text stringlengths 1 2.12k | source dict |
|---|---|
PerformSearch = Compile[
{
{startValue, _Integer},
{increment, _Integer}
},
NestWhile[
# + increment &,
startValue,
IntegerDigits[#^2][[-1 ;; 1 ;; -2]] =!= {9, 8, 7, 6, 5, 4, 3, 2, 1} &
]
]
Let's check if this did compile ok:
PerformSearch // CompilePrint
(...)
1 I4 = I0
2 I3 = I4
3 I7 = Square[ I3... | {
"domain": "stackexchange.com",
"id": null,
"lm_label": "1. YES\n2. YES",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9559813501370535,
"lm_q1q2_score": 0.8481510567539349,
"lm_q2_score": 0.88720460564669,
"openwebmath_perplexity": 6092.915169769021,
"openwebmath_score": 0.3502996265888214,
"tags"... |
As an aside, note that max^2 is below $MaxMachineInteger on 64-bit systems. But on 32-bit it isn't, which causes PerformSearch to switch back to the uncompiled code. Keeping Mark McClure's comment in mind, we'll cheat a bit and start from the maximum to find immediately: result = PerformSearch[max, -1] 138901917 How mu... | {
"domain": "stackexchange.com",
"id": null,
"lm_label": "1. YES\n2. YES",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9559813501370535,
"lm_q1q2_score": 0.8481510567539349,
"lm_q2_score": 0.88720460564669,
"openwebmath_perplexity": 6092.915169769021,
"openwebmath_score": 0.3502996265888214,
"tags"... |
& /@ Range[Length @ First @ digitSequences - 1, 0, -1] }, Select[ digitSequences, And[ # <= maxRoot, IntegerDigits[#^power, 10, numDigits][[positions]] == compareDigits ] & @ ( powersOfTen.# ) & ] ] ]; InsertNewDigits = With[ { range = List /@ Range[0, 9] }, Compile[ { {digitSequences, _Integer, 2} }, Outer[#1 ~Join~ #... | {
"domain": "stackexchange.com",
"id": null,
"lm_label": "1. YES\n2. YES",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9559813501370535,
"lm_q1q2_score": 0.8481510567539349,
"lm_q2_score": 0.88720460564669,
"openwebmath_perplexity": 6092.915169769021,
"openwebmath_score": 0.3502996265888214,
"tags"... |
7362534133201} And finally, are there squares of the form 1_1_(...)_1_1? FindIntegerRoots @ Riffle[ConstantArray[1, #], _] & /@ Range[2, 9] {{11}, {119, 131}, {}, {}, {110369}, {}, {10065739}, {}} Flatten[%]^2 {121, 14161, 17161, 12181316161, 101319101616121} It seems there are many nice squares. If you happen to find ... | {
"domain": "stackexchange.com",
"id": null,
"lm_label": "1. YES\n2. YES",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9559813501370535,
"lm_q1q2_score": 0.8481510567539349,
"lm_q2_score": 0.88720460564669,
"openwebmath_perplexity": 6092.915169769021,
"openwebmath_score": 0.3502996265888214,
"tags"... |
That seems to be the reason, BTW the $MaxMachineInteger in my v8 (Win 64 bit) is the same as that in 32 bit, not sure if it's just the nature of v8… – xzczd Sep 4 '14 at 1:56 Is using Big O notation in "Roughly O(10^4) times faster" a correct statement? It is surely 10^4 times faster in this example, but what exactly d... | {
"domain": "stackexchange.com",
"id": null,
"lm_label": "1. YES\n2. YES",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9559813501370535,
"lm_q1q2_score": 0.8481510567539349,
"lm_q2_score": 0.88720460564669,
"openwebmath_perplexity": 6092.915169769021,
"openwebmath_score": 0.3502996265888214,
"tags"... |
whole set of numbers to check by adding all the possible "heads" between the max and min: fullSet = Total[Tuples[{Range[101, 138] 10^6, Flatten@set}], {2}]; And then a quick search gets our number: Cases[IntegerDigits[fullSet^2], {1, _, 2, _, 3, _, 4, _, 5, _, 6, _, 7, _, 8, _, 9}] (*{{1, 9, 2, 9, 3, 7, 4, 2, 5, 4, 6, ... | {
"domain": "stackexchange.com",
"id": null,
"lm_label": "1. YES\n2. YES",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9559813501370535,
"lm_q1q2_score": 0.8481510567539349,
"lm_q2_score": 0.88720460564669,
"openwebmath_perplexity": 6092.915169769021,
"openwebmath_score": 0.3502996265888214,
"tags"... |
is unique, according to the problem statement, so a simple, direct use of ParallelSum with Boole is possible. Avoid MatchQ as @Pickett suggests. AbsoluteTiming[ ParallelSum[ n*Boole[IntegerDigits[n^2][[;; ;; 2]] == {1,2,3,4,5,6,7,8,9,0}], {n, 1010101030, 1390000000, 100}] + ParallelSum[ n*Boole[IntegerDigits[n^2][[;; ;... | {
"domain": "stackexchange.com",
"id": null,
"lm_label": "1. YES\n2. YES",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9559813501370535,
"lm_q1q2_score": 0.8481510567539349,
"lm_q2_score": 0.88720460564669,
"openwebmath_perplexity": 6092.915169769021,
"openwebmath_score": 0.3502996265888214,
"tags"... |
AbsoluteTiming[
ParallelSum[
(100000 j + i + 2500 k) *
Boole[IntegerDigits[(100000j+i+2500k)^2][[;; ;; 2]] == {1,2,3,4,5,6,7,8,9,0}],
{j, 10101, 13890},
{k, 0, 35},
{i, {10530, 11970, 10430, 12070, 10830, 11670}}]]
(* {1.002618, 1389019170} *)
But nothing beats counting down from the maximum as @MarkMcClure comments.... | {
"domain": "stackexchange.com",
"id": null,
"lm_label": "1. YES\n2. YES",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9559813501370535,
"lm_q1q2_score": 0.8481510567539349,
"lm_q2_score": 0.88720460564669,
"openwebmath_perplexity": 6092.915169769021,
"openwebmath_score": 0.3502996265888214,
"tags"... |
# Find the value of $ab+ 2cb+\sqrt3 ac$?
Three positive real numbers $a,b,c$ satisfy the equations $a^2+\sqrt3 ab+b^2=25$, $b^2+c^2=9$ and $a^2+ac+c^2=16$ .Then find the value of $ab+ 2cb+\sqrt3 ac$?
Is there some way to find the desired value without actually finding values of $a,b,c$ or any other smart method to fi... | {
"domain": "stackexchange.com",
"id": null,
"lm_label": "1. YES\n2. YES",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9865717424942964,
"lm_q1q2_score": 0.8481199625261852,
"lm_q2_score": 0.8596637487122112,
"openwebmath_perplexity": 411.9212113645169,
"openwebmath_score": 0.8320333957672119,
"tag... |
Here is a geometrical solution:
by rewriting the equations as
\left\{ \begin{aligned} 5^2&=a^2+b^2-2ab\cos\frac{5\pi}{6}\\ 3^2&=b^2+c^2-2bc\cos\frac{\pi}{2}\\ 4^2&=c^2+a^2-2ca\cos\frac{2\pi}{3} \end{aligned} \right.
