Search is not available for this dataset
url string | text string | date timestamp[s] | meta dict |
|---|---|---|---|
http://clrs.skanev.com/02/problems/01.html | # Problem 2.1
## Insertion sort on small arrays in merge sort
Although merge sort runs in $\Theta(\lg{n})$ worst-case time and insertion sort runs in $\Theta(n^2)$ worst-case time, the constant factors in insertion sort can make it faster in practice for small problem sizes on many machines. Thus, it makes sense to c... | 2017-03-25T07:48:08 | {
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http://math.stackexchange.com/questions/732445/my-first-induction-proof-very-simple-number-theory-please-mark-grade | ## Theorem
The sum of the cubes of three consecutive natural numbers is a multiple of 9.
## Proof
First, introducing a predicate $P$ over $\mathbb{N}$, we rephrase the theorem as follows. $$\forall n \in \mathbb{N}, P(n) \quad \text{where} \quad P(n) \, := \, n^3 + (n + 1)^3 + (n + 2)^3 \text{ is a multiple of 9}$$ ... | 2015-07-30T17:02:45 | {
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http://math.stackexchange.com/questions/263640/how-can-i-algebraically-prove-that-2n-1-is-not-always-prime | # How can I algebraically prove that $2^n - 1$ is not always prime?
This question is from Elementary Number Theory by W. Edwin Clark.
Is $2^n - 1$ always prime, or not? Prove.
Is this a start? $x^n - 1 = ( x - 1)(1 + x + x^2 \cdots x^{n - 1})$. So, $2^n - 1 = \sum \limits _{i = 0}^{n - 1} 2^i.$
Will I reach a solut... | 2014-04-20T21:55:58 | {
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http://www.virtualmuseum.finearts.go.th/sudbury-cable-lcpi/page.php?12d573=diagonal-of-parallelogram | Calculations include side lengths, corner angles, diagonals, height, perimeter and area of parallelograms. where is the two-dimensional cross product and is the determinant.. As shown by Euclid, if lines parallel to the sides are drawn through any point on a diagonal of a parallelogram, then the parallelograms not cont... | 2021-07-25T00:15:17 | {
"domain": "go.th",
"url": "http://www.virtualmuseum.finearts.go.th/sudbury-cable-lcpi/page.php?12d573=diagonal-of-parallelogram",
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"lm_q1_score": 0.97557690710554... |
https://gateoverflow.in/500/gate-cse-1991-question-01-iii | 3,977 views
Consider the number given by the decimal expression:
$$16^3*9 + 16^2*7 + 16*5+3$$
The number of $1’s$ in the unsigned binary representation of the number is ______
### 1 comment
$16^3=2^{12}$ and multiplying a number in binary with $2^x$ means that we are shifting that number to the left by $x$ bits.
So,... | 2021-09-27T21:33:20 | {
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https://www.physicsforums.com/threads/chain-and-spinning-disk-problem.741529/ | # Chain and spinning disk problem
## Homework Statement
A chain is wrapped around a disk of radius R. The tension of chain is T. What is the coefficient of friction, if when the disk is spinning at angular velocity ω, the chain slips down?
See image attached.
## Homework Equations
II Newton law
$a_{centripetal} = ... | 2020-12-02T00:53:20 | {
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... |
https://walkingrandomly.com/?p=5215 | ## Simple nonlinear least squares curve fitting in Python
December 6th, 2013 | Categories: math software, programming, python | Tags:
A question I get asked a lot is ‘How can I do nonlinear least squares curve fitting in X?’ where X might be MATLAB, Mathematica or a whole host of alternatives. Since this is such a c... | 2020-12-03T08:23:19 | {
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https://math.stackexchange.com/questions/3871593/proving-lim-x-to-infty-frac2xx1-2-using-definition | # Proving $\lim_{x \to \infty}\frac{2|x|}{x+1} = 2$ using definition
I'm trying to prove this limit here
Prove $$\lim_{x \to \infty}\frac{2|x|}{x+1} = 2$$, using epsilon-delta or sequence limit definition
Here's the answer I've come up so far
Let $$\epsilon > 0$$, by Archimedian Property, then exist $$m \in N$$ suc... | 2021-04-16T20:59:53 | {
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https://math.stackexchange.com/questions/2918372/where-have-i-made-a-mistake | # Where have I made a mistake?
I have been trying the integral below, but cannot get the right answer and I am not sure where I have gone wrong. Let $$I=\int_0^{1/2}\arcsin(\sqrt{x})dx$$ and make the substitution $\sqrt{x}=\sin(u)$ so $dx=2\sin(u)\cos(u)du$. Now, \begin{align} I &= \int_0^{\pi/4}2u\sin(u)\cos(u)du = \... | 2020-01-28T20:05:02 | {
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https://math.stackexchange.com/questions/1213727/counting-all-possibilities-that-contain-a-substring | Counting all possibilities that contain a substring
How many strings are there of seven lowercase letters that have the substring tr in them?
So I am having a little problem with this question, I know that the total number of combinations is $26^6$ but there is double counting on some of the combinations.
For exampl... | 2019-10-16T09:42:37 | {
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http://mathhelpforum.com/math-challenge-problems/240584-can-grid-filled.html | # Thread: Can the grid be filled?
1. ## Can the grid be filled?
Given binary sequences of equal length, let the "distance" between them be defined as the number of bits that would need to be flipped to convert one binary sequence to another. For example, the sequences 1111 and 1110 are a distance of 1 apart, because ... | 2018-08-20T11:02:48 | {
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http://math.stackexchange.com/questions/291892/what-is-the-converse-of-this-statement-and-is-it-true | # What is the converse of this statement and is it true?
If $a$ and $b$ are relatively prime, $a\mid c$ and $b\mid c$, then $(ab)\mid c$.
I am lost. Would the converse be "If $(ab)\mid c$, then $a$ and $b$ are relatively prime and $a\mid c$ and $b\mid c$" or is it "if $a$ and $b$ are relatively prime, and $(ab)\mid c... | 2015-07-05T12:55:49 | {
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"lm_q1_score": 0.... |
https://betaprojects.com/project-euler-28/ | Select Page
#### Project Euler 28 Problem Statement
Starting with the number 1 and moving to the right in a clockwise direction a 5 by 5 spiral is formed as follows:
21 22 23 24 25
20 7 8 9 10
19 6 1 2 11
18 5 4 3 12
17 16 15 14 13
It can be verified that the sum of both diagonals is 101.
What is the sum of both d... | 2020-04-03T22:37:40 | {
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"l... |
https://www.pythonlikeyoumeanit.com/Module2_EssentialsOfPython/Problems/MarginPercentage.html | Within Margin Percentage¶
An algorithm is required to test out what percentage of the parts that a factory is producing fall within a safety margin of the design specifications. Given a list of values recording the metrics of the manufactured parts, a list of values representing the desired metrics required by the des... | 2019-08-19T18:31:12 | {
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https://math.stackexchange.com/questions/773686/why-does-2n-choose1n-choose2-ldotsn-choosen-1-11n | # Why does $2+{{n}\choose{1}}+{{n}\choose{2}}+\ldots+{{n}\choose{n-1}}=(1+1)^n$
$${{n}\choose{0}}+ {{n}\choose{1}}+{{n}\choose{2}}+\ldots+{{n}\choose{n-1}}+{{n}\choose{n}}=(1+1)^n$$
I don't see why this is true, because (if I'm not mistaken)
\begin{align}&{{n}\choose{0}}+ {{n}\choose{1}}+{{n}\choose{2}}+\ldots+{{n}\... | 2020-01-18T12:21:52 | {
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"lm_label": "1. YES\n2. YES",
"lm_q1_score": 0.990... |
http://bueteeearchives.net/o3ddr4ei/0c6f4b-fraction-exponents-calculator | Dividing fractions calculator online. Welcome to the Exponent Calculator. Negative exponent ; A negative exponent represents which fraction of the base, the solution is. Sometimes the exponent itself is a fraction. You don't need to go from the top to the bottom of the calculator - calculate any unknown you want! In th... | 2021-03-02T01:38:16 | {
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"url": "http://bueteeearchives.net/o3ddr4ei/0c6f4b-fraction-exponents-calculator",
"openwebmath_score": 0.7745479941368103,
"openwebmath_perplexity": 1244.501551708118,
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"lm_label": "1. Yes\n2. Yes\n\n",
"lm_q1_score": 0.982287698185481,
"lm_... |
http://math.stackexchange.com/questions/608465/is-there-a-proof-for-this-fibonacci-relationship | # Is there a proof for this Fibonacci relationship?
