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

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0
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29 views

Guess the rule of transformation of a natural number

I came across a playful problem. On a sheet of paper it is written the number $\overline{1234xy}$, where \begin{equation}\overline{1234xy}=1*10^5+2*10^4+3*10^3+4*10^2+x*10^1+y\end{equation} Five ...
1
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0answers
20 views

What formula can I use to calculate how much protein per 100 calories a given food has?

I have an Excel spreadsheet of 529 items all with calories, carbs, fats, and protein listed. I'd like to add a grams of protein per 100 calories column but my math ability is embarrassingly ...
5
votes
4answers
79 views

Which is more simplified: $a\sqrt{b}$ or $\sqrt{c}$?

Which is considered more simplified (if it matters)? $a \sqrt{b}$ or $\sqrt{c}$ For example: $2 \sqrt{3}$ or $\sqrt{12}$
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1answer
30 views

Distribute coins fairly

$10$ coins weigh $10$ grams each, and another $10$ coins weigh $11$ grams each. So the average weight is: $$\frac{10 \cdot 10 + 10 \cdot 11}{20} = 10.5\text{ grams}.$$ Now I need to distribute coins ...
3
votes
2answers
55 views

What is this method of calculating int number times int number called?

I saw this video on Facebook and I'm curious about this. I have very basic questions on this because I can use it but I can't understand the technique. Link to the video explaining this method on ...
4
votes
2answers
96 views

Consecutive sets of consecutive numbers which add to the same total

I'm looking at examples of numbers that can be written as the sum of integers from $j$ to $k$ and from $k+1$ to $l$. For example $15$ which can be written as $4+5+6$ or $7+8$. Or $27 = 2+3+4+5+6+7 = ...
2
votes
1answer
26 views

How many unique numbers can be obtained by adding two numbers from two different sequences?

Let the two integer sequences $\{a_m\}$ and $\{b_m\}$, be defined as: $a_n+D_n=a_{n+1}$ and $b_n=a_n-k$, where $D_n$ may be any natural number (and $D_i$ may or may not be equal to $D_j$), $k$ is an ...
6
votes
1answer
58 views

“there exists” and “for some” are the same, right?

I think "there exists" and "for some" are the same, but still want to make sure. Ex: $x > ky$ for some k or there exists a k such that $x > ky$
0
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3answers
34 views

Arithmetic and geometric sequence

Which two numbers should be placed between -5 and 49 so that the first three numbers form an arithmetic sequence, whereas the last three numbers form a geometric sequence?
-1
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0answers
13 views

Highest Yielding Array [on hold]

If I have 2 arrays of simple numbers and I add all the numbers for each one so I have 2 sums such as 250 and 400. Is the highest number equal the highest yielding over a period of time dispite ...
3
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1answer
17 views

Check algebraic transformation with trial numbers?

I did some algebraic transformations on equations with multiple real variables $x_i$, and I'd like to check whether the transformed equation is still valid. The equations are basically only rational ...
3
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2answers
27 views

Order of parsing + and -

This seems like an absurdly simply question, and is possibly below the level of this forum, but it seems the most sensible place. I'm building an arithmetic equation parser, and currently working on ...
10
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2answers
127 views

When is $\sqrt{a^2}=\pm a$ and when is $\sqrt{a^2}=a$?

When we derive some formula and have to do huge algebraic expansions that deal with raising powers we use exponent rules mindlessly and we never write down the $\pm$ symbol. Why is this right? My ...
-1
votes
2answers
63 views

2+2=square root of 16. What's the appropriate answer? [closed]

4? Positive and negative 4? I just got into an argument with a buddy about this. He argues if it's not an i, it's not included as a imaginary number, but only the real positive number.
0
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3answers
49 views

Exponential Function, Help Appreciated :-)

my text book asks me to 'Simplify, and express in terms of positive indices'. But my answer always seems to come up with: $x^{\frac {35} {36}}$. The term is $$\frac{ (x^{-\frac 1 2})^{\frac 2 3} \ ...
6
votes
1answer
62 views

Tzaloa 2015 game problem (piles with $1,2,4 \dots 2^{19}$ coins each)

We have $20$ piles with $1,2,4,8\dots 2^{19}$ coins repectively and two players. In each turn a player must select five piles that have at least one coin and remove exactly one coin from each. Player ...
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votes
1answer
75 views

How to make the expression from the left of the equation look like the expression to the right of the equation? [closed]

I cannot see how my teacher rewrites this equation.. : The answer is the expression to the right of the equation. I want to know how my teacher gets this expression from the left of the equation. ...
1
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2answers
55 views

Combination of $n$ objects taken $p$ at a time where $n$ contains $r$, $s$, and $t$ identical objects.