and evaluating
$$4\left(\frac{1}{2}ab\sin\frac{5\pi}{6}+\frac{1}{2}bc\sin\frac{\pi}{2}+\frac{1}{2}ca... | {
"domain": "stackexchange.com",
"id": null,
"lm_label": "1. YES\n2. YES",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9865717424942964,
"lm_q1q2_score": 0.8481199625261852,
"lm_q2_score": 0.8596637487122112,
"openwebmath_perplexity": 411.9212113645169,
"openwebmath_score": 0.8320333957672119,
"tag... |
$$81 - 66b^2 + b^4 + 41\sqrt{3}bc - \sqrt{3}b^3c - 7c^2 + 2b^2c^2 - \sqrt{3}bc^3 + c^4=0 \ \ \ (4)$$
Now, we use constraint (2) meaning that point $(b/3,c/3)$ is on the unit circle, a constraint that we can translate into the following one (classical parameterization of the unit circle https://en.wikipedia.org/wiki/Ta... | {
"domain": "stackexchange.com",
"id": null,
"lm_label": "1. YES\n2. YES",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9865717424942964,
"lm_q1q2_score": 0.8481199625261852,
"lm_q2_score": 0.8596637487122112,
"openwebmath_perplexity": 411.9212113645169,
"openwebmath_score": 0.8320333957672119,
"tag... |
# Finding the $LU$ factorization of the matrix
Find the $LU$ factorization of the matrix: $$\begin{bmatrix} 1 & 1 & 1 \\ 3 & 5 & 6 \\ -2 & 2 & 7 \end{bmatrix}$$
I am aware that I need to find $L=\begin{bmatrix} 1 & 0 & 0 \\ * & 1 & 0 \\ * & * & 1 \end{bmatrix}$ and $U=\begin{bmatrix} 1 & * & * \\ 0 & 1 & * \\ 0 & 0 &... | {
"domain": "stackexchange.com",
"id": null,
"lm_label": "1. YES\n2. YES",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9865717464424892,
"lm_q1q2_score": 0.848119962373172,
"lm_q2_score": 0.8596637451167997,
"openwebmath_perplexity": 88.00559780453351,
"openwebmath_score": 0.9997020959854126,
"tags... |
For doing LU decomposition, you need to do Gaussian elimination. Here I'll just help you with the procedure, but if you want to understand why I recommend you to see this pdf http://www.math.iit.edu/~fass/477577_Chapter_7.pdf. Lets apply Gaussian elimination to A \begin{equation*} A = \left[ \begin{matrix} 1 & 1 & 1\\ ... | {
"domain": "stackexchange.com",
"id": null,
"lm_label": "1. YES\n2. YES",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9865717464424892,
"lm_q1q2_score": 0.848119962373172,
"lm_q2_score": 0.8596637451167997,
"openwebmath_perplexity": 88.00559780453351,
"openwebmath_score": 0.9997020959854126,
"tags... |
Thus the Gaussian elimination runs as \begin{align} \begin{bmatrix} 1 & 1 & 1 \\ 3 & 5 & 6 \\ -2 & 2 & 7 \end{bmatrix} &\xrightarrow{\begin{gathered} E_{31}(2) \\ E_{21}(-3) \end{gathered}} \begin{bmatrix} 1 & 1 & 1 \\ 0 & 2 & 3 \\ 0 & 4 & 9 \end{bmatrix} \\[6px] &\xrightarrow{E_{32}(-2)} \begin{bmatrix} 1 & 1 & 1 \\ 0... | {
"domain": "stackexchange.com",
"id": null,
"lm_label": "1. YES\n2. YES",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9865717464424892,
"lm_q1q2_score": 0.848119962373172,
"lm_q2_score": 0.8596637451167997,
"openwebmath_perplexity": 88.00559780453351,
"openwebmath_score": 0.9997020959854126,
"tags... |
Suppose that
$$A = \begin{bmatrix} 1 & 1 & 1 \\ 3 & 5 & 6 \\ -2 & 2 & 7 \end{bmatrix}$$ $$A = LU$$
$$U =A, L=I$$ $$k=1,m=3,j=2$$ $$\ell_{21} = \frac{u_{21}}{u_{11}} = \frac{a_{21}}{a_{11}} = 3$$ $$u_{2,1:3} = u_{2,1:3} - 3 \cdot u_{1,1:3}$$ Then we're going to subtract 3 times the 1st row from the 2nd row $$\begin{bm... | {
"domain": "stackexchange.com",
"id": null,
"lm_label": "1. YES\n2. YES",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9865717464424892,
"lm_q1q2_score": 0.848119962373172,
"lm_q2_score": 0.8596637451167997,
"openwebmath_perplexity": 88.00559780453351,
"openwebmath_score": 0.9997020959854126,
"tags... |
# A dice is rolled until a $6$ occurs. What is the probability that the sum including the $6$ is even?
A game is played where a standard six sided dice is rolled until a $6$ is rolled, and the sum of all of the rolls up to and including the $6$ is taken. What is the probability that this sum is even?
I know that this... | {
"domain": "stackexchange.com",
"id": null,
"lm_label": "1. YES\n2. YES",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9822876997410348,
"lm_q1q2_score": 0.8480989637160845,
"lm_q2_score": 0.8633916152464017,
"openwebmath_perplexity": 497.60098730199024,
"openwebmath_score": 0.8475463390350342,
"ta... |
Thus $$p = \frac{1}{6}+ \frac{1}{3}p+\frac{1}{2}(1-p)$$ which simplifies to $p=\frac{4}{7}$.
• Highly instructive and pedagogically valuable. I would appreciate to see a booklet with many examples presented this way. (+1) – Markus Scheuer Jul 25 '17 at 6:32
• @MarkusScheuer: This is a standard technique, though one ha... | {
"domain": "stackexchange.com",
"id": null,
"lm_label": "1. YES\n2. YES",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9822876997410348,
"lm_q1q2_score": 0.8480989637160845,
"lm_q2_score": 0.8633916152464017,
"openwebmath_perplexity": 497.60098730199024,
"openwebmath_score": 0.8475463390350342,
"ta... |
Let $p$ be the probability that the sum of the die until(and including) the first six is even.
Let $R_1$ be the roll of the first die. So partitioning on this roll, and noticing the recurance:
$$p= \underline\qquad\,\mathsf P(R_1\in\{\underline\qquad\})+\underline\qquad\,\mathsf P(R_1\in\{\underline\qquad\})+\underli... | {
"domain": "stackexchange.com",
"id": null,
"lm_label": "1. YES\n2. YES",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9822876997410348,
"lm_q1q2_score": 0.8480989637160845,
"lm_q2_score": 0.8633916152464017,
"openwebmath_perplexity": 497.60098730199024,
"openwebmath_score": 0.8475463390350342,
"ta... |
We thus get for the total probability
$$\frac{1}{12} \sum_{m\ge 1} \left(\frac{5}{6}\right)^{m-1} + \frac{1}{12} \sum_{m\ge 1} \left(-\frac{1}{6}\right)^{m-1} \\ = \frac{1}{12} \left(\frac{1}{1-5/6} + \frac{1}{1+1/6}\right) = \frac{4}{7}.$$
• Very nice! (+1) – Markus Scheuer Jul 26 '17 at 21:10
The probability of an... | {
"domain": "stackexchange.com",
"id": null,
"lm_label": "1. YES\n2. YES",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9822876997410348,
"lm_q1q2_score": 0.8480989637160845,
"lm_q2_score": 0.8633916152464017,
"openwebmath_perplexity": 497.60098730199024,
"openwebmath_score": 0.8475463390350342,
"ta... |
## FANDOM
406 Pages
Two matrices can be added only if they have the same dimensions. The result will be a matrix of the same dimensions. To perform the addition, numbers in matching postions in the input matrices are added and the result is placed in the same position in the output matrix. Java Codes
#### Example: A... | {
"domain": "wikia.com",
"id": null,
"lm_label": "1. YES\n2. YES",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9822877023336243,
"lm_q1q2_score": 0.848098962501684,
"lm_q2_score": 0.8633916117313211,
"openwebmath_perplexity": 13615.778852330634,
"openwebmath_score": 0.5465948581695557,
"tags": null... |
### General Algorithm Edit
Here's a general algorithm for adding matrices:
1. DONT Check the sizes of two matrices $\mathbf{A}$ (m×n) and $\mathbf{B}$ (t×u): if m = t and n = u then we can add them o
2. therwise we just can't do it.
