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

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1answer
108 views

Dividing x by (1+x) the unusual way

Why this way of dision is not correct; that is, changing the order of the terms of divisor as and when required? Even though $1+x$ is same as $x+1$ Check: (quotient)X(divisor)+(remainder) ...
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2answers
35 views

Mathematic function that takes any number above 90 and returns 90 minus the quantity above 90

For instance: 100 returns 10 101 returns 11 150 returns 60 but 87 returns 87 Is this possible exclusively with mathematics?
3
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2answers
198 views

Proving $mn=nm$ for all $n,m\in \mathbb N$

How can I prove that $mn=nm ,\forall m,n \in \mathbb N$, by using just the following axioms? $(\forall n \in \mathbb N)(n\cdot 0=0)$ $(\forall m,n \in \mathbb N)(m(n+1)=mn+m)$, The axioms and ...
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1answer
31 views

How to evaluate $\pm$ operations

When finding the root of a number with an even exponent, $x^y$ becomes $\pm x$. How would this work in a situation such as $a = \sqrt{(5x + 12)^2 + m}$? I know that the result is not $a = \pm 5x + ...
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1answer
78 views

Adding weightage to number.

I have four numbers x=50 y=30 z=20 sum of x+y+z=100 if i want to add a number n where n=(x+y)/2 Edit: ...
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1answer
99 views

Find the sale price given the 40% markup over wholesale and later 20% discount

A retailer pays $\$86$ to a wholesaler for an article. The retail price is set using a $40\%$ rate of markup on selling price. To increase traffic to his store, the retailer marks the article down ...
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2answers
71 views

Math question from the GMATprep

If $xy=1$ what is the value of: $2^{(x+y)^2}/2^{(x-y)^2}$ A 1 B 2 C 4 D 16 E 19 $(x+y)^2/(x-y)^2$ because $2$ just cancels out from numerator and denominator, ...
4
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1answer
91 views

Simplify $\sum_{k=0}^n \frac{1}{k!(n-k!)}.$

Is there a way to simplify the expression $$\sum_{k=0}^n \frac{1}{k!(n-k)!}?$$ This came up when I was trying to determine $\mathbb{P}(X+Y =r)$ given a joint mass probability $$m_{X,Y}(j,k) = ...
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1answer
21 views

How to calculate payment based on ratio [closed]

This is probably trivial math for most, but it's got me stumped. What I want to do is calculate payments on amounts based on the ratio of two other amounts. Example: Bob has 4000 Joe has 2000 Bob ...
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1answer
50 views

Percentage ratio [closed]

Correctly: I have order (100%) $\$1500$ and I have two workers for this order: 1st worker and 2nd worker has percent rate from order. If they have 10% it's simple: 10% from 1500$ and /2(case they ...
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2answers
33 views

on visualising arithmetic with roots ansd radicals

Is there a visual way to simplify $4\sqrt{12}+4\sqrt{27}$? I know the answer is $20\sqrt{3}$, but I want to geometrically explain it to a 14 year old. Is there also a way to geometricaly interpret ...
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2answers
890 views

How many times vs how many times greater?

I keep on coming into these problems while my gre prepration How many times vs how many times greater or a is what % of b or a is what % greater than b What is the right convention to solve ...
3
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1answer
73 views

comparing bit lengths of binary numbers

Suppose I have two binary numbers x and y that have bit lengths of nx and ...
0
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2answers
33 views

Proving Multiplication by Positive Element

I need help proving this simple fact. If $a,b,c \in \mathbb{Z}$, all $a,b,c>0$, and $a>b$, then $ca>b$. How do I prove this?
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2answers
76 views

SOLVED — For $a,n \in \mathbb{Z}$, where $n>a>0$, prove that $\nexists x \in \mathbb{Z}$ s.t. $nx=a$

Suppose $a,n \in \mathbb{Z}$, and $n>a>0$. How do I prove that $\nexists x \in \mathbb{Z}$ s.t. $nx = a$ ? I'm really not sure where to start on this one. I'd be happy if someone could give me a ...
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2answers
70 views

FACE divided by D (base 16 arithmetic problem) [closed]

I am doing my college math homework, and I am stuck on this question that has to do with dividing in the base 16. FACE (base 16) divided by D (base 16)
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4answers
651 views

Proof that $n^3 + 3n^2 + 2n$ is a multiple of $3$.

