiments for that n, such that two people in that test have the same birthday.

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Which is a false statement considering copyright law? a. when people upload something to the internet they automatically receive a copyright for the work b. the work does not have to contain a copyright notice to be considered having a copyright c. copyright is legal term describing rights given to the creators for literary and artistic works d. personal pictures are always covered by copyrights

The volume v and paper surface area a of a conical paper cup are given by where r is the radius of the base of the cone and h is the height of the cone. a. by eliminating h, obtain the expression for a as a function of r and v. b. create a user-de ned function that accepts r as the only argument and computes a for a given value of v. declare v to be global within the function. c. for v ! 10 in.3 , use the function with the fminbnd function to compute the value of r that minimizes the area a. what is the corresponding value of the height h? investigate the sensitivity of the solution by plotting v versus r. how much can r vary about its optimal value before the area increases 10 percent above its minimum value?