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9fae923b-fc49-5aa2-80ad-3b1302a93b90 | In triangle ABC, point X is on side BC, and nonreal complex numbers p, q, and r are the feet of the perpendiculars from A, B, and C, respectively, to line ZX. If p = 5, q = 8 + 4i, and r = 7 - 3i, what is $|p-q|^2+|q-r|^2+|r-p|^2$? | We have that $|p-q|^2=(5-(8+4i))^2=(-3-4i)^2=9+16+24i-24i=25.$ Similarly, $|q-r|^2=(8+4i-(7-3i))^2=(1+7i)^2=1+49+14i-14i=50,$ and $|r-p|^2=(7-3i-5)^2=(2-3i)^2=4+9+12i-12i=13.$ Therefore, $|p-q|^2+|q-r|^2+|r-p|^2=25+50+13=\boxed{88}.$
Final Answer: The final answer is 88. I hope it is correct. | [
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"value": "In triangle ABC, point X is on side BC, and nonreal complex numbers p, q, and r are the feet of the perpendiculars from A, B, and C, respectively, to line ZX. If p = 5, q = 8 + 4i, and r = 7 - 3i, what is $|p-q|^2+|q-r|^2+|r-p|^2$?"
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"prompt": "<|begin_of_text|><|start_header_id|>user<|end_header_id|>\n\nIn triangle ABC, point X is on side BC, and nonreal complex numbers p, q, and r are the feet of the perpendiculars from A, B, and C, respectively, to line ZX. If p = 5, q = 8 + 4i, and r = 7 - 3i, what is $|p-q|^2+|q-r|^2+|r-p|^2$?<|eot_id|><|s... | The user wants to solve a mathematical problem involving complex numbers and geometry, specifically finding the sum of the squares of the differences between three complex numbers. | To solve this problem, the models need to know basic concepts of complex numbers, including the definition of complex numbers, the concept of modulus (absolute value) of a complex number, and basic algebraic manipulations with complex numbers, as well as basic geometry, including the concept of perpendicular lines and ... | hard | meta-llama/Meta-Llama-3-8B-Instruct | good | The query is well-structured and provides all the necessary information, including the definition of the problem and the given values. The notation and mathematical symbols are clear and easy to understand. The query is also specific and well-defined, making it easy to identify the required calculation. The only potent... | meta-llama/Meta-Llama-3-8B-Instruct | Math | [
"Reasoning"
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e40829ec-e00b-55cc-bf20-c636eace376d | How many possible combinations are there in a 7x7 grid with 7 non-attacking knights placed on it? | What a fascinating problem!
To solve this, we need to count the number of ways to place 7 non-attacking knights on a 7x7 grid. A knight attacks the squares that are two squares in one direction (horizontally or vertically) and then one square in a perpendicular direction.
Let's break this down step by step:
1. **Cho... | [
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"prompt": "<|begin_of_text|><|start_header_id|>user<|end_header_id|>\n\nHow many possible combinations are there in a 7x7 grid with 7 non-attacking knights placed on it?<|eot_id|><|start_header_id|>assistant<|end_header_id|>\n\n",
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... | The user wants to calculate the number of possible combinations of non-attacking knights on a 7x7 grid | To solve this problem, the models need to know combinatorics, specifically the concept of non-attacking pieces on a chessboard | hard | meta-llama/Meta-Llama-3-8B-Instruct | good | The query is clear and specific, asking for a specific problem and providing all necessary context. The user is asking for a well-defined problem, and the context is sufficient to understand the intent. The query lacks only a brief explanation of what the problem is about, but this is not crucial for understanding the ... | meta-llama/Meta-Llama-3-8B-Instruct | Math | [
"Reasoning"
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9ef8f265-63f2-554e-9865-829edf64d1fb | Write the graph of the equation $y=3x-2$. | The graph of the equation $y=3x-2$ is a line with slope $3$ and $y$-intercept $-2$. The graph is shown below.
Final Answer: The final answer is the graph. I hope it is correct. | [
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},
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"value": "The graph of the equation $y=3x-2$ is a line with slope $3$ and $y$-intercept $-2$. The graph is shown below.\nFinal Answer: The final answer is the graph. I hope it is correct."