I was looking at the decomposition of Fibonacci numbers using the definition of $F_n = F_{n-1} + F_{n-2}$, and noted the pattern in the coefficients of the terms were Fibonacci numbers. It appears to hold, and I believe it's true, but I haven't seen a proof for it. D... | 2014-08-29T08:28:03 | {
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"lm_label": "1. YES\n2. YES",
"lm_q1_score": 0.99168422... |
https://math.stackexchange.com/questions/2065622/how-many-multisets-of-size-4-that-can-be-constructed-from-n-distinct-element/2065636 | # How many multisets of size $4$ that can be constructed from $n$ distinct elements?
How many multisets of size $4$ that can be constructed from $n$ distinct elements so that at least one element occurs exactly twice ?
Example : For $n=3$ and element set as $\{1,2,3\}$ I am getting multisets as: $\{1,1,3,3\}, \{1,1,2... | 2021-09-26T01:06:01 | {
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"openwebmath_score": 0.8861674070358276,
"openwebmath_perplexity": 190.9249164476898,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. Y... |
http://linear.ups.edu/fcla/section-S.html | A subspace is a vector space that is contained within another vector space. So every subspace is a vector space in its own right, but it is also defined relative to some other (larger) vector space. We will discover shortly that we are already familiar with a wide variety of subspaces from previous sections.
Here is t... | 2020-05-28T07:06:22 | {
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"lm_q1_score": 0.9933071498682252,
"lm_q2_score": 0.8918110526265554,
"lm_q1q2_sco... |
https://stats.stackexchange.com/questions/185683/distribution-of-ratio-between-two-independent-uniform-random-variables | # Distribution of ratio between two independent uniform random variables
Supppse $X$ and $Y$ are standard uniformly distributed in $[0, 1]$, and they are independent, what is the PDF of $Z = Y / X$?
The answer from some probability theory textbook is
$$f_Z(z) = \begin{cases} 1/2, & \text{if } 0 \le z \le 1 \\ 1/(2z^... | 2019-12-12T15:00:53 | {
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"url": "https://stats.stackexchange.com/questions/185683/distribution-of-ratio-between-two-independent-uniform-random-variables",
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"openwebmath_perplexity": 194.34591193416304,
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... |
https://mathhelpboards.com/threads/displacement-and-distance.2253/ | # Displacement and Distance
#### alane1994
##### Active member
Here is my question.
The function $$v(t)=15\cos{3t}$$, $$0 \leq t \leq 2 \pi$$, is the velocity in m/sec of a particle moving along the x-axis. Complete parts (a) through (c).
a.Graph the velocity function over the given interval. then determine when th... | 2020-09-26T02:30:23 | {
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"lm_q2_score"... |
http://math.stackexchange.com/questions/182617/counterexample-check-for-sum-of-limit-points-of-subsequences | # Counterexample Check for Sum of Limit Points of Subsequences
Let $c$ be a limit point of a sequence of real numbers $\langle a_n \rangle$ and $d$ a limit point of $\langle b_n \rangle$. Is $c+d$ necessarily a limit point of $\langle a_n + b_n \rangle$?
My Question:
When considering this question, do I have to sum ... | 2014-08-23T20:32:57 | {
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"url": "http://math.stackexchange.com/questions/182617/counterexample-check-for-sum-of-limit-points-of-subsequences",
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https://math.stackexchange.com/questions/1738331/sequence-of-functions-that-fails-certain-conditions-of-arzela-ascoli-theorem | # Sequence of functions that fails certain conditions of Arzela-Ascoli theorem
For a closed, bounded interval $[a,b]$, let $\{ f_{n}\}$ be a sequence in $C[a,b]$. If $\{f_{n}\}$ is equicontinuous, does $\{f_{n}\}$ necessarily have a uniformly convergent subsequence?
I would think not, because according to the Arzela-... | 2021-03-09T08:24:33 | {
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http://www.appeton.co.id/future-currency-tosgcr/63e023-linear-function-graph | By … By graphing two functions, then, we can more easily compare their characteristics. In this section, 8th grade and high school students will have to find the missing values of x and f(x). In $f\left(x\right)=mx+b$, the b acts as the vertical shift, moving the graph up and down without affecting the slope of the lin... | 2021-04-13T17:23:29 | {
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"lm_label": "1. Yes\n2. Yes",
"lm_q1_score": 0.983596967483837,
"lm_q2_score": 0.90... |
https://chemistry.stackexchange.com/questions/61117/probability-of-finding-a-molecule-in-the-ground-vibrational-level | # Probability of finding a molecule in the ground vibrational level
I wanted to estimate the probability of finding a molecule in the ground vibrational level using the Boltzmann distribution:
$$p_i = \frac{e^{-\epsilon_i/kT}}{\sum_{i=0}^{N}e^{-\epsilon_i/kT}}$$
Using the quantum harmonic oscillator as a model for t... | 2021-12-03T17:33:49 | {
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"url": "https://chemistry.stackexchange.com/questions/61117/probability-of-finding-a-molecule-in-the-ground-vibrational-level",
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"... |
https://math.stackexchange.com/questions/2235805/dimension-of-image-kernel-of-linear-transformation | # Dimension of Image/Kernel of Linear Transformation
Consider the vector spaces $P_n$ (polynomials of degree no more than n). The differentiation D gives a linear transformation from $P_n$ to $P_{n-1}$. What is the dimension of the image and the kernel of D? Is D a valid linear transformation from $P_n$ to $P_n$? If i... | 2020-04-02T23:20:25 | {
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https://math.stackexchange.com/questions/3714641/does-this-double-integral-exists | # Does this double integral exists?
I've calculated $$\iint_D\frac{y}{x^2+y^2}\,dA$$ where D is bounded by $$y=x$$, $$y=2x$$, $$x=2$$, in this way: $$\iint_D\frac{y}{x^2+y^2}\,dA=\int_0^2\int_x^{2x}\frac{y}{x^2+y^2}\,dy\,dx=\cdots = \ln \frac{5}{2}.$$ However, I wonder if the fact that the $$\frac{y}{x^2+y^2}$$ is not... | 2022-01-20T12:18:00 | {
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... |
http://test.marbellaphysio.com/chronic-fatigue-civ/page.php?page=4e714e-correlation-coefficient-worksheet-with-answers | 2) The direction of the relationship, which can be positive or negative based on the sign of the correlation coefficient. correlation is rather strong, so the correlation coefficient should be closer to 1. Correlation Coefficient WorksheetName: Calculator steps for creating a scatter plot: Stat. Students estimate the c... | 2021-06-21T19:26:44 | {
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"lm_label": "1. Yes\n2. Yes\n\n... |
https://math.stackexchange.com/questions/3482467/find-value-of-a-1-such-that-a-101-5075 | # Find value of $a_1$ such that $a_{101}=5075$
Let $$\{a_n\}$$ be a sequence of real numbers where $$a_{n+1}=n^2-a_n,\, n=\{1,2,3,...\}$$
Find value of $$a_1$$ such that $$a_{101}=5075$$.
I have
$$a_2=1^2-a_1$$
$$a_3=2^2-a_2=2^2-1^2+a_1$$
$$a_4=3^2-2^2+1^2-a_1$$
$$a_5=4^2-3^2+2^2-1^2+a_1$$
$$\vdots$$
$$a_{101}... | 2020-05-28T05:18:13 | {
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http://mathhelpforum.com/math-topics/137961-vector-intersection.html | 1. ## Vector Intersection
Hi, I have a mechanics question here I can't quite get.
