Questions on basic arithmetic, e.g. addition, subtraction, multiplication, division, powers, radicals, etc.

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Arithmetic, geometric and harmonic means: adding a constant to data values

If to each observation $x_i$ we add a constant $c$, then $\frac{\sum(x_i+c)}{n}=\bar{x}+c$ Can we find an expression for the new geometric mean as a function of the old geometric mean? What about the ...
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1answer
40 views

Arithmetic Progression question on finding the 25th term

In AP, sum of n terms is $\dfrac{3n^2 + 5n}{2}$. Find 25th term. My work : $S_n = \dfrac{n}{2}\left({3n + 5}\right)$ $2a + (n-1)d = \left({3n + 5}\right)$ $2a + 24d = 80$ $a + 12d = 40$ 13th ...
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1answer
43 views

Non standard vector addition [closed]

If addition was defined as $(a_1, a_2) + (b_1, b_2) = (a_1 + b_1, 0)$ over a a set $V$, the set of all ordered pairs of real numbers, does that special addition only apply to ordered pairs and vectors ...
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2answers
369 views

logic Accounting trick

Tom went to shop with a fake \$1000 for shopping.He bought items worth \$800 from shopkeeper A A.The shopkeeper had no change so he went to borrow from shopkeeper B. He came back and gave Tom his ...
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2answers
83 views

Time speed and distance.

Two Indian tourists in the US cycled towards each other,one from point A and the other from point B. The first tourist left point A $6$ hrs later than the second left point B, and it turned out on ...
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1answer
31 views

Two sequences such that $a_i,b_i\in \{-1,0,1\} $ for all $i$

Let $(a_i)_{i\in \mathbb{N}}$ and $(b_i)_{i\in \mathbb{N}}$ be two sequences such that : $$\forall i\in \mathbb{N}\ \ a_i,b_i\in \{-1,0,1\} $$ Assuming that for all $n\in\mathbb{N^+}$: ...
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1answer
14 views

Find weight given it can be up to $34 $ times more than $3^{-2}$

A newborn baby chicken weighs $3^{-2}$ pounds ($3$ raised to negative $2$). If an adult chicken can weigh up to $34$ times more than the newborn chicken, how much does an adult chicken weigh? A. $9$ ...
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0answers
60 views

Polynomial change of basis

We got asked to solve this problem: Express the polynomial $f(x) = (1 + x)^6, f \in \mathbb{Z}[x]$, in the basis $(1 + x^2)$. I don't really understand how a polynomial change of basis ...
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3answers
132 views

Why is $(-1)^3=(-1)^{6/2}=((-1)^6)^{1/2}=1^{1/2}=1$ wrong? [duplicate]

Why is this wrong? $$(-1)^3=(-1)^{6/2}=((-1)^6)^{1/2}=1^{1/2}=1$$ It seems logical but I know it's wrong.
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0answers
77 views

Tough mathematics question [duplicate]

If $a,b,q=\frac{a^2+b^2}{ab+1}$ are positive integers then $q$ is a perfect square.
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3answers
541 views

Solving the equation $-5a = 15$: is it possible to multiply a negative number by a positive and make it positive?

I'm stuck with a question which says this $$-5a = 15$$ What is $a$? I'm confused; is it possible to multiply a negative number by a positive and make it positive?
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2answers
28 views

Simple SAT question concerning percents

Here is a simple question I am struggling with: Allison, Jonathan, and Jennifer are teachers at a school. There classes contain a total of 82 students. Jonathan's class is 25% larger than ...
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2answers
48 views

Which of following inequalities hold in interval 0 to pi/2

i tried using calculator and i got 1,2,4 correct .But i am not sure about how to prove them
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0answers
45 views

Is there a difference between induction in Peano Arithmetic and Presburger Arithmetic

Following this question I still do not get clearly the difference between defining exponentiation in PA but impossiblity of recursively define multiplication in Presburger Arithmetics I was thinking ...
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1answer
17 views

Concerning averages.

Here is a simple test question: The average of 5 different integers is 33. The smallest of the 5 integers is 30. The largest of the five integers is N. How many possible values of N are there? ...
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1answer
32 views

What is the correct name for a “summable” number?