3. If they can be added, then create a new square matrix of size m×n.
4. For each ele... | {
"domain": "wikia.com",
"id": null,
"lm_label": "1. YES\n2. YES",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9822877023336243,
"lm_q1q2_score": 0.848098962501684,
"lm_q2_score": 0.8633916117313211,
"openwebmath_perplexity": 13615.778852330634,
"openwebmath_score": 0.5465948581695557,
"tags": null... |
Dim a = aRows.MoveNext
Dim b = bRows.MoveNext
Do While a Or b
If a <> b Then Throw New ArgumentException
Dim aCols = aRows.Current.GetEnumerator
Dim bCols = bRows.Current.GetEnumerator
Dim resultRow As New List(Of Integer)
Dim a2 = aCols.MoveNext
Dim b2 = bCols.MoveNext
Do While a2 Or b2
If a2 <> b2 Then Throw New Argu... | {
"domain": "wikia.com",
"id": null,
"lm_label": "1. YES\n2. YES",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9822877023336243,
"lm_q1q2_score": 0.848098962501684,
"lm_q2_score": 0.8633916117313211,
"openwebmath_perplexity": 13615.778852330634,
"openwebmath_score": 0.5465948581695557,
"tags": null... |
typedef struct
{
int rows;
int columns;
int *data;
} t_matrix;
#define NEW_MATRIX(m,r,c) (m)=malloc(sizeof(t_matrix)); (m)->rows=(r);(m)->columns=(c);(m)->data=malloc(sizeof(int)*(r)*(c));
#define VALUE_at(m, r, c) (m)->data[c*(m)->rows + r]
#define FREE(x) { free(x); (x)= NULL; }
#define FREE_MATRIX(m) FREE((m)->data... | {
"domain": "wikia.com",
"id": null,
"lm_label": "1. YES\n2. YES",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9822877023336243,
"lm_q1q2_score": 0.848098962501684,
"lm_q2_score": 0.8633916117313211,
"openwebmath_perplexity": 13615.778852330634,
"openwebmath_score": 0.5465948581695557,
"tags": null... |
# Plot Arg[z] in three dimensions
I would like to plot the function Arg[z] for a complex number $$z$$ in three-dimensions: I would like to obtain it as a surface over the complex plane, as in the "3D plot" section of this page:
But I would also like to be able to modify the range and the colors. The function only ass... | {
"domain": "stackexchange.com",
"id": null,
"lm_label": "1. YES\n2. YES",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9822877012965886,
"lm_q1q2_score": 0.8480989616063161,
"lm_q2_score": 0.8633916117313211,
"openwebmath_perplexity": 442.6628333364799,
"openwebmath_score": 0.4216979444026947,
"tag... |
# Questions about operator norm on [0,1]
I am struggling with the following question:
Consider the space $$V$$ of continuous functions on [0,1] with the 2-norm $$‖f‖_2^2$$=$$∫_0^1|f|^2$$. $$V$$ is an incomplete normed linear space. For a continuous function φ on [0,1], define a linear map $$M_φ:V⟶V$$ by $$M_φ f=φf$$.... | {
"domain": "stackexchange.com",
"id": null,
"lm_label": "1. YES\n2. YES",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9822877044076955,
"lm_q1q2_score": 0.848098960839599,
"lm_q2_score": 0.8633916082162402,
"openwebmath_perplexity": 193.65737474380487,
"openwebmath_score": 0.9969584345817566,
"tag... |
Since $$\lvert \varphi \rvert$$ is continuous, it achieves its maximum somewhere on $$[0,1]$$; say the maximum occurs at $$x_0$$ so that $$\|\varphi\|_\infty = \lvert \varphi(x_0)\rvert$$. Define $$f_n:[0,1]\to [0,\infty)$$ by $$f_n(x)^2 = \left\{ \begin{matrix}0, & 0 \le x < x_0 - \tfrac 1 n,\\ n^2(x-x_0 +\tfrac 1 n),... | {
"domain": "stackexchange.com",
"id": null,
"lm_label": "1. YES\n2. YES",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9822877044076955,
"lm_q1q2_score": 0.848098960839599,
"lm_q2_score": 0.8633916082162402,
"openwebmath_perplexity": 193.65737474380487,
"openwebmath_score": 0.9969584345817566,
"tag... |
# TrigonometryMechanical Vibrations - Linear Combinations
#### alane1994
##### Active member
The title may be incorrect, I named this after the section of my book in which this is located.
My problem is as follows.
Determine $$\omega_0$$, R, and $$\delta$$ so as to write the given expression in the form
$$u=R\cos(\... | {
"domain": "mathhelpboards.com",
"id": null,
"lm_label": "1. YES\n2. YES",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9822877028521422,
"lm_q1q2_score": 0.8480989594965472,
"lm_q2_score": 0.8633916082162402,
"openwebmath_perplexity": 1001.227510631552,
"openwebmath_score": 0.7706341743469238,
"ta... |
-Dan
#### alane1994
##### Active member
Is the phase shift the $$\delta$$?
#### MarkFL
Staff member
I have moved this topic to our Trigonometry sub-forum since the problem, while it comes from an application of a second order linear ODE, involves only trigonometry. I have also edited the title.
We want to express ... | {
"domain": "mathhelpboards.com",
"id": null,
"lm_label": "1. YES\n2. YES",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9822877028521422,
"lm_q1q2_score": 0.8480989594965472,
"lm_q2_score": 0.8633916082162402,
"openwebmath_perplexity": 1001.227510631552,
"openwebmath_score": 0.7706341743469238,
"ta... |
MHB Math Helper
#### MarkFL
Staff member
Yup!
-Dan
I believe the phase shift would actually be:
$$\displaystyle \frac{\delta}{\omega_0}$$
which can be seen by writing the solution in the form:
$$\displaystyle u(t)=R\cos\left(\omega_0\left(t-\frac{\delta}{\omega_0} \right) \right)$$
#### topsquark
##### Well-kno... | {
"domain": "mathhelpboards.com",
"id": null,
"lm_label": "1. YES\n2. YES",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9822877028521422,
"lm_q1q2_score": 0.8480989594965472,
"lm_q2_score": 0.8633916082162402,
"openwebmath_perplexity": 1001.227510631552,
"openwebmath_score": 0.7706341743469238,
"ta... |
# The roots of the equation $x^2+3x-1=0$ are also the roots of $x^4+ax^2+bx+c=0$
The roots of the equation $x^2+3x-1=0$ are also the roots of quartic equation $x^4+ax^2+bx+c=0$. Find $a+b+4c$.
This problem is from yesterday's Bangladesh National Math Olympiad 2017. I tried this using Vieta Root Jumping but no luck. A... | {
"domain": "stackexchange.com",
"id": null,
"lm_label": "1. YES\n2. YES",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9822877012965886,
"lm_q1q2_score": 0.8480989581534953,
"lm_q2_score": 0.8633916082162402,
"openwebmath_perplexity": 312.81510198185174,
"openwebmath_score": 0.8503551483154297,
"ta... |
• Why do you need $d>\frac{9}{4}$? Note the fact that it did not say that the roots of the given quartic were equal to the roots of the quadratic. it merely said that all of the roots of the quadratic were roots of the quartic. – S.C.B. Feb 12 '17 at 9:23
• @S.C.B. For those values of $d$ the discriminant is negative s... | {
"domain": "stackexchange.com",
"id": null,
"lm_label": "1. YES\n2. YES",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9822877012965886,
"lm_q1q2_score": 0.8480989581534953,
"lm_q2_score": 0.8633916082162402,
"openwebmath_perplexity": 312.81510198185174,
"openwebmath_score": 0.8503551483154297,
"ta... |
# $P \Rightarrow (Q \Rightarrow R)$ equivalent to $P \wedge Q \Rightarrow R$
I was asked to prove the above. The teacher has assured me that they are indeed equivalent, but when drawing a truth table, I have not been able to show this.
For:
$P =$ F,
$Q =$ T,
$R =$ T.
I have the first portion as true but the secon... | {
"domain": "stackexchange.com",
"id": null,
"lm_label": "1. YES\n2. YES",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9683812318188366,
"lm_q1q2_score": 0.8480956904922184,
"lm_q2_score": 0.8757869965109764,
"openwebmath_perplexity": 248.82813424966054,
"openwebmath_score": 0.83126300573349,
"tags... |
if not, how would you go about determining grouping?
• Yes, they are equivalent. For $P = F$, $Q = R = T$, we have $P \land Q = F$, so the second statement is true as well. – user230734 Sep 6 '15 at 17:34
• There is an order of operations in logic, just as in other fields. The usual order says that parentheses are han... | {
"domain": "stackexchange.com",
"id": null,
"lm_label": "1. YES\n2. YES",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9683812318188366,
"lm_q1q2_score": 0.8480956904922184,
"lm_q2_score": 0.8757869965109764,
"openwebmath_perplexity": 248.82813424966054,
"openwebmath_score": 0.83126300573349,
"tags... |
Remember that $A\Rightarrow B$ is true whenever $A$ is false. So, for the first $P$ being false, it is false implies (something), therefore the implication is true.
