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

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0answers
22 views

Computing composite functions

This may not be strictly a math question but is related. Whenever there is some function that computes more than two elements, is it possible that all elements are computed at once? Or is computing ...
0
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1answer
45 views

How many (decimal) digits does $2^{3021 377}$ have?

I was wondering, how many (decimal) digits does $2^{3021377}$ have? We have $2^4=16,\, 2^5=32,\, 2^6=64$ and $2^7=128,\, 2^8=256, \, 2^9=512$ but $2^{10}=1024,\, 2^{11}=2048, \, 2^{12}=4096, \, ...
5
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4answers
75 views

Find the limit as x approaches negative infinity for $\sqrt{x^2+x-1} +x$

Find the limit as x approaches negative infinity for $\sqrt{x^2+x-1} +x$ My solution: multiplying by: $\displaystyle\frac{\sqrt{x^2+x-1}-x}{\sqrt{x^2+x-1}-x}$ Which gives us: ...
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2answers
39 views

Running 3 miles in 20 minutes, how many miles can one run in 50 minutes?

Maria can run 3 miles in 20 minutes. At this rate, how many miles could she run in 50 minutes? I have tried dividing 3 by 20 to get the unit rate.
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2answers
11 views

Converting units and currency

A supermarket in Japan sells soy milk for 398 yen per liter. If there are 83.35 yen per dollar, then what is the price in dollars per quart? Conversions that were given. Dollars per foreign =0.0120 ...
2
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0answers
25 views

Significance of formulas similar to summation formula

We all know formula $n(n+1)/2$ for adding up the numbers from $1$ to $n$. But I would like to know if there is any significance and use of formulas of type $n(n^{p-1}+p-1)/p$, where $p$ is a prime. ...
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1answer
61 views

Can we solve variable questions without using algebra - for example age problems?

I am not sure on what should be the quick way of approach to solve these kind of questions. As we grow, we can think of other possible ways to solve the same problem. Many genius can solve the algebra ...
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2answers
43 views

Are there real extensions of the operations of addition, multiplication, exponentiation, etc in the other direction?

We have $\underbrace{a+a+a...+a}_{n\:times}$ which equals $a \times n$, and also $\underbrace{b \times b \times b.... \times b}_{p\: times}$ is $b^p$, so I was wondering if the generalization would ...
3
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2answers
156 views

Is it allowed to use “equal to” and “approximately equal to” in the same sentence?

Let's use the following example: $$17! = 16!*17 \approx 2 \cdot 10^{13} * 17 = 3.4 \cdot 10^{14} $$ Are you allowed to do this? I am in doubt whether or not this indicates that $17! = 3.4 \cdot ...
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1answer
36 views

how many questions did D answer correctly

Each of A, B, C, and D took a test. Each of them answered at least one question correctly, and altogether they answered 67 questions correctly. A had more correct answers than anyone else. B and C ...
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2answers
44 views

What is the sum of one + one in a 26 letter number system

A number system based on 26 uses the letters of the alphabet as its digits, with $A = 0, B = 1, C = 2, D = 3, E = 4, . . . , Y = 24,$ and $Z = 25. $ What is the the sum: ONE + ONE = in this system
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1answer
60 views

x / 3 + y /3 + z / 3 = (x + y + z) / 3?

Is the following equation always true? x / 3 + y /3 + z / 3 = (x + y + z) / 3 I hope this is not too simple of a question. Every example I can think of, this equation is true. However, in a ...
1
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1answer
53 views

Is this assertion true or false? $(\exists x)(\exists y)(\forall z)(y \ne x+z \Rightarrow y\lt x)$ Cohn - Classic Algebra P7

$x,y,z\in\mathbb{N}$ with $0$ $(\forall x)(\forall y)(\exists z)(y \geq x \Rightarrow y=x+z)$ Can you help me with trivial thing above? I imagine it is because I am tired, but I can't see if this is ...
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1answer
23 views

An inequality question involving non-negative integers

I am trying to prove something then I hit a stumbling block in the form of this problem. Let $a,b,c,d$ be non-negative integers such that: $c,d$ are fixed $\max a=d$ $$a\geq b$$ $$c\geq b$$ ...
2
votes
2answers
73 views

What means $23_4$?

Sorry, I just show this on a mathematical clock for $11$, i.e $23_4=11$: http://ecx.images-amazon.com/images/I/51nsaGqFoUL.jpg I guess it is some notation from algebra. But since algebra was never ...
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0answers
83 views

Why is $2^{16} = 65536$ the only power of $2$ less than $2^{31000}$ that doesn't contain the digits $1$, $2$, $4$ or $8$ in its decimal representation

$65536$ is the only power of $2$ less than $2^{31000}$ that does not contain the digits $1$, $2$, $4$ or $8$ in its decimal representation. http://en.wikipedia.org/wiki/65536_%28number%29
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0answers
56 views

A challenge question in elementary number theory!