A destroyer sights a ship at a point with position vector 600(3i + j)m relative to it and moving with velocity 5j m/s. The destroyer alters course so that it moves with speed v m/s in the direction of the vector 4i + 3j. Find v so that ... | 2017-09-26T09:54:08 | {
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"openwebmath_score": 0.8040945529937744,
"openwebmath_perplexity": 948.0050107983985,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. YES\n2. YES",
"lm_q1_score": 0.9865717468373085,
"lm_q2_score"... |
https://gmatclub.com/forum/if-the-set-s-consists-of-five-consecutive-positive-integers-what-is-218964.html | It is currently 25 Feb 2018, 19:42
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"openwebmath_score": 0.6206461191177368,
"openwebmath_perplexity": 2145.6368674994515,
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"lm_label": "1. Yes\n2. Yes\n",
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https://gmatclub.com/forum/if-x-is-a-positive-integer-is-x-1-a-factor-of-126421.html | It is currently 22 Mar 2018, 20:16
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"openwebmath_perplexity": 1108.1858722364714,
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http://bootmath.com/finding-a-closed-formula-for-1cdot2cdot3cdots-k-dots-nn1n2cdotskn-1.html | # Finding a closed formula for $1\cdot2\cdot3\cdots k +\dots + n(n+1)(n+2)\cdots(k+n-1)$
Considering the following formulae:
(i) $1+2+3+..+n = n(n+1)/2$
(ii) $1\cdot2+2\cdot3+3\cdot4+…+n(n+1) = n(n+1)(n+2)/3$
(iii) $1\cdot2\cdot3+2\cdot3\cdot4+…+n(n+1)(n+2) = n(n+1)(n+2)(n+3)/4$
Find and prove a ‘closed formula’ f... | 2018-06-22T17:08:32 | {
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"url": "http://bootmath.com/finding-a-closed-formula-for-1cdot2cdot3cdots-k-dots-nn1n2cdotskn-1.html",
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"openwebmath_perplexity": 421.3720734986149,
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"lm_label": "1. YES\n2. YES",
"lm_q1_score": 0.988130879652718... |
https://math.stackexchange.com/questions/2586523/evaluating-an-integral-2 | # Evaluating an integral 2.
I'm calculating the following integral: $\int \frac{1}{\sqrt{x^2+2}}dx$
I tried the following:
Performing $u$ substitution:
Let $x=\sqrt{2}\tan(u)$
$x^2=2\tan^2(u)$
$dx=\sqrt{2}(1+\tan^2(u))du$
$\int \frac{1}{\sqrt{x^2+2}}dx=\int \frac{\sqrt{2}(1+\tan^2(u))du}{\sqrt{2\tan^2(u)+2}}= \i... | 2019-11-19T12:42:07 | {
"domain": "stackexchange.com",
"url": "https://math.stackexchange.com/questions/2586523/evaluating-an-integral-2",
"openwebmath_score": 0.972143828868866,
"openwebmath_perplexity": 244.08938928784292,
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"lm_label": "1. YES\n2. YES",
"lm_q1_score": 0.9912886170864413,
"lm_q2_s... |
https://math.stackexchange.com/questions/1041325/probability-that-someone-will-pick-a-red-ball-first | # Probability that someone will pick a red ball first?
A father and son take turns picking red and green balls from a bag. There are 2 red balls and 3 green balls. The first person to pick a red ball wins. There is no replacement. What is the probability that the father wins if he goes first?
I drew a binary tree to ... | 2022-01-24T23:00:51 | {
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"url": "https://math.stackexchange.com/questions/1041325/probability-that-someone-will-pick-a-red-ball-first",
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"openwebmath_perplexity": 785.5544343391575,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. YES\n2. YES",
"lm_q1_score": 0.9... |
http://edenwhitemusic.com/6rm5l89/viewtopic.php?e57fe7=inverse-of-product-of-two-matrices | Lecture 3: Multiplication and inverse matrices Matrix Multiplication We discuss four different ways of thinking about the product AB = C of two matrices. Suppose $A$ is an invertable matrix. In Problem, examine the product of the two matrices to determine if each is the inverse of the other. Step by Step Explanation. C... | 2021-01-22T00:19:22 | {
"domain": "edenwhitemusic.com",
"url": "http://edenwhitemusic.com/6rm5l89/viewtopic.php?e57fe7=inverse-of-product-of-two-matrices",
"openwebmath_score": 0.7859293818473816,
"openwebmath_perplexity": 350.9617148648594,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. Yes\n2. Yes",
"lm_q1_score": 0.98481094940... |
http://manami.pl/site/ymvno.php?tag=fe20d3-set-notation-examples | Adopted or used LibreTexts for your course? Let's cover one more thing about set notation. We can use the braces to show the empty set: { }. For example, the set { 1, 2, 3, 4, 5, 6, 7, 8, 9 } list the elements. So let's name this set as "A". Let us start with a definition of a set. | {{course.flashcardSetCount}} The nu... | 2022-05-19T09:12:23 | {
"domain": "manami.pl",
"url": "http://manami.pl/site/ymvno.php?tag=fe20d3-set-notation-examples",
"openwebmath_score": 0.6804498434066772,
"openwebmath_perplexity": 616.9135748554941,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. YES\n2. YES",
"lm_q1_score": 0.9817357259231532,
"lm_q2_score": 0.90192067... |
https://plainmath.net/7256/situations-comparing-proportions-described-determine-situation-proportions | # TWO GROUPS OR ONE? Situations comparing two proportions are described. In each case, determine whether the situation involves comparing proportions fo
TWO GROUPS OR ONE? Situations comparing two proportions are described. In each case, determine whether the situation involves comparing proportions for two groups or ... | 2022-06-26T02:34:07 | {
"domain": "plainmath.net",
"url": "https://plainmath.net/7256/situations-comparing-proportions-described-determine-situation-proportions",
"openwebmath_score": 0.7326516509056091,
"openwebmath_perplexity": 1204.4285773342365,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. Yes\n2. Yes",
"lm_q1_score": 0.974... |
https://mathematica.stackexchange.com/questions/134106/which-root-does-findroot-give | # Which root does FindRoot give?
I think that usually, FindRoot will give the root that's closest to the starting point. But see the example below, where I try to find the root of $\cos x=0$. If I started from $x=0.1$, then I get $10.9956$, but if I started from 1, I get $1.5708$. What's wrong?
• Draw a graph of the ... | 2021-04-14T09:04:05 | {
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"openwebmath_perplexity": 2313.082319097427,
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"lm_label": "1. YES\n2. YES",
"lm_q1_score": 0.9615338123908151... |
https://mathhelpboards.com/threads/rule-of-sum-and-rule-pf-product-how-many-distinct-sums-are-possible-using-from-1-to-all-of-the-15-cards.25841/ | Rule of sum and rule pf product: How many distinct sums are possible using from 1 to all of the 15 cards
Dhamnekar Winod
Active member
There are 8 cards with number 10 on them, 5 cards with number 100 on them and 2 cards with number 500 on them. How many distinct sums are possible using from 1 to all of the 15 cards?... | 2020-07-09T02:47:37 | {
"domain": "mathhelpboards.com",
"url": "https://mathhelpboards.com/threads/rule-of-sum-and-rule-pf-product-how-many-distinct-sums-are-possible-using-from-1-to-all-of-the-15-cards.25841/",
"openwebmath_score": 0.8201991319656372,
"openwebmath_perplexity": 529.3834386670821,
"lm_name": "Qwen/Qwen-72B",
"lm_... |
https://math.stackexchange.com/questions/2453591/difference-between-infty-and-infty | # difference between $+\infty$ and $\infty$
I'm taking Mathematical Analysis "I" and I'm studying limits where I have limits to the infinity, but I don't know what's the difference between $\lim_{x \to \infty}$ and $\lim_{x \to +\infty}$ I suppose that they are the same but I'm not sure. If you could help me I would a... | 2019-06-25T23:34:48 | {
"domain": "stackexchange.com",
"url": "https://math.stackexchange.com/questions/2453591/difference-between-infty-and-infty",
"openwebmath_score": 0.9814448356628418,
"openwebmath_perplexity": 230.86852229597366,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. YES\n2. YES",
"lm_q1_score": 0.9702399086356109,... |
http://math.stackexchange.com/questions/29638/how-do-we-find-a-fraction-with-whose-decimal-expansion-has-a-given-repeating-pat | # How do we find a fraction with whose decimal expansion has a given repeating pattern?