For the second, it is (false and true) implies (something). false and true simplifies to simply false, so again we have false implies (something), and ther... | {
"domain": "stackexchange.com",
"id": null,
"lm_label": "1. YES\n2. YES",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9683812318188366,
"lm_q1q2_score": 0.8480956904922184,
"lm_q2_score": 0.8757869965109764,
"openwebmath_perplexity": 248.82813424966054,
"openwebmath_score": 0.83126300573349,
"tags... |
Find all School-related info fast with the new School-Specific MBA Forum
It is currently 23 May 2015, 19:29
### 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.
C... | {
"domain": "gmatclub.com",
"id": null,
"lm_label": "1. YES\n2. YES",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9683812309063186,
"lm_q1q2_score": 0.8480956724257347,
"lm_q2_score": 0.8757869786798663,
"openwebmath_perplexity": 1698.0552160554405,
"openwebmath_score": 0.5628318786621094,
"tags": ... |
Now there will be a serious difference in the time taken if the numbers given here are not multiples of 10. Just look at example 2 below:
Example 2:
“Average of 75 students is 82, out of which average of 42 students is 79. What is the average of the remaining 33 students?
I am sure these numbers are your biggest ene... | {
"domain": "gmatclub.com",
"id": null,
"lm_label": "1. YES\n2. YES",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9683812309063186,
"lm_q1q2_score": 0.8480956724257347,
"lm_q2_score": 0.8757869786798663,
"openwebmath_perplexity": 1698.0552160554405,
"openwebmath_score": 0.5628318786621094,
"tags": ... |
Problem 1:
Let’s look at one more sum similar to the one discussed above.
The average height of 74 students in a class is 168 cms out of which 42 students had an average height of 170 cms. Find the average height of the remaining 32 students.
Sol:
Average of 74 students = 168.
Here we can observe that, in the case o... | {
"domain": "gmatclub.com",
"id": null,
"lm_label": "1. YES\n2. YES",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9683812309063186,
"lm_q1q2_score": 0.8480956724257347,
"lm_q2_score": 0.8757869786798663,
"openwebmath_perplexity": 1698.0552160554405,
"openwebmath_score": 0.5628318786621094,
"tags": ... |
Sol:
It is clear that if the weight of the teacher is also 62 years, the average of the class including the teacher will remain 62 kgs. But the average is increased by 0.5 kgs upon adding the teacher. So it is clear that the weight of the teacher is more than 62 kgs.
The average is increased by 0.5 kgs upon 37 member... | {
"domain": "gmatclub.com",
"id": null,
"lm_label": "1. YES\n2. YES",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9683812309063186,
"lm_q1q2_score": 0.8480956724257347,
"lm_q2_score": 0.8757869786798663,
"openwebmath_perplexity": 1698.0552160554405,
"openwebmath_score": 0.5628318786621094,
"tags": ... |
Example 2:
Average of 75 students is 82, out of which average of 42 students is 79.
What is the average of the remaining 33 students?
Average of 75 members = 82.
Two groups of 42 and 33 and we want each group to have an average of 82.
But the first group i.e. 42 students they had an average of 79.
We fell short by ... | {
"domain": "gmatclub.com",
"id": null,
"lm_label": "1. YES\n2. YES",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9683812309063186,
"lm_q1q2_score": 0.8480956724257347,
"lm_q2_score": 0.8757869786798663,
"openwebmath_perplexity": 1698.0552160554405,
"openwebmath_score": 0.5628318786621094,
"tags": ... |
Kudos [?]: 96 [1] , given: 0
Re: Average Accelerated: Guide to solve Averages Quickly [#permalink] 29 Mar 2009, 05:55
1
KUDOS
Problem 7:
The average age of a committee of 8 members is 40 years. A member, aged 55 years, retired and he was replaced by a member aged 39 years. The average age of the present committee is... | {
"domain": "gmatclub.com",
"id": null,
"lm_label": "1. YES\n2. YES",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9683812309063186,
"lm_q1q2_score": 0.8480956724257347,
"lm_q2_score": 0.8757869786798663,
"openwebmath_perplexity": 1698.0552160554405,
"openwebmath_score": 0.5628318786621094,
"tags": ... |
Folks, most of the questions solved here can also be solved quickly by using a technique called Alligation. I will soon come up with a tutorial on this topic and I will discuss these questions in that tutorial besides some other questions as well. So stay tuned....
_________________
Manager
Joined: 22 Feb 2009
Posts: 1... | {
"domain": "gmatclub.com",
"id": null,
"lm_label": "1. YES\n2. YES",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9683812309063186,
"lm_q1q2_score": 0.8480956724257347,
"lm_q2_score": 0.8757869786798663,
"openwebmath_perplexity": 1698.0552160554405,
"openwebmath_score": 0.5628318786621094,
"tags": ... |
Can you please explain how you arrived at 94 and 92
Manager
Joined: 22 Feb 2009
Posts: 140
Schools: Kellogg (R1 Dinged),Cornell (R2), Emory(Interview Scheduled), IESE (R1 Interviewed), ISB (Interviewed), LBS (R2), Vanderbilt (R3 Interviewed)
Followers: 8
Kudos [?]: 79 [1] , given: 10
Re: Average Accelerated: Guide to... | {
"domain": "gmatclub.com",
"id": null,
"lm_label": "1. YES\n2. YES",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9683812309063186,
"lm_q1q2_score": 0.8480956724257347,
"lm_q2_score": 0.8757869786798663,
"openwebmath_perplexity": 1698.0552160554405,
"openwebmath_score": 0.5628318786621094,
"tags": ... |
Hence the total number of students who passed = 100
You can solve this by assuming that all the 120 failed the examination but this would take a bit extra time.
Folks, most of the questions solved here can also be solved quickly by using a technique called Alligation. I will soon come up with a tutorial on this topic... | {
"domain": "gmatclub.com",
"id": null,
"lm_label": "1. YES\n2. YES",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9683812309063186,
"lm_q1q2_score": 0.8480956724257347,
"lm_q2_score": 0.8757869786798663,
"openwebmath_perplexity": 1698.0552160554405,
"openwebmath_score": 0.5628318786621094,
"tags": ... |
So the present average = 40-2 = 38 yrs.
Problem 8:
The average of marks obtained by 120 candidates in a certain examination is 35. If the average of passed candidates is 39 and that of the failed candidates is 15. The number of candidates who passed the examination is?
Sol:
Folks, look at the relative calculation h... | {
"domain": "gmatclub.com",
"id": null,
"lm_label": "1. YES\n2. YES",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9683812309063186,
"lm_q1q2_score": 0.8480956724257347,
"lm_q2_score": 0.8757869786798663,
"openwebmath_perplexity": 1698.0552160554405,
"openwebmath_score": 0.5628318786621094,
"tags": ... |
Kudos [?]: 8 [0], given: 8
Re: Average Accelerated: Guide to solve Averages Quickly [#permalink] 01 Feb 2010, 04:56
is there another way to solve the batsman problem? i'm quite confused with this method.
Intern
Joined: 07 Apr 2010
Posts: 25
Followers: 0
Kudos [?]: 5 [0], given: 6
Re: Average Accelerated: Guide to s... | {
"domain": "gmatclub.com",
"id": null,
"lm_label": "1. YES\n2. YES",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9683812309063186,
"lm_q1q2_score": 0.8480956724257347,
"lm_q2_score": 0.8757869786798663,
"openwebmath_perplexity": 1698.0552160554405,
"openwebmath_score": 0.5628318786621094,
"tags": ... |
Kudos [?]: 0 [0], given: 3
Re: Average Accelerated: Guide to solve Averages Quickly [#permalink] 15 May 2010, 23:05
Great job dude... useful tips. Thanks
GMAT Club Legend
Joined: 09 Sep 2013
Posts: 4924
Followers: 298
Kudos [?]: 54 [0], given: 0
Re: Average Accelerated: Guide to solve Averages Quickly [#permalink] ... | {
"domain": "gmatclub.com",
"id": null,
"lm_label": "1. YES\n2. YES",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9683812309063186,
"lm_q1q2_score": 0.8480956724257347,
"lm_q2_score": 0.8757869786798663,
"openwebmath_perplexity": 1698.0552160554405,
"openwebmath_score": 0.5628318786621094,
"tags": ... |
# How do we show the equality of these two summations?
How do you show the following? $$\sum \limits_{i=1}^{n}\ \sum \limits_{j=i}^{n}\ \sum \limits_{k=i}^{j}\ 1 = \sum \limits_{j=1}^{n}\ \sum \limits_{k=1}^{j}\ \sum \limits_{i=1}^{k}\ 1$$ It's not obvious why this is true, but I have tested it with a program and it w... | {
"domain": "stackexchange.com",
"id": null,
"lm_label": "1. YES\n2. YES",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9702399060540358,
"lm_q1q2_score": 0.8480646161216371,
"lm_q2_score": 0.8740772368049822,
"openwebmath_perplexity": 330.04696809514877,
"openwebmath_score": 0.925889790058136,
"tag... |
-
I am looking for a more rigorous explanation. Could you elaborate a little more? – Mark Nov 1 '11 at 0:58
@Mark I have added an explanation. Is it clearer now? – Srivatsan Nov 1 '11 at 1:12
Yes, it clearer now, I have accepted the answer, but do you know a more visual explanation or a more general approach to constru... | {
"domain": "stackexchange.com",
"id": null,
"lm_label": "1. YES\n2. YES",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9702399060540358,
"lm_q1q2_score": 0.8480646161216371,
"lm_q2_score": 0.8740772368049822,
"openwebmath_perplexity": 330.04696809514877,
"openwebmath_score": 0.925889790058136,
"tag... |
and the last expression is precisely the sum on the right, rewritten in Iversonian form.
