Tagged Questions

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

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0
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0answers
39 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 ...
0
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0answers
38 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 ...
0
votes
2answers
23 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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votes
1answer
27 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
votes
1answer
90 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 ...
0
votes
2answers
43 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
26 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
50 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 ...
0
votes
2answers
39 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 ...
2
votes
3answers
59 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
26 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 ...
-1
votes
0answers
166 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
votes
2answers
28 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. ...
0
votes
1answer
13 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
vote
1answer
27 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 ...
1
vote
1answer
103 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, ...
0
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0answers
7 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
votes
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.
2
votes
2answers
63 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
votes
2answers
39 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 , ...
0
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3answers
52 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 ...
1
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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 ...
0
votes
1answer
17 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 ...
-1
votes
1answer
22 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 ...
0
votes
0answers
23 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 ...
1
vote
4answers
54 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?
3
votes
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 ...
1
vote
3answers
39 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
36 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
votes
5answers
45 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 ...
0
votes
0answers
52 views

Is there any shortcut to find if a number is a perfect cube?

Is there any shortcut to find if a number is a perfect cube? I am taking for instance finding if a number is a perfect square. So , if a number ends with 2,3,7,8. It cannot be a square. But if it ...
0
votes
1answer
24 views

a factor in the numerator is the opposite of the denominator - simplifies to -1

I'm working on a little khan academy problem, finding the limit as x -> 36 in the solution the program explains in the last step that since there are opposite ...
2
votes
1answer
65 views

Cube and Numbers

my question is the following. On an cube are numbers. The numbers are v, l, r, o, u and h. The twelve absolute amounts of the differences of these numbers are the numbers from 1 to 12. The ...
0
votes
1answer
46 views

How many times must you square a number to get $<1/2$

Let $0\leq x<1$. Be given. How many times must you square $x$ to get less than $1/2$? Clearly this depends on $x$. But is there a nice formula to determine this? Such as: To make ...
0
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1answer
26 views

Use charts to calculate time frames

$$ \begin{array}{|c|c|c|c|c|c|} \hline \text{Artist} & \text{Bernard} & \text{Meg} & \text{Clayton} & \text{Ivy} & \text{Anderson}\\\hline \text{Number ...
1
vote
3answers
100 views

Sum of the digits

Let $N$ be the greatest number that will divide $1305,4665$ and $6905$, leaving the same remainder in each case. Then what is the sum of the digits in $N$?
0
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0answers
39 views

Sum of roots of terms of an Arithmetic Progression

Is there any easy way or formula to calculate sum of roots of an Arithmetic progression? For example if the arithmetic progression is $a+d$,$a+2d$,$a+3d$, $\ldots$, $a+nd$: How can I calculate ...
0
votes
2answers
26 views

Solving a linear equation

I need to solve: $$\frac{1}{2}\left[10\beta+(1-\beta)(-10)\right]-\frac{c}{i}= 5-c$$ for $\beta$ to get to: $$\beta = 1 – \left( 1 - \frac{1}{i}\right)\frac{c}{10}$$ But i get stuck somewhere in the ...
1
vote
0answers
39 views

Is $\sum_{i=1}^n i = \sum_{i=n}^1 i$

When I enter these expressions into wolfram I get that they're not equal. Why is this? Essentially I'm trying to say $$ 1+2+\cdots+n = n+(n-1)+\cdots+1 $$
0
votes
1answer
30 views

From an expression raised in a power of 2 to an expression raised in the power or 10

Is there a simple/"easy" way to convert a big number from a power of $2$ to a power of $10$ equivalent. Example: I had $2^{127}\cdot 1.9999999$ which I did the multiplication got the result and from ...
23
votes
5answers
4k views

In primary school I was showed this. Why does it work?

When I was in primary school a teacher showed us the following exercise in arithmetic. Take any 3 digit number between 201 and 998 provided that the hundreds digit is bigger than the ones digit and ...
0
votes
2answers
47 views

Multiplication of repeating decimal $0.3333\overline{3}$ by $3$ [duplicate]

Let's start considering a simple fractions like $\dfrac {1}{2}$ and $\dfrac {1}{3}$. If I choose to represent those fraction using decimal representation, I get, respectively, $0.5$ and ...
1
vote
0answers
76 views

Types realized in ultrapowers consisting of definable functions

Let $\mathcal{M}$ be a nonstandard model of arithmetic and let $M$ be its universe. Let $U$ be a nonprincipal ultrafilter over $M$ and let $\mathcal{N}$ be the ultrapower $\mathcal{M}^M / U$. Let $F$ ...
4
votes
4answers
72 views

Rationalize $\left(\sqrt{3x+5}-\sqrt{5x+11} -\sqrt{x+9}\right)^{-1}$

I was trying to find if there a method similar to multiplying and dividing by the conjugate $$\frac{1}{\sqrt{3x+5}-\sqrt{5x+11} - \sqrt{x+9}},$$ but that doesn't seem to work here. Also, is there a ...
0
votes
1answer
19 views

SAT Math Problem about decimal

In the decimal representation of $\frac{1}{k}$, where $0 < \frac{1}{k} < 1$. the tenths digit is $1$, hundredths digit is $3$ and at least one other digit is nonzero. What is the tenths digit ...
6
votes
4answers
1k views

Why exactly does the distributive property work?

Suppose I have this expression that needs to be simplified: $$4(2x + 4)$$ It can be simplified down to this: $$8x + 16$$ In this case, this expression has been simplified down using the ...
0
votes
1answer
32 views

General formula for a series

I am trying to solve series of the form, T(n) = T(n/4) + clog(n) I am able to formulate a general formula for the T(n) term for the nth term. Its of the form ...
0
votes
1answer
36 views

Formula for the floor of $n/2$, to be proved by induction

How do you compute this when the base case is all wrong?