Counting Definition and 413 Threads

We got some cool weather today along with some scattered showers. My wife was sitting there in deep concentration so I asked her what she was thinking. She said she was counting the seconds between the lighting flash and the thunder. She said that the light gets here much faster than the sound...

In an electric circuit a branch is a part of the network between two points or junctions... I have attached a circuit diagram...Can anyone please confirm how many branches are there in the circuit.I m getting a little bit confused. I think the answer is 7. Plz tell me. V1=Emf source 1...

Homework Statement Hi, I am trying to solve the following question: count the number of homomorphism between Z/mZ and Z/nZ? Can you tell me is my solution correct? Homework Equations The Attempt at a Solution Let f be a homorphism. f(mZ + a) = nZ + b ; a,b belong to G Now...

can someone tell me what is wrong with my code? i am trying to make a code that has 1000000 randomly choosing A or B 1000 times. if A is bigger than B, i want to increment the variable called 'aWins'... when i try to get it to print the screen is blank. i left out the int main and #include parts...

Hi I want to know how astronomers count the number of stars (or any other celestial object for that matter) in the sky. Will they take a photograph and do some signal processing like counting the number of brightest spots? Is it possible to count accurately since there are billions and...

Dear Friends, I have a question and would be pleased if you help me by suggesting a paper or book to study. Let A={1,2,...,n}. We consider all the subsets with k elements. How many of these sets have a sum of r ? e.g. for n=6, k=3, r=10 {1,3,6} {1,4,5} {2,3,5} Hense the...

So I am taking intro to stats and probability and I am having trouble understanding something that may be quite difficult to explain in counting. Let me start by telling you what i understand The choose function i.e (6 C 2) will take six elements and create a SET of 15 TUPLE's, in which...

Homework Statement #include <stdio.h> main() { long nc; nc=0; while (getchar() !=EOF) ++nc; printf("%ld\n", nc); } Homework Equations The Attempt at a Solution I'm trying to learn C and am using the book "C Programming Language". It says that...

Homework Statement Z plays a game where independent flips of a coin are recorded until two heads in succession are encountered. Z wins if 2 heads in succession occurs. Z loses if after 5 flips, we have not encounter two heads in succession. 1) What is the probability that Z wins the game...

Homework Statement Let A = {1,2,3} and B = {1,2,3,4,5} Find the number of functions f: A -> B so that f(1) = f(2) Homework Equations The Attempt at a Solution I'm just reviewing random questions for my final on Tuesday and I came upon this question. Seems to be a counting...

Homework Statement 1. How many strings of eight English letters are there if no letter can be repeated? 2. How many strings of eight English letters are there if X is the first letter and no letter can be repeated? 3. How many strings of three decimal digits do not contain the same digit...

I was confonoted with the following problem today, and thought it was interesting enough to discuss it here: Homework Statement You have a box with balls numbered 1,2,3...n. Suppose you began, by taking out balls numbered 1–100 and then put ball 1 back. Suppose you then removed balls...

Homework Statement Prove that, in any set of n + 1 positive integers (n ≥ 1) chosen from the set {1, 2, . . . 2n}, it must be that two of them are relatively prime (i.e. have no common divisor except 1). ( Hint: two consecutive integers are relatively prime. Make boxes labelled by pairs of...

Let K1, K2, K3, . . . be an infnite sequence of sets, where each set Kn is countable. Prove that the union of all of these sets K = Union from n=1 to infinity, Kn is countable. I tried to start, but I don't even understand the question Need some idea on how to start

Hi, I wondered if anyone can help. I have some linear equations in which I've found various possible solutions to the variables using NSolve function. For example, for x1, x2, x3 and x4, it has given me ~14 different possible combinations for each x. Is it possible to do a count so if the...

I'm taking a course that uses matlab, and for one assignment, we need to write a function that, among other things, counts the number of rows and columns in any given numeric matrix. The thing is that we're not allowed to use any built-in functions. No x = size(mat). No length(mat). It all...

Homework Statement Specifically, How many ways can you divide up 20 distinct balls into 5 distinct boxes so that no box contains more than 10 balls? Homework Equations This is similar to another problem in which we have to find the number of ways to divide up r balls into k boxes...