We know $\frac{1}{81}$ gives us $0.\overline{0123456790}$
How do we create a recurrent decimal with the property of repeating:
$0.\overline{0123456789}$
a) Is there a method to construct such number?
b) Is there a solution?
c)... | 2014-08-01T01:47:35 | {
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"url": "http://math.stackexchange.com/questions/29638/how-do-we-find-a-fraction-with-whose-decimal-expansion-has-a-given-repeating-pat",
"openwebmath_score": 0.9437023997306824,
"openwebmath_perplexity": 871.6057100813944,
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"lm_label": "1. YES\n2. ... |
https://mathhelpboards.com/threads/a-probability-question-choosing-3-from-25.5240/#post-23851 | # [SOLVED]A probability question: choosing 3 from 25
#### first21st
##### New member
In a class, there are 15 boys and 10 girls. Three students are selected at random. The probability that 1 girl and 2 boys are selected, is:
A. 21/46
B. 25/117
C. 1/50
D. 3/25
Could you please solve this problem with proper explanati... | 2022-05-17T10:23:37 | {
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"url": "https://mathhelpboards.com/threads/a-probability-question-choosing-3-from-25.5240/#post-23851",
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"openwebmath_perplexity": 381.7450872745894,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. YES\n2. YES",
"lm_q1_score": 0.9926541... |
https://orinanobworld.blogspot.com/2020/ | ## Monday, February 17, 2020
### Reversing Differences
Fellow blogger Håkan Kjellerstrand posted an interesting question on OR Stack Exchange recently. Starting from a list of integers, it is trivial to compute the list of all pairwise absolute differences, but what about going in the other direction? Given the pairw... | 2020-02-22T07:02:48 | {
"domain": "blogspot.com",
"url": "https://orinanobworld.blogspot.com/2020/",
"openwebmath_score": 0.6736919283866882,
"openwebmath_perplexity": 405.9040934732411,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. YES\n2. YES",
"lm_q1_score": 0.9926541727735793,
"lm_q2_score": 0.8918110396870287,
"lm_q1q2_... |
http://mathhelpforum.com/algebra/109037-determining-formula-sequence.html | # Math Help - Determining the formula of this sequence?
1. ## Determining the formula of this sequence?
I was given the sequence
0, 1, 4, 11, 26, 57, 120, 247, 502, 1013, ...
and I'm looking for a method to determine an explicit formula for this.
I've tried doing difference columns, and I always end up with 2^n being... | 2015-11-26T06:08:17 | {
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"lm_q2_... |
https://math.stackexchange.com/questions/1763978/can-you-use-both-sides-of-an-equation-to-prove-equality | # Can you use both sides of an equation to prove equality?
For example:
$\color{red}{\text{Show that}}$$\color{red}{\frac{4\cos(2x)}{1+\cos(2x)}=4-2\sec^2(x)}$$ In high school my maths teacher told me To prove equality of an equation; you start on one side and manipulate it algebraically until it is equal to the othe... | 2019-07-19T01:57:50 | {
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"url": "https://math.stackexchange.com/questions/1763978/can-you-use-both-sides-of-an-equation-to-prove-equality",
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"openwebmath_perplexity": 481.2578683796757,
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"lm_label": "1. YES\n2. YES",
"lm_q1_score":... |
https://math.stackexchange.com/questions/1436296/is-the-probability-of-picking-an-ace-as-the-second-card-of-a-deck-the-same-if-th | # Is the probability of picking an Ace as the second card of a deck the same if the deck is shuffled after the first card?
Here's the situation:
You have a deck of 52 cards that is already shuffled. You pick the first card, and the first card is not an Ace. Is the probability of drawing an Ace as second card the same... | 2019-06-17T02:33:48 | {
"domain": "stackexchange.com",
"url": "https://math.stackexchange.com/questions/1436296/is-the-probability-of-picking-an-ace-as-the-second-card-of-a-deck-the-same-if-th",
"openwebmath_score": 0.7584448456764221,
"openwebmath_perplexity": 192.16351161095074,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. YES\... |
https://math.stackexchange.com/questions/1845889/integrals-over-subset-of-measure-space | # Integrals over subset of measure space
Let $(X, \mathcal{M}, \mu)$ be a measure space. Suppose $E \in \mathcal{M}$ and $f \in L^+$ where $L^+$ is a space of measurable functions from $X$ to $[0, \infty]$. $\int_E f$ is defined by $\int_X f\chi_E$ where $\chi_E$ is a characteristic function of $E$. Now every time we ... | 2019-05-27T07:05:26 | {
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"url": "https://math.stackexchange.com/questions/1845889/integrals-over-subset-of-measure-space",
"openwebmath_score": 0.9362642765045166,
"openwebmath_perplexity": 160.88799488823398,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. YES\n2. YES",
"lm_q1_score": 0.9814534316905... |
http://math.stackexchange.com/questions/429842/how-many-triangles-in-picture | How many triangles in picture
How many triangles in this picture:
-
I only count 40...and unless someone can explain me how this is a mathematics question I think I'm going to vote to close it as off-topic – DonAntonio Jun 26 '13 at 9:16
I do not think one needs mathematics to solve the puzzle. – Avitus Jun 26 '13 ... | 2014-10-21T07:21:38 | {
"domain": "stackexchange.com",
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"openwebmath_perplexity": 397.4700085710202,
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"lm_label": "1. YES\n2. YES",
"lm_q1_score": 0.9728307676766118,
"lm_q2... |
https://math.stackexchange.com/questions/1063724/convergence-of-sum-n-1-infty-left-frac1n-frac1n-2-righ | # Convergence of $\sum_{n=1}^{\infty}\left(\, \frac{1}{n} - \frac{1}{n + 2}\,\right)$
What criteria can I use to prove the convergence of $$\sum_{n=1}^{\infty}\left(\,{1 \over n} - {1 \over n + 2}\,\right)\ {\large ?}$$
My idea was to use ratio test: $$\displaystyle{1 \over n} - {1 \over n+2} = {2 \over n^{2} + 2n}$$... | 2020-02-21T06:36:12 | {
"domain": "stackexchange.com",
"url": "https://math.stackexchange.com/questions/1063724/convergence-of-sum-n-1-infty-left-frac1n-frac1n-2-righ",
"openwebmath_score": 0.8874070644378662,
"openwebmath_perplexity": 204.44323439052374,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. YES\n2. YES",
"lm_q1_score":... |
https://math.stackexchange.com/questions/2339821/how-to-prove-that-a-sequence-diverges-using-the-cauchy-definition | # How to prove that a sequence diverges using the Cauchy definition?
It was a question of my integral calculus exam:
Write the Cauchy definition of $\lim_{n\rightarrow\infty} a_n = L$
So, I literally wrote:
" $\{a_n\}$ is a Cauchy sequence if given $\epsilon>0$ there exists $N \in \mathbb{N}$ such that $\forall\ m,... | 2019-07-18T02:07:22 | {
"domain": "stackexchange.com",
"url": "https://math.stackexchange.com/questions/2339821/how-to-prove-that-a-sequence-diverges-using-the-cauchy-definition",
"openwebmath_score": 0.9682406783103943,
"openwebmath_perplexity": 145.87265261899606,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. YES\n2. YES",
"lm... |
https://math.stackexchange.com/questions/3372929/which-sets-of-sequence-is-countable-and-uncountable | # Which sets of sequence is countable and Uncountable.
Consider the sequences
$$\displaystyle X=\left\{(x_n): x_n \in \left\{0,1\right\},n \in \mathbb{N} \right\}$$ $$and$$ $$\displaystyle Y=\left\{(x_n)\in X:x_n=1 \;\;\text{for at most finitely many n} \right\}$$
I have to choose which is uncountable and which is c... | 2021-04-14T13:59:39 | {
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"url": "https://math.stackexchange.com/questions/3372929/which-sets-of-sequence-is-countable-and-uncountable",
"openwebmath_score": 0.9329140782356262,
"openwebmath_perplexity": 174.8466598034546,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. YES\n2. YES",
"lm_q1_score": 0.9... |
https://gmatclub.com/forum/in-how-many-different-ways-can-a-group-of-8-people-be-divide-85707-20.html | GMAT Question of the Day: Daily via email | Daily via Instagram New to GMAT Club? Watch this Video
It is currently 28 May 2020, 00:56
### GMAT Club Daily Prep
#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Pr... | 2020-05-28T08:56:24 | {
"domain": "gmatclub.com",
"url": "https://gmatclub.com/forum/in-how-many-different-ways-can-a-group-of-8-people-be-divide-85707-20.html",
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"lm_q1_score": 0.97557... |
https://math.stackexchange.com/questions/1977626/help-needed-with-different-approach-to-a-combinatorics-question | # Help needed with different approach to a combinatorics question
Every day, the 15 students in Mr. Singh`s Advanced Chemistry class are randomly divided into 5 lab groups of 3 students each. What is the probability that three students - Linda, Martin, and Nancy - are in the same lab group today?
The answer to the qu... | 2019-05-19T13:00:01 | {
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"url": "https://math.stackexchange.com/questions/1977626/help-needed-with-different-approach-to-a-combinatorics-question",
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"openwebmath_perplexity": 148.78251876948974,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. YES\n2. YES",
"lm_q... |
https://math.stackexchange.com/questions/1187351/how-many-ways-are-there-to-divide-elements-into-equal-unlabelled-sets | # How many ways are there to divide elements into equal unlabelled sets?