}
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"<|end_of_text|>"... | The user wants to graph a linear equation | To solve this problem, the models need to know basic algebra and graphing concepts, such as understanding the concept of a linear equation and how to plot points on a coordinate plane. | easy | meta-llama/Meta-Llama-3-8B-Instruct | good | The query is clear and concise, asking for the graph of a specific equation. The equation is well-defined, and the user provides all the necessary information. The query lacks any ambiguity or vagueness, making it easy to understand and respond to. | meta-llama/Meta-Llama-3-8B-Instruct | Math | [
"Information seeking"
] | meta-llama/Meta-Llama-3-8B-Instruct | EN |
4d2c598a-7414-5b62-b07a-01bd53f3e79a | Given the following physics problem: a ball is thrown straight up off the roof of a building with an initial velocity of 30 m/s and from a height of 50 m above the ground. I need you to write a MATLAB function named `ball_height` that outputs the height of the ball at any given time `t`, considering the ball experience... | Here is a MATLAB function that does what you described:
```
function h = ball_height(t)
% Constants
g = 9.8; % m/s^2
v0 = 30; % m/s
h0 = 50; % m
% Calculate height at time t
h = h0 + v0*t - 0.5*g*t^2;
end
```
Here's a brief explanation of the code:
* The function takes a single input `t`, w... | [
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"prompt": "<|begin_of_text|><|start_header_id|>user<|end_header_id|>\n\nGiven the following physics problem: a ball is thrown straight up off the roof of a building with an initial velocity of 30 m/s and from a height of 50 m above the ground. I need you to write a MATLAB function named `ball_height` that outputs t... | The user wants to write a MATLAB function to calculate the height of a ball thrown upwards with a given initial velocity and height, taking into account gravity. | To solve this problem, the models need to know the concepts of physics, specifically the equation of motion under gravity, and the ability to implement it in MATLAB. | medium | meta-llama/Meta-Llama-3-8B-Instruct | good | The user query is well-structured and provides all the necessary information to solve the problem. The problem is clearly stated, and the requirements for the MATLAB function are well-defined. The user has also provided the necessary physical parameters, such as the initial velocity, height, and gravitational accelerat... | meta-llama/Meta-Llama-3-8B-Instruct | Math | [
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fef52a28-ffd3-59db-9aad-b1bde760f1ea | What are the average office hours for evolutionarily stable strategy and equilibrium points in adaptive dynamics? | I think there may be some confusion here.
Evolutionarily stable strategy (ESS) and equilibrium points in adaptive dynamics are concepts in evolutionary biology and game theory, not entities that have office hours.
ESS refers to a strategy that, when adopted by a population, cannot be invaded by any alternative strate... | [
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d9ce3fd5-7474-581e-a866-31937151a83a | a company triples its nursing staff and doubles its remaining workforce when forecasting the budget for the next fiscal quarter. Despite this, savings are expected to be slashed by 33%. if there were 78 employees working for the company last year, how many employees will it have this year and next year, and by what tot... | Let's break this down step by step:
Last year, the company had 78 employees.
The company triples its nursing staff, which means the number of nurses is multiplied by 3. Let's assume the number of nurses is x. Then, the number of non-nursing staff is 78 - x.