Homework Statement Billy has 1 penny, 1 nickel, 1 dime and 1 quarter. How many different ways can he put his coins in the following board by placing one coin in each cell? Juan walks to school everyday. His walking speed is 1/15 mile per minute, and it takes him 30 minutes to get to...

Hi everyone. I thought I understood this problem, but now I'm unsure. Everything is worked out step by step with the answers, but when I try to duplicate it, I get something different. Can anyone shed some light on it? Homework Statement Suppose there is a steady current of 0.50 A in a...

Homework Statement I am wondering is there a way to count the number of bits to the left or right of a given 1 in a 32-bit integer? For example, if I give the function the number 32 = 0b100000, there are 5 bits to the right of the 1 and hence, 26 bits to the left of the 1. The catch...

Hi all, I am wondering is there a way to count the number of bits to the left or right of a given 1 in a 32-bit integer? For example, if I give the function the number 32 = 0b100000, there are 5 bits to the right of the 1 and hence, 26 bits to the left of the 1. The catch is, is there a way...

How many divisors does 55,125 have? For example, 55,125 = (3)^2 . (5)^3 . (7)^2

Homework Statement let f(x)=x^3+x^5. Evaluate int((f(x)^-1)^2, x = 0 .. 2) The Attempt at a Solution i have a feeling that it has a relation with counting volume of a solid revolution.but i don't know how to answer it...

PI(N) = N /{A * LOG(N)^2 +B * LOG(N) + C}. Note: LOG(N) is the common log. This formula works for N up to 10^23. The accuracy depends on the number of digits after the decimal point in the coefficients A, B & C. I used a Lotus123 spreadsheet to calculate them. My calculated values are...

In a math contest, the question goes somehow like this: A lattice point is a point wherein the value of (x,y) is an integer. Determine the total number of lattice points in a circle which has a radius of 6 and the its center is at the origin. Any one knows the solution or shortcut for this?

I have trouble finding the following information on the coincidence counting in a Bell experiment: - Is there a fraction of single photons (not entangled) produced in the experiment and how are the final results corrected for this? - No-hits on both side can never be counted (nothing is...

A calculator has an eight -digit display and a decimal point that is located at the extreme right of the number displayed, at the extreme left or between any pair of digits. The calculator can also display a minus sign at the etreme left of the number. How many distinct numbers can the...

Homework Statement How can you get from this \frac {z(i-1) +i +1} {z(1-i) +i +1} to this = \frac { z-1 } {-z -i} ? The Attempt at a Solution SageMath does not simplify the result any further from the beginning. The equivalence is based on some high Math. I am not sure how you...

Let’s say i have n identical classical non interacting particles and N sites where i can put them in. BUT the total energy is given. The number of possible states is (N)^n/n!/(n/2)! Where N^n is the total possibilities to arrange the particles. We divide it by n! since they are identical...

Jackson: t-minus three semesters and counting! Okay, help me with this thought-experiment: I was wondering how well-prepared for graduate (Jackson) electromagnetism I would be if I had studied the entirety of Griffith's "Intro...Electrodynamics" one year beforehand. What subject-matter would I...

Theorem: Let {N(t): t≥0} be a Poisson process of rate λ. Suppose we are given that for a fixed t, N(t)=n. Let Ti be the time of the ith event, i=1,2,...n. Then the (conditional) density function of Tn given that N(t)=n is the exactly the same as the density function of X(1)=min{X1,X2,...,Xn}...

Let {N(t): t≥0} be a Poisson process of rate λ. We are given that for a fixed t, N(t)=n. Let Ti be the time of the ith event, i=1,2,...,n. Then the event {T1≤t1, T2≤t2,...,Tn≤tn, and N(t)=n} occurs if and only if exactly one event occurs in each of the intervals [0,t1], (t1,t2]...

Homework Statement Show that there is a one to one correspondence between even and odd subsets of the set {0, 1...n}. Homework Equations They want a combinatorial proof so basically a proof based on counting? Perhaps (n choose k) = (n choose n-k) The Attempt at a Solution I've...

