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

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-2
votes
1answer
32 views

I do not know how to slove it [on hold]

If a child can run 10 meters while a car travels 30 meters, how many meters can the child run while the car travels 66 meters
2
votes
1answer
45 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
33 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 ...
1
vote
3answers
45 views

Maths problem on distance and time. [on hold]

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.
0
votes
1answer
16 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 ...
0
votes
3answers
11 views

Percentage Increase [on hold]

Bilal's weekly salary increased from Rs.175 to Rs.201.25. Find the percent of increase? $A) 1.15 %$ $B. 1.5 %$ $C. 8.7 %$ $D. 87 %$ $E. 15 %$
-7
votes
0answers
33 views

arithmetic sequence of 3 numbers please solve [on hold]

Please solve this sequence of numbers: 1000, 1,850, 6,500 Please give at least 6 numbers following after 6,500. Rough estimate is ok. Thank you. Please solve this too: 660, 1000, 3000. What are ...
-1
votes
0answers
104 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
22 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
10 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
20 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
86 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
votes
0answers
6 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: ...
5
votes
1answer
55 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
1answer
57 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
36 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
25 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
47 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
10 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
16 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
19 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
21 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
53 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
29 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
28 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
34 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
37 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
41 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
17 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
62 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
votes
1answer
25 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
96 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
votes
0answers
32 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
29 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 ...
22
votes
5answers
3k 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
44 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
59 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
69 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
17 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
30 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
votes
1answer
16 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
38 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
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
267 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 ...
-1
votes
3answers
45 views

How to find the total amount from given percentage

I am trying to answer this question from internet for my mathematics practice. ...