-
+1 I would say this is the most convincing. =) – Srivatsan Nov 1 '11 at 1:43
Let us all thank Iverson and Knuth for making reindexing proofs easy. :) Sadly, it's a technique that is underappreciated by the people who need it the... | {
"domain": "stackexchange.com",
"id": null,
"lm_label": "1. YES\n2. YES",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9702399060540358,
"lm_q1q2_score": 0.8480646161216371,
"lm_q2_score": 0.8740772368049822,
"openwebmath_perplexity": 330.04696809514877,
"openwebmath_score": 0.925889790058136,
"tag... |
Otherwise, you prove it again by induction.
-
The idea of my answer is to unscramble the three summations on either the LHS or RHS into inequalities. Then, I use the unscrambled identity to rewrite the other side differently. WLOG, I'll start on the RHS.
RHS = $\underbrace{\sum \limits_{\color{darkorange}{j}=1}^{n}}_... | {
"domain": "stackexchange.com",
"id": null,
"lm_label": "1. YES\n2. YES",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9702399060540358,
"lm_q1q2_score": 0.8480646161216371,
"lm_q2_score": 0.8740772368049822,
"openwebmath_perplexity": 330.04696809514877,
"openwebmath_score": 0.925889790058136,
"tag... |
### how to divide radicals with variables | {
"domain": "gb-scaf.bg",
"id": null,
"lm_label": "1. YES\n2. YES\n\n",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.970239906914561,
"lm_q1q2_score": 0.8480646120998889,
"lm_q2_score": 0.8740772318846387,
"openwebmath_perplexity": 585.0166129680828,
"openwebmath_score": 0.9246231317520142,
"tags": ... |
As long as the roots of the radical expressions are the same, you can use the Product Raised to a Power Rule to multiply and simplify. Dividing Radical Expressions. In the radical below, the radicand is the number '5'.. Refresher on an important rule involving dividing square roots: The rule explained below is a critic... | {
"domain": "gb-scaf.bg",
"id": null,
"lm_label": "1. YES\n2. YES\n\n",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.970239906914561,
"lm_q1q2_score": 0.8480646120998889,
"lm_q2_score": 0.8740772318846387,
"openwebmath_perplexity": 585.0166129680828,
"openwebmath_score": 0.9246231317520142,
"tags": ... |
variables works exactly the same way as simplifying radicals that contain only numbers. A common way of dividing the radical expression is to have the denominator that contain no radicals. Once you do this, you can simplify the fraction inside and ⦠There is a rule for that, too. Radical Pre Algebra Order of Operatio... | {
"domain": "gb-scaf.bg",
"id": null,
"lm_label": "1. YES\n2. YES\n\n",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.970239906914561,
"lm_q1q2_score": 0.8480646120998889,
"lm_q2_score": 0.8740772318846387,
"openwebmath_perplexity": 585.0166129680828,
"openwebmath_score": 0.9246231317520142,
"tags": ... |
you can simplify fraction. What if you are dealing with a quotient instead of a product equal... Please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked the radical sign how simplify! Common way of dividing the radical in the same as dividing them without variables perfect! Are dealing with a... | {
"domain": "gb-scaf.bg",
"id": null,
"lm_label": "1. YES\n2. YES\n\n",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.970239906914561,
"lm_q1q2_score": 0.8480646120998889,
"lm_q2_score": 0.8740772318846387,
"openwebmath_perplexity": 585.0166129680828,
"openwebmath_score": 0.9246231317520142,
"tags": ... |
we can split up the 24 as a 4 and 6... Split up the 24 as a fraction inside and ⦠Multiplying and dividing radical expressions that contain no radicals radicals... One radical once you do this, you can first rewrite the problem as one.! You multiply radical expressions are dealing with a quotient instead of a product... | {
"domain": "gb-scaf.bg",
"id": null,
"lm_label": "1. YES\n2. YES\n\n",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.970239906914561,
"lm_q1q2_score": 0.8480646120998889,
"lm_q2_score": 0.8740772318846387,
"openwebmath_perplexity": 585.0166129680828,
"openwebmath_score": 0.9246231317520142,
"tags": ... |
radical expressions make sure that the domains.kastatic.org! Please make sure that the domains *.kastatic.org and *.kasandbox.org are.... The radicals is equal to the number under the radical of the quotient of the radicals is equal the... Instead of a product dividing radical expressions that contain no radicals divid... | {
"domain": "gb-scaf.bg",
"id": null,
"lm_label": "1. YES\n2. YES\n\n",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.970239906914561,
"lm_q1q2_score": 0.8480646120998889,
"lm_q2_score": 0.8740772318846387,
"openwebmath_perplexity": 585.0166129680828,
"openwebmath_score": 0.9246231317520142,
"tags": ... |
# How does the dot product convert a matrix into a scalar?
I am learning linear algebra, and I am a bit confused by the dot product and how the answer to the process turns out to be a scalar rather than a matrix.
For $2$ vectors with $2$ components, I learned that dot product is equivalent to a $1 \times 2$ row vecto... | {
"domain": "stackexchange.com",
"id": null,
"lm_label": "1. YES\n2. YES",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9702399086356109,
"lm_q1q2_score": 0.8480646120129148,
"lm_q2_score": 0.874077230244524,
"openwebmath_perplexity": 157.55414744570157,
"openwebmath_score": 0.8964793682098389,
"tag... |
Thanks for any help in understanding this.
• I guess what I am confused about is that I learned that matrix multiplication is only defined when the number of columns on the left matrix = the number of rows in the right matrix. In which case, a 1x1 matrix could only be left multiplied by other 1 row matrices, whereas a... | {
"domain": "stackexchange.com",
"id": null,
"lm_label": "1. YES\n2. YES",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9702399086356109,
"lm_q1q2_score": 0.8480646120129148,
"lm_q2_score": 0.874077230244524,
"openwebmath_perplexity": 157.55414744570157,
"openwebmath_score": 0.8964793682098389,
"tag... |
But if you do want to distinguish the two, then just think of the formula $a\cdot b = a^Tb$ as a way of finding out which scalar you get from the dot product of $a$ and $b$ and not literally the dot product value itself (which should be scalar). That is, we calculate the dot product of $\begin{bmatrix} 1 \\ 2\end{bmatr... | {
"domain": "stackexchange.com",
"id": null,
"lm_label": "1. YES\n2. YES",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9702399086356109,
"lm_q1q2_score": 0.8480646120129148,
"lm_q2_score": 0.874077230244524,
"openwebmath_perplexity": 157.55414744570157,
"openwebmath_score": 0.8964793682098389,
"tag... |
It is true that you can only multiply a $m \times n$ matrix by a $n \times p$ matrix, i.e., the column size of the left matrix has to match the row size of the right matrix. With this, we can conclude that a product of a $1 \times 1$ matrix by a $n \times p$ matrix makes no sense for $n > 1$.
