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

learn more… | top users | synonyms (1)

0
votes
1answer
26 views

Summation problem (probability)

I have the equation $$\Pr(X\le6)=\sum_{x=6}^{∞}\left({e^{-4.8}}\cdot\frac{4.8^{x}}{x!}\right).$$ And it is not equating to when I sum each term manually. Plugging this into my calculator I get ...
2
votes
1answer
38 views

Why does complement arithmetic work?

I'm learning about how computers store and manipulate integers, and I want to understand two's complement. Despite an abundance of web-sites demonstrating how to perform complement arithmetic, the ...
1
vote
2answers
39 views

How to calculate so that when width increases, height will decrease

As stated in title. Width is dynamic, hence the calculation :p The tricky part is that width can not be on the right side of the divide sign (\), as defined by the css ...
0
votes
1answer
371 views

Irrational inequalities question: $\sqrt { -3x+1 } + \sqrt {6x+1} < \sqrt {3x+4}$ and $\sqrt { -6x+10 } + \sqrt {-x+2} \gt \sqrt {4x+5}$

Consider the following inequalities: $\sqrt { -3x+1 } + \sqrt {6x+1} \lt \sqrt {3x+4}$ $\sqrt { -6x+10 } + \sqrt {-x+2} \gt \sqrt {4x+5}$ Attempt at a solution; after performing all the ...
3
votes
1answer
94 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 ...
1
vote
2answers
43 views

Find the fraction that creates a repeating decimal that repeats certain digits

Is there any way to find the fraction $x/y$ that, when converted to a decimal, repeats a series of digits $z$? For example: ${x}/{y} = z.zzzzzzzz...$ or with actual numbers, $x/y = 234.234234234...$ ...
2
votes
1answer
82 views

When is $(p - 2)! \equiv 1 (\bmod p)$

I want to show when the following is true for $p$ a prime number. $(p - 2)! \equiv 1 \pmod p$. Could someone help me prove this? It worked for $p = 2$, $p = 3$, $p = 5$, so I believe it may work for ...
0
votes
1answer
37 views

help in simplifying an easy but nasty expression

I would like double check my work, I am trying to simplify the following summation, \begin{align} \sum_{\substack{(i,j) \in \mathcal{S}}} A_i v_i v_j \end{align} with the assumption that $$v_iv_j= c ...
1
vote
3answers
38 views

Operations and Identities [duplicate]

We have the binary operation addition on numbers. It has an additive identity ( 0 ) and it is commutative. Multiplication is simply repeated addition. It is a binary operation on numbers. Its ...
4
votes
1answer
19 views

Sum of numbers in a grouping question

A person grouped numbers in the following way: $$\left \{ 1 \right \},\left \{ 3,5 \right \},\left \{ 7,9,11 \right \},\left \{ 13,15,17,19 \right \},...$$ What is the sum of the numbers in the $9$th ...
2
votes
2answers
83 views

What fraction is $\frac{2}{5}$ of $\frac{3}{4}$?

$\frac{2}{5}$ of blood donors at a centre have group O blood. $\frac{3}{4}$ of these donors are under 30. What fraction of the group O blood donors at the centre are under 30? What I did was divide ...
0
votes
0answers
24 views

Solving equations with 3 variables

Is there any simple way to solve those 3 equations of the 2nd question in this page? There are three variables v, u, x. http://www.campusgate.co.in/2012/10/time-speed-and-distance-iii-challenging.html ...
2
votes
0answers
24 views

Arbitrarily long arithmetic progressions?

I found a theorem that states that if $A\subset \mathbb{Z}$ such that the upper Banach density is non-zero, then $A$ contains arbitrarily long arithmetic progressions, this is called Szemerédi's ...
1
vote
3answers
12k views

How to get the aspect ratio of an image?

