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

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1answer
16 views

decimal to fractions

When being asked how to solve the Arithmetic Means of 8, 7, 7, 5, 3, 2, and 2, I understand that adding these numbers then dividing by 7 (the amount of numbers) gives me the decimal 4.85714... But ...
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2answers
78 views
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0answers
18 views

Simple interest ( Instalments) [on hold]

A sum of Rs 10 is lent to be returned in 11 monthly instalments of Re 1 each, interest being simple. The rate of interest is? 100/11 % 10 % 11 % 240/11 % What I understand is this - Rs 1 for 11 ...
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1answer
24 views

Instalments ( simple interest)

The price of a T.V set worth Rs. 20,000 is to be paid in 20 instalments of Rs. 1000 each. If the rate of interest be 6% per annum, and the first instalments be paid at the time of purchase, then the ...
0
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1answer
25 views

IEEE-754 Format Conversion

Represent 11.0011 x 2^10 using the IEEE-754 standard for 32-bit floating point representation. 0-Sign Bit 10001010-Exponent 1001100000000000000000-Mantissa Is this answer is correct ? I am bit ...
7
votes
4answers
92 views

How to position negative sign of fraction

For example we have: $$ \frac{-1}{2} $$ Does this mean that only the numerator of the fraction is negative? Can we put it like this? $$ -\frac{1}{2} $$ Does this means that the whole fraction is ...
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votes
2answers
96 views

How do we add numbers?

How do we compute sums in general? How can we tell the result of the operation $A+B$? Even when we talk about very basic numbers like $\Bbb{N}$ I find it hard to understand the algorithm we use to ...
1
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2answers
46 views

Alternating Sum of Cubes [on hold]

How is it possible to evaluate: $$\sum_{k=1}^n{((-1)^{n-k}\cdot k^3)}=n^3 - (n-1)^3 + (n - 2)^3 - \cdots \pm 1^3$$ The fact that there is the $\pm$ at the end makes it difficult.
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3answers
32 views

find nth term of a few sequences

first $4,-1,-11,-26,-46$ I found a recurrence relation of $U_{n-1} - 5(n-1)$ but I don't know how to find an explicit nth term formula second $0,3,8,15,24$ It goes up by $+3,+5,+7,+9$ I'm not sure ...
4
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5answers
172 views

Which are the operations used in mathematics? [on hold]

Everyone knows +,-,x,:,^. But I would really like to know which other operations exist, and what they do.
5
votes
2answers
177 views

Find $x;y$ such that: $\frac{x^2+y^3}{xy-1} \in \mathbb{Z}$

Let $x;y \in \mathbb{Z}$ such that: $\dfrac{x^2+y^3}{xy-1} \in \mathbb{Z}$ Find $x;y$? P/s; I don't have any ideas about this problem :( Thanks :)
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votes
1answer
14 views

Finding parts per million of number

Problem: A maximum deviation of $\pm$ 20 ppm (parts per million) from $x= 60.48*10^9$ is allowed. My Solution $Maximum Deviation = (0.02)(60.48*10^9) $ However the answer is $\pm 3024 $. Can ...
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votes
1answer
35 views

Representing a 5 star rating weighted arithmetic mean [on hold]

I have a working set of equations to find a "True Value" from a 5 star rating. For example, if I have 119(a) five-stars, 25(b) four-stars, 13(c) three-stars, 6(d) two-stars, and 3(e) one-stars. Then ...
2
votes
1answer
42 views

Speeding up integer division if only certain bits in result are needed

Let's say I need to divide two integers $x$ and $y$, but I only care about the lowest 8 bits of the answer, i.e. I'm calculating: $$r = \frac{x}{y}\,\,\%\,\,256$$where % is the modulus operator. Is ...
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votes
1answer
39 views

simple formula to get %? [on hold]

How to get % how much is y and how much is x ? x = 200 y = 800 result must be: x = 20% y = 80% what the formula ? Thanks
0
votes
1answer
29 views

Subtraction of trigonometric functions

I was working on a problem booklet and came across the following equation. $$\sqrt2\sin(2x)-\cos(2x)=\sqrt3\sin(2x-a)$$ $a \in \mathbb{R}$ is a specific value that I'm supposed to find, but I don't ...
2
votes
5answers
79 views

The sum of what 2 odd numbers above 1 make 443.

