Assignment #2 1) Improve the result from problem 4 of the previous assignment by showing that for every e> 0, no matter how small, given n real numbers x1,...,xn where each xi is a real number in the interval [0, 1], there exists an algorithm that runs in linear time and that will output a permutation of the numbers, say y1, ...., yn, such that ∑ ni=2 |yi - yi-1| < 1 + e. (Hint: use buckets of size smaller than 1/n; you might also need the solution to problem 3 from the first assignment!) 2) To evaluate FFT(a0,a1,a2,a3,a4,a5,a6,a7) we apply recursively FFT and obtain FFT( a0,a2,a4,a6) and FFT(a1,a3,a5,a7). Proceeding further with recursion, we obtain FFT(a0,a4) and FFT(a2,a6) as well as FFT(a1,a5) and FFT(a3,a7). Thus, from bottom up, FFT(a0,a1,a2,a3,a4,a5,a6,a7)
To multiply and divide radicals, perform the indicated operation on the radicands and then simplify: (You do not need radicand to be the same in order to multiply or divide) Example 1: (85) (42) = (8)(4) 5 2 = 3210 Example 2: (105) ÷ (25)= (10 ÷ 2) (5 ÷ 5) = 5 (1) = 5 Example 3: (320 ) (32) sometimes it is easier to simplify first (64 ∙ 5) (16 ∙ 2 (85) (42) Answer = 3210 Example 4: (6500) ÷ 220 ← Rewrite as a fraction and divide =
1. Factor a trinomial whose leading coefficient is 1. Pick any one of the problems and solve the trinomial. If the trinomial is prime, state this and explain why. a. x2+8x+15 b. x2–4x –5 c. x2–14x+45 2.
Unit 3 – Algebra Basics Module 3C Sections 10.3 – 10.8 3C Addition of Real Numbers Addition on the Number Line To do the addition a + b on the number line, start at 0, move to a, and then move according to b. a) If b is positive, move from a to the right. b) If b is negative, move from a to the left. c) If b is 0, stay at a. Copyright 2011, 2007, 2003, 1999 Pearson Education, Inc. Slide 2 3C Addition of Real Numbers Add real numbers without using the number line. Add: –4 + 9.
It is four octets of numbers from 0-255 represented in decimal form. Class A always has the first bit of their address set to 0. They have an 8 bit network mask that is why they leave it zero so they can have 7 bits for the network portion. They have 128 possible networks. Class B addresses always has the first bit set to 1 and their second bit set to 0.
Using the Internet and the Help files in Excel, explain why creating a converter from decimal to binary would be more difficult to construct. Hint: you should consider the conditional evaluation of whether the decimal value remaining is larger than the binary digit value. = Creating a decimal converter form in excel would be more difficult because there would be a lot of different formulas that you would have to use depending on the equation that you are trying to solve. Lab 1.2 1. Determine the result of 100100002+11011102.
One times x^1 leaves x when simplified. * Using the product of powers property, we add the exponents together to get the 11th root of x^11. By finding the 11th root of x^11 we cancel both 11s out to get simply
We can conclude that the data are Poisson distributed. Chi-Square test of independence Problem 12.12 Use the following contingency table to determine whether variable 1 is independent of variable 2. Let α = .01 | Variable 2 | Variable1 | 24 | 13 | 47 | 58 | | 93 | 59 | 187 | 244 | Step 1 Ho: the two classifications are independent Ha: the two classifications are dependent Step 2 d.f = (r – 1) (c – 1) Step 3 α = 0.01 x 2 0.01, 3df = 11.3449 Step 4 Reject Ho if x 2 > 11.3449 | Variable 2 | Total | Variable1 | 24 (22.92) | 13 (14.10) | 47 (45.83) | 58 (59.15) | 142 | | 93 (94.08) | 59 (57.90) | 187 (188.17) | 244 (242.85) | 583
What are you going to do with the outlier? Please provide a rationale for your decision. (0 marks as this question is part of data screening for the writing of the results in Task 10) Participant two’s score was changed to 256, which was one unit higher than the next most extreme score identified. Perform data screening. Was there a normal distribution?
4,25,000 d.None of these 80. Total property of Ghosh Babu (in Rs.lakh) is (a) 5.0 (b) 7.5 81. (c) 10.0 (d) 12.5. If Ghosh Babu had equal number of gold and silver bars, the number of silver bars he has is (a) 90 (b) 60 (c) 75 (d) 55 CAT 1990 Actual Paper Page 11 Questions 82-84 : The following questions relate to a game to be played by you and your friend. The game consists of a 4 x 4 board (see below) where each cell contains a positive integer.