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

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55 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
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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
48 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 ...
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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 ...
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5answers
51 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
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0answers
54 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
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1answer
28 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
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1answer
66 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 ...
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1answer
48 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 ...
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1answer
27 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
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3answers
104 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 $N$?
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0answers
43 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
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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
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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
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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
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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
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2answers
48 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 ...
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0answers
80 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
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4answers
75 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
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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 ...
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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
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1answer
34 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
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?
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1answer
23 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
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2answers
44 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 ...
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3answers
48 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
289 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 ...
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3answers
108 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
25 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
21 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
51 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
29 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
34 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
54 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
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2answers
31 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 ...
0
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0answers
23 views

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

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
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1answer
26 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 ...
1
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2answers
55 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
73 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
51 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 = ...
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votes
5answers
2k 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
98 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 ...
1
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1answer
33 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 ...
0
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1answer
105 views

Evaluate $\sqrt{1 + 2\sqrt{1 + 3 \sqrt{1 + \dots}}}$ [duplicate]

I was asked to show that the answer is 3. I don't have any idea on how to proceed. Thanks!
5
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4answers
364 views

General formula of repeated roots.

Prove that $$\underbrace{\sqrt{k\sqrt{k\sqrt{k\sqrt{\cdots\sqrt{k}}}}}}_{n\text { times}}=k^{1-1/2^n}$$ How do I derive this formula?
2
votes
2answers
42 views

Square grid , sum of elements

I am trying to solve the following problem : Find all the positive integers $n$ and $k$ such that it is possible to write integers in an $n \times n$ grid so that the sum of all elements in the grid ...
0
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2answers
46 views

How do break down this addition?

I've been given the following expression: $2(a + b) + (n + 1)(2a + c) + 2n(2a + d + b) + (a + r)$ And I've been told that it can be simplified to: $n(6a + 2b + c + 2d) + (5a + 2b + c + r)$ I've ...
4
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3answers
239 views

The proof of $\sqrt{2}$ is not rational number via fundamental theorem of arithmetic.

I assume that $\sqrt{2}$ is positive number satisfies $(\sqrt{2})^2=2$. proof) Let $m$, $n$ as natural number,$\ $ $M$ is the number of prime factor of $m$,$\ $ $N$ is also the number of prime ...
0
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1answer
80 views

Divisibility rule for 22

Divisibility rule for 22: Under what conditions a natural number $N$ is divisible by $22$ ? My thought is The divisibility rule for $22$ is that the number is divisible by $2$ and by $11$. ...
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1answer
21 views

Calculation of a value for number divisible by 11

Calculates the value $x$ for the number $M=5278x$ is divisible by 11 my attempt, $11\mid M=5278x \Longleftrightarrow (5-2)+(7-8)+x=2+x$ is multiple of $11$ $ 2+x$ is multiple of $11 ...