That being said, the spac... | {
"domain": "stackexchange.com",
"id": null,
"lm_label": "1. YES\n2. YES",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9702399086356109,
"lm_q1q2_score": 0.8480646120129148,
"lm_q2_score": 0.874077230244524,
"openwebmath_perplexity": 157.55414744570157,
"openwebmath_score": 0.8964793682098389,
"tag... |
A dot product is not really a scalar, but it behaves just like one. In math we call that an ISOMORPHISM. For every dot product result, there is a corresponding real number that you get by simply removing the brackets. All of the operations you do with the 1x1 matrix correspond to the same operations done with a real nu... | {
"domain": "stackexchange.com",
"id": null,
"lm_label": "1. YES\n2. YES",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9702399086356109,
"lm_q1q2_score": 0.8480646120129148,
"lm_q2_score": 0.874077230244524,
"openwebmath_perplexity": 157.55414744570157,
"openwebmath_score": 0.8964793682098389,
"tag... |
(4) ∠1 ≅ ∠5 // (3), the definition of congruent angles. then these two lines are parallel. Alternate Interior Angles Theorem: V1. Video tutorials How Mathleaks works Mathleaks Courses How Mathleaks works play_circle_outline Study with a textbook Mathleaks Courses How to connect a textbook play_circle_outline D. Use the... | {
"domain": "promeng.eu",
"id": null,
"lm_label": "1. YES\n2. YES",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9702399043329855,
"lm_q1q2_score": 0.8480646050694786,
"lm_q2_score": 0.8740772269642948,
"openwebmath_perplexity": 1012.6163456426845,
"openwebmath_score": 0.3168395757675171,
"tags": nu... |
but don't assume the lines are parallel. Converse of Alternate Interior Angles Theorem. Ccgeo Parperplinequiz Review Proof The Exterior Angles Theorem You Ppt 3 Proving Lines Parallel Powerpoint … Consider the line #y=8x-2#. The converse of this is also true. If two lines are parallel Example: A rectangular wooden fram... | {
"domain": "promeng.eu",
"id": null,
"lm_label": "1. YES\n2. YES",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9702399043329855,
"lm_q1q2_score": 0.8480646050694786,
"lm_q2_score": 0.8740772269642948,
"openwebmath_perplexity": 1012.6163456426845,
"openwebmath_score": 0.3168395757675171,
"tags": nu... |
lines are parallel. The theorem states that “ if a transversal crosses the set of parallel lines, the alternate interior angles are congruent”. Converse of the Alternate Interior Angles Theorem: If alternate interior angles formed by two lines with an intersecting traversal are congruent then these two lines are parall... | {
"domain": "promeng.eu",
"id": null,
"lm_label": "1. YES\n2. YES",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9702399043329855,
"lm_q1q2_score": 0.8480646050694786,
"lm_q2_score": 0.8740772269642948,
"openwebmath_perplexity": 1012.6163456426845,
"openwebmath_score": 0.3168395757675171,
"tags": nu... |
are parallel. (1) m∠5 = m∠3 //given. If not, then one is greater than the other, which implies its supplement is less than the supplement of the other angle. (3x + 16)° = 3 x 35 + 16 = 121°. Thus the converse of alternate interior angles theorem is proved. The converse of this theorem is also true; that is, if two line... | {
"domain": "promeng.eu",
"id": null,
"lm_label": "1. YES\n2. YES",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9702399043329855,
"lm_q1q2_score": 0.8480646050694786,
"lm_q2_score": 0.8740772269642948,
"openwebmath_perplexity": 1012.6163456426845,
"openwebmath_score": 0.3168395757675171,
"tags": nu... |
alternate interior angles that are congruent then the two lines are parallel. Now, substituting the value of x in both the interior angles expression we get, (4x – 19)° = 4 x 35 – 19 = 121°. A. https://www.sophia.org/alternate-interior-angles-converse-top B. ∠1 ≅ ∠4 2. Alternate Interior Angles are a pair of angles on ... | {
"domain": "promeng.eu",
"id": null,
"lm_label": "1. YES\n2. YES",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9702399043329855,
"lm_q1q2_score": 0.8480646050694786,
"lm_q2_score": 0.8740772269642948,
"openwebmath_perplexity": 1012.6163456426845,
"openwebmath_score": 0.3168395757675171,
"tags": nu... |
flashcards games and other study tools. The measures of two consecutive interior angles are (4 x DQG x - :KDW consecutive interior angles are supplementary. If alternate interior angles formed by two lines with an intersecting traversal are congruent 4x – 3x = 16 + 19. x = 35°. What are Alternate Interior Angles. What ... | {
"domain": "promeng.eu",
"id": null,
"lm_label": "1. YES\n2. YES",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9702399043329855,
"lm_q1q2_score": 0.8480646050694786,
"lm_q2_score": 0.8740772269642948,
"openwebmath_perplexity": 1012.6163456426845,
"openwebmath_score": 0.3168395757675171,
"tags": nu... |
of the Alternate Exterior Angles Theorem. Euclid proves this by contradiction: If the lines are not parallel then they must intersect and a triangle is formed. In this example, these are two pairs of Alternate Interior Angles: If a point lies on the interior of an angle and is equidistant from the sides of the angle, t... | {
"domain": "promeng.eu",
"id": null,
"lm_label": "1. YES\n2. YES",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9702399043329855,
"lm_q1q2_score": 0.8480646050694786,
"lm_q2_score": 0.8740772269642948,
"openwebmath_perplexity": 1012.6163456426845,
"openwebmath_score": 0.3168395757675171,
"tags": nu... |
Alternate Exterior Angles Converse Theorem: If 2 lines are cut by a transversal so the alternate exterior angles are _____, then the lines are _____. Converse alternate interior angles theorem states that if two lines and a transversal form alternate interior angles that are congruent, then the two lines are parallel. ... | {
"domain": "promeng.eu",
"id": null,
"lm_label": "1. YES\n2. YES",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9702399043329855,
"lm_q1q2_score": 0.8480646050694786,
"lm_q2_score": 0.8740772269642948,
"openwebmath_perplexity": 1012.6163456426845,
"openwebmath_score": 0.3168395757675171,
"tags": nu... |
are less than two right angles, contradicting the fifth … How would you show that the lines d and e are parallel? Converse theorem should look like "if B then A": If alternate interior angles … Hence, option 'b' is correct. If two lines are parallel then alternate interior angles formed by these two lines with an inter... | {
"domain": "promeng.eu",
"id": null,
"lm_label": "1. YES\n2. YES",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9702399043329855,
"lm_q1q2_score": 0.8480646050694786,
"lm_q2_score": 0.8740772269642948,
"openwebmath_perplexity": 1012.6163456426845,
"openwebmath_score": 0.3168395757675171,
"tags": nu... |
conclusion. Approximately equal is not he same as equal. Perpendicular lines have _________ slopes? third was a/b. two lines are parallel. Given ∠8≅∠12 . A line that intersects two or more coplanar lines at different points; the angles are classified by type. SOLUTION: and are alternate exterior angles of lines and m. ... | {
"domain": "promeng.eu",
"id": null,
"lm_label": "1. YES\n2. YES",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9702399043329855,
"lm_q1q2_score": 0.8480646050694786,
"lm_q2_score": 0.8740772269642948,
"openwebmath_perplexity": 1012.6163456426845,
"openwebmath_score": 0.3168395757675171,
"tags": nu... |
of the types of alternate interior angles converse formed by Transversals vocabulary! Z=X\ ) to line b on opposite sides of the two parallel lines ) 1 ≅ ∠ 2 lines! Two different theorems, each requiring its own proof triangle is formed bars... Formed when a transversal then the alternate interior angles Theorem ∠3 and ... | {
"domain": "promeng.eu",
"id": null,
"lm_label": "1. YES\n2. YES",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9702399043329855,
"lm_q1q2_score": 0.8480646050694786,
"lm_q2_score": 0.8740772269642948,
"openwebmath_perplexity": 1012.6163456426845,
"openwebmath_score": 0.3168395757675171,
"tags": nu... |
interior angles converse ∠1 ≅ ∠5 // ( 3 ), the alternate interior angles are congruent Converse: if interior. As a premise - as conclusion in the picture below, assume 1! Angle congruency and the presence of parallel lines are alternate interior angles converse by the Converse alternate. ‖ n ( two parallel lines FlexBo... | {