My math/CS teacher mentioned a function to me a few days ago (I don't remember the context), but didn't know the real name for it, so he just called it a summable function. We didn't really go into ...
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0answers
50 views

Proving a simple inequality on three parameters

Given $0<\alpha, p, q<1$, let, $$ C=1-2[\alpha(1-p)d_{0} +(1-\alpha)(1-q)(1-d_{0})+\alpha p d_{1} +(1-\alpha)q(1-d_{1})] $$ where, ...
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1answer
123 views

Log or Antilog tables, which ones are more useful?

I'm trying to make a Log or Antilog table small enough to fit in the back of a wallet calendar (or a business card). My intend is to build a mathematically useful gift that can be used by anybody ...
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1answer
34 views

Calculating expressions to the power of two with radicals

How do we calculate $(2\sqrt{22})^2$? I tried but failed: $$ 2*2+2*\sqrt{22}+ \sqrt{22}*2+\sqrt{22}*\sqrt{22} $$ The answer is 88. Thanks!
3
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2answers
205 views

Product of Sums: Show that the following is a Polynomial by converting it into standard form. [duplicate]

$$\prod_{k=0}^n (1+x^{2^k})$$ The given expression simplifies to $(1+x)(1 + x^2)...(1 + x^{2^n})$ I am not able to proceed further. How do I express this in Summation form?
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0answers
26 views

Doubt about semigroups in this article (anyone can help).

I need help in this article. My doubt is very arithmetical and I think follows directly from the definitions. So I think anyone could help me. The author defines what is a semigroup, gaps and ...
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0answers
15 views

Simple odds calculation

I'm stuck with a simple expression creation problem. I'd like to express odds by removing values from $100$ and arriving at a number. Every variable I use has value, that can either be $+10$ or $-10$, ...
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0answers
61 views

On $1/7$ in base $12$

Remember something from seventh grade: \begin{align} & 142857 \\ {}+ {}& 142857 \\ \\ & 285714 \\ {}+{} & 142857 \\ \\ & 428571 \\ {}+{} & 142857 \\ \\ & 571428 \\ ...
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1answer
32 views

Show an arithmetic progression has infinitely many elements

How would I Show this arithmetic progression has infinitely many elements. $$A_{a,b}=\left\lbrace a+nb:n\in\mathbb{Z}\right\rbrace$$
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4answers
111 views

How come $\left(\frac{n+1}{n-1}\right)^n = \left(1+\frac{2}{n-1}\right)^n$

I'm looking at one of my professor's calculus slides and in one of his proofs he uses the identity: $\left(\frac{n+1}{n-1}\right)^n = \left(1+\frac{2}{n-1}\right)^n$ Except I don't see why that's ...
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4answers
146 views

Efficiently producing certain kinds of examples of the application of Euclid's algorithm

Is there some efficient way to churn out pairs of integers $n,m$ such that $\gcd(n,m)=1$; $n,m$ both have fairly large numbers of fairly small prime factors; and Euclid's algorithm applied to $n,m$ ...
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1answer
29 views

Exponents [Discrete Maths]

Had to prove something by induction. Can you please help me by explaining what magic happened after the red $\color{red}=$ in this solution?! ...
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3answers
72 views

Splitting $\frac{1}{n}$ for $n\geq 2$ as a sum of $m\geq 2$ unit fractions (Various proofs)

So the problem is to write $\frac{1}{n}=\sum_{1}^{m}\frac{1}{a_{k}}$ for $a_{k}\in \mathbb{N}$ (distinct if it is too easy). The only proof I've seen is with ...
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0answers
27 views

Order of operations for log transformation

I am working with a large dataset of positive values with a positive skew. I will be using a Ln transformation in SPSS to normalize my dataset. However, I am not sure of the order of operations. For ...
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1answer
44 views

polynomials such that $P(k)=Q(l)$ for all integer $k$

In a book I have read this problem: Given $P\in \mathbb{R}[X]$, if $P(X)$ takes at every integer, a value which is the $k$-th power of an integer, then $P(X)$ itself is the $k$-th power of a ...
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1answer
65 views

How to define addition (of natural number) in ZF

The picture is from Enderton's "elements of set theory"(1977) page79. My question is: How to construct the set "+" by using the axioms in ZF set theory? In the picture above, those one-place ...
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3answers
60 views

Swimming pool problem: Time required to empty the swimming pool

In a swimming pool, 6 swimmers have to swim such that 3 swimmers start from end A at intervals of 1 minute and the remaining 3 start from end B at intervals of 2 minutes where A and B are opposite ...
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2answers
55 views

Solve the equation, hat consists on an arithmetical progression.

$$1+x+x^2+x^3+\cdots+x^{99}=0.$$ I said to prove with $0+1+2+3+\cdots+99=0$. How should I proceed?
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2answers
35 views

Prove that this is an arithmetic progression.

