Use induction on the number of components to prove that any acyclic graph with c components and nvertices must have n−c edges, for any n and any c ≥ 1. acyclic graphs are sometimes referred to as forests.

Ariana starts with 100 milligrams of a radioactive substance. the amount of the substance decreases by 20% each week for a number of weeks, w. the expression 100(1−0.2)w finds the amount of radioactive substance remaining after w weeks. which statement about this expression is true? a) it is the difference between the initial amount and the percent decrease. b) it is the difference between the initial amount and the decay factor after w weeks. c) it is the initial amount raised to the decay factor after w weeks. d) it is the product of the initial amount and the decay factor after w weeks.

Find each value of the five-number summary for this set of data. [note: type your answers as numbers. do not round.] 46, 19, 38, 27, 12, 38, 51 minimum maximum median upper quartile lower quartile

For the sequence [tex]a_{n} = 2n/(n+1)[/tex], what is the value of [tex]a_{10}[/tex]