Find an expression for the following sum: $$\sum_{i:(i,n)=1}(i-1,n)$$ I guess that this sum equals to $\phi(n)d(n).$
3
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1answer
59 views

Write $1681$ using four $4$s

Write $1681$, using $4$, four times only, and you can use any mathematical operation available within mathematics(except catenation or $4.4$ etc, it should be an operation), like factorial and cube ...
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0answers
42 views

How do we get from one to another?

I am doing an assignment, and have no idea where my teacher is getting his numbers from. I'll give you all the calculations, and maybe you can help me out? A person consumes $\frac{200}{7}$ of a ...
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0answers
44 views

Monotonically decreasing function for multiplication product?

I have a set of numbers $S = [100,999]$ for which I want the maximum product $p$ such that $p = a \times b$ for all $a,b \in S$ also fulfilling some condition $C$. I would like $p$ to be monotonically ...
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2answers
25 views

Patlak equation

For solute flux across microvessel wall, these two equations are supposed to be equivalent: $$ \begin{align} J_s &= J_v(1-\sigma_f)\frac{C_i - C_Le^{\mathrm{Pe}}}{1 - e^{\mathrm{Pe}}} \\ J_s ...
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1answer
29 views

Elementary arithmetic question

2 groups of people $A$ and $B$ are trying to build a road. For the first 40 days, only one group was working at any time. At first, only group $A$ worked. They worked for an unknown amount of days, ...
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3answers
51 views

Is my arithmetical proof using induction correct?

The exercise 2.b of my textbook ask me to prove that: $$\text{(P): }\;\forall n\in \mathbb{N}, 13\;|\;(3^{n+2}+4^{2\cdot n+1})$$ I would like to know if my proof is correct and if not what I need to ...
3
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1answer
97 views

What is the remainder when ${2222}^{5555}+{5555}^{2222}$ is divided by $7$? [duplicate]

The question is multiple-choice. What is the fastest approach to solve it? One suggested solution is: It can be seen that $[2222\equiv3\pmod7]\wedge[5555\equiv4\pmod7]$ Therefore ...
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2answers
68 views

Is this correct - confused in this riddle - where does the one rupee come from…? [closed]

I have 50 rupees, and spending like this and where does that ONE rupee come from.... am right or wrong ??????
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3answers
29 views

Which is simpler, a mixed fraction, or an improper fraction?

My son's homework sheet says to solve problems like: (5) / (15/4) and to write the "quotient" in its "simplest" form. The crux of my question is, which form is generally considered the "simplest" ...
2
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1answer
51 views

How prove this$\lfloor \sqrt{2x-\lfloor\sqrt{2x}\rfloor}\rfloor=\lfloor\frac{\sqrt{8x+1}-1}{2}\rfloor$

Question: let $x\ge 0$, show that $$\lfloor \sqrt{2x-\lfloor\sqrt{2x}\rfloor}\rfloor=\lfloor\dfrac{\sqrt{8x+1}-1}{2}\rfloor$$ My idea: let $\lfloor \sqrt{2x}\rfloor =m$ then ...
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2answers
47 views

Multiplication and addition, but in a weird way.

'calculate the product of x and y by accumulating the sum of x copies of y' I'm stumped, what is it this exercise actually wants me to do? Express $x$ * $y$ as something else? I'm allowed to use an ...
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3answers
61 views

Maths problem on distance and time. [closed]

A snail climbs up a 20 m wall 5 m every hour then slides back 3 m. How long does it take the snail to climb up the wall? Possible solutions and working out please.
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1answer
31 views

What's known about magic cubes of order 4?

An earlier question asked for a demonstration that there is no magic cube of order 4. The question was closed and deleted. I think it's worth having some information on magic cubes on m.se, so I'm ...
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0answers
172 views

Prove that $(x + y + z)!$ is divisible by $x!y!z!$ [duplicate]

I am posting this question for Abdo, who asked it but had it closed because some people thought it was unclear what he was asking. However, I understood what he was asking and was ready to answer. So ...
3
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2answers
30 views

Why is $\displaystyle\sum_{k=j}^{i+j}(j+i-k) = \displaystyle\sum_{k=1}^{i}(k)$

$\displaystyle\sum_{k=j}^{i+j}(j+i-k) = \displaystyle\sum_{k=1}^{i}(k)$ I know the above are equal through testing it out with arbitrary values, but I can't get an intuitive grasp as to why this is. ...
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0answers
17 views