I have an image that is: 320 original width 407 original height I want to let users resize the image via a form I am building on a webpage. They can adjust ...
4
votes
1answer
46 views

$f(x) = k^n$ for infinitely many integers $k$

Let $f(x)$ be a polynomial of $n^{th}$ degree with integer coefficients and let the leading coefficient be 1. Is it true that $f(x) = k^n$ for infinitely many integers $k$ and $x$ if and only if all ...
-1
votes
2answers
37 views

Extremely basic arithmetic simplification

For the life of me I can't understand my lecturer's working on this. I have $$\frac{1}{j\omega{L}}$$ Where $\omega=5000$ and $L=0.0001$ He somehow ended up with $$-2j$$ Whereas I simly got ...
-1
votes
1answer
72 views

How to solve a quintic congruence equation? [duplicate]

My textbook has this quadratic equation that I have to solve, any ideas how I could show that? $$15 | (21n^5+10n^3+14n),\;\forall n\in\mathbb{Z}$$
2
votes
1answer
65 views

Find these prime numbers $p, q$?

Let $p, q$ be prime numbers such that $p = 3p_1 + 2; q = 3q_1 + 2$; $p + q + 3$ and $3p + 3q + pq + 3$ are square numbers. Find $p, q$? P.S. I don't have any ideas about this problem :( Thanks ...
1
vote
0answers
23 views

How to find a relation between given numbers to get a given result?

I have f(2, 3, 6) = 5/6; f(4, 3, 12) = 17/6; f(3, 3, 9) = 11/6; f(2, 0, 2) = 2; How can I find the relation f for the given values?
1
vote
2answers
37 views

How can I scale a value from -255 to 255 or -100 to 100 to a scale of 0-100?

For Brightness, I have a formula that takes in a value from -255 to 255 and contrast from -100 to 100. What if I wanted to use the same formula but I wanted to convert/adjust the scaling so that I ...
1
vote
1answer
22 views

re-arrange equation $L=2^{10(v-1)} v^2$

Is it possible to re-arrange this equation to make v the subject? $$L=v^2 . 2^{10(v-1)}$$ If so, what is the answer? If it helps (which by excluding zero it should)... $$0<v<1$$ I have tried ...
0
votes
1answer
12 views

How to form a 'master rank' from a list of other ranked items?

This is my first question across the StackExchange network, and it seems a lot easier than other questions I've seen on here (so I hope it doesn't bore you!), but I can't seem to come up with the ...
0
votes
1answer
26 views

Base three numbers and expanded form

I need help understanding this. Write each of the following base three numerals in expanded notation. $22_3$ $212_3$ $12110_3$
2
votes
1answer
20 views

order of operation

For the following expressions,why we can get the right answer even we do addition /subtraction first ? $3+4\times 11-5 = (3+4)\times(11-5) = 42$ $6+4\times7-4$ $5+2\times13-10$ $4+7\times16-6$ ...
2
votes
4answers
57 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 ...
5
votes
1answer
69 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 ...
2
votes
3answers
2k views

How to convert from 10s complement to base 10/decimal

I finally understood how to convert from base 10 to 10's complemnt here But how do I convert back? How do I know what sign it is? In 2s complement, its the LSB, 1 means negetive else positive. For ...
1
vote
3answers
65 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 $4$.
1
vote
0answers
18 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, ...
6
votes
4answers
402 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?
0
votes
0answers
31 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
33 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
41 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 ...
4
votes
2answers
76 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 ...
35
votes
10answers
5k views

Is it possible to simulate a floor() function with elementary arithmetic?

I'm using a "programming language" that only allows basic operations: addition, subtraction, multiplication, and division. Is it possible to emulate a floor function (i.e. drop the decimals a number) ...
1
vote
1answer
29 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
11 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
50 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
128 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
76 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.
0
votes
3answers
540 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?
2
votes
2answers
26 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
46 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
6
votes
4answers
145 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
0answers
42 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 ...
3
votes
2answers
2k views

Square root of surds?

I got this question Find the square root of $12+2\sqrt{6}$ expressing your answer in the form $\sqrt{m}+\sqrt{n}$. I have no idea what this means and how to go about it.
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
30 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
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, ...
1
vote
4answers
109 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 ...