I'm struggling with this problem: For any natural number $n$, prove that $n^3 + 3n^2 + 2n$ is a multiple of $3$. That $n^3 + 3n^2 + 2n$ is a multiple of $3$ means that: $n^3 + 3n^2 + 2n = 3 ...
2
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2answers
76 views

How to find $p$ and $q$ if we have $\operatorname{lcm}(p,q)=b$ and $p+q=a$ where ($a,b \in \mathbb{N}$) and $p>q$.

What is the general formula to find $p$ and $q$ if we have $\def\lcm{\operatorname{lcm}}\lcm (p,q)=b$ or $\gcd(p,q)$ and $p+q=a$ where ($a,b \in \mathbb N$) and $p>q$? Example: $\lcm(p,q)=84$ and ...
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2answers
44 views

How to find the rate of interest?

Q. The simple interest in 3 yrs and the compound interest in 2 yrs on the same principal and at the same rate are 1200 and 832 respectively. Calculate the rate. What I've done: SI in 3 years = ...
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1answer
30 views

Centering the image

How should i calculate the left offset to center align the image inside the container? Example container width: 190mm image width: 63,5 mm left offset: ?
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3answers
81 views

time and distance problem related to speed

2 workers,One Young And One Old, Live Together and Work at the same office . It takes 20 mins for the young man to walk to office . the old man takes 30 mins for the same distance. when will the young ...
0
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1answer
676 views

men and women problem in time and work

4 men or 5 women can construct a wall in 82 days . How long will it take 5 men and 4 women to do the same?? Not able to grasp the problem in contention intuitively. Any help is greatly appreciated . ...
0
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1answer
125 views

How to get average of Arun's weight?

This is an aptitude problem I found in a website, question no 9: In Arun's opinion, his weight is greater than 65 kg but less than 72 kg. His brother does not agree with Arun and he thinks that ...
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2answers
80 views

Why are the roots of the polynomial $z^N = a^N$ equal to $z_k = a \ e^{j\frac{2 \pi k}{N}}$?

I am trying to understand equation 3.28 from this image in my book. I get everything that the author is saying, except for when he finds the roots, (zeros), of $z^N = a^N$. Of course, there are ...
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1answer
822 views

Is there something similar for division as this Japanese multiplication method?

In this youtube link, a really cool method to multiply two big numbers is given. Only works of integers. I was wondering if something unconventional and similar to this exists for dividing two big ...
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3answers
91 views

Roots Calculation Question

How does one calculate the roots: $$ \sqrt {57-40\sqrt{2}} - \sqrt {57+40\sqrt{2}}$$ manually? Also, how can one determine which of the pair is bigger: $ \sqrt {3} +\sqrt {5} $ vs. $ \sqrt {2} ...
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2answers
42 views

New hourly rate after a pay raise

Show the correct equation and solve for the indicated items. Jim is earning $12.50 per hour as a cook. He has earned an 8.5% pay raise this year. What will his new hourly rate be? Source: ...
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2answers
198 views

Special subdivision of numbers from 1 to 99

I've been lately working on a problem I still can't solve. The problem is: Can we divide numbers from 1 to 99 into 33 groups of three numbers, such that in every group one number is the sum of the ...
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1answer
201 views

How does adding big O notations works

can someone please explain how adding big O works. i.e. $O(n^3)+O(n) = O(n^3)$ why does the answer turn out this way? is it because $O(n^3)$ dominates the whole expression thus the answer is still ...
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1answer
62 views

Order of operations: problem evaluating an expression

Well I have the expression below can be evaluated in tow different ways according to my knowledge of order of operations: $$\begin{matrix} 3+8\div2\left(10-2^3\right)-7 \end{matrix}$$ OK my try: ...
4
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1answer
232 views

How to sort numbers from 1 to 20 into 6 piles where sum in each pile is the same?

How to sort numbers from 1 to 20 into 6 piles where sum in each pile is the same? This question, my son got in school and I can't figure out what is the correct approach to solve this.
2
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3answers
2k views

Find the sum of all the integers between 1 and 1000 which are divisible by 7

How can I work this one out (with workings)? "Find the sum of all the integers between 1 and 1000 which are divisible by 7" Thanks!
0
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1answer
27 views

We suppose: $a, b, c \in \mathbb{N}$ and $b$ and $c$ are multiples of $a$ then $b+c$ is a multiple of $a$.

