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)
-0011 0110 0011 represents 3 0110 represents 6 - 36 Exercise 1.3.6 Represent the hexadecimal value f6 16 in binary and decimal. Show the steps of conversion that you used. - The best way I feel to do this propose is to change it to binary first. - F is 1111 - 6 is 0110 - 11110110 in binary - Then do the decimal step , 246 Lab 1.3 Reviews Explain why it is important to know how many system words will fit in a primary storage device on a computer (such as the hard drive). -So that you know how much ad primary storage unit can hold.
Radicals Tips 1. Make sure that one of the two factors of the radicand (expression under the radical) is the largest perfect square: Example: Simplify 72 Correct 72 = 36 ∙ 2 = 62 Incorrect 72 = 9 ∙ 8 = 38 2. To be able to add or subtract radicals, the radicands must be the same. Example 1: Add 32 + 52 Answer: Since radicands are the same, (3 + 5)2 = 82 Example 2: Subtract 73 - 3 Answer: (7 – 1)3 = 63 Example 3: 318 - 52 (Must simplify first) 39 2 - 52 3 ∙ 3 ∙ 2 - 52 92 - 520 Answer: 42
8 5 7 8 (a) 7 7 8 6 6 11 7 5 5 7 9 9 6 7 6 7 Construct a frequency table from the above data and add a cumulative frequency column. For this data, find: (i) the median; (ii) the lower quartile; (iii) the upper quartile. 2 (b) 1 1 1 2 (c) Construct a boxplot for this data. [Turn over [ X100/201] Page three Marks 3. The diagram below represents a sphere.
A. 1.99 x 10-25 B. 9.55 x 10-25 C. 6.62 x 1016 D. 1.51 x 10-17 E. 1.51 x 10-26 4. Of the following transitions in the Bohr hydrogen atom, the __________ transition results in the emission of the highest-energy photon. A. n = 3 n
Randy Michael NT 1210 Lab 1.1 Professor Chibuzo Onukwufor 4/1/15 Lab 1.1 1: Convert the decimal value 127 to binary. Explain the process of conversion that you used. Decimal Number | Binary Number | Remainder | 127 - | 64 | 63 | 63 - | 32 | 31 | 31 - | 16 | 15 | 15 - | 8 | 7 | 7 - | 4 | 3 | 3 - | 2 | 1 | 1 - | 1 | 0 | Binary | 27 | 26 | 25 | 24 | 23 | 22 | 21 | 20 | Decimal | 128 | 64 | 32 | 16 | 8 | 4 | 2 | 1 | Conversion | 0 | 1 | 1 | 1 | 1 | 1 | 1 | 0 | I took the decimal and divided it by two giving 1 for the remainders and 0 if it did not have a remainder. 2: Explain why the values 102 and 00102 are equivalent. They are equivalent because they represent the powers of 10 3: Based on the breakdown of the decimal and binary systems in this lab, describe the available digit values and the first four digits of a base 5 numbering system.
What is always true about the meaning of 7.14 g/mL? The correct answer choice is choice f). This is correct because g/mL means that for every 1 mL, there is x amount of grams. 4. What is the graphical (graph shape), mathematical (equation of the graph) and numerical (value of slope and y-intercept) relationship between the mass of a piece of zinc and the volume of space it occupies?
2) Define weighted average- An average that takes into account the proportional relevance of each component, rather than treating each component equally. 3) Place one atom of each isotope on the scale. Divide the mass by 3 to fine the straight average. How is this number different from your average atomic mass? Number – 19g average mass 1.7g 4) If a 4th isotope of beanium, D (green), were added to the pool, how would the average atomic mass change?
(no, 4.29 nm is too short) _______________15. How many Joules of energy are there in one photon of yellow light whose wavelength is 630 nm? (3.16 X 10-19 J) _______________16. Find the color of light whose photon has 4.75 X 10-19 J of energy. (violet) ________________17.
It tends to be most accurate when values are distributed across multiple orders of magnitude. It is named after physicist Frank Benford, who stated it in 1938, although it had been previously stated by Simon Newcomb in 1881. A set of numbers is said to satisfy Benford's law if the leading digit d (d ∈ {1, ..., 9}) occurs with probability P(d)=\log_{10}(d+1)-\log_{10}(d)=\log_{10} \left(\frac{d+1}{d}\right)=\log_{10} \left(1+\frac{1}{d}\right). Numerically, the leading digits have the following distribution in Benford's law, where d is the leading digit and P(d) the probability: d P(d) Relative size of P(d) 1 30.1% 2 17.6% 3 12.5% 4 9.7% 5 7.9% 6 6.7% 7 5.8% 8 5.1% 9 4.6% Application :- Accounting fraud detection In 1972, Hal Varian suggested that the law could be used to detect possible fraud in lists of socio-economic data submitted in support of public planning decisions. Based on the plausible assumption that people who make up figures tend to distribute their digits fairly uniformly, a simple comparison of first-digit frequency distribution from the data with the expected