## Timmy has a collection of jelly beans in a jar. If he groups them

,Timmy has a collection of jelly beans in a jar. If he groups them in 4’s, there is one jelly bean left over at the end. If he groups them in 6’s, there is again one left over. If he groups them in 9’s, there is again one left over. Finally, Timmy is thrilled to discover that if he groups them in 7’s, there are no beans left over. What is the smallest number of jelly beans in Timmy’s jar?, ## 1. Find n when a 1 = 45, d = 9, and a n = 81. 2. Expand (2x=5y) 6

,1.  Find n when a,1 ,= 45, d = 9, and a,n, = 81.,2.  Expand (2x=5y),6  ,      What is the expansion?,3.  From the 12 male and 9 female sales representatives for an insurance company, a team of 3 men and 4 women will be selected to attend a national conference on insurance fraud.,-  In how many ways can the team of 7 be selected?,4.  How many 4 – digit numbers can be formed using the digits 2,3,4, and 6 without repetition? With repetition?,-  A total of ___ different 4 – digit numbers can be formed using the digits 2,3,4, and 6 without repetition.,-  A total of ___ different 4 – digit numbers can be formed using the digits 2,3,4, and 6 with repetition.,5.  Find the sum, if it exists.,     75+45+27+ …,6.  Determine the nth term of the geometric sequence.,     1,4,16,64, …,7.  A theater has 24 rows of seats.  The first row has 18 seats, the second row has 20 seats, the third row has 22 seats, and so on.  How many seats are in the theater?,8.  Suppose we select, without looking, one marble from a bag containing 3 red marbles and 11 green marbles.  What is the probability of selecting each of the following?,       a) A red marble                  b) A green marble,       c) A purple marble            d) A red or a green marble,9.  Rewrite the sum using sigma notation.,     1/1*4 + 1/2*5 + 1/3*6 + 1/4*7 + …,     , ## Suppose that the compact submanifold X in Y intersects another

Suppose that the compact submanifold X in Y intersects another submanifold Z, but dim X + dim Z < dim Y. Prove that X may be pulled away from Z by an arbitrarily small deformation, i.e. given e > 0 there exists a deformation Xt = it(X) such that X1 does not intersect Z and |x – i1(x)| < e for all x in X. ## Python CSC2421. Develop a program that displays a GUI window

Python CSC242,,1. Develop a program that displays a GUI window with your picture on the left side and your first name, last name, and place and date of birth on the right. The picture has to be in the GIF format. If you do not have one, find a free online converter tool and a JPEG image online and convert the image to GIF.,,2. Modify the phone dial GUI from Section 9.1 so it has buttons instead of labels. When the user dials a number, the digits of the number should be printed in the interactive shell.,,,Following is the original code from the text:,,from tkinter import *,,root = Tk(),,labels = [[‘1′,’2′,’3’], [‘4′,’5′,’6’], [‘7′,’8′,’9’], [‘*’,’0′,’#’]],,for r in range(4):,,for c in range(3):,,label = Label(root, relief=RAISED, padx=10, text=labels[r][c]),,label.grid(row=r, column=c) #Using grid, not pack. ## Is There a Place for Ethics in IT? On March 15, 2005, 