Questions on basic arithmetic involving numerical quantities only. Questions involving variable values (other than the result of the operation) should be placed under the (algebra-precalculus) tag.

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3 views

question of mixtures and aliigations

whats the solution for this question of mixtures and aliigations ? http://i.stack.imgur.com/01Ujl.png
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4answers
247 views

Why does the symbol for the multiplication operation change shape?

Why does the "$\times$" used in arithmetic change to a "$\cdot$" as we progress through education? The symbol seems to only be ambiguous because of the variable $x$; however, we wouldn't have chosen ...
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1answer
15 views

Convert currency base from one base to another

Consider a list of currency rates where the base is USD: 1 USD = 0.90390 EUR 0.74771 GBP 1.30101 CAD how can I convert the base from USD to GBP, such that I ...
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1answer
14 views

Ratios question [on hold]

Two water taps , One big , one small , are used to fill a rank of capacity 4 $m^3$ with water . Small water tap supplies water to the tank at a rate of p $m^3$ per min and the big water tap supplies ...
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2answers
46 views

Maximizing product of five-digits numbers

From a French 2016 puzzle and math contest, where no calculator is allowed Using each of the digits $0,1,2,3,4,5,6,7,8,9$ exactly once, find two five-digit integers such that their product is ...
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1answer
38 views

Finding the sum of numbers between any two given numbers

I tried to derive this type of formula and ended up with this . But it's not holding true for all the numbers. Can you please tell what I've done wrong !!
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2answers
31 views

Why shift the result of subtracting vectors?

Why do we shift the resulting vector after subtracting any two vectors a and b? I learned that when you add any two vectors a and b, the sum vector looks like the one that can be seen in the picture ...
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1answer
25 views

Finding the original value of a quantity when final value and the ratio in which it is altered is given. [on hold]

Question: A liquid when heated expands $0.00236$ of it's original volume. If it is finally $624.7 cm^3$ after expanding, what was it before heating?
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2answers
23 views

Inequality on sequence of integers whose only prime factors are $2$ or $3$

Let $M=\lbrace 2^i 3^j | i,j \geq 0\rbrace$ and denote by $m_k$ the $k$-th element of $M$ ; so $m_1=1,m_2=2,m_3=3,m_4=4,m_5=6\ldots$. Is it true that $3m_k\geq 2m_{k+1}$ for every $k>1$ ? My ...
3
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1answer
77 views

An Olympiad question on arithmetic progressions.

I stuck in the following problem that was one of math Olympiad questions. Can anybody give me some hints please? Suppose that $s_1,s_2,s_3,\ldots$ is a strictly increasing sequence of positive ...
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1answer
25 views

simple integration artimethic error

I am trying to integrate a polynomial but I couldn't get the correct answer somehow. I feel like I'm making a mistake when evaluating the integral. $$\pi\int_{-1}^1{1-2x^2+x^4}dx=[{x-{2x^3\over3}+{x^...
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0answers
13 views

Round up/Round down to Decimal and Significant

(1) 30.9955 is round up to 2 decimal places. 31.00 (2) 30.9955 is round down to 3 significant digits. 30.9000 Is this right?
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0answers
27 views

For SAT test… [closed]

What is the maximum number of rectangular blocks measuring $3$ inches by $2$ by $1$ inch that can be packed into a cube-shaped box whose interior measure 6 inches on an edge? A) $24$ B) $28$ C) $30$ ...
3
votes
6answers
684 views

Real and Non-real Numbers; Value of Zero? [closed]

There are several things that I don't understand. I know that zero is a real number, but I'm confused on the how and why aspects. What defines a real number, compared to a number that's considered non-...
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5answers
90 views

find $u,v\in \mathbb Z$ such that $231u+45v=1$. [duplicate]

I have to find $u,v\in \mathbb Z$ such that $231u+45v=1$. By Euclide algorithm, \begin{align*} 231&=5\cdot 45+6\\ 45&=6\cdot 7+3\\ 7&=3\cdot 2+1 \end{align*} The first equation gives $$6=...
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1answer
46 views

Question about mathematical logic

Let say that you think you have 10 dollars in your pocket and you find out that you have two more dollars than what you thought you had, so you have 12 dollars. But what does it mean to say that you ...
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0answers
22 views

Area of an ellipse, Grid points, Approximation

Let $f(x,y)=ax^2 + bxy + cy^2$ with $a,b,c \in \mathbb{Z}$ a primitive and positiv definite quadratic form with discriminante $D < 0$. Then $ax^2 + bxy + cy^2 = N$ with $N \in \mathbb{N}$ describes ...
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5answers
459 views

What is the fastest method to find which of $\frac {3\sqrt {3}-4}{7-2\sqrt {3}} $ and $\frac {3\sqrt {3}-8}{1-2\sqrt {3}} $ is bigger manually?

