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

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Figuring a loan payoff amount

I have a loan for a principal amount of \$117,000.00 at 9.75% interest and a total amount due (including the interest for 84 months) of \$191,805.60. I had 84 months to pay it off, or I could pay it ...
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2answers
454 views

What is a fancy way to say “same sign” for two numbers?

If $xy > 0$, then $x$ and $y$ are [insert fancy smart term for same sign] Does "sign parity" work here?
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1answer
450 views

Calculating difference of percentages

Sometimes, in research articles the difference between two percentage is reported directly. How is it right? Example: State A has 75% of people of X kind. State B has 80% of people of X kind. The ...
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3answers
2k views

Product of consecutive even numbers

Prove that the product of three consecutive even numbers is a multiple of 8? show This into as much detail as possible!
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1answer
1k views

Help with $\sum (x_i- \bar{x})(y_i - \bar{y}) = \sum x_i(y_i - \bar{y})$

I can not understand how to get from one side to the other. $$\sum [(x_i- \bar{x})(y_i - \bar{y})] = \sum[x_i(y_i - \bar{y})]$$
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4answers
1k views

Why not to extend the set of natural numbers to make it closed under division by zero?

We add negative numbers and zero to natural sequence to make it closed under subtraction, the same thing happens with division (rational numbers) and root of -1 (complex numbers). Why this trick ...
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1answer
92 views

Power / Root function issue

I'm having trouble finding the answer for this, or really any Nth root problem. Here is the particular problem that I cannot figure out. A simple explanation of how to solve this would go a long ...
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1answer
126 views

Convert natural exponent, $e^{c\cdot x}$, into the form $a^{x}$

How does one convert a natural exponent written as $e^{c\cdot x}$ into the form $a^{x}$ ?
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3answers
149 views

Progessive terms adding and minusing

What is the value of $$1+2+3-4+5+6+7-8+9+10+11+12...+97+98+99-100 \ ?$$ Any help is appreciated, thank you! I added the terms as an AP then subtracted 10 then all the numbers that were missed out, ...
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2answers
301 views

Equivalence of quadratic forms over p-adic fields.

There is a theorem that states that two quadratic forms over $\mathbb{Q}_p$ are equivalent iff they have the same rank, discriminant and the same $\epsilon$ invariant. (The last is defined as ...
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2answers
5k views

Standard way to divide numbers of base other than 10.

I have some homework where I am supposed to divide two numbers that are base 5 or 3. And I did it. I basically converted the numbers to decimal, divided, and then convert the result to the original ...
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2answers
113 views

Get the increased amount based on Percentage

Suppose I have $\$100$ and it increased $2850\%$. How much money will I have? Can you also share the formula? thanks.
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2answers
106 views

Percentage calculation

I am trying to figure out the win-loss/accuracy of stock trades exported to excel. I have thousand of lines of trades. Unfortunately the software exports the win/loss as a fraction and not two ...
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2answers
1k views

How to find the first and last n/2-digits from an n-digit number?

I have an n-digit number, say X. Now, what-is-the/how-can-I-come-up-with-an equation [or function] that I should use to get the ...
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1answer
2k views

Chinese Remainder theorem with non-pairwise coprime moduli

Let $n_1,...,n_k \in \mathbb{N}$ and let $a_1,...,a_k \in \mathbb{Z}$. How to prove the following version of the Chinese remainder theorem (see here): There exists a $x \in \mathbb{Z}$ satisfying ...
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2answers
289 views

A Very Short Question On Surd Notation{Square Root}

What makes $\sqrt[7]{9}$ = $9^\frac{1}{7}$ Can this be explained using laws of indices?
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1answer
166 views

How does mutliplication work?

I was wondering how Al Khwarizmi's method of multiplication worked? I was hoping for a simple explanation in layman's terms. For those of you unfamiliar with the method its basically this: If you ...
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1answer
72 views

Please help with this simple question?

My problem says that 1 out of 2 people in the neighborhood have a car. How many people out of 100 neighbors have a car? I don't understand what that means. First they say 2 people then 100...
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1answer
259 views

What does it mean if a number has a remainder of 1?

I have this problem: linesize = 20 counter % linesize == 1 // what does this line mean?
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1answer
95 views

How fast is a low denominator encountered, when using only mediants?