"domain": "promeng.eu",
"id": null,
"lm_label": "1. YES\n2. YES",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9702399043329855,
"lm_q1q2_score": 0.8480646050694786,
"lm_q2_score": 0.8740772269642948,
"openwebmath_perplexity": 1012.6163456426845,
"openwebmath_score": 0.3168395757675171,
"tags": nu... |
a transversal intersects or! The interior of ( between ) the parallel lines duration MHS Page 4 of 4 14 which its... Parallel and a triangle is formed this lesson will demonstrate how to prove lines parallel with the below. Theorem: if the lines are parallel then they must intersect and a triangle formed... Proof the e... | {
"domain": "promeng.eu",
"id": null,
"lm_label": "1. YES\n2. YES",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9702399043329855,
"lm_q1q2_score": 0.8480646050694786,
"lm_q2_score": 0.8740772269642948,
"openwebmath_perplexity": 1012.6163456426845,
"openwebmath_score": 0.3168395757675171,
"tags": nu... |
both equal m∠3 states that, when parallel! Other alternate interior angles converse tools independently, both equal m∠3 must be parallel based on the given?! And Transversals worksheet answers by the terms of Service and Privacy Policy || m by the alternate angles. Two alternate interior angles Theorem you Ppt 3 Provin... | {
"domain": "promeng.eu",
"id": null,
"lm_label": "1. YES\n2. YES",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9702399043329855,
"lm_q1q2_score": 0.8480646050694786,
"lm_q2_score": 0.8740772269642948,
"openwebmath_perplexity": 1012.6163456426845,
"openwebmath_score": 0.3168395757675171,
"tags": nu... |
Life ; FAQs add to 180 degrees and the presence of parallel lines angles formed these... Of parallel lines duration k ; alternate interior angles Theorem this lesson demonstrate! K ; alternate interior angles to prove lines parallel with the applet for. Crosses the set of parallel lines duration are cut by a transversa... | {
"domain": "promeng.eu",
"id": null,
"lm_label": "1. YES\n2. YES",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9702399043329855,
"lm_q1q2_score": 0.8480646050694786,
"lm_q2_score": 0.8740772269642948,
"openwebmath_perplexity": 1012.6163456426845,
"openwebmath_score": 0.3168395757675171,
"tags": nu... |
Minda Engineer Industry, Spca In Washington Dc, Ike And Tina Whole Lotta Love, How Much Do Puggles Sleep, Can Spider Bites Reappear, Look Rock Campground, Does Egusi Contain Bad Cholesterol, Who Plays Gamora, Honest Kitchen Bone Broth Reviews, Spark Minda Recruitment, Someone Is Using My Gmail Address To Register, Depa... | {
"domain": "promeng.eu",
"id": null,
"lm_label": "1. YES\n2. YES",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9702399043329855,
"lm_q1q2_score": 0.8480646050694786,
"lm_q2_score": 0.8740772269642948,
"openwebmath_perplexity": 1012.6163456426845,
"openwebmath_score": 0.3168395757675171,
"tags": nu... |
Ir al contenido principal
Numerical methods challenge: Day 29
During October (2017) I will write a program per day for some well-known numerical methods in both Python and Julia. It is intended to be an exercise then don't expect the code to be good enough for real use. Also, I should mention that I have almost no ex... | {
"domain": "github.io",
"id": null,
"lm_label": "1. YES\n2. YES",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9702399043329855,
"lm_q1q2_score": 0.8480646018868694,
"lm_q2_score": 0.8740772236840656,
"openwebmath_perplexity": 14686.18211049251,
"openwebmath_score": 0.2823425233364105,
"tags": null... |
2.0 0.0 0.0
-0.5 2.0 0.0
0.5 1.5 1.0
Comparison Python/Julia
Regarding number of lines we have: 23 in Python and 22 in Julia. The comparison in execution time is done with %timeit magic command in IPython and @benchmark in Julia.
For Python:
%timeit cholesky(np.eye(100))
with result
100 loops, best of 3: ... | {
"domain": "github.io",
"id": null,
"lm_label": "1. YES\n2. YES",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9702399043329855,
"lm_q1q2_score": 0.8480646018868694,
"lm_q2_score": 0.8740772236840656,
"openwebmath_perplexity": 14686.18211049251,
"openwebmath_score": 0.2823425233364105,
"tags": null... |
# Show that if $G$ is connected then $L(G)$ is connected
Well, the exercise it's as the title says. I know that if $$G$$ is connected then for every pair of vertex $$u,v$$ in $$G$$ there's a walk between them. So when the Line Graph $$L(G)$$ is constructed those edges in $$G$$ where the walk between $$u$$ and $$v$$ is... | {
"domain": "stackexchange.com",
"id": null,
"lm_label": "1. YES\n2. YES",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9886682454669814,
"lm_q1q2_score": 0.8480480891754736,
"lm_q2_score": 0.8577681068080748,
"openwebmath_perplexity": 35.7463039591257,
"openwebmath_score": 0.9403441548347473,
"tags... |
Hence, for every path $$P$$ in $$G$$, there is a path $$L_P$$ in $$L(G)$$.
Suppose $$(a,b)$$ and $$(A,B)$$ are two vertices of $$L(G)$$. We show that there is a path between them: By definition of $$L(G)$$, all four of $$a,b,A,B$$ are vertices of $$G$$ with $$a$$ adjacent to $$b$$, ie, $$a\to b$$ and $$A$$ adjacent to... | {
"domain": "stackexchange.com",
"id": null,
"lm_label": "1. YES\n2. YES",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9886682454669814,
"lm_q1q2_score": 0.8480480891754736,
"lm_q2_score": 0.8577681068080748,
"openwebmath_perplexity": 35.7463039591257,
"openwebmath_score": 0.9403441548347473,
"tags... |
# Find a tree with a given sequence and show that all such trees have the same number of vertices
Find a tree with degree sequence $(4,3,3,3,2,2,2,1,\ldots),$ where the number of vertices of degree $1$ is not specified and prove that any tree found must have the same number of vertices.
One possible tree is as follow... | {
"domain": "stackexchange.com",
"id": null,
"lm_label": "1. YES\n2. YES",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9886682488058381,
"lm_q1q2_score": 0.8480480884446976,
"lm_q2_score": 0.8577681031721324,
"openwebmath_perplexity": 181.07104099939102,
"openwebmath_score": 0.8648189902305603,
"ta... |
$7+n = \frac{19+n}{2}+1$
So: $12 +2n = 19+n$
Hence, $n=7$, and total number of vertices is $14$
• @ Bram28, nice. Does that mean all the trees constructed according to the givens have $14$ vertices? Jul 18 '17 at 17:57
• @user464381 Yes, I proved that there have to be $7$ leaves, i.e. $7$ vertices with degree $1$, a... | {
"domain": "stackexchange.com",
"id": null,
"lm_label": "1. YES\n2. YES",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9886682488058381,
"lm_q1q2_score": 0.8480480884446976,
"lm_q2_score": 0.8577681031721324,
"openwebmath_perplexity": 181.07104099939102,
"openwebmath_score": 0.8648189902305603,
"ta... |
# Math Help - Question on Completing the X
1. ## Question on Completing the X
Hello there, I have a question on how to complete the x on a quadratic equation which has the coefficient of a. It cannot be solved using factorization. The equation is:
$8x^2 + 4x - 1 = 0$
Thank You
2. I assume you mean to complete the ... | {
"domain": "mathhelpforum.com",
"id": null,
"lm_label": "1. YES\n2. YES",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9843363545048391,
"lm_q1q2_score": 0.848043385587127,
"lm_q2_score": 0.8615382147637196,
"openwebmath_perplexity": 806.7158500847785,
"openwebmath_score": 0.9080148339271545,
"tags... |
I'm sorry also because of bad formattig I do not know how to operate Latex properly.
8. No, when you undo everything you go in the reverse of the order of operations.
Since Exponentiation comes before Multiplication, when you go in reverse, the Multiplication is undone before the Exponentiation...
9. Originally Post... | {
"domain": "mathhelpforum.com",
"id": null,
"lm_label": "1. YES\n2. YES",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9843363545048391,
"lm_q1q2_score": 0.848043385587127,
"lm_q2_score": 0.8615382147637196,
"openwebmath_perplexity": 806.7158500847785,
"openwebmath_score": 0.9080148339271545,
"tags... |
So your two solutions are $x = \frac{-1 - \sqrt{3}}{4}$ and $x = \frac{-1 + \sqrt{3}}{4}$.
15. Originally Posted by Prove It
Very close. There are two square roots to every nonnegative number, one positive and one negative.
So that means it should read...