How many ways are there to divide N elements into K sets where each set has exactly N/K elements.
For the example of 6 elements into 3 sets each with 2 elements. I started by selecting the elements that would go in the first set (6 choose 2) and... | 2020-01-18T17:41:16 | {
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"openwebmath_perplexity": 191.1003331146527,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. YES\n2. YES",
... |
https://math.stackexchange.com/questions/4194996/representing-a-linear-transformation-with-respect-to-a-new-basis | # Representing a linear transformation with respect to a new basis
I have a question about the following exercise:
Let $$f:\mathbb{R}^3\to\mathbb{R}^3$$ be the linear transformation such that $$f(x,y,z)=(x-y+2z,-2x+y,x+z).$$ Represent the transformation with respect to the basis $$\{(1,1,0),(0,1,-1),(1,1,1)\}$$.
Wha... | 2021-12-07T22:51:59 | {
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https://math.stackexchange.com/questions/2839456/finding-orthonormal-basis-from-orthogonal-basis | # Finding orthonormal basis from orthogonal basis
The following is example C.5 from Appendix C (Linear Spaces Review) of Introduction to Laplace Transforms and Fourier Series, Second Edition, by Phil Dyke:
Example C.5 Show that $\{\sin(x),\cos(x)\}$ is an orthonormal basis for the inner product space $V=\{a\sin(x)+b\... | 2021-05-06T17:04:14 | {
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"openwebmath_perplexity": 350.798848385106,
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"lm_label": "1. YES\n2. YES",
"lm_q1_score": 0.9875683... |
https://math.stackexchange.com/questions/3114318/computing-the-product-fracddxxn-fracddxxn/3114413 | # Computing the product $(\frac{d}{dx}+x)^n(-\frac{d}{dx}+x)^n$
I want to compute the product $$(\frac{d}{dx}+x)^n(-\frac{d}{dx}+x)^n,$$ for a natural number $$n$$. For $$n$$ equal to 0 or 1, the computation is very simple obviously, but for such a low number as 2 the brute force calculation begins to be rather cumber... | 2019-06-19T11:32:52 | {
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"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. YES\n2. YES",
"lm_q1_score": 0.9875... |
https://www.physicsforums.com/threads/pendulum-dilemma.546677/ | # Pendulum dilemma
## Homework Statement
I am suppose to find a linear graph for the equation T=2pie(√L/√g)
## The Attempt at a Solution
The best linear graph I could think of was L/T^2.
Am I doing it right? Thanks.
Yes.
T$^{2}$ on y-axis and L on x-axis.
Yes.
T$^{2}$ on y-axis and L on x-axis.
Thank you very... | 2022-05-16T06:24:07 | {
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"lm_q2_score... |
http://math.stackexchange.com/questions/270564/what-is-the-argument-for-not-using-the-average-of-an-average | what is the argument for not using the average of an average?
I want to disprove someone's calculation of percentage of cash sales for a year by taking summing percentage of cash sales by month and dividing by 12. I sense the correct way is to take total cash sales for the year and divide by total sales for year to ar... | 2013-12-21T22:54:05 | {
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"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. YES\n2. YES",
"lm_q1_sco... |
https://stacks.math.columbia.edu/tag/00D3 | Definition 4.21.1. Let $I$ be a set and let $\leq$ be a binary relation on $I$.
1. We say $\leq$ is a preorder if it is transitive (if $i \leq j$ and $j \leq k$ then $i \leq k$) and reflexive ($i \leq i$ for all $i \in I$).
2. A preordered set is a set endowed with a preorder.
3. A directed set is a preordered set $... | 2022-12-08T16:02:30 | {
"domain": "columbia.edu",
"url": "https://stacks.math.columbia.edu/tag/00D3",
"openwebmath_score": 0.8227077126502991,
"openwebmath_perplexity": 393.8887121005783,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. YES\n2. YES",
"lm_q1_score": 0.9857180639771091,
"lm_q2_score": 0.8976952873175982,
"lm_q1q2... |
https://gmatclub.com/forum/what-is-x-more-than-y-1-x-of-y-is-9-2-y-more-than-x-is-260828.html | GMAT Question of the Day - Daily to your Mailbox; hard ones only
It is currently 20 Nov 2018, 07:47
### GMAT Club Daily Prep
#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.
Customize... | 2018-11-20T15:47:04 | {
"domain": "gmatclub.com",
"url": "https://gmatclub.com/forum/what-is-x-more-than-y-1-x-of-y-is-9-2-y-more-than-x-is-260828.html",
"openwebmath_score": 0.56454998254776,
"openwebmath_perplexity": 7392.551180880582,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. Yes\n2. Yes",
"lm_q1_score": 0.97112909472487,... |
https://brilliant.org/discussions/thread/euclidean-algorhytm/ | # Euclidean algorithm
I found something interesting about solving this question:
If p is the number of pairs of values (x, y) that can make the equation 84x + 140y = 28 true, what is true about p?
I noticed while solving that I could simplify the equation:
84x - 140y = 28
42x – 70y = 14
21x – 35y = 7
3x – 5y = 1... | 2018-10-15T11:47:55 | {
"domain": "brilliant.org",
"url": "https://brilliant.org/discussions/thread/euclidean-algorhytm/",
"openwebmath_score": 0.9645053148269653,
"openwebmath_perplexity": 1666.9390768969245,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. Yes\n2. Yes\n\n",
"lm_q1_score": 0.9658995703612219,
"lm_q2_score": 0.91... |
https://mathhelpboards.com/threads/arc-length-question.13986/ | # Arc length question
##### Member
The length of the minor arc of a circle is 10cm, while the area of the sector AOB is 150cm2.
a) Form two equations involving r and θ, where θ is measured in radians.
b) Solve these equations simultaneously to find r and θ.
Help to solve? Cant understand the question very well.
I ... | 2021-09-26T03:42:26 | {
"domain": "mathhelpboards.com",
"url": "https://mathhelpboards.com/threads/arc-length-question.13986/",
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"lm_label": "1. YES\n2. YES\n\n",
"lm_q1_score": 0.9840936110872273,
"lm_q2_score": 0... |
https://math.stackexchange.com/questions/2456373/optimal-route-consisting-of-rowing-then-walking | # Optimal route consisting of rowing then walking
Problem
You're in a boat on point A in the water, and you need to get to point B on land. Your rowing speed is 3km/h, and your walking speed 5km/h.
See figure:
Find the route that takes the least amount of time.
My idea
I started by marking an arbitrary route:
Fr... | 2021-05-16T16:16:33 | {
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"url": "https://math.stackexchange.com/questions/2456373/optimal-route-consisting-of-rowing-then-walking",
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"openwebmath_perplexity": 372.64045876237503,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. YES\n2. YES",
"lm_q1_score": 0.9904... |
https://brilliant.org/discussions/thread/magnetic-dollars/ | # Magnetic Dollars
Imgur
Suppose that I have two urns, with one magnetic dollar in each urn. I begin randomly throwing more magnetic dollars in the general vicinity of the urns, and the coins fall in the urns by a simple rule:
Let's say that Urn A has $$x$$ coins, and Urn B has $$y$$ coins. The probability that the ... | 2018-09-26T07:53:38 | {
"domain": "brilliant.org",
"url": "https://brilliant.org/discussions/thread/magnetic-dollars/",
"openwebmath_score": 0.9101695418357849,
"openwebmath_perplexity": 965.1188540119305,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. YES\n2. YES\n\n",
"lm_q1_score": 0.9808759649262344,
"lm_q2_score": 0.901920... |
https://math.stackexchange.com/questions/2542068/asymptotic-behavior-of-x-n1-x-n-frac1x-n-space-space-space-x-0-1 | # Asymptotic behavior of $x_{n+1}=x_n+\frac{1}{x_n}, \space\space\space x_0=1$
I have defined a sequence $x_n$ as follows: $$x_{n+1}=x_n+\frac{1}{x_n}, \space\space\space x_0=1$$ After convincing myself that there is no nice closed-form formula for $x_n$, I decided to try and find an asymptotic formula for $x_n$ (unfo... | 2019-09-19T14:30:55 | {
"domain": "stackexchange.com",
"url": "https://math.stackexchange.com/questions/2542068/asymptotic-behavior-of-x-n1-x-n-frac1x-n-space-space-space-x-0-1",
"openwebmath_score": 0.9949032068252563,
"openwebmath_perplexity": 127.60192712234979,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. YES\n2. YES",
"lm_... |
http://mathhelpforum.com/discrete-math/280796-help-combinatorics-exercise.html | # Thread: Help in combinatorics exercise
1. ## Help in combinatorics exercise
Hey everyone I'm stuck in the exercise, I will be happy to work out a solution
Find how many integers - n, have the attribute:
n is divisible by 7 and is not divisible by any natural number - k that sustains:
Thanks friends.
