Problem. Prove by contradiction that v2 is an irrational number. Hint: In a fraction you may...
5. Assume that we have proved that V2 and 13 are irrational numbers. Prove that 12+13 is an irrational number.
all parts A-E please.
Problem 8.43. For sake of a contradiction, assume the interval (0,1) is countable. Then there exists a bijection f : N-> (0,1). For each n є N, its image under f is some number in (0, 1). Let f(n) :-0.aina2na3n , where ain 1s the first digit in the decimal form for the image of n, a2 is the second digit, and so on. If f (n) terminates after k digits, then our convention will be...
please prove 9.6 and 9.7
The next three theorems formalize what you may have discovered in the preceding group of questions. 9.6 Theorem. Let K be a positive integer Then, among any k real num- bers, there is a pair of them whose difference is within 1/K of being an integer When we take our collection of real numbers to be multiples of an ir- rational number, then we can find good rational approximations for the irrational number. Remember how...
F1.
need help solving this problem.
1. (25 pts) Here's a neat theorem. Suppose that f la, b] [a, b] is continuous; then f will always map some s-value to itself (a so-called fixed point): i.e. 3 c E (a, b) for which f(c)-c (a) Give a "visual proof" of this theorem. Hint: take your inspiration from our "visual proofs" of Theorem 15 and IVT And notice here that the domain and range of f are the same interval; this...
2. [9 marks] Number representation Some of you may be familiar with the fact that in basc 10, the sum of the digits of a multiple of nine is also a multiple of 9. The following questions have to do with number represntation in bas 11, so we would count from 0 to 12 as follows S SC 0,1, 2, 3, 4, 5, 6, 7,8,9, Л, 10, 11 In general (2A) mind that this means 2A is not could say...
Suppose that insurance companies did a survey. They randomly
surveyed 410 drivers and found that 300 claimed they always buckle
up. We are interested in the population proportion of drivers who
claim they always buckle up.
NOTE: If you are using a Student's t-distribution, you may
assume that the underlying population is normally distributed. (In
general, you must first prove that assumption, though.)
Part (a)
(i) Enter an exact number as an integer, fraction, or decimal.
x =
(ii) Enter...
please help if you know Optimization with Quadratic
Functions
Could you please prove 89.
Thank you so much !
Quadratic Functions A quadratic function is a mapping Q R R that is a scalar combination of single variables and pairs of variables. Thus, there are coefficients Cli,] and Ell, and a real number q, such that for X E IRn, we have The m atrix notation for C is suggestive. Indeed, C is n × n, and we take E...
4.11.3
P4.11.3 Prove the claim at the end of the section about the Euclidean Algorithm and Fibonaci numbers. Specifically, prove that if positive naturals a and b are each at most F(n), then the Euclidean Algorithm performs at most n -2 divisions. (You may assume that n >2) P4.11.4 Suppose we want to lay out a full undirected binary tree on an integrated circuit chip, wi 4.11.3 The Speed of the Euclidean Algorithm Here is a final problem from number...
IN JAVA PLEASE HELP!
ALSO PLEASE ADD COMMENTS
Summary Build two classes (Fraction and Fraction Counter) and a Driver for use in counting the number of unique fractions read from a text file. We'll use the ArrayList class to store our list of unique Fraction Counters. Rather than designing a monolithic chunk of code in main like we did in the previous homework, we'll practice distributing our code into containers (called classes) that you will design specifically to tackle this...
need to check my work. Just
need B and C
Problem 2. Recall that a discrete random variable X has Poisson distribution with parameter λ if the probability mass function of X is fx (x) = e-λ- XE(0, 1,2, ) ar! This distribution is often used to model the number of events which will occur in a given time span, given that λ such events occur on average a Prove by direct cornputation that the mean of a Poisson randoln...