The sum of what $2$ odd numbers above $1$ make $443$. I honestly cannot figure this out - I got this question for my Year $7$ - NAPLAN numeracy test and I don't know it. Please someone help me get the ...
0
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3answers
36 views

Nicolas Choquet problem of bottles

In 1484 Nicolas Choquet wrote the first french algebra book. In a problem, he wants to split $21$ bottles between $3$ people. $7$ of them are full $7$ others are half filled $7$ others are empty ...
0
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1answer
17 views

Find the lower and upper bounds

I'm stuck with this question: $-2 < x < 6$ and $-4<y<-2$ What are the bounds of $x^2-y^2$? I thought that they are $(-2)^2-(-4)^2 = -12$ and $6^2-(-2)^2 = 32$, but apparently they are ...
0
votes
1answer
90 views

Why is $\sqrt{X}\times\sqrt{X}=X$?

Today I was solving the limit $(\ln(x))/(2*(x^{1/2})$ but then faced the step after applying the derivation that ended up with $(1/x)/(1/x^{1/2})$ and the result of that was $1/x^{1/2}$. When I asked ...
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4answers
59 views

Dividing fractions in real life scenario / application

First of all sorry if this question sounds too stupid or offends anyone. One apple divide by two you get half an apple. $\large{\frac{1}{2} = 0.5}$ I couldn't get my head around with dividing ...
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3answers
41 views

Cube roots of complex numbers [closed]

I need help with finding the cube roots of the complex number 27... I know that the obvious answer is three, but what is the less simple method to solving this?
4
votes
0answers
60 views

$d$ and $d+1$ both dividing certain integers

\begin{align} & 1\cdot 72 \\ & 2\cdot 36 \\ & 3\cdot 24 \\ & 4\cdot 18 \\ & 6\cdot 12 \\ & 8\cdot 9 \end{align} When the divisors of a number are listed in this way, let us ...
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2answers
42 views

Proving that $a \dot{-} (b+1) = (a \dot{-} b) \dot{-} 1$

This should be an easy exercise from Hodel's Introduction to Mathematical Logic, but for some reason I'm not getting it right. Define $a \dot{-} b$ as $a-b$ if $a \geq b$ and as $0$ otherwise. ...
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2answers
530 views

How to avoid stupid mistakes in calculus exams without checking the whole process?

Few days ago I failed my Calculus exams. And again it was mostly due to simple mistakes such as forgetting about minus in front of fraction, switching y coordinates of two points etc. The assignments ...
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1answer
15 views

How many rows & columns do 1,028 equal spaces create…

I have a board that is 17.5" wide and 67" long. I need to divide this board into 1,028 equal spaces. How many rows and how many columns will this equate to?
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4answers
69 views

Find all numbers divisible by 25, that begin with 6.

please, help me solve this problem: Find all numbers divisible by 25, that begin with 6. Regards.
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2answers
29 views

Cone mensuration sum

I am a tenth grade student. I am normally good in mensuration, but a question stumped me. The height of a cone is 30 cm. A small cone is cut off at the top by a plane parallel to it's base. If ...
4
votes
3answers
43 views

Find all 4 digits numbers that $ABCD=(CD)^2$

Please help me to solve following problem: Find all 4 digits numbers such that $ABCD=(CD)^2$.(any of $A,B,C,D$ is a digit!) I know one of solutions is $5776=(76)^2$.
0
votes
1answer
26 views

How to calculate the number of combinations of $x$ integers, each with a value between $y$ and $z$?

For example, if I have 4 integers, and each can be between 0 and 36, how many combinations are there? If the numbers have appeared before, but in a new order, then this still counts as a new ...
4
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2answers
61 views

Are $+, -,\times,\div$ the “base” calculations?

My friend told me that every equation possible with modern mathematical notation boils down to only $+, -,\times,\div$ What that means is that you can take any function and if you dive deep enough ...
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6answers
396 views

Is $15/52$ equal to $17/59$?

Is $\frac{15}{52} = \frac{17}{59}$? I typed it into the calculator and found: $$\frac{15}{52} = 0.2884615 $$ $$\frac{17}{59} = 0.2881356 $$ So I thought they were different. But then my friend said ...
2
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2answers
51 views

How to understand the principles of the rule of three? By the way, who invented it?