What is the fastest method to find which number is bigger manually? $\frac {3\sqrt {3}-4}{7-2\sqrt {3}} $ or $\frac {3\sqrt {3}-8}{1-2\sqrt {3}} $
1
vote
4answers
114 views

find a formula to explain this set:$\{3,7,-11,-15,19,23,…\}$ [closed]

I want a formula to explain this set:$\{3,7,-11,-15,19,23,...\}$ Our teacher asked us to do.If they are one negative and one positive it was easy but now It become hard I think a lot, but no results....
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0answers
60 views

What is difference between the “usual multiplication” and multiplication?

I have been reading books in the algebra, and I noticed that some books use terms "usual multiplication" and "usual addition". Do they carry different meaning that multiplication and addition? If "...
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4answers
74 views

How to approximate

I was reading a book and saw this approximation $(1 - 10^{-3})^{1023} \approx 2^{-1.476}$ I am wondering how it is calculated.
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2answers
47 views

Algebraic equation solving for X

Solve for x $1^x + 2^x + 3^x = 6^2 $ I have misconceptions here as I keep linking it to the laws of indices and therefore I do not know how to add $1^x + 2^x ... $ can I get a hint ? Thanks !
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votes
5answers
289 views

Which number is greater, $11^{11}$ or $9^{12}$?

Which number is greater than $11^{11}$ or $9^{12}$? My work so far: $11^{11}=285311670611>9^{12}=282429536481$. But to verify the validity of equality should be in the range of easily ...
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votes
2answers
38 views

Mixtures and solutions [closed]

Suppose we have two solutions of sulphuric acid in water. The first is 40% strong and second is 60% strong. We mix the two solutions, add 5 kg of pure water and obtain a 20% solution. If instead of ...
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1answer
24 views

LCM (remainders)

A section of soldiers are rehearsing for the march past for the National Day parade . If they march in Pairs , one soldier will be without a partner . If they march in 3s , 5s, 7s , they will be a ...
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1answer
36 views

Adding coins and Multiplication Game

I am currently creating a maths game and need a little help. Inside the Game you can add up coins. maximum 1 each (1p,2p,5p,10p,20p,50p,£1,£2) You can also multiply the current sum maximum 1 each ...
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1answer
31 views

XOR equation with multiplication arrangment

How can I move all the X to one side so the equation will become x=y XOR <somthing>... $$\begin{align} &2x \oplus y = x \end{align}$$ ...
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1answer
68 views

Prove that $2+2\sqrt{12n^2+1}$ is perfect square

Problem: Let $n \in \mathbb{N}$ such that $2+2\sqrt{12n^2+1}$ is the integer. Prove that $2+2\sqrt{12n^2+1}$ is perfect square. I tried to found $n$ such that $\sqrt{12n^2+1}$ is integer, i.e. $...
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3answers
61 views

How to calculate $(-\frac{1}{3} - 3)(-\frac{1}{3} + 5) - (-\frac{1}{3} + 4)(-\frac{1}{3} - 5)$

$(-\frac{1}{3} - 3)(-\frac{1}{3} + 5) - (-\frac{1}{3} + 4)(-\frac{1}{3} - 5)$ multiply and calculate left $(-\frac{1}{3} - 3)(-\frac{1}{3} + 5)$ = $-15\frac{5}{9}$ Same for right $(-\frac{1}{3} + 4)(...
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2answers
32 views

How to resolve this proportion/equivalence calculation? [simple one]

Let's suppose I have one cat and when buying food for him I have to take into account this: 1 cat eats 2kg of food each 20 days How can I get a formula to know how many days my food will last based ...
2
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1answer
56 views

What's the numerator and the denominator of a fraction called?

Just a quick question, is it right to call the numerator and the denominator of a fraction by "terms"? I don't think that "terms" is the right word here, but i don't know any alternatives. Can any ...
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1answer
9 views

combining 3 ratio together with no equal volumes

An Alloy A contains copper and tin in the ratio of 3 : 5 by weight. Another Alloy B contains tin and zinc in the ratio 3:7 by weight . Find the ratio of copper : tin : zinc in a new alloy containing ...
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1answer
24 views

The future and present value of an annuity of $100 payable at the start of each quarter for 15 yrs if the rate is 12% compounded quarterly is?

What are the future and present value of an annuity of $100 payable at the beginning of each quarter for 15 years if the interest rate is 12% compounded quarterly?
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2answers
37 views

What amount can be paid at the end of every month in perpetuity from an endowment of $350,000 which is earning 5.4% compounded monthly?

