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

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1
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0answers
29 views

Among 10 packet each having weight 100grams 1 packet is defective and weight is 90 grams. How to find out the defective one in only one measurement?

I have 10 packets of cigars. Each packet consists of 10 cigar and weight of each cigar is 10 grams.So weight of each pack will be 100 grams.But Somehow my friend measures packets of cigars and said ...
0
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2answers
21 views

Computing an academic grade when relative weights are changed

My grade is 88.6% (High B) and we get 80%(Assessment Grade) and 10%(Homework). My teacher is now making this 70%(Assessment Grade) and 30%(Homework). I have done all my homework 100% and I've been ...
1
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2answers
28 views

How to recognise the digit multiplication, subtraction or addition when checking for divisibility by 7, 11, 13, 17 and 19?

I was studying this page Divisibility by prime numbers under 50 to check for the divisibility by 7, 11, 13, 17, 19 etc. Is there any way to recognise whether to add or sub the given times of unit ...
-6
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1answer
64 views

you know root square of -1, what is the larger of the square? [on hold]

there is a square ABDC, $BD = \sqrt{-1}$ what is the value of AB=BC=DC=AD?
0
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3answers
45 views

The meaning of dot centered vertically, as in $3\cdot 5$

I just went to a site to practise some maths as I am studying some maths on my OU course in computing and IT and I ran into some symbols that I did not understand The questions were solve ...
-1
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1answer
38 views

How to find the formula of S3n? [on hold]

I have series $$1+2+3+4+4+3+5+5+6+...$$ if $n \in N$ then the formula of $S_{3n}=...$ Even I'm confused the pattern of the sequence. Anyone can help me? 4 first terms is like natural number, but at ...
3
votes
5answers
55 views

Manually obtainining a list of primes $\leq n$, by using the root of n?

In my abstract math class I learned that if we want to get a list of primes $\leq n$ manually, we have to calculate the root of n, and the floor of that result will be the greatest number for which to ...
0
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1answer
22 views

Calculating how much money I spent? (23-73 gives

I'm a very simple person with basic math knowledge. Recently I run into huge problems when calculating how much I spent. Sometimes to calculate how much I spent I do a calculation $final sum - start ...
0
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2answers
23 views

Use of arithmetic progression to find the sum of numbers

How can I find the sum of numbers divisible by 3 that are between 1 and 1000 if I don't know how many elements there are in the arithmetic progression?
1
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1answer
20 views

Bézout's identity on a polynome sequence

I'm stuck on an exercise which is split in 3 questions : 1) Prove that : $$\exists (U_n, V_n) \in \mathbb{R}[X]^2 \text{ s.t. } (1-X)^{n+1}U_n+X^{n+1}V_n=1$$ 2) Let $(R_n, ...
1
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4answers
134 views

Proving that $p_1p_2\mid n$ iff $p_1\mid n$ and $ p_2\mid n.$

Let $p_1$, $p_2$ be distinct primes. Using the Fundamental Theorem of Arithmetic prove that a natural number $n$ is divisible by $p_1p_2$ if and only if $n$ is divisible by $p_1$ and $n$ is divisible ...
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0answers
26 views

Number sense. Math help please. [on hold]

You go shopping at sportchek for a new pair of skates and you know you are allowed to spend between $\$100$ and $\$125$ with taxes included. One pair of skates has a ticket price of $\$184.99$. What ...
1
vote
1answer
36 views

$a=2, b=2$; then using what operation make 32, that is, $a\circ b=32$ [on hold]

$a=2, b=2$ then using what operation make 32...Using only two "2" can you make 32? You can use any binary operation. Furthermore is there or will there be any other pair $(a,b)$ for which $a\circ ...
0
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1answer
29 views

Dividing by zero the answer is undefined

I know that $\frac{1}{0}$ is undefined. What about $\frac{1}{0}-0.5$ it's undefined as well?
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1answer
17 views

Covering deficits with values with different weights

SO I have a couple of assessments with specific weights as follows: Assignment 1: 5% => Mark 60% Assignment 2: 5% => Mark 53% Assignment 3: 5% Assignment 4: 5% Test 1: 30% => 47% Test 2: 30% ...
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votes
2answers
40 views

216 BGN in Euros [closed]

I am trying to convert $216$ BGN to Euros. I know $10$ Euros are $18$ Dollars and $4$ Dollars are $6$ BGN. From this is got, as $36 \times 6 = 216$, that $216$ BGN are $4 \times 36 = 130$ ...
1
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1answer
39 views

How and why can it be true that some decimals that sometimes go on forever in base 10 such as $1\over 3$ change to good numbers in base 12?