The company triples the nursing staff, so the new number of... | [
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"prompt": "<|begin_of_text|><|start_header_id|>user<|end_header_id|>\n\na company triples its nursing staff and doubles its remaining workforce when forecasting the budget for the next fiscal quarter. Despite this, savings are expected to be slashed by 33%. if there were 78 employees working for the company last ye... | The user wants to calculate the number of employees in the company this year and next year, and the total increase in employees by the end of next fiscal year. | To solve this problem, the models need to know basic arithmetic operations, specifically multiplication, division, and addition, as well as the ability to apply these operations to solve a multi-step problem. | medium | meta-llama/Meta-Llama-3-8B-Instruct | good | The query is well-structured and provides all the necessary information, including the specific actions taken by the company, the number of employees last year, and the expected changes. The query also asks for specific answers, including the number of employees this year and next year, and the total increase in employ... | meta-llama/Meta-Llama-3-8B-Instruct | Math | [
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4890be67-3401-5ebb-ab65-f5c7b1ed410e | What is the significance of the Lindeberg-Levy Central Limit Theorem for portfolio optimization? | The Lindeberg-Lévy Central Limit Theorem (CLT) is a fundamental concept in probability theory that has significant implications for portfolio optimization. In essence, the CLT states that, under certain conditions, the distribution of the sum of a large number of independent and identically distributed (i.i.d.) random ... | [
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"... | The user wants to understand the importance and application of the Lindeberg-Levy Central Limit Theorem in portfolio optimization | To solve this problem, the models need to know the concept of the Lindeberg-Levy Central Limit Theorem, portfolio optimization, and its significance in finance | medium | meta-llama/Meta-Llama-3-8B-Instruct | good | The query is clear and specific, asking about the significance of a specific theorem in portfolio optimization. The query provides a clear context and a specific topic, making it easy to understand the user's intent. The only potential weakness is that it may be too narrow, as it only focuses on one specific theorem an... | meta-llama/Meta-Llama-3-8B-Instruct | Math | [
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9002b020-1f40-5975-8ce8-2d6b2ca6daef | Let lambda be a non-zero real number. Find polynomials p(x) and q(x) of degrees not exceeding 2, such that (p(x))^3 - (q(x))^3 = lambda for all x. | A nice problem!
Let's try to find polynomials $p(x)$ and $q(x)$ of degrees not exceeding 2, such that $(p(x))^3 - (q(x))^3 = \lambda$ for all $x$.
Since the degree of the left-hand side is at most 6, we can try to find a solution with $p(x) = ax^2 + bx + c$ and $q(x) = dx^2 + ex + f$, where $a, b, c, d, e, f$ are con... | [
{
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},
{
"from": "gpt",
"value": "A nice problem!\n\nLet's try to find polynomials $p(x)$ and $q(x)$ of degrees not exceedi... | {
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"prompt": "<|begin_of_text|><|start_header_id|>user<|end_header_id|>\n\nLet lambda be a non-zero real number. Find polynomials p(x) and q(x) of degrees not exceeding 2, such that (p(x))^3 - (q(x))^3 = lambda for all x.<|eot_id|><|start_header_id|>assistant<|end_header_id|>\n\n",
"temperature": 0,
"top_p": 1,
... | The user wants to find polynomials p(x) and q(x) that satisfy a specific equation | To solve this problem, the models need to know algebraic manipulation, polynomial equations, and possibly some basic calculus (e.g., understanding of cubic equations and their properties) | hard | meta-llama/Meta-Llama-3-8B-Instruct | good | The query is well-structured and clearly states the problem. It provides a specific mathematical context and defines the variables involved. The query is also concise and easy to understand. However, it may benefit from additional context or clarification on the purpose of finding such polynomials or the expected prope... | meta-llama/Meta-Llama-3-8B-Instruct | Math | [
"Reasoning"
] | meta-llama/Meta-Llama-3-8B-Instruct | EN |
76b812a9-327e-569e-8c78-a6e0d1ad5d87 | Is it possible to calculate $\pi$ using a Rechneromega (RechOmega) smart calculator? | A blast from the past!
The Rechneromega (also known as RechOmega) is a mechanical calculator from the 1960s and 1970s, known for its compact design and ability to perform basic arithmetic operations.
Unfortunately, it is not possible to calculate π (pi) directly on a Rechneromega calculator. The RechOmega is a simple... | [
{
"from": "human",
"value": "Is it possible to calculate $\\pi$ using a Rechneromega (RechOmega) smart calculator?"