2. ## Re: Help... | 2018-08-20T11:04:25 | {
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"lm_label": "1. YES\n2. YES",
"lm_q1_score": 0.9869795095031688,
"lm... |
http://gunb.nomen.pw/predator-prey-model-simulation-matlab.html | • Predator Prey Model Simulation Matlab
• Design, simulation and analysis in Simulink. Aggregate models consider a population as a collective group, and capture the change in the size of a population over time. The link to this assignment on github is here. ) Wilensky, U. GIBSON1*, DAVID L. I have a program called Pred... | 2020-06-04T10:21:04 | {
"domain": "nomen.pw",
"url": "http://gunb.nomen.pw/predator-prey-model-simulation-matlab.html",
"openwebmath_score": 0.4283117651939392,
"openwebmath_perplexity": 1332.7149487413285,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. Yes\n2. Yes",
"lm_q1_score": 0.9901401423688666,
"lm_q2_score": 0.893309407... |
https://math.stackexchange.com/questions/1694666/how-to-prove-the-result-of-this-definite-integral | # How to prove the result of this definite integral?
During my work I came up with this integral:
$$\mathcal{J} = \int_0^{+\infty} \frac{\sqrt{x}\ln(x)}{e^{\sqrt{x}}}\ \text{d}x$$
Mathematica has a very elegant and simple numerical result for this, which is
$$\mathcal{J} = 12 - 8\gamma$$
where $\gamma$ is the Eule... | 2019-12-10T19:09:29 | {
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"url": "https://math.stackexchange.com/questions/1694666/how-to-prove-the-result-of-this-definite-integral",
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"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. YES\n2. YES",
"lm_q1_score": 0.988... |
http://mathhelpforum.com/statistics/121412-probibality-problem-pls-help.html | # Math Help - Probibality problem, Pls help
1. ## Probibality problem, Pls help
A market research study is being conducted to determine if a product modification will be well received by the public. A total of 910 consumers are questioned regarding this product. The table below provides information regarding this sam... | 2014-04-17T10:40:53 | {
"domain": "mathhelpforum.com",
"url": "http://mathhelpforum.com/statistics/121412-probibality-problem-pls-help.html",
"openwebmath_score": 0.7383276224136353,
"openwebmath_perplexity": 699.3556623555581,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. YES\n2. YES\n\n",
"lm_q1_score": 0.9884918509356966,
"... |
http://bajecznyogrod.com.pl/canadian-dollar-afy/diagonal-matrix-and-scalar-matrix-c0406f | Work Study Job Postings, Schoko Bons Halal, Ontology Database Example, Strawberry Fruit Price In Kerala, Factory Kitchen Design, Financial Advisor Logo Images, South Block Meaning, Is Dlf Mall Noida Open Tomorrow, Foreclosures Brenham, Tx, 20 Mil Commercial Vinyl Plank, How Much Is A Car Wash At 7/11, Ryobi P2009 Trimm... | 2021-04-13T01:08:34 | {
"domain": "com.pl",
"url": "http://bajecznyogrod.com.pl/canadian-dollar-afy/diagonal-matrix-and-scalar-matrix-c0406f",
"openwebmath_score": 0.776803195476532,
"openwebmath_perplexity": 985.6655599754145,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. Yes\n2. Yes",
"lm_q1_score": 0.9777138183570424,
"lm_q... |
https://math.stackexchange.com/questions/980941/calculate-112123-cdots123-cdotsn | # Calculate $1+(1+2)+(1+2+3)+\cdots+(1+2+3+\cdots+n)$
How can I calculate $1+(1+2)+(1+2+3)+\cdots+(1+2+3+\cdots+n)$? I know that $1+2+\cdots+n=\dfrac{n+1}{2}\dot\ n$. But what should I do next?
## 8 Answers
Hint: use also that $$1^2 + 2^2 + \dots + n^2 = \frac{n(n+1)(2n+1)}6$$
$$1 + (1+2) + \dots + (1 +2+\dots +n) ... | 2019-09-21T09:45:48 | {
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"lm_label": "1. YES\n2. YES",
"lm_q1_score": 0.985271387015241,
"l... |
https://mlpro.io/problems/absolute-error/ | 6
# Absolute Error
Unsolved
###### Prob. and Stats
Difficulty: 2 | Problem written by mesakarghm
##### Problem reported in interviews at
If x is the actual value of a quantity and x0 is the predicted value, then the absolute error can be calculated using the formula:
$$\delta x = x_0 - x$$
For multiple prediction... | 2022-01-22T02:44:40 | {
"domain": "mlpro.io",
"url": "https://mlpro.io/problems/absolute-error/",
"openwebmath_score": 0.2139071822166443,
"openwebmath_perplexity": 4694.177720383252,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. YES\n2. YES",
"lm_q1_score": 0.9719924818279465,
"lm_q2_score": 0.909906997487259,
"lm_q1q2_scor... |
http://distriktslakaren.se/k552h6wj/python-modulo-negative-numbers-4d02a4 | rev 2021.1.18.38333, Stack Overflow works best with JavaScript enabled, Where developers & technologists share private knowledge with coworkers, Programming & related technical career opportunities, Recruit tech talent & build your employer brand, Reach developers & technologists worldwide, Surprisingly, Python's modul... | 2021-04-17T20:25:53 | {
"domain": "distriktslakaren.se",
"url": "http://distriktslakaren.se/k552h6wj/python-modulo-negative-numbers-4d02a4",
"openwebmath_score": 0.5023279190063477,
"openwebmath_perplexity": 1372.441624422156,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. YES\n2. YES",
"lm_q1_score": 0.9653811611608242,
"lm_q2... |
https://math.stackexchange.com/questions/1918355/is-cos-alpha-x-cosx-periodic | # Is $\cos(\alpha x + \cos(x))$ periodic?
Consider the function $f: \mathbb{R} \to [-1, 1]$ defined as
$$f(x) = \cos(\alpha x + \cos(x))$$
What conditions must be placed on $\alpha \in \mathbb{R}$ such that the function $f$ is periodic?
First of all, I tried plotting some values on Wolfram|Alpha, and for all the va... | 2019-07-17T15:19:37 | {
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"url": "https://math.stackexchange.com/questions/1918355/is-cos-alpha-x-cosx-periodic",
"openwebmath_score": 0.9016054272651672,
"openwebmath_perplexity": 185.1782319914737,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. YES\n2. YES",
"lm_q1_score": 0.9835969641180276,
"lm_... |
http://mathhelpforum.com/math-topics/162319-measure-angle-formed-minute-hour-hands-print.html | # Measure of angle formed by minute and hour hands
• Nov 6th 2010, 03:31 PM
Hellbent
Measure of angle formed by minute and hour hands
Hi,
What is the measure of the angle formed by the minute and hour hands of a clock at 1:50?
(A) $90^o$
(B) $95^o$
(C) $105^o$
(D) $115^o$
(E) $120^o$
My guess was $90^o$ after menta... | 2017-08-22T06:32:57 | {
"domain": "mathhelpforum.com",
"url": "http://mathhelpforum.com/math-topics/162319-measure-angle-formed-minute-hour-hands-print.html",
"openwebmath_score": 0.6861971616744995,
"openwebmath_perplexity": 584.658362151656,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. YES\n2. YES",
"lm_q1_score": 0.979035761... |
https://mathoverflow.net/questions/71736/number-of-closed-walks-on-an-n-cube | # Number of closed walks on an $n$-cube
Is there a known formula for the number of closed walks of length (exactly) $r$ on the $n$-cube? If not, what are the best known upper and lower bounds?
Note: the walk can repeat vertices.