I've noticed on a math channel on YouTube that some of these decimals from fractions in the decimal system such as $1\over 3$, which equals $0.\overline3$, which goes on forever, doesn't show off this ...
1
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3answers
85 views

Which number is higher $2^{600}$ or $3^{400}$?

Which number is higher $2^{600}$ or $3^{400}$ ? I know that the solution is $3^{400}>2^{600}$ bot how to explain that. without using a calculator.
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1answer
24 views

Fundamental Algebra and Intermediate [closed]

There are 24 students and 6 teachers driving to a sporting event. Assuming each car holds 5 people, what’s the least number of cars needed to transport everyone to the event?
0
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2answers
49 views

Converting American to Canadian

Paid \$1012 American for a group of items, which worked out to \$1248.99 Canadian. How do I calculate the conversion rate so I can figure out the total cost Canadian of each item?
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2answers
28 views

Simplify the radical expression [closed]

Simplify the following: $$\sqrt{48 a^2 b^7}$$ All I have so far is 16 I think i forgot how to do this, can anyone help?
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1answer
29 views

What is the proof-theoretic ordinal of $PA+TI(\epsilon_0)$?

what is the proof-theoretic ordinal for $PA+TI(\epsilon_0)$, where $PA+TI(\epsilon_0)$ is Peano arithmetic where transfinite induction up to $\epsilon_0$ was added? Is it known? Thank you
1
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0answers
5 views

algorithm related to dyadic decomposition

Starting from an integer $n >0$, iterate the two operations of substracting one and dividing by $2$ (when the number is even) until $1$ is reached. Thus when the number is odd we can only substract ...
0
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3answers
51 views

simple question [closed]

How would you say 4,954,000? I forgot
1
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1answer
34 views

Roots of polynomial equation $2a x^\gamma + ax^{\gamma - 1} - 2 = 0$

I would like to find roots of the following polynomial equation $$2a x^\gamma + ax^{\gamma - 1} - 2 = 0$$ where $a,\gamma>0$ (we might also assume that $\gamma \in\mathbb{N}$ if needed). Playing a ...
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2answers
35 views

Two person working together

If Person A can deliver papers in 40 min, and person B can do the same papers in 50 min, how long does it take when they work together? This is a rational expression problem. Is there an easy, or ...
1
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0answers
36 views

sigma divisor function with gcd

For computational reasons, I want to show that the following holds true: Let $n_1,n_2,N\in \mathbb{N}$. One has $$ \sum_{a\mid \gcd(n_1,N)}\sum_{b\mid \gcd(n_2,\frac{n_1N}{a^2})} ab =\sum_{g\mid ...
0
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1answer
23 views

Converge on square root of 3 with tree.

If a rule is set for generating a tree whereby: both the children of a node with out-degree 2 each have an out-degree of 3; and the children of a node with out-degree 3 will have out-degrees of ...
4
votes
2answers
106 views

Second Grade Homework Problem - Methodology

Ashamed to admit that I cannot aid my friend's niece with her second grade homework problem. So much for that college education, eh? Here's the problem. Using only the natural numbers 1 through 9 ...
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1answer
31 views

company as none-binary tree [closed]

Company's structure is depicted as none-binary tree where each node represents an employee. Root of the tree is CEO of the company and every node that has children is their supervisor. When assigning ...
11
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3answers
754 views

How to raise -1 to non-integer powers

How do you calculate $(-1)^x$ where $x$ is some real number. For example, what is $(-1)^{\sqrt{5}}$. This question came as I was trying to computer $e^{i\pi a}$ where $a$ is irrational.
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4answers
40 views

Prove Summation to Some Number $n$ [duplicate]

Let $n\in \mathbb{N}$. Can someone help me prove this by induction: $$\sum _{i=0}^{n}{i} =\frac { n\left( n+1 \right) }{ 2 } .$$
3
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1answer
32 views

How many divisors of N ended by 5

I must know how to find how many divisor of N ended by 5 ? In my exercise, I have $\ N=63'000 = 2^3*3^2*5^3*7 $ and I can found the number of divisors of N using $\ (3+1)*(2+1)*(3+1)*(1+1)=96$ Among ...
0
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0answers
17 views

Binary Overflow Detection

I am trying to solve several problems, which are binary and encoded using the 2's complement system. One problem has stuck out to me: 0111 + 0001 Both are positive, with 0111 being 1+2+4 or 7, and ...
21
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12answers
5k views

Is there a law that you can add or multiply to both sides of an equation?

