For each of the following claims, determine whether they are true or false. justify your determination (show your work). if the claim is false, state the correct asymptotic relationship as o, θ, or ω. unless otherwise specified, lg is log2.(a) (b) (c) (d) (e) (f) (g) (h) (i) (j)n+1 =22n =2n =1 =ln2 n =n2 +2n−4 =33n = 2n+1 =√n = 10100 =o(n4) o(2n)θ(2n+7 ) o(1/n)θ(lg2 n) ω(n2 )θ(9n ) θ(2n lg n )o(lg n) θ(1)

Digital information is stored using a series of ones and zeros. computers are digital machines because they can only read information as on or off –1 or 0. this method of computation is known as the system

This first part of the film shows the early history of motion pictures. how accurate do you think the portrayal of the early motion picture industry is? why? is historical accuracy important in films and theatre productions? explain. in the scene where don is going to the party (starting at time code 14: 51), we see a street scene as he first rides with cosmo and then with kathy. what aspects did the filmmaker include to make the scene look and feel like don, cosmo, and kathy are riding in a car on a street? think about elements such as scenery, sound, props, lighting, and so on. a "talkie" picture is shown starting around time code 21: 15. how does the audience in the film react to the "talkie"? what influence do audiences have on film and theatre performances? how do film and theatre actors influence audiences? in the musical scene with cosmo (starting at time code 27: 00), how does the actor use props? what is the result? do you think the use of props effectively fulfilled the artistic vision for this musical number? why or why not?

A911 dispatcher is the sole sender of messages to all police officers. while on patrol, officers communicate with the dispatcher who, in turn, relays messages to other officers. the officers do not communicate directly with one another. this illustrates a network.