This question is (remotely) related to How to find a "simple" fraction between two other fractions?, but is not answered in that older post. Let $f_1=\frac{a}{b}$ and $f_2=\frac{c}{d}$ be ...
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1answer
104 views

Is there a direct proof of this inequality between quotients of integers?

Let $\frac{a}{b}$ and $\frac{c}{d}$ be two reduced fractions with $bc-ad > 1$ (and hence $\frac{a}{b} \lt \frac{c}{d}$) and $a,b,c,d$ positive. It is well known that there are integers $u,v$ ...
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4answers
344 views

Divide inside a Radical

It has been so long since I have done division inside of radicals that I totally forget the "special rule" for for doing it. -_- For example, say I wanted to divide the ...
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1answer
108 views

When are quantities considered mere numbers?

I don't understand how an angle (radians) is considered a mere number, while degrees (for example) aren't. I think that degrees are different in that they are defined arbitrarily, but I don't find ...
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2answers
114 views

Which roots of a negative number can be done?

I'm an Android programmer and am working on a graphing calculator. I have been looking for the limits on which roots can be done. I have a decent understanding of mathematics but can not seem to find ...
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1answer
4k views

Effective Annual Rate Calculation: Tricky periods and payout frequencies

For calculating the Effective Annual Rate (EAR) from various stated interest rates, I'm using the formula: $$EAR= \left(1+\frac{r}{p}\right)^{pt}-1$$ where, $p$ = no. of payouts in a period, $t$ = ...
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2answers
5k views

Is the average of the averages equal to the average of all the numbers originally averaged?

I am tempted to say yes because of the following pseudo-proof (I say pseudo-proof because I am not convinced): $$ \frac{\frac{w+x}{2}+\frac{y+z}{2}}{2}=\frac{w+x}{4}+\frac{y+z}{4}=\frac{w+x+y+z}{4} ...
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1answer
581 views

Priority of parentheses and brackets in basic arithmetic.

Wolfram alpha is giving inconsistent results to this problem: When I enter: 16÷2( 8-3(4-2) )+1 the result is 17. When I enter: 16÷2[ 8-3(4-2) ]+1 the result is 5. and 16÷2*[ 8-3(4-2) ]+1 brings ...
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4answers
6k views

Indian claims finding new cube root formula

Indian claims finding new cube root formula It has eluded experts for centuries, but now an Indian, following in the footsteps of Aryabhatt, one of the earliest Indian mathematicians, claims to ...
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1answer
8k views

Calculating CRC by long division: How to decide the top number of long division?

Ok, I know how to use long division by using regular numbers, but when comes to binary numbers I'm getting confused. In following calculation I can see the equation solved but I don't understand ...
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1answer
3k views

Problem while calculating Frame Check Sequence (FCS) in Cyclic Redundancy Check (CRC)

I am asked, in homework assignment, to calculate the CRC of the message and pattern that are given. Question states: For P = 110011 and M = 11100011, find the Cyclic Redundancy Check (CRC). My ...
3
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1answer
90 views

Game analysis : Is it worth it to steal the box?

There are $N$ dollars in a box. You have a probability $P$ (fixed) to win everything in the box and $1-P$ to pay a fee of $200$ dollars ($100$ go in the box, the other half is lost). You can try it as ...
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1answer
95 views

Why are we adding instead of subtracting?

The problem statement: Distance between two stations A and B is 230 km. Two motorcyclist starts simultaneously from A and B in opposite directions and the distance between them after 4 hours ...
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1answer
165 views

Is there any recursive definition, using only addition, of the set of values of $x^2+y^2$?

There is a recursive definition of the set of squares which uses only addition: $CS(x,y) := IS(x) \wedge IS(y) \wedge x \lt y \wedge \forall z: (x \lt z) \wedge (z \lt y)⇒\neg IS(z)$ $IS(x)⇔ x=0 ...
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1answer
790 views

On the commutative property of multiplication (domain of integers, possibly reals)

$ab = ba$ This is, inherently, true. Some texts drop it like an axiom without any justification. But I'm a bit curious where it stems from or basically why/how it works. If anyone could enlighten me ...
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2answers
217 views

$\wedge,\cap,\times$ and $\vee,\cup,+$ are always interchangeable?