What amount can be paid at the end of every month in perpetuity from an endowment of $350,000 which is earning 5.4% compounded monthly? Am trying to apply the compound interest formula but it isn't ...
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2answers
35 views

Convert the following between octal, decimal and hexadecimal

(a) Convert $61502$ from base $8$ to decimal. (b) Convert $EB7C5$ from base $16$ to octal. My answer: a) $6\times8^4+1\times8^3+5\times8^2+\times8^1+2\times8^0=25410$ b) not sure: converting $E=14$,...
3
votes
2answers
46 views

Football:What is the minimum number of points to guarantee qualification in a group of 4 teams?

In a group of 4 teams, each team plays 3 matches ( against the 3 other teams). A win gives a team 3 points, a draw 1 point, and a loss 0 points. In the end the top two teams of the group qualify. It ...
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2answers
29 views

For some $w$,$x$,$y$,$z$ it holds that $w+x>y+z$. Does that mean that $\sqrt w+\sqrt x> \sqrt y+\sqrt z$ and the other way around?

For some $w$,$x$,$y$,$z$ it holds that $$w+x>y+z. \quad \quad (1)$$Does that mean that $$\sqrt w+\sqrt x> \sqrt y+\sqrt z \quad \quad (2)$$ and the other way around, so if (2) holds then (1) ...
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0answers
15 views

The representation of finite and infinite ternary's

In my notes I came across a sentence that says "every ternary may also be written as an infinite ternary with infinitely many trailing 3's". I dont understand this statement, what does it mean?
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1answer
27 views

Evaluating an arithmetic abstract syntax tree [closed]

This might be very simplistic for this forum (apologies, if so). How does one evaluate the tree below. I am not looking for a solution, just assistance in how to evaluate it: I assume I start at ...
2
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1answer
49 views

Algebraic problem solving technique

In a "seven-eleven" (7-11) store, a customer selected four items to buy. The check-out clerk says that he multiplied the costs of the items and obtained exactly $7.11$, the very name of the store! The ...
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7answers
768 views

What is the sum of the $81$ products in the $9 \times 9$ multiplication grid?

What is an easy way to solve this problem? I believe that the value in each box is the product of $x$ and $y$. Suppose the 9 × 9 multiplication grid, shown here, were filled in completely. What ...
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3answers
50 views

$25$ men are employed to do a work

$25$ men are employed to do a work, which they could finish it in $20$ days but the drop off by $5$ men at the end of every $10$ days. In what time will the work be completed? My Attempt In $20$ ...
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2answers
90 views

How to remove parentheses from $x/(y-z)$

To remove parentheses from $x(y-z)$ I reword it to $xy-xz$. How do I remove parenthesis from $x/(y-z)$?
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2answers
58 views

Finding the min/max of consecutive numbers which equal a given sum

Given a consecutive list of numbers of size $n$, and a total sum figure $t$, what is the simplest way of finding the minimum $min$ and maximum $max$ numbers of that consecutive list? For example, $...
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votes
1answer
23 views

Speed Distance Time(RACES) [closed]

PLEASE GIVE THE DETAILED SOLUTION. Tom, Jerry and Snoopy participate in a race. Tom covers the same distance in $49$ steps as Jerry covers in $50$ steps and Snoopy in $51$ steps. Tom takes $10$ steps ...
0
votes
1answer
30 views

A,B and C can do a piece of

A can do a piece of work in $10$ days, B in $20$ days and C in $30$ days. If A is assisted by B and C turn by turn in alternate days, in how many days the work might have been completed? My Attempt: ...
14
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9answers
432 views

Why does every number of shape ababab is divisible by $13$?

Why does it seems like every number $ababab$, where $a$ and $b$ are integers $[0, 9]$ is divisible by $13$? Ex: $747474$, $101010$, $777777$, $989898$, etc...
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6answers
478 views

How to determine the remainder of $ \frac{7^{369}}{350} $?

How to determine the remainder of the following : $$ \frac{7^{369}}{350} $$ Is there any tricky way to determine this? I start as $$\frac{7^{368}}{50} \ \ , $$ This type of problem are highly ...
1
vote
2answers
58 views

Basic arithmetic - trick question.

I have the following question: A baker filled a measuring cup with $3/4$ cup of water. He poured $1/2$ of the water into the batter, and then spilled $1/8$ of the water on the floor. How much ...
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0answers
18 views

Convert double precision number to rational fraction plus exponent

I have a double precision quantity (either pixels per cm or pixels per inch) that gets converted into pixels per meter. I then need to convert this number into a rational fraction, with numerator and ...