Yes (assuming a closed walk can repeat vertices). For any finite graph $G$ with adjacen... | 2021-11-27T21:19:42 | {
"domain": "mathoverflow.net",
"url": "https://mathoverflow.net/questions/71736/number-of-closed-walks-on-an-n-cube",
"openwebmath_score": 0.9175300598144531,
"openwebmath_perplexity": 120.13085606220396,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. YES\n2. YES",
"lm_q1_score": 0.9883127399388855,
"lm_q... |
https://mathhelpboards.com/threads/eigenvalues.1117/ | # [SOLVED]Eigenvalues
#### Sudharaka
##### Well-known member
MHB Math Helper
saravananbs's question from Math Help Forum,
if A and B are similar matrices then the eigenvalues are same. is the converse is true? why?
thank u
Hi saravananbs,
No. The converse is not true in general. Take the two matrices, $$A=\begin{pm... | 2021-06-20T19:05:13 | {
"domain": "mathhelpboards.com",
"url": "https://mathhelpboards.com/threads/eigenvalues.1117/",
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"openwebmath_perplexity": 340.24618773285397,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. YES\n2. YES",
"lm_q1_score": 0.98504291340685,
"lm_q2_score": 0.897695292107... |
https://math.stackexchange.com/questions/2218855/how-to-find-the-distance-between-two-non-parallel-lines | # How to find the distance between two non-parallel lines?
I am tasked to find the distance between these two lines.
$p1 ... x = 1 + t, y = -1 + 2t, z = t$
$p2 ... x = 1 - t; y = 3 - t; z = t$
Those two lines are nonparallel and they do not intersect (I checked that).
Using the vector product I computed the normal... | 2019-04-24T13:51:32 | {
"domain": "stackexchange.com",
"url": "https://math.stackexchange.com/questions/2218855/how-to-find-the-distance-between-two-non-parallel-lines",
"openwebmath_score": 0.7590815424919128,
"openwebmath_perplexity": 261.0994649340746,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. YES\n2. YES",
"lm_q1_score":... |
https://gmatclub.com/forum/four-integers-are-randomly-selected-from-the-set-238726.html | GMAT Question of the Day - Daily to your Mailbox; hard ones only
It is currently 25 Jun 2019, 13:01
### GMAT Club Daily Prep
#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.
Customize... | 2019-06-25T20:01:57 | {
"domain": "gmatclub.com",
"url": "https://gmatclub.com/forum/four-integers-are-randomly-selected-from-the-set-238726.html",
"openwebmath_score": 0.7639310956001282,
"openwebmath_perplexity": 2586.3598944138034,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. Yes\n2. Yes",
"lm_q1_score": 0.9759464415087019,
... |
http://mathhelpforum.com/calculus/77945-freaky-series-using-limit-comparison-test.html | # Math Help - Freaky series using limit comparison test!
1. ## Freaky series using limit comparison test!
How in the world do you determine the following series' convergence/divergence specifically using the limit comparison test?
from n=1 to n=infinity
ln (2n+1)/ (n^2 + 2n)
I'm bamboozled and befuddled!
2. Origi... | 2015-01-30T07:12:07 | {
"domain": "mathhelpforum.com",
"url": "http://mathhelpforum.com/calculus/77945-freaky-series-using-limit-comparison-test.html",
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"openwebmath_perplexity": 391.8554818226111,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. YES\n2. YES",
"lm_q1_score": 0.9773708006261042,... |
https://math.stackexchange.com/questions/2863510/between-any-two-powers-of-5-there-are-either-two-or-three-powers-of-2 | # Between any two powers of $5$ there are either two or three powers of $2$
Is this statement true?
Between any two consecutive powers of $5$, there are either two or three powers of $2$.
I can see that this statement is true for cases like $$5^1 < 2^3 < 2^4 < 5^2$$ or $$5^3 < 2^7 < 2^8 < 2^9 < 5^4$$
But I am havin... | 2019-11-13T01:46:35 | {
"domain": "stackexchange.com",
"url": "https://math.stackexchange.com/questions/2863510/between-any-two-powers-of-5-there-are-either-two-or-three-powers-of-2",
"openwebmath_score": 0.974236249923706,
"openwebmath_perplexity": 84.0521815525579,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. YES\n2. YES",
"l... |
http://mathrefresher.blogspot.com/2007/04/properties-of-matrix-multiplication.html | ## Tuesday, April 17, 2007
### Properties of Matrix Multiplication
Multiplication can only occur between matrices A and B if the number of columns in A match the number of rows in B. This presents the very important idea that while multiplication of A with B might be a perfectly good operation; this does not guarante... | 2018-05-25T20:19:41 | {
"domain": "blogspot.com",
"url": "http://mathrefresher.blogspot.com/2007/04/properties-of-matrix-multiplication.html",
"openwebmath_score": 0.8964815735816956,
"openwebmath_perplexity": 4432.601708256597,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. YES\n2. YES",
"lm_q1_score": 0.9930961615201183,
"lm_... |
https://math.stackexchange.com/questions/931839/expected-number-of-output-letters-to-get-desired-word | # Expected number of output letters to get desired word
I am using a letter set of four letters, say {A,B,C,D}, which is used to output a random string of letters. I want to calculate the expected output length until the word ABCD is obtained; that is, the letters A B C D appearing consecutively in that order.
I have... | 2019-07-16T06:03:02 | {
"domain": "stackexchange.com",
"url": "https://math.stackexchange.com/questions/931839/expected-number-of-output-letters-to-get-desired-word",
"openwebmath_score": 0.7974311709403992,
"openwebmath_perplexity": 788.5972785961158,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. YES\n2. YES",
"lm_q1_score": 0.... |
https://math.stackexchange.com/questions/1999358/is-there-a-closed-form-expression-for-these-combinatorial-sums | # Is there a closed form expression for these combinatorial sums?
I needed to compute this sum: $$\sum_{i=0}^n\binom{n}{i}i^2$$ I don't want any proofs or formulae, but just a yes/no answer. Is there a closed form expression for this sum?
Just to share, I was able to find a closed form expression for this sum: $$\sum... | 2020-02-24T02:10:04 | {
"domain": "stackexchange.com",
"url": "https://math.stackexchange.com/questions/1999358/is-there-a-closed-form-expression-for-these-combinatorial-sums",
"openwebmath_score": 0.8920262455940247,
"openwebmath_perplexity": 358.2792575451208,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. YES\n2. YES",
"lm_q1_... |
https://math.stackexchange.com/questions/3185610/very-indeterminate-form-lim-x-to-infty-left-sqrtx22x3-sqrtx23 | # Very indeterminate form: $\lim_{x \to \infty} \left(\sqrt{x^2+2x+3} -\sqrt{x^2+3}\right)^x \longrightarrow (\infty-\infty)^{\infty}$
Here is problem:
$$\lim_{x \to \infty} \left(\sqrt{x^2+2x+3} -\sqrt{x^2+3}\right)^x$$
The solution I presented in the picture below was made by a Mathematics Teacher
I tried to solv... | 2020-12-03T05:27:22 | {
"domain": "stackexchange.com",
"url": "https://math.stackexchange.com/questions/3185610/very-indeterminate-form-lim-x-to-infty-left-sqrtx22x3-sqrtx23",
"openwebmath_score": 0.9431429505348206,
"openwebmath_perplexity": 575.1508586668708,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. YES\n2. YES",
"lm_q1_s... |
https://nndcgroup.com.ng/blog/1k4v2s2.php?c0ec0e=latex-math-symbols | Below is the comprehensive list of Greek symbols/characters/alphabets generally used for preparing a document using LaTex. Note that The following table provides a comprehensive list/guide of mathematical Integral symbols using an appropriate example. command to add a little whitespace between them: The choices availab... | 2021-03-04T08:46:10 | {
"domain": "com.ng",
"url": "https://nndcgroup.com.ng/blog/1k4v2s2.php?c0ec0e=latex-math-symbols",
"openwebmath_score": 0.7525127530097961,
"openwebmath_perplexity": 13979.083181375348,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. YES\n2. YES",
"lm_q1_score": 0.9648551566309688,
"lm_q2_score": 0.9161096... |
http://tex.stackexchange.com/questions/53702/wrapping-text-in-enumeration-environment-around-a-table?answertab=active | # Wrapping text in enumeration environment around a table
I would like to wrap the text in an enumerate environment around a table, this is my actual situation (sorry for including so much code, but I wanted to give a precise idea of the number of lines in the enumerate environment):
\subsection{Given the following d... | 2014-10-31T05:54:20 | {
"domain": "stackexchange.com",
"url": "http://tex.stackexchange.com/questions/53702/wrapping-text-in-enumeration-environment-around-a-table?answertab=active",
"openwebmath_score": 1.0000078678131104,
"openwebmath_perplexity": 5530.152522412758,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. YES\n2. YES",
"... |
https://www.mathworks.com/help/symbolic/piecewise.html | # piecewise
Conditionally defined expression or function
## Description
example
pw = piecewise(cond1,val1,cond2,val2,...) returns the piecewise expression or function pw whose value is val1 when condition cond1 is true, is val2 when cond2 is true, and so on. If no condition is true, the value of pw is NaN.