Update : Should have left the Arithmetic out of this question, the new modified question is posted here : $\wedge,\cap$ and $\vee,\cup$ between Logic and Set Theory always interchangeable? ...
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2answers
354 views

Finding the bitrate of source

I am doing a math homework but I'm not understanding one part of the question. What would be the 32 intensity values in following question: Suppose that a digitized TV picture is to be transmitted ...
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4answers
100 views

Is it true that $\sum_{k=1}^n(p_k\prod_{i=1}^k(1-p_i)) \stackrel{\mbox{?}}{=} 1 - \prod_{i=1}^n(1-p_i)$

Prove that $$ p_1 + \sum_{k=2}^n \left(p_k\prod_{i=1}^{k-1}(1-p_i)\right) = 1 - \prod_{k=1}^n(1-p_k)\ . $$ I'm working in a code where I have to do those computations. I want to see if this ...
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0answers
127 views

1/3+2/3 in double precision

When I add 1/3 and 2/3 in double precision, I ended up with $1.\boxed{111\ldots1}1\times2^{-1}$, where the boxed part is the 52-bit mantissa. By the rounding to even rule, I should round it up, right? ...
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1answer
247 views

Solve an inequality with fractions [closed]

How can an inequality with fractions should be solved ? Let say : $$ \displaystyle \frac{2}{4}\quad?\quad\frac{5}{21} $$ Please give me examples, information (step by step). I should multiply ...
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2answers
155 views

When is a calculation undefined and when is it indeterminate?

I have the sense that f(x0,y0, ...) is indeterminate if the limit can be any complex number if we choose the right path to (x0, y0, ....). MathWorld and Wikedidia mention the subject, but it wasn't ...
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2answers
737 views

How hard is it to do arithmetic?

People in computing are often observed saying that a computation takes $\operatorname{O}(n^3\log n)$ steps or that it's NP-hard or that it's not computable, or that it's primitive recursive, etc. I ...
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1answer
196 views

Why is $\frac{x}{0}$ undefined? [duplicate]

Possible Duplicate: Division by $0$ The way I see things (and I know most will scoff) is some math doesn't align to common sense. Why does $x^{0}=1$? You are taking x zero times. Why not ...
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2answers
1k views

Measuring equal distances between points on a line

I have a 36 inch piece of wood (Length) I will placing 6 coat hanger hooks along the length of the wood. The first hook will be placed 1 inch down the length from one end and the last hook will be ...
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2answers
270 views

A line moving along the hypotenuse of a right triangle

ABC is a triangle with sides $AB = 6 m$, $BC = 8m$, and $AC = 10m$. A line $k$ in the plane of the triangle $ABC$ moves along the segment $AC$ at the rate of $1cm$ per sec. The line starts at A and ...
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4answers
343 views

Perfect Squares ending in 576

I want to find out perfect squares ending in 576, after the number 576. Here is my derivation to arrive at such a number. Let the perfect square ending in $576$ be $1000k+576$. Every perfect square ...
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7answers
2k views

Doing simple math in your head

I thought I was pretty good at doing math in my head until yesterday I saw someone do $17.4/4$ in their head, without writing anything down and it took them less than 20 seconds. What do you do to do ...
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1answer
305 views

Word problems - Sum of squares & a strange function

These were two of 20 problems I had to do in a test today that I didn't manage to solve. 1) Find the least $k$ such that $1^2 + 2^2 + 3^2 + 4^2 + \dots + k^2$ is a multiple of 200. 2) ...
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8answers
2k views

Which of the numbers $99^{100}$ and $100^{99}$ is the larger one?

Which of the numbers $99^{100}$ & $100^{99}$ is the larger? Solve without using logarithms.
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2answers
171 views

Absolute value around numbers Example: y = 2|x + 2|

I know this is a super basic question but I can't find an answer. Is it that the result of anything within $|\quad|$ must be evaluated first and given a positive value? I knew this years ago but ...
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1answer
95 views

rearrange $z \mapsto z^2 + c$

Mathematics, some of its magic is that a lot is known about how to rearrange its statements (equations). Given the Mandelbrot Set: $z \mapsto z² + c$ (or more precisely) $z_{i+1} = z_i ^2 + c$ ...