If a, b, c is an arithmetic progression prove that $$a^2-bc, b^2-ac, c^2-ab$$ is an arithmetic progression. Well firstly I stated that: b-a=c-b, then I showed that $$b^2-ac-a^2+bc=c^2-b^2-ab+ac$$ What ...
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2answers
32 views

Problem with arithmetic series

Define the arithmetic series if $A_3 + A_7 = 28$, $S_{10} = 155$. We have this for homework, I browsed the internet and I tried to find a formula or the way but there is nowhere I can find anything. ...
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35 views

Performing arithmetical operations (with binary numbers) using propositional logic

Clarifying some terms. By arithmetical operations I mean the four basic operations of addition, subtraction, multiplication and division. By binary numbers I mean numbers in the binary system. By ...
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1answer
61 views

How can I show that if $m ≥ 2^k $(with k ≥ 2 integer), then $n ≥ 2^{k + 1} -1$? [closed]

Let $m, n$ be positive integers and $P ∈ Z [X] $ a polynomial of degree $n$ such that all its coefficients are odd. Assume that $(x - 1)^m$ divides $P$. How can I show that if $m ≥ 2^k $(with k ≥ 2 ...
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2answers
33 views

Betting System Payout Equation

I am currently programming a betting system. I am a little confused as to the logic for working out the payouts (math is not my strong point) I will explain this the best i can. Scenario: Max Bet ...
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1answer
35 views

The name for numbers with a certain digit sum.

What is the term for a number that has a certain digit sum? For instance 12 is the "digit sum" of 84, 138, 525 and so on. But what kind of number is 84, 138 and 525 to the number 12? Is there a term ...
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12 views

how this arithmetic series is getting its values?

I have been reading a book of data mining and I am not quite sure of the results of the following example; the author presents us with the following figure: and it says: Each sucessive line ...
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1answer
38 views

Addition Problem with Missing Digits

In the addition problem shown each $\ast$ denotes a missing digit and the $\ast$'s are not necessarily identical. What final four digit sum will result from the proper restoration of the missing ...
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3answers
76 views

Usage of Mathematical Induction

How do I prove this with Mathematical Induction? Whereby $$u_1, u_2...u_n$$ are all positive and are in an arithmetic progression for $$n\geq2$$ ...
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3answers
143 views

The number $90$ is a polite number, what is its politeness?

The number $90$ is a polite number, what is its politeness? A. $12$ B. $9$ C. $6$ D. $14$ E. $3$ How did you get that answer? I tried Wikipedia to figure out what a polite number was ...
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2answers
46 views

Savings Accounts

A father has 4 children each with a savings account. Each account already has money in and the money cannot be transferred between accounts or taken out. Only money can be placed in the accounts at ...
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5answers
149 views

Fake proof $2=1$ [closed]

let $$x=y \implies 2x-x=2y-y \implies 2x-2y=x-y$$ $$2(x-y)=(x-y) \implies 2=1 \ \ \ \ \operatorname{By Cancellation Law}$$
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6answers
70 views

How to find the multiplicative inverse of $2^{29} \mod 9$

I just started studying this topic and from my understanding I have to find an integer $x$ such that: $2^{29}x \equiv 1 \mod 9$ However, I have no idea of how to find a linear combination of $9$ and ...
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1answer
28 views

Need to determine work hours formula [closed]

I am trying to do some resource planning for a project but the math just isnt working out. for example I have 768 hours worth of work, but only 4 hours to complete it. I am trying to determine the ...
2
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1answer
44 views

Which integers can be written in two different ways as a sum of $n$ distinct factorials?

Problem 11 from the 1966 IMO Shortlist asks: Does there exist an integer $z$ that can be written in two different ways as $z = x! + y!$, where $x$, $y$ are natural numbers with $0 < x \leq y$? ...
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2answers
57 views

Pedro's barn and how to find constant

"In Pedro's barn, the number of mice is inversely proportional to the number of cats. When he owned 5 cats, there were 48 mice in the barn. He increased the number of cats to 8. Based on the increased ...
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1answer
65 views

How can you multiply without adder?

Now, I'm trying to implement like this. "How many $4\times4$ multiplier would you need to perform an $8\times8$ multiply. how an $8\times8$ multiplier would be created using only $4\times4$ ...