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

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6
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1answer
91 views

What's the digit sum of $4444^{4444}$? [duplicate]

For a natural number $n$ say that $d(n)$ is the sum of the digits of $n$ (in base $10$). Then what is the value of $$d(d(d(4444^{4444}))) ?$$ I have been trying with modular arithmetic, but can't do ...
1
vote
0answers
20 views

Tratchenberg Division Method

$ 743567 \div 256 =$? I get the following method: $ 7 4 3 5 6 7 \div 256 = 2$ __24, 7, 23, And since $23 \div 2 > 9$, I choose $23 \div 3$ to get: $ 7 4 3 5 6 7 \div 256 = 27$ __24, ...
0
votes
3answers
121 views

How to put a fraction in simplest form, such as $140/255$?

Given the fraction $$\dfrac{140}{255}$$ How do I find a common factor so it can be easily simplified? I have already tried $2$, $3$ and $4$.
5
votes
4answers
453 views

Why is $-5^2=-25$?

If $-5^2$ is equal to $(-5)(-5)$, doesn't that mean the negatives should cancel each other out and become $25$? Why is this not the case?
2
votes
4answers
66 views

Why does the least common denominator work?

Take for instance the following problem. You have two beakers of the same height. One has tick marks that break it into thirds. The other has tick marks that separate it into fourths. The water levels ...
0
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0answers
75 views

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 ...
1
vote
1answer
103 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 ...
-2
votes
1answer
63 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 ...
1
vote
2answers
587 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 ...
4
votes
2answers
155 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 ...
1
vote
1answer
37 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 $n\in\mathbb{N^+}$: ...
0
votes
1answer
70 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. $9$ ...
1
vote
0answers
96 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 ...
1
vote
3answers
148 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.
2
votes
0answers
80 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.
1
vote
3answers
556 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?
0
votes
1answer
242 views

How to explain this question (about square perimeter and area) to a 6 year old

My daughter who is in 1st grade is learning to grasp he meaning of multiplication and has not yet been introduced to division. she is appearing for Kangaroo Math Competition. Following question has ...
2
votes
2answers
33 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 ...
1
vote
2answers
50 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
1
vote
1answer
74 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 ...
0
votes
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? ...
2
votes
1answer
48 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 ...
0
votes
0answers
51 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, ...
2
votes
2answers
63 views

Proving square of nonzero integer is natural number

I am learning proofs with $\mathbb N$ and have this proposition: Let $m \in\mathbb Z$. If $m \ne 0$, then $m^2 \in\mathbb N$. Previously, I have proven: For $m \in\mathbb Z$, one and only one of the ...
3
votes
2answers
714 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 ...
0
votes
1answer
35 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
votes
2answers
222 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?
2
votes
0answers
28 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 ...
0
votes
0answers
19 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 $-10$, ...
4
votes
0answers
66 views

On $1/7$ in base $12$

Remember something from seventh grade: \begin{align} & 142857 \\ {}+ {}& 142857 \\ \\ & 285714 \\ {}+{} & 142857 \\ \\ & 428571 \\ {}+{} & 142857 \\ \\ & 571428 \\ ...
0
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1answer
38 views

Show an arithmetic progression has infinitely many elements

How would I Show this arithmetic progression has infinitely many elements. $$A_{a,b}=\left\lbrace a+nb:n\in\mathbb{Z}\right\rbrace$$
2
votes
4answers
143 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 ...
6
votes
4answers
152 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 $n,m$ ...
1
vote
1answer
51 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?! ...
0
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3answers
82 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 ...
0
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0answers
59 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 ...
2
votes
1answer
50 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 ...
1
vote
1answer
92 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 ...
0
votes
3answers
125 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 ...
1
vote
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?
0
votes
2answers
38 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 ...
0
votes
2answers
34 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. ...
0
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0answers
46 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 ...
1
vote
1answer
62 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 ...
0
votes
2answers
71 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 ...
1
vote
1answer
41 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 ...
0
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0answers
18 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 ...
-2
votes
1answer
77 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 ...
0
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3answers
84 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 $$n\geq2$$ ...
7
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3answers
321 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 ...