Are those statements true? We suppose: $ a, b, c \in \mathbb{N}$. We suppose: $b$ and $c$ are multiples of $a$ then $b+c$ is a multiple of $a$. We suppose: $b$ and $c$ are multiples of $a$ and $(b ...
2
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2answers
61 views

Easy Algebra Question

Its been too long since my highschool algebra class, and now I need those skills again. I'm reviewing all my math on khanacademy.org but I need this answered sooner than that. What algebraic ...
0
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2answers
141 views

Rational exponents: prove some states

In some rational exponent expressions the solution isn't a real number why? Example (explain what I mean): $$\begin{align} \Big(-x\Big)^{1/n}=\left\{\text{is not a real number}\right\} \end{align}$$ ...
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2answers
124 views

Calculation of bucks missing

Lets say I bought 1000 bucks from a friend of mine and 500 bucks from another.Now I went to the market and there I accidentally lost 1000 bucks. Ok then I did some shopping which costs me 300 bucks. ...
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0answers
33 views

Generate Max Value Expression

How to insert * AND + OPERATORS between a given set of integers so that the expression evaluates to the max possible value if Set is [3,4,5,6,-2] it should give 3*4*5*6+-2 and also note that * gets ...
6
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3answers
731 views

Explanation for $\lim_{x\to\infty}\sqrt{x^2-4x}-x=-2$ and not $0$

I am trying to intuitively understand why the solution to the following problem is $-2$. $$\lim_{x\to\infty}\sqrt{x^2-4x}-x$$ ...
1
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1answer
300 views

How many $n$-disk legal configurations are there for the Tower of Hanoi?

This question comes from this homework assignment from ECS20 at UC Davis. How many $n$-disk legal configurations are there for the Tower of Hanoi? A "legal configuration" means that no disk is ...
0
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1answer
66 views

algebra, solving equations with variables on both sides

Janine has job offers at two companies. One company offers a starting salary of $\$28,000$ with a raise of $\$3000$ each year. The other company offers a starting salary of $\$36,000$ with a raise of ...
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2answers
70 views

Why is $0^0=1$, given the following information? [duplicate]

Why is $0^0=1$, given the following information? We really have two separate rules that are at odds with each other. Typically we have $0^n=0$ (provided n is positive) and $a^0=1$. Each of these ...
1
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2answers
292 views

Remainder when $26^{3008} + 3008^{26}$ is divided by $4$

I want to find the Remainder when $26^{3008} + 3008^{26}$ is divided by $4$. What should I do? Even though I've included the tag modular arithmetic I've very limited knowledge about it. How should I ...
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1answer
48 views

Is there any way to write this number with these limits?

Is there any way to write this number: $$ \frac{17+15\sqrt{5}}{7+15\sqrt{5}} $$ Just using the digits $1$, $4$, $7$, $8$, $9$ once each with the following criteria: A maximum of two square root ...
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2answers
73 views

How to find the remainder of $(2010^{1020} + 1020^{2010})$ divided by $3$

What is the remainder when $2010^{1020} + 1020^{2010}$ is divided by 3?
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3answers
141 views

Where do variables outside of a square root go?

This is a formatting question. Example, $\sqrt{4}x^2 \text{ or } x^2\sqrt{4}$. Which is less ambiguous? Is there a style guideline for things like this?
1
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1answer
129 views

How to justify the rule for the product of square roots of real numbers?

Why $\sqrt{a}$ * $\sqrt{b}$ = $\sqrt{ab}$ ? It's easy to verify that it works in some cases, like in $\sqrt{4}$ * $\sqrt{9}$ = $\sqrt{36}$. But why does the general rule work?
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5answers
373 views

How to explain infinty to a $3^{rd}$ grader?

In my country in $3^{rd}$ grade in math kids learn the four basic arithmetic operation (addition, subtraction, multiplication and divison) up to $10 000$. My sister this year goes to $3^{rd}$ grade ...
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0answers
28 views

Positive Arithmetic Complexity

Define the binary operator $[k]$ as an operator that takes an integer $k$ and operates between two integers $a,b$ such that: $$a[k]b = (...((((a)[k-1]a)[k-1]a)[k-1]...a)[k-1]a$$ (b times) And: ...
4
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2answers
76 views

Arithmetic sequence and a rectangular triangle

Task: Calculate the smallest angle in a rectangular (or right) triangle whose sides form an arithmetic sequence. That's it.. and I can't solve it. The solution is 36°52'. p.s.: thank you in advance! ...
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1answer
60 views

Solving linear inequalities and expressing in interval notation…

I have a set of problems for my algebra class dealing with expressing linear inequalities in interval notation. I get the solution but I'm not sure how to express the infinity, here's an example. ...