I am talking about something like this: $ N = \{2, 3, 3, 3, 5, 5, 7\}$ $ n = 7$ $ s=3 $ $t=2$ In my case specifically, those numbers in $N$ are the prime factors of a number $Z$ repeated the number ...
0
votes
3answers
24 views

average of an inequality

what is the result of $<1 + <1$? ; $<1 + <1 = <2$? or <1 + <1 = <1? Now what is that number divided by 2? Either we have: <2 / 2 = <1 or <1 / 2 = <0.5
3
votes
0answers
48 views

If $(x^2+y^2+z^2)=2(x+z-1)$, then show that $x^3+y^3+z^3$ is constant and find its numeric value.

I am trying to solve this question, If $(x^2+y^2+z^2)=2(x+z-1)$, then show that $x^3+y^3+z^3$ is constant and find its numeric value. I've tried this, $$x^2-2x + z^2-2z + 2 + y^2 = 0$$ $$ ...
10
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2answers
175 views

What would Gauss do in this case: adding $1+\frac12+\frac13+\frac14+ \dots +\frac1{100}$?

We all know the story related to Gauss that Gauss' class was asked to find the sum of the numbers from $1$ to $100$ as a "busy work" problem and and he came up with $5050$ in less than a minute. He ...
2
votes
0answers
36 views

Solving $-1=e^a-2e^{av}$ as part of a equation system

Problem Given $f_2(x)=e^{ax-b}+c$ with $x \in \left(0,1\right)$, I am trying to calculate the parameters $a,b,c$ in respect to the following constraints: $$ \begin{align} f_2(0) &= 0 \\ ...
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0answers
39 views

Getting fractions [closed]

Just wondering if there is a better algo/formula to get fractions (I don't know the correct Math term): Given: x and y Get this list: ...
1
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0answers
19 views

Definition arithmetic progressions of any given length.

I have been studying erdős conjecture on arithmetic progressions for some time and have an interesting question for you : How do I strictly define "a set containing arithmetic progressions of any ...
1
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1answer
82 views

Number puzzle : “You can't determine my sum.”

Albert said to Bob, "I have two unequal positive integers; the smaller is at least 2; the larger is at most 25. I will only tell you their product." So he did. Later, Albert has forgotten the numbers ...
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1answer
42 views

Does 0/0 = a new branch of numbers? Have I made a mistake in the equation? [duplicate]

So I thought... 0/0 = x... then 0 = x*0... then 0x = 0... then its technically possible to divide by 0 again 0x/0 = 0/0 ... since 0/0 = x and 0x/0 = 0/0.. then x = 0x/0 ... 0x = 0 ... x = 0/0 ...
3
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0answers
28 views

Comparing Large Exponents with different bases.

How to compare large exponents with different bases? Is there any way to roughly approximate their values? For example, sort the elements of list below based on their magnitude. ...
0
votes
2answers
34 views

calculating costs of manufacture [closed]

I apologize in advance if I'm asking this question in the wrong forum, but I'm having trouble with the Math, not the spreadsheet here. I'm calculating the cost per round of hand made ammunition, and ...
0
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1answer
39 views

Understanding A simple mathematical addition operation

I was just doing a simple maths operation: $s = 158 + 46 \times -1: \Rightarrow s = 112$ and $s = (158 + 46) \times -1:\Rightarrow s = -204$ In the latter case $158 + 48$ gets calculated first ...
4
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1answer
86 views

Infinite exponentiation $n^{n^{n^{…^n}}} \equiv m \pmod q$ , find m?

let $(n,q) \in \mathbb N^{*^2}$ I was wondering if it was possible to find a function $f_q$ such that : $f_q(n)=m$ where $m$ is such that $n^{n^{...^n}} \equiv m \mod q$ or at least an easy way to ...
1
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2answers
21 views

division of fraction simplification

The expression is this: ${{y^2 - y} \over 1 {}} \div {{y^2 - 1} \over 3}$ The first step is to swap the second expression round to: ${{y^2 - y} \over 1 {}} \div {3 \over {y^2 - 1}}$ The answer ...
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0answers
8 views

I want to find the % taken from the gross amount to reach the net amount

I know the gross amount and I know the net amount I want to know how to find the % of the gross taken to get the net amount
5
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0answers
60 views

imo question to be explained in a manner so as to a layman

Suppose that you mark a finite collection of points on an infinite plane in such a way that you cannot draw a straight line through any three marked points. We define a windmill to be the following ...
1
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2answers
49 views

Proving that an expression returns a real non-integer number (Number 2)

Let $$a=443372888629441 = 17*31*41*43*89*97*167*331$$ $$b=(3+\sqrt{13})/2$$ $$c=(2+\sqrt{8})/2$$ $$d=(1+\sqrt{5})/2$$ How can you prove that the expression ...
1
vote
3answers
55 views