It seems that given a statement a = b, that a + c = b + c is assumed also to be true. Why isn't this an axiom of arithmetic, like the commutative law or associative law? Or is it a consequence of ...
3
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0answers
18 views

Finding lower bounds for solution of linear Diophantine equation in two varuables

I am currently encountering the following arithmetical problem : given four nonzero integers $A,B,C,D$, let $\Omega=\bigg\lbrace (x,y)\in{\mathbb N_{\geq 0}}^2 \ \bigg| \ \frac{Ax+By}{Cx+Dy} \in ...
0
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4answers
99 views

What is $10 \times 10-10+10$? [duplicate]

I was just surfing a social site and found this question posted by someone. People were arguing or different answers like 80, 100, 120. So, what is the correct answer for $10 \times 10-10+10$? I used ...
3
votes
6answers
125 views

Show that $\sqrt[3]{3\sqrt{21} + 8} - \sqrt[3]{3\sqrt{21} - 8} = 1$

Show that $$\sqrt[3]{3\sqrt{21} + 8} - \sqrt[3]{3\sqrt{21} - 8} = 1$$ Playing around with the expression, I found a proof which I will post as an answer. I'm asking this question because I ...
6
votes
7answers
175 views

why is $\sqrt{-1} = i$ and not $\pm i$? [duplicate]

this is something that came up when working with one of my students today and it has been bothering me since. It is more of a maths question than a pedagogical question so i figured i would ask here ...
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1answer
76 views

factor and simplify $x^{7/8} - x^{1/8}$ [on hold]

I do not know how to factor this AND simplify after I factor. I need help please and as soon as possible. I've been trying to figure it out for the past 3 hours and I don"t know how to get the answer. ...
4
votes
1answer
117 views

Can someone prove why $\sqrt{ab}=\sqrt{a}\sqrt{b}$ is only valid when a and b are positive?

I have seen many people say that a and b can't be positive for example in this false proof : $$1=\sqrt{1}=\sqrt{(-1)(-1)}=\sqrt{-1} \sqrt{-1} = i^2 = -1$$ Trust me, I understand that $1\neq -1$ and ...
5
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9answers
191 views

How do I explain why multiplying $0.8 \times 0.8$ is less than $0.8$?

I'm math is very rusty so forgive me for a trivial question. In my daughters home work she had the sum $4.8 \times 4.8$. Her thought process was to multiply $4 \times 4 =16$ and then $0.8 \times 0.8$ ...
0
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1answer
24 views

Multiplying numbers splitting the number into 4 digit numbers

Doing some programming exercise how to sum big numbers,I split the numbers into $n$ numbers of $4$-digit numbers $1240135981395813958$ I split into $1240$,$1359$,$8139$,$5813$,$958$ and summing with ...
2
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2answers
61 views

get 100 with the help of five 2

how to get 100 with the help of +, -, /, * and five 2s? 22222 = 100 I should put arithmetic operants between two s and get 100. PLease help
11
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7answers
168 views

Arithmetic pattern $1 + 2 = 3, 4 + 5 + 6 = 7 + 8$, and so on

I am noticing this pattern: \begin{align} 1+2&=3\\ 4+5+6&=7+8\\ 9+10+11+12&=13+14+15 \\ 16+17+18+19+20&=21+22+23+24 \\ &\vdots \end{align} Is there a general formula that expresses ...
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2answers
40 views

Solving a number with a fraction as exponent [closed]

How would I solve the following problem? $$256^{1/4}$$ In words, what is 256 to the power of 1/4? Thanks.
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0answers
69 views

Can you subtract two integers using multiplication and division?

The multiplication operation is traditionally defined as "repeated addition", and division (with remainder) can be defined using repeated subtraction. Can we define subtraction the other way round? ...
2
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1answer
40 views

Order of Operations Game Solution

My AP Computer Science teacher likes to play a game with his students where he writes 4 random numbers on the board and a fifth, target number. The objective is to use the four basic operations ...
2
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2answers
49 views

Why does the limit behavior of this function take over at 35?

I've been working with this function on an semi-related question: $$f(N)=\left\lfloor \frac{10N}{\lceil \frac{3}{4} N \rceil} \right\rfloor$$ It's clear that $10\leq f(N) \leq 13$, and that ...
3
votes
2answers
91 views

Is there a name for property $n+k=m+k\implies n=m$?

Monoid of natural numbers with addition have such property, that for any $n,m, k \in \mathbb{N}$ if $n+k=m+k$ then $n=m$. Does this property have some name in English?