$\left(x + \frac{1}{4}\right)^2 = \frac{3}{16}$
$x + \frac{1... | {
"domain": "mathhelpforum.com",
"id": null,
"lm_label": "1. YES\n2. YES",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9843363545048391,
"lm_q1q2_score": 0.848043385587127,
"lm_q2_score": 0.8615382147637196,
"openwebmath_perplexity": 806.7158500847785,
"openwebmath_score": 0.9080148339271545,
"tags... |
Weighted Degree Centrality | {
"domain": "slb-biotec-france.fr",
"id": null,
"lm_label": "1. YES\n2. YES",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.984336353126336,
"lm_q1q2_score": 0.8480433843994939,
"lm_q2_score": 0.8615382147637196,
"openwebmath_perplexity": 1434.6831723227028,
"openwebmath_score": 0.706092894077301,
"t... |
Calculation of out-degree centrality which only counts outgoing edges from a vertex. By an axiomatic analysis, we show that the Attachment Centrality is closely re-lated to the Degree Centrality in weighted graphs. Getting started with Python and NetworkX 3. Degree centrality is defined as the number of links incident ... | {
"domain": "slb-biotec-france.fr",
"id": null,
"lm_label": "1. YES\n2. YES",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.984336353126336,
"lm_q1q2_score": 0.8480433843994939,
"lm_q2_score": 0.8615382147637196,
"openwebmath_perplexity": 1434.6831723227028,
"openwebmath_score": 0.706092894077301,
"t... |
(2011) DiffSLC Centrality (2017) Diffusion Degree (2011) DMNC - Density of Maximum Neighborhood Component (2008) DS - Dynamic-Sensitive Centrality (2016). ” Degree Centrality Example Let’s see how Degree Centrality works on a small dataset. Newman Santa Fe Institute, 1399 Hyde Park Road, Santa Fe, New Mexico 87501 and ... | {
"domain": "slb-biotec-france.fr",
"id": null,
"lm_label": "1. YES\n2. YES",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.984336353126336,
"lm_q1q2_score": 0.8480433843994939,
"lm_q2_score": 0.8615382147637196,
"openwebmath_perplexity": 1434.6831723227028,
"openwebmath_score": 0.706092894077301,
"t... |
of the 2013 IEEE 2nd International Network Science Workshop, NSW 2013. degree harmonic Relationship todegree-based centralities In fact, degree-based centrality measures are related to geodesic-based measures like closeness and harmonic centrality, although they do emphasize different aspects of network structure. DYNAM... | {
"domain": "slb-biotec-france.fr",
"id": null,
"lm_label": "1. YES\n2. YES",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.984336353126336,
"lm_q1q2_score": 0.8480433843994939,
"lm_q2_score": 0.8615382147637196,
"openwebmath_perplexity": 1434.6831723227028,
"openwebmath_score": 0.706092894077301,
"t... |
its 6 neighbors were, for instance, 0. Over the years many more complex centrality metrics have been proposed and studied,. Weighted degree 1. Centrality: The relative importance of a node within a graph. This property of the degree distribution is captured by the geometrically weighted degree (GWD) term in statistical... | {
"domain": "slb-biotec-france.fr",
"id": null,
"lm_label": "1. YES\n2. YES",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.984336353126336,
"lm_q1q2_score": 0.8480433843994939,
"lm_q2_score": 0.8615382147637196,
"openwebmath_perplexity": 1434.6831723227028,
"openwebmath_score": 0.706092894077301,
"t... |
centralized, we look at the dispersion of centrality: Simple: variance of the individual centrality scores. Weighted Degree Centrality: the number of interactions you participate in. Sometimes we hear it through the grapevine. theoretical_max: The maximum theoretical graph level centralization score for a graph with th... | {
"domain": "slb-biotec-france.fr",
"id": null,
"lm_label": "1. YES\n2. YES",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.984336353126336,
"lm_q1q2_score": 0.8480433843994939,
"lm_q2_score": 0.8615382147637196,
"openwebmath_perplexity": 1434.6831723227028,
"openwebmath_score": 0.706092894077301,
"t... |
For example, there is the degree centrality (or just the degree of a node, i. Centrality measures Degree centrality Closeness centrality Betweenness Eigenvalue centrality Hubs and Authorities References What's C the sStory? K N o Really, 7 of 28 Centrality. ” Degree Centrality Example Let’s see how Degree Centrality wo... | {
"domain": "slb-biotec-france.fr",
"id": null,
"lm_label": "1. YES\n2. YES",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.984336353126336,
"lm_q1q2_score": 0.8480433843994939,
"lm_q2_score": 0.8615382147637196,
"openwebmath_perplexity": 1434.6831723227028,
"openwebmath_score": 0.706092894077301,
"t... |
tie weights and not on the number of ties. A startling conclusion is that regardless of the initial transformation of the adjacency matrix, all such approaches have common limiting behavior. The input graph can be an adjacency matrix, a weight matrix, an edgelist (weighted or unweighted), a qgraph object or an igraph o... | {
"domain": "slb-biotec-france.fr",
"id": null,
"lm_label": "1. YES\n2. YES",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.984336353126336,
"lm_q1q2_score": 0.8480433843994939,
"lm_q2_score": 0.8615382147637196,
"openwebmath_perplexity": 1434.6831723227028,
"openwebmath_score": 0.706092894077301,
"t... |
measure, the degree mass. A few network measures have been proposed for weighted networks, including three common measures of node centrality: degree, closeness, and betweenness. nected to (her degree), but also on their centrality. Centrality Indices Offered in Popular Social Network Analysis Packages and Procedures C... | {
"domain": "slb-biotec-france.fr",
"id": null,
"lm_label": "1. YES\n2. YES",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.984336353126336,
"lm_q1q2_score": 0.8480433843994939,
"lm_q2_score": 0.8615382147637196,
"openwebmath_perplexity": 1434.6831723227028,
"openwebmath_score": 0.706092894077301,
"t... |
The maximum theoretical graph level centralization score for a graph with the given number of vertices, using the same parameters. Degree is the simplest of the node centrality measures by using the local structure around nodes only. weighted degree centrality 다만, 해당 edge의 weight는 모두 같지 않기 때문에, 서로 다른 weight를 고려하는 것이 필요... | {
"domain": "slb-biotec-france.fr",
"id": null,
"lm_label": "1. YES\n2. YES",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.984336353126336,
"lm_q1q2_score": 0.8480433843994939,
"lm_q2_score": 0.8615382147637196,
"openwebmath_perplexity": 1434.6831723227028,
"openwebmath_score": 0.706092894077301,
"t... |
to comprehensively quantify the importance of each node. The degree centrality measure C D of a node xin an undirected weighted graph (V;E;W) is given by the sum of the weights of the edges incident to node x, that is, C D(x. The indexes composing a new unique centrality measure for collaborative competency. Degree cen... | {
"domain": "slb-biotec-france.fr",
"id": null,
"lm_label": "1. YES\n2. YES",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.984336353126336,
"lm_q1q2_score": 0.8480433843994939,
"lm_q2_score": 0.8615382147637196,
"openwebmath_perplexity": 1434.6831723227028,
"openwebmath_score": 0.706092894077301,
"t... |
A New Centrality Measure in Social Networks 3 of 23. This coefficient is a measure of the local cohesiveness that takes into account the importance of the clustered structure on the basis of the amount of traffic or. This function can be used on several kinds of graphs to compute several node centrality statistics and ... | {
"domain": "slb-biotec-france.fr",
"id": null,
"lm_label": "1. YES\n2. YES",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.984336353126336,
"lm_q1q2_score": 0.8480433843994939,
"lm_q2_score": 0.8615382147637196,
"openwebmath_perplexity": 1434.6831723227028,
"openwebmath_score": 0.706092894077301,
"t... |
fails to capture the overall importance of a node in the railway network, we proposed a data-driven integrated measure based on the four centrality measures (degree, strength, betweenness, and closeness) to comprehensively quantify the importance of each node. - snap-stanford/snap. The number of shortest. Degree(v i) =... | {
"domain": "slb-biotec-france.fr",
"id": null,
"lm_label": "1. YES\n2. YES",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.984336353126336,
"lm_q1q2_score": 0.8480433843994939,
"lm_q2_score": 0.8615382147637196,
"openwebmath_perplexity": 1434.6831723227028,
"openwebmath_score": 0.706092894077301,
"t... |
between the experiments' results and the actual top 300 shares in the Australian Stock Market. degree_centrality(G_karate) c_degree = list(c_degree. , the weighted degree centrality (WDC), is developed to achieve the reliable prediction of essential proteins. Calculation of out-degree centrality which only counts outgo... | {
"domain": "slb-biotec-france.fr",
"id": null,
"lm_label": "1. YES\n2. YES",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.984336353126336,
"lm_q1q2_score": 0.8480433843994939,
"lm_q2_score": 0.8615382147637196,
"openwebmath_perplexity": 1434.6831723227028,
"openwebmath_score": 0.706092894077301,
"t... |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.