example... | 2022-05-17T22:05:37 | {
"domain": "mathworks.com",
"url": "https://www.mathworks.com/help/symbolic/piecewise.html",
"openwebmath_score": 0.7444276213645935,
"openwebmath_perplexity": 3955.442450780083,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. YES\n2. YES",
"lm_q1_score": 0.9755769049752756,
"lm_q2_score": 0.90598981530676... |
https://math.stackexchange.com/questions/2812614/question-on-probability-of-winning-a-game-of-dice/2812717 | # question on probability of winning a game of dice
QUESTION:
A and B are playing a game by alternately rolling a die, with A starting first. Each player’s score is the number obtained on his last roll. The game ends when the sum of scores of the two players is 7, and the last player to roll the die wins. What is the... | 2021-10-15T21:36:44 | {
"domain": "stackexchange.com",
"url": "https://math.stackexchange.com/questions/2812614/question-on-probability-of-winning-a-game-of-dice/2812717",
"openwebmath_score": 0.7995924949645996,
"openwebmath_perplexity": 127.69045875533342,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. YES\n2. YES",
"lm_q1_scor... |
https://www.exaton.hu/qn573/c5fe24-tangent-of-a-circle-example | This point is called the point of tangency. Rules for Dealing with Chords, Secants, Tangents in Circles This page created by Regents reviews three rules that are used when working with secants, and tangent lines of circles. AB 2 = DB * CB ………… This gives the formula for the tangent. Solution This problem is similar to ... | 2021-03-05T04:04:23 | {
"domain": "exaton.hu",
"url": "https://www.exaton.hu/qn573/c5fe24-tangent-of-a-circle-example",
"openwebmath_score": 0.4151161313056946,
"openwebmath_perplexity": 358.98978621027345,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. Yes\n2. Yes",
"lm_q1_score": 0.9861513881564148,
"lm_q2_score": 0.896251372... |
https://www.lil-help.com/questions/7852/in-the-game-of-two-finger-morra-2-players-show-1-or-2-fingers-and-simultaneously-guess-the-number-of-fingers-their-opponent-will-show | In the game of Two-Finger Morra, 2 players show 1 or 2 fingers and simultaneously guess the number of fingers their opponent will show
# In the game of Two-Finger Morra, 2 players show 1 or 2 fingers and simultaneously guess the number of fingers their opponent will show
A
45 points
In the game of Two-Finger Morra, ... | 2018-11-14T01:36:12 | {
"domain": "lil-help.com",
"url": "https://www.lil-help.com/questions/7852/in-the-game-of-two-finger-morra-2-players-show-1-or-2-fingers-and-simultaneously-guess-the-number-of-fingers-their-opponent-will-show",
"openwebmath_score": 0.7249987721443176,
"openwebmath_perplexity": 255.606206917506,
"lm_name": "Q... |
https://wild.maths.org/comment/1010 | Pairwise Puzzler
You may wish to take a look at Pairwise Adding before trying this problem
Alison reckons that if Charlie gives her the sums of all the pairs of numbers from any set of five numbers, she'll be able to work out the original five numbers.
Charlie gives her this set of pair sums: $0$, $2$, $4$, $4$, $6$... | 2022-12-10T06:06:29 | {
"domain": "maths.org",
"url": "https://wild.maths.org/comment/1010",
"openwebmath_score": 0.6365929245948792,
"openwebmath_perplexity": 344.7798361841747,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. YES\n2. YES",
"lm_q1_score": 0.9893474879039229,
"lm_q2_score": 0.8933094110250331,
"lm_q1q2_score": ... |
https://math.stackexchange.com/questions/1056982/probability-a-is-before-b-when-the-26-letters-are-arranged-randomly | # Probability $A$ is before $B$ when the 26 letters are arranged randomly
The 26 letters A, B, ... , Z are arrange in a random order. [Equivalently, the letters are selected sequentially at random without replacement.]
a) What is the probability that A comes before B in the random order?
b) What is the probability t... | 2021-04-13T20:54:11 | {
"domain": "stackexchange.com",
"url": "https://math.stackexchange.com/questions/1056982/probability-a-is-before-b-when-the-26-letters-are-arranged-randomly",
"openwebmath_score": 0.8802695870399475,
"openwebmath_perplexity": 300.8157627126416,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. YES\n2. YES",
"l... |
https://stats.stackexchange.com/questions/50274/probability-of-a-pair-in-cards | # probability of a pair in cards
I have a simple problem involving probability of drawing at least 1 pair of cards in a four card hand. I am not getting the right answer but I dont understand the flaw in my logic. Can anyone explain to me why my approach is wrong?
The problem:
Bill has a small deck of 12 playing car... | 2021-03-07T22:06:27 | {
"domain": "stackexchange.com",
"url": "https://stats.stackexchange.com/questions/50274/probability-of-a-pair-in-cards",
"openwebmath_score": 0.6800057291984558,
"openwebmath_perplexity": 241.87707813867704,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. YES\n2. YES",
"lm_q1_score": 0.9783846684978779,
"l... |
https://www.physicsforums.com/threads/questions-about-linear-transformations.887744/ | # I Questions about linear transformations
1. Oct 3, 2016
### Chan Pok Fung
We learnt that the condition of a linear transformation is
1. T(v+w) = T(v)+T(w)
2. T(kv) = kT(v)
I am wondering if there is any transformation which only fulfil either one and fails another condition. As obviously, 1 implies 2 for rational... | 2017-11-21T14:27:29 | {
"domain": "physicsforums.com",
"url": "https://www.physicsforums.com/threads/questions-about-linear-transformations.887744/",
"openwebmath_score": 0.8395922780036926,
"openwebmath_perplexity": 1244.7749528275344,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. YES\n2. YES",
"lm_q1_score": 0.9783846634557752... |
https://math.stackexchange.com/questions/2668314/multiplication-of-moduli-in-modular-congruences | # Multiplication of Moduli in Modular Congruences
Lately it's come up in my discrete mathematics class that proving things for smaller congruences, namely those where the modulus is a prime is much easier than attempting to do so for larger congruences.
For example, one such problem was to prove that $a^5 \equiv a \p... | 2019-09-16T20:46:06 | {
"domain": "stackexchange.com",
"url": "https://math.stackexchange.com/questions/2668314/multiplication-of-moduli-in-modular-congruences",
"openwebmath_score": 0.9810587167739868,
"openwebmath_perplexity": 147.5086358032251,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. YES\n2. YES",
"lm_q1_score": 0.98756... |
https://mathhelpboards.com/threads/combinatorics-challenge.6224/ | # Combinatorics Challenge
#### anemone
##### MHB POTW Director
Staff member
For $n=1,2,...,$ set $$\displaystyle S_n=\sum_{k=0}^{3n} {3n\choose k}$$ and $$\displaystyle T_n=\sum_{k=0}^{n} {3n\choose 3k}$$.
Prove that $|S_n-3T_n|=2$.
#### MarkFL
Staff member
My solution:
For the first sum, we may simply apply the ... | 2021-10-16T15:16:12 | {
"domain": "mathhelpboards.com",
"url": "https://mathhelpboards.com/threads/combinatorics-challenge.6224/",
"openwebmath_score": 0.9442697167396545,
"openwebmath_perplexity": 1185.4687731455952,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. YES\n2. YES",
"lm_q1_score": 0.9925393565360598,
"lm_q2_score": ... |
https://math.stackexchange.com/questions/2890157/what-is-the-difference-between-lim-h-to0-frac0h-and-lim-h-to-infty | What is the difference between $\lim_{h\to0}\frac{0}{h}$ and $\lim_{h\to\infty}\frac{0}{h}$?
What is the difference (if any) between-
$$\lim_{h\to0}\frac{0}{h} \text{ and } \lim_{h\to\infty}\frac{0}{h}$$
I argue that both must be $=0$ since the numerator is exactly $0$. But one fellow refuses to agree and argues tha... | 2019-07-18T17:41:44 | {
"domain": "stackexchange.com",
"url": "https://math.stackexchange.com/questions/2890157/what-is-the-difference-between-lim-h-to0-frac0h-and-lim-h-to-infty",
"openwebmath_score": 0.8766734004020691,
"openwebmath_perplexity": 328.29831887739505,
"lm_name": "Qwen/Qwen-72B",
"lm_label": "1. YES\n2. YES",
"l... |
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