Questions

See the attachment. where (a, b) = gcd(a, b), mu = Mobius functions, phi = Euler function

If start out with 300,000peso and earn 10% a month in interest. I roll over all the interest back into the business each month how much will it be worth in . 1 year2 years 3 years Thank you for your h...

**Please let me know an appropriate bounty for this. I am also open to partial solves or "pointers" in the correct direction so I am putting the bounty where it is right now. If there is a partial com...

Let $L_1, L_2 \subseteq \mathbb{R}^n$  be full-rank Euclidean lattices with generating matrices $A, B$ respectively (representing Minkowski-reduced bases), and let $d(A,B)< \epsilon$, for some fixe...

Let $L_1, L_2 \subseteq \mathbb{R}^n$  be full-rank Euclidean lattices with generating matrices $A, B$ respectively, and let $d(A,B)< \epsilon$, for some fixed positive real $\epsilon$. Then do the...

Let $C$ be a vector subspace of $\mathbb{F}_q^n$, and define the Hamming distance as follows: If $v, w \in C$, then $d(v,w) =$ number of non-$0$ coordinates of $v-w$, and $d(v) = d(v,0)$. For a linear...

I am wondering if 0/0 is an impossibility vs Undefined. Given that 0 is a privation of quantity. I'm wondering if 0/0 is really just asking if "nothing" can go into "nothing". If this is what the equa...

A motorcyclist passes 2 independent traffic lights, each red, with a probability of 0.25, with waiting times in units of minutes, which are independent random variables, exponentially distributed with...

I've been trying to understand the formula P = Fv, but I don't really like the traditional way of explaining it. My math background is much stronger than my physics background, so I often try to come...

The constant product is used in decentralized finance. It is used to calculate how much someone gets for currency $Y$ when giving funds of currency $X$. $X$ and $Y$ indicate the size of funds in the c...

My apologies if this is not a valid question. I come from a computer science background, and this question came to mind while attempting to provide privacy protection for my use case.Assume there are...

Sorry, I made a mistake in the first equation and forgot a bracket. In fact it has the following form, which might complicate the proof: $f(X_n)=Y*(\sum_{n}^{N}X_n)^A$and the 2nd one remains to be$g(X...

1. There are 52 cards in a deck of cards, of which 4 are aces. Anna and Benjamin (father and his daughter) play a game in which each one of them, in turn, draws four cards without return. Whoever draw...

I have two functions:$f\left ( X_n \right ) =B*\sum_{n}^{N}X_n^A $and$g\left ( X_n \right ) =\sum_{n}^{N}(Z_n*X_n^B) $with $A$ and $B$ as the exponents of $X_n$.It alway must hold that $f\left ( X_n \...

Consider the map $\phi(z):= \tanh(\frac{\pi}{4}z)$, which is a conformal bijection from the strip $\{z\in\mathbb{C} ; |\text{Im} (z)|<1\}$ to the unit disc $\{z\in\mathbb{C} ; |z|<1\}$. Prove th...

I have a function $\varphi \in L^2(\mathbb{R})$ such that $\text{supp}(\widehat{\varphi})\subset [0,1]$ and a $2\pi$-periodic Fourier series $R(x):=\sum_{k\in \mathbb{Z}} a_k e^{ikx}$ (of some continu...

Find harmonic function in cartesian coordinates u(x,y) which satisfies in polar coordinates the next condition: u(rcos(0),rsin(0))=u(rcos(pi/4),rsin(pi/4))=agiven that:u(x0,y0)=2a for 0<y0<x0

Searcing for solution to part c) (pieri s rule is attached last,where the sum is taken over all λ obtained from ν by removing one box )

1. Let f(x,y) = 3$x^{2} $ -10xy+3$y^{2} $ on the region [0,4] x [0,4]; evaluate the double integral 2. Change the region to 0 < x < 3 and 0 < y < $\sqrt{9-x^2}$ ; evaluate the double integ...

Hey, lets say I have an orthogonal projection matrix $M(n)$ which is n x n so it depends on the number of observations $n$. Lets say I am projecting some vector $z(n)$, a n x 1 vector,  on this space....

Hi,  Can I add these 2 percentages together?  Let's say the scrap loss of 1 part is 2% over 150 transactions and the scrap loss of an assembly that the scrap loss part goes into is 4 percent o 137 tra...

This question is from a high school level Canadian secondary 4 text book. I added the question as an attachment. Please show and name all of the steps clearly written. Please use high school level mat...