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

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0
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2answers
43 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 $20$. $$ 1+\frac{i}{n}=\frac{1+\frac{i}{4}}{1+\frac{i}{5}} $$
0
votes
0answers
33 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
votes
3answers
59 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
vote
1answer
17 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
29 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
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1answer
52 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
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0answers
32 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
62 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
85 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
116 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
vote
1answer
105 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 ...
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votes
5answers
81 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 ...
1
vote
0answers
156 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
265 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
70 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
51 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
77 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
115 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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2answers
32 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
44 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
38 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 ...
26
votes
5answers
4k views

Trick with 3-digit numbers, always get 1089

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
63 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 ...
0
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0answers
119 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 $F$ ...
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4answers
91 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
21 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
2k 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 ...
1
vote
1answer
61 views

Associative law with negative sign

We know that $a+b+c$ is meaningful for, say, the group $\left( \mathbb{Z}% ,+\right) $. Since for any $b,c$, we must have $b^{-1},c^{-1}$, therefore $% a+b^{-1}+c^{-1}$ has to be meaningful, too, but ...
0
votes
1answer
39 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 ...
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1answer
49 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?
0
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1answer
73 views

Operations on a set of numbers to leave the median unchanged

Set Q contains 14 distinct numbers. Which of the following operations would decrease the average of set Q while leaving the median unchanged? A. Decreasing all 14 numbers by 2 each B. Increasing the ...
0
votes
2answers
46 views

Inversing fraction

I'm having a little trouble understanding the logic behind solving the following equation: $(24/25)\times a = b \times \cos(12)$ we need to seperate a from the equation so it becomes $a = (b \times ...
1
vote
3answers
52 views

How to find $n$-th value in a series

Let $(x_n, y_n, z_n) = (3, 1, 0)$ for $n=0$ For $n \ge 1$, $$\begin{align} x_n &= x_{n-1} +3 z_{n-1}\\ y_n &= x_{n-1} +2 z_{n-1}\\ z_n &= 5 y_{n-1} \end{align}$$ Please let me know the ...
4
votes
4answers
398 views

Mean/Median/Mode question?

I came across the following problem: A list of 11 positive integers has a mean of 10, a median of 9, and a unique mode of 8. What is the largest possible value of an integer in the list? From the ...
0
votes
3answers
1k views

How to find the total amount from given percentage

I am trying to answer this question from internet for my mathematics practice. ...
0
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1answer
26 views

Check whether an image is proportional to a given one

I wonder how can I test whether the size of an image is proportional to $250\times 167$. For example, I have an image size of $1000\times 668$ and would like to see if it is proportional to ...
0
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1answer
22 views

Find base of numbers in a sum?

is there an easier way to find the base A in the following without essentially brute-forcing it with different conversions until I get the result? Again, trying to find base A such that the following ...
0
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3answers
142 views

How to find the total investment from interest received

Dave Horn invested half of his money at $5$%, one-third of his money at $4$%, and the rest of his money at $3.5$%. If his total annual investment income was $\$530$, how much had he invested? I found ...
0
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3answers
35 views

Generiloze: the difference of two squares is equal to a odd number.

For example, 3 = 2^2 - 1^2 5 = 3^2 - 2^2 7 = 4^2 - 3^2 ... Is there a general formula to explain this phenomenon?
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1answer
35 views

$ \sqrt[5]{x^3} = (\sqrt[5]{x})^3 $?

$ \sqrt[5]{x^3} = (\sqrt[5]{x})^3 $ ? I would suppose so given that $ x^{3/5} = x^{3(1/5)} = \sqrt[5]{x^3} $ or $ x^{3/5} = x^{(1/5)3} = (\sqrt[5]{x})^3 $
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2answers
55 views

Is there a general way to do arithmetic involving binomials more quickly?

I'm talking about exercises like these for example: $ (a+2b)^3 - (a-2b)^3 $ $(a+b+c)(a+b-c)(a-b+c)(a-b+c)(-a+b+c)$ Of course these can be done the time-consuming and mentally easy way, but are ...
0
votes
2answers
35 views

Simplifying $0.300 (1 \pm 0.0633)$

This problem had to do with finding area with uncertainty, I got this far but I'm not sure how to go on. The answer to the next step is $(0.300 \pm 0.0190)$. How do they get this? What do we do with ...
2
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0answers
33 views

when to use ( end point/date - start point/date + 1) , and when to use end point /date - start point /date? [duplicate]

This is a simple question on difference. I have seen the following situation - for example how many day you spend on a travel when the travel date was 14-Aug-2014 till 25-August-2014. The answer for ...
2
votes
1answer
35 views

Shared groceries expenses between roommates to be divided as per specific consumption ratio and attendance

My apologies if this question is in the wrong section. Couple of my roommates & I (total 5 people) share the groceries expenses. We record the purchases in an Excel sheet, and also have the ratio ...
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2answers
92 views

How to reduce large combinations?

The result of a hypergeometric distribution question that I posted about earlier this evening is what follows: $$\frac{{30 \choose 10}{20 \choose 5}}{{50 \choose 15}}$$ This becomes: ...
4
votes
1answer
88 views

What is $\sqrt{-x^3}$?

What is $\sqrt{-x^3}$, assuming $x \in \mathbb R$ and $x < 0$? It seems as if there are two possibilities: $\sqrt{-x^3} = \sqrt{-x\times x \times x} = \sqrt{-x \times x^2} = x\sqrt{-x}$ ...
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5answers
75 views

Not clear on what we mean with numbers with infinite digits

I am confused on a rather simplistic question. 1/3 = 0.333333333333 to infinity. So it has infinite digits. How is it possible to multiply such a number with another one and get a finite number? 6/3 = ...
7
votes
5answers
3k views

Arithmetic mean. Why does it work?

I've been using the formula for the arithmetic mean all my life, but I'm not sure why it works. My current intuition is this one: The arithmetic mean is a number that when multiplied by the number ...
5
votes
2answers
202 views

Efficiently factoring polynomials over $\Bbb F_2$

I am attempting to write some software which is intended to generically answer the question of which Cyclic Redundancy Code (CRC) generating polynomial is used for a given set of sample messages using ...
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1answer
37 views

Yet another product of irrational numbers

Let $~\alpha~$ and $~\beta~$ be irrational numbers such that $$~\alpha \notin \{\beta, -\beta\}$$ and $$~\alpha \notin \left\{\frac{1}{\beta}, -\frac{1}{\beta}\right\}$$ I suppose that in this case ...