I'm looking to learn all the basic math now, because now I'm an adult math looks much more interesting and easier than ever! As I saw no exact answer for my doubt here on Math SE I resolved to ask ...
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2answers
47 views

problem of arithmetic [duplicate]

You can only use the numbers $1,3,5,7,9,11,13,15$. You can also repeat the numbers. Fill in the blanks: ____ $+$ ____ $+$ ____ $=30$
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5answers
2k views

Is there any explanation for the repetitions after decimal point on divisions like 24/7

I was trying to divide 24 by 7 using a pen and a paper. After I had no more space on my checkerboard paper, I decided to put it on a calculator. The calculator returned 3.428571428571429 and I ...
5
votes
3answers
67 views

How to get all the decimals on a division with decimal point and without remainder?

I divided 4.18 by 5 by hand, like this: As you see I removed the decimal point since I was dividing by a whole number, then I put the decimal point back and got 0.83 as result. It's correct, the ...
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0answers
34 views

Arithmetic progression Find first term and common difference when sum of 10 terms and the 8th term is given

Sigma is a car company that sell cars. Sigma sells $x$ cars in the first month and its sales increase constantly by $y$ cars every subsequent month. It sells $96$ cars in the $8^{th}$ month and the ...
3
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0answers
83 views

Looking for handy arithmetic tricks [closed]

A few days ago my grandfather taught me a trick to make it easier to calculate squares of quintuples in decimal numbers. What he told can be expressed in this way: $$ (10n+5)^ 2\quad = \quad ...
7
votes
2answers
112 views

Prove: if $n\mid 7^n+6^n$ and $n>1$, then $13\mid n$

Prove: if $n\mid 7^n+6^n$ and $n>1$, then $13\mid n$ Let $p$ be the least prime number such that $p\mid n$. And I want to show that $p=13$ Let $d$ be the least number such that: $14^d\equiv 0 ...
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2answers
49 views

$1$kilogram -$ 200$grams [closed]

I use 200g out of a 1kg packet of sugar. How many grams of sugar are left?
2
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1answer
43 views

How prove this fact about consecutive square numbers?

I saw somewhere that the sum of three consecutive squares minus $2$ is divisible by $3$. For example, $$2^2+3^2+4^2-2=4+9+16-2=27=3\cdot 9$$ But, I'm not sure how to give proof for this "property" of ...
0
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1answer
31 views

MLE of Integer Valued Normal Distribution

If Z is a normal random variable on $\mathbb{R}^d$ with parameters $(\mu,\Sigma)$ and we know that $\mu\in \mathbb{Z}^d$ and $\Sigma \in \mathbb{Z}^{d+}$; then how can we solve this MLE problem for ...
2
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5answers
85 views

How does 9 mod -7 = -5?

Forgive me if this question does not belong on this site for it is simplistic and this is my first post, however I do not seem to understand the modulo function when it comes to negative numbers. I'd ...
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2answers
30 views

word problem with addition [closed]

if every 100 points is \$10 and every survey is worth 5 points, how many surveys do I have to take to reach \$200 ?
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2answers
40 views

An infinite square arithmetic progression? [duplicate]

How to prove that there does not exist and infinite arithmetic sequence that all of it's terms are distinct squares of integers?
0
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1answer
15 views

Time And Distance (Train Journey)

The average speed of a train in the onward journey is 25% more than that in the return journey. The train halts for one hour on reaching the destination. The total time taken for the complete to and ...
2
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5answers
119 views

Solving $ \sqrt{x - 4} + \sqrt{x - 7} = 1 $.

I have the equation $ \sqrt{x - 4} + \sqrt{x - 7} = 1 $. I tried to square both sides, but then I got a more difficult equation: $$ 2 x - 11 + 2 \sqrt{x^{2} - 11 x - 28} = 1. $$ Can someone tell me ...
1
vote
1answer
23 views

Time, Speed and Distance

A walks around a circular field at the rate of one round per hour while B runs around it at the rate of six rounds per hour. They start in the same direction from the same point at 7.30 a.m. They ...
0
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0answers
19 views

Percentage Increase and Dates

Suppose we have the following data: ...
43
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11answers
7k views

What exactly IS a square root?

It's come to my attention that I don't actually understand what a square root really is (the operation). The only way I know of to take square roots (or nth root, for that matter) it to know the ...