Evan pulls one marble randomly from a bag containing 6 red marbles, 3 green marbles, and 1 yellow marble. What is P(red or yellow)

Homework Statement A committee of seven is to be chosen from 8 men and 9 women. a) how many possible committees are there? b) how many committees contain at least 6 woment? c) if bob and alice cannot be on the same committee because they cannot work together well, how many committees are...

Homework Statement how many 4 digit positive integers have at least one digit that is a 2 or a 3? Homework Equations - this is what I need - The Attempt at a Solution I cannot find the equation to this problem. Can someone give me a hand?

could some1 help me in these 3 questions of C language Q1 Write a program to count the number to count the number of zero’s, one's, blank spaces and other characters using switch statement. Q2 Write a program to evaluate the series x-(x^3)/3!+)(x^5)/5!-(x^7)/7! ... up to (x^n)/n! Q3...

Three drugs: A, B and C 50 subjects reported relief from: 21 drug a 21 drug b 31 drug c 9 a&b 14 a&c 15 b&c 41 report relief from at least one drug Note that some of the subjects who reported results from A might have done so for B and C etc. a. How many got relief from...

Homework Statement Suppose you have an a x b rectangular array of distinct integers (think of it as a matrix if you would like). Now suppose we first move across the columns and take a permutation of the entries in each column. Informally, we can imagine the integers in the array as cards, and...

Is there a longest repeated sequence (congruency) in the prime counting function \pi (x) (that which gives the number of primes less than or equal to x)? Recall that \pi (x) , although infinite, may not be random, and itself starts out with an unrepeated sequence \pi (2)=1 and \pi (3)=2...

Homework Statement An organization of 100 members, 6 of whom are officers, plans to elect delegates to attend a convention. There are to be 2 delegates; one must be an officer and the other cannot be an officer. In addition, an alternate delegate, either an officer or not, will be elected and...

1. Homework Statement [/b] There are N 3-dimensional quantum harmonic oscillators, so the energy for each one is: E_i = \hbar \omega (\frac{1}{2} + n_x^i + n_y^i + n_z^i). What is the total number of states from energy E_0 to E, and what is the density of states for E? The Attempt at a...

my question is, let us suppose we can find an expansion for the prime number (either exact or approximate) \pi (x) = \sum _{n=0}^{\infty}a_n log(x) and we have the expression for the logarithmic integral Li (x) = \sum _{n=0}^{\infty}b_n log(x) where the numbers a(n) and b(n)...

how many 1 dimensional subspaces of Z_3^3 are there? Z_3^3 has 3^3 = 27 vectors 26 of which are non zero then we can say v and 2v have the same span and so there are in fact 13 1 dimensional subspaces. is this true?

Homework Statement Suppose that tosses of a biased coin in which it comes up heads with probability 1/4 are independant. The coin is tossed 40 times and the number of heads X is counted. The coin is tossed X more times. A) Determine the expected total number of heads generated by this...

I have heard many people use the term power counting before but I can't find any explanation of what it means. All I know is that it is related to renormalisation somehow. Could someone explain to me what power counting is? thanks

The problem statement Suppose you have n beads, each with a different color. You need to string these beads into a necklace. How many distinct necklaces can you make? (A necklace flipped over remains the same and does not count as a distinct necklace.) The attempt at a solution I...

The problem statement There are 26 letters in the English Alphabet, how many seven-letter palindromes can be made? The attempt at a solution There are 26 letters in the alphabet, so there are 26^7 possible strings of length 7 (order being important for palindromes, i don't think 26...

Wikipedia article Hilbert-Polya conjecture has a link to an article H=xp and the Riemann zeros by Berry & Keating. They mention that the number of energy levels below given E could be counted by computing the area enclosed by the contour H(x,p)=E in the phase space. What is that all about? Does...

Homework Statement Here's the problem. We define the triple primes as triples of natural numbers (n,n+2,n+4) for which all three entries are prime. How many triple primes are there? (Hint:mod 3.) (By way of contrast, it is not yet known whether the twin primes-that is, pairs (n,n+2) with both...