Proof of the division algorithm

I wasn't happy with the proof provided by the book, so I had an attempt at it, but I don't know if it's right. The theorem is: Let $a,b\in\mathbb{Z}$ and $b\neq0$. Then there exist unique ...
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2answers
36 views

An Elementary Algebra (Ratios & Proportions) Problem

Let $a,b,c,d$ be positive real numbers in Continued Proportion (i.e., $\frac{a}{b} = \frac{b}{c} = \frac{c}{d}$), then show that $$d-a \ge 3(c-b).$$ or $$d -a = 3 + (some\ algebraic\ expression) $$
0
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1answer
15 views

how many distinct number group possibilities exist in a powerball drawing if you exclude the powerball [closed]

in a powerball lottery draw you choose 5 numbers out of 59 with no repeating numbers how many distinct number groupings does this amount to is there an equation that can be used to calculate this?
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3answers
121 views

What is the value of $-(-6)$?

I know this is not absolute value, so what do the parentheses mean? If it was absolute value, it would have lines so I can rule that out. And I guess I should mention, the question I was asked is ...
5
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1answer
101 views

A beautiful book on arithmetic doesn't treat you like a little baby

The state of arithmetic today is disgusting. The textbooks on it are absolutely repelling, the authors treat it like a subject that will be of concern to only babies. They don't show any love, they ...
1
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1answer
34 views

Compound interest question

A property is mortgaged over $20$ years at an interest rate of $5.6$% per annum compounded annually. If the mortgage is £$120,000$, what are the annual repayments if payments are made at the end of ...
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0answers
22 views

Calculating percentages of margins

If a company has three tiers of pricing for its product and its overall margin is $20\%$, is it possible to calculate the percentage margin of each tier from following information? Tier 1 = base ...
4
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5answers
827 views

If $x^3+y^3=72$ and $xy=8$ then find the value of $x-y$.

I recently came across a question, If $x^3+y^3=72$ and $xy=8$ then find the value of $(x-y)$. By trial and error I found that $x=4$ and $y=2$ satisfies both the conditions. But in general how ...
1
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2answers
39 views

Solving proportion problems involving three quantities

How do you solve proportion if 3 variables are given? I have looked in this site but i could not undertand it completely http://www.beatthegmat.com/ratio-proportion-3-variables-t34902.html 15 robots ...
0
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2answers
54 views

Arithmetic Sequence - Find the Last Number of Terms

The sequence is: $11, 13, 15, ... 59$ I need to find $i$ so that the sum of all terms before $i$ equals the sum of all terms after $i$ The simple way would be to calculate: $S_{i-1} = S_{n} - S_{i}$ ...
5
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4answers
140 views

How do I find the remainder of $4^0+4^1+4^2+4^3+ \cdots + 4^{40}$ divided by 17?

Recently I came across a question, Find the remainder of $4^0+4^1+4^2+4^3+ \cdots + 4^{40}$ divided by 17? At first I applied sum of G.P. formula but ended up with the expression $1\cdot ...
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votes
1answer
80 views

Proving that an expression returns a real non-integer number [closed]

Let $$a = 443372888629441$$ $$b = \frac{2+\sqrt{8}}{2}$$ $$c = \frac{1+\sqrt{5}}{2}$$ How to prove that the expression $$\frac{b^a-b^{-a} - 2(c^a-c^{-a})}{a}$$ is a real non-integer number?
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2answers
46 views

Take $\sqrt[n]{m}$ where $n$ is a positive non-integer number. Is this possible?

The title pretty much says it all. I am trying to figure out how to take the $n$-th root of a number $m$ where $n$ is a fractional number. Unfortunately all I could turn up on Google was how to take a ...
0
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3answers
75 views

If $ab(a+b)=2$ then what will be the value of $\frac{1}{(ab)^3}-a^3-b^3$?

The question given is, If $ab(a+b)=2$ then show that $\dfrac{1}{(ab)^3}-a^3-b^3=?$ $(a)\ \ \ \ \ 0$ $(b)\ \ \ \ \ 1$ $(c)\ \ \ \ \ 3$ $(d)-1$ I noted that $a=1$ and $b=1$ satisfy the ...
1
vote
0answers
18 views

A manufacturer discount to allow a buy-two-get-one sale [closed]

Could you help with right result, please? XD Thanks!!! The SuperSave supermarket sells Sudsy washing up liquid for $1.20 a bottle. At this price they are charging 50% more than the price at which ...
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0answers
17 views

Immediate Annuities

For a house loan of $\$300000$ at $4.65\% \ p.a$, the repayment is an $\$2,210$ per month for the first 60 months and then finishes the loan at $\$1960$. What are the total repayments of loan and how ...