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Prove that every nontrivial tree has at least two vertices of degree 1 by filling in the details and completing the following argument: Let T be a nontrivial tree and let S be the set of all paths from one vertex to another of T. Among all the paths in S, choose a path P with the most edges. (Why is it possible to find such a P?) What can you say about the initial and final vertices of P? Why?
When the sides are turned up to form the box, its volume is 765 cubic inches. Find the dimensions, in inches, of the original piece of cardboard.
Find the best investment using the following decision criteria.
Set up a system of equations and solve the problem. The college theatre, collected $1300 from the sale of 450 tickets. If the tickets were sold for $2.50 and $3.50, how many tickets were sold at each price?
1. In the 2000 U.S. Census, a small city had a population of 50.000. By the 2010, the population had reached 74,012. If the population grows by the same percent each year, when will the population reach 100,000?
one soccer field is an rectangle 375 feet long and 230 feet wide what is the area and perimeter of it. but what if the area of the soccer field in square yard? What is the perimeter in yards?
What fraction of the time does he take the bus
Probability : Dice and Payoff c) in part a, if you bet one dollar that a sum of 10 will turn up, what should the house pay (plus returning your one dollar bet) if a sum of 10 turns up for the game to be fair?
A charity sells tickets for a fund raising dinner. Each adult's ticket costs $10 and each child's ticket costs $5. A total of $1050 was raised by selling 130 tickets.
This problem is basically from Mathematics and it is about finding the log for the given number.
A series of equal quarterly deposits of $1,000 extends over a period of three years. It is desired to compute the future worth of this quarterly deposit series at 12% compounded monthly
Evaluate the integral ∫01 ∫0√1-x2 ∫√x2+y2√2-x2-y2 xy dz dy dx by changing to spherical coordinates. Evaluate the integral ∫∫∫E(x2 + y2) dV where E is the part of the sphere x2 + y2+z2 = 1 above the xy-plane.
Describe what is meant by the functional decomposition of a Boolean function of n variables and discuss procedures for decomposing Boolean functions into a composition of Boolean functions with fewer variables.
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