Calculating annual occurrence of an event that happens less than once per year

If an event happens less than once per year, how would I calculate how many times a year it actually happens? For example, I have something that will happen every $5.47$ years, but I need to break ...
1
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1answer
37 views

Simple Elementary Word Problem

I'm trying to help my little sister out but I can't seem to figure it out. Here is the question: John fish weight 8 times as much as her parakeet. Together the pet's weight 63 ounces. How much ...
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1answer
127 views

Arithmetic sequence of natural numbers

Consider an arithmetic progression of natural numbers with a non-zero common difference. For each of the members of the progression its square root is taken, and if the square root is not an integer, ...
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0answers
8 views

Constrain the precision of the operands and the solution of a simple arithmetic expression

I'm developing a game where users will have to solve simple arithmetic expressions containing two operands and an operator. For instance: ...
4
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1answer
59 views

Algebra problem solve for a,b,c and d?

Can anyone find the values of these integers: a,b,c and d? $$1+\sqrt{2}+\sqrt{3}+\sqrt{6} = \sqrt{a+\sqrt{b+\sqrt{c+\sqrt{d}}}}$$ a+b+c+d = ? Thank you.
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2answers
66 views

Finding the integer solutions of the equation $3\sqrt {x + y} + 2\sqrt {8 - x} + \sqrt {6 - y} = 14$

$ 3\sqrt {x + y} + 2\sqrt {8 - x} + \sqrt {6 - y} = 14 $ . I already solved this using the Cauchy–Schwarz inequality and got $x=4$ and $y=5$. But I'm sure there is a prettier, simpler solution ...
0
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2answers
41 views

Getting the value of $n$

It's strange. I can't get the value of $n$. Could someone give me the step by step way of getting the value of $n$. The answer key says $20$. $$ 1+\frac{i}{n}=\frac{1+\frac{i}{4}}{1+\frac{i}{5}} $$
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0answers
28 views

How to denote combinations of differences?

Let $ \mathcal{A} $, $ \mathcal{B} $ and $ \mathcal{C} $ be sets defined by $ \mathcal{A} = \{ A_k \} $, $ \mathcal{B} = \{ B_k \} $ and $ \mathcal{C} = \{ C_k \} $ where $ k \in \{1 , 2 , \ldots , ...
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3answers
55 views

Question on Fermats Last Theorem

$a^n + b^n = c^n$, for any integer value of n greater than two where a,b,c are positive integers. Since this is too hard for me to solve, I tried to change the question a little. I believe Fermat ...
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1answer
11 views

Operators Game that really confusing

I saw this question on the newspaper and can't solve it, help. Use the four operation sign, substitute them into the question marks between the digits such that the outcome is two(the order of ...
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1answer
22 views

Antisymmetric asymptotic curve with only simple binary arithmetic?

I'm looking for an s-curve formula with similar properties to $Sigmoid$ or $\tan^{-1}$, but without 'expensive' unary functions or their binary generalizations (e.g. $^x\log y$). The only allowed ...
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1answer
29 views

Biking uphill and downhill

During an interview, I was asked "If you can bike 20 mph uphill and 30mph downhill, and you have 1 hour to bike, how far or how long should you ride uphill before turning back." While a very ...
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0answers
24 views

Calculate value based on previous purchase value

I'm looking to make sure a customer is not short changed (or given stuff for free) when their commission band changes. The setup is the following: A customer can top up an account. When topping up ...
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4answers
56 views

Prove that $n_1 n_2 > 10(n_1+n_2)$ when $n_i > 20$

How would one prove that $n_1 n_2 > 10(n_1+n_2)$ if $n_i > 20$? I have no idea where to start. Can you give me a hint?
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2answers
30 views

What does the modulo of a non-integer mean?

For example, in the equation $ x=\frac{3}{5} \bmod 11$ The value of $x$ is $5$ according to wolfram alpha. I know how to manipulate the equation to to get the value but I dont understand what the ...
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3answers
56 views

Percentage of total voters captured by two political candidates

In an election, 2.8 million votes were cast and each vote was either for candidate I or candidate II. candidate I received 28,000 more votes than candidate II. What percent of the 2,8 million votes ...
1
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1answer
38 views

How does this card trick work?

Pick a card from the deck and keep it secret. Double the face value of the card (aces = 1, jacks = 11, queens = 12, and kings = 13). Add 3 to the result. Multiply this by 5. Add 1 if the card is a ...
0
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5answers
53 views

Recursive formula - alternating addition and suntraction

So i got this formula that basically does this: $$f(n) = n^2-(n-1)^2+(n-2)^2...$$ until it gets to $f(1)$ which is $1$. The recursive form is: $$f(n)=n^2-f(n-1)$$ So is there a way to get to the ...