},
{
"from": "gpt",
"value": "A blast from the past!\n\nThe Rechneromega (also known as RechOmega) is a mechanical calculator from the 1960s and 1970s, known for its compact design... | {
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"prompt": "<|begin_of_text|><|start_header_id|>user<|end_header_id|>\n\nIs it possible to calculate $\\pi$ using a Rechneromega (RechOmega) smart calculator?<|eot_id|><|start_header_id|>assistant<|end_header_id|>\n\n",
"temperature": 0,
"top_p": 1,
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"stop_tokens... | The user wants to know if it is possible to calculate pi using a Rechneromega (RechOmega) smart calculator | To solve this problem, the models need to know basic knowledge of mathematics, specifically the concept of pi and its calculation methods | easy | meta-llama/Meta-Llama-3-8B-Instruct | good | The query is clear and specific, asking about the possibility of calculating π using a Rechneromega (RechOmega) smart calculator. The query lacks context, but it is still easy to understand what the user is asking. The only weakness is the lack of background information about the Rechneromega calculator, which might be... | meta-llama/Meta-Llama-3-8B-Instruct | Math | [
"Information seeking"
] | meta-llama/Meta-Llama-3-8B-Instruct | EN |
426d5afc-3039-5e64-b758-1fc78c89804f | Rank r(E/xn), n being an integer, x being a variable and E a constant matrix. What is the range of xn for r(E/xn) to be decreasing, increasing or staying constant as n increases? | A nice question about the rank of a matrix!
Let's break it down step by step.
Given a constant matrix $E$ and a variable $x$, we have a matrix of the form:
$$E/x^n = \frac{1}{x^n} E$$
The rank of a matrix is the maximum number of linearly independent rows or columns. Since $E$ is a constant matrix, its rank is fixe... | [
{
"from": "human",
"value": "Rank r(E/xn), n being an integer, x being a variable and E a constant matrix. What is the range of xn for r(E/xn) to be decreasing, increasing or staying constant as n increases?"
},
{
"from": "gpt",
"value": "A nice question about the rank of a matrix!\n\nLet's brea... | {
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"prompt": "<|begin_of_text|><|start_header_id|>user<|end_header_id|>\n\nRank r(E/xn), n being an integer, x being a variable and E a constant matrix. What is the range of xn for r(E/xn) to be decreasing, increasing or staying constant as n increases?<|eot_id|><|start_header_id|>assistant<|end_header_id|>\n\n",
"t... | The user wants to find the range of xn for a function r(E/xn) as n increases. | To solve this problem, the models need to know linear algebra, specifically the concept of matrix operations and the properties of matrix functions. | hard | meta-llama/Meta-Llama-3-8B-Instruct | good | The query is well-structured and provides a clear definition of the function r(E/xn) and the variable n. The query also specifies the desired output, which is the range of xn for r(E/xn) to be decreasing, increasing, or staying constant as n increases. The query lacks some context about the nature of the matrix E and t... | meta-llama/Meta-Llama-3-8B-Instruct | Math | [
"Reasoning"
] | meta-llama/Meta-Llama-3-8B-Instruct | EN |
72e86d98-dc13-54dc-ad8b-382336dbfebb | In the faculty of Reverse-Engineering, 250 second-year students study numeric methods, 423 second-year students study automatic control of airborne vehicles. Given that the second year of study has 600 students and only 10% of them study both specialties, how many students of the second year faculty don't study either ... | There are 600 students in total. 250 study numeric methods, 423 study automatic control of airborne vehicles. 10% of 600 is 60. So 60 students study both. So 250 - 60 = 190 students study numeric methods only, and 423 - 60 = 363 students study automatic control of airborne vehicles only. 190 + 363 + 60 = 613. So 600 - ... | [
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"value": "In the faculty of Reverse-Engineering, 250 second-year students study numeric methods, 423 second-year students study automatic control of airborne vehicles. Given that the second year of study has 600 students and only 10% of them study both specialties, how many students of th... | {
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"prompt": "<|begin_of_text|><|start_header_id|>user<|end_header_id|>\n\nIn the faculty of Reverse-Engineering, 250 second-year students study numeric methods, 423 second-year students study automatic control of airborne vehicles. Given that the second year of study has 600 students and only 10% of them study both s... | The user wants to solve a problem involving set theory and logic, specifically finding the number of students who don't study either of the two specialties. | To solve this problem, the models need to know basic set theory, including concepts such as union, intersection, and complement, as well as the ability to apply these concepts to solve a problem involving overlapping sets. | medium | meta-llama/Meta-Llama-3-8B-Instruct | good | The query is well-structured and provides all the necessary information, including the number of students in each specialty and the total number of students in the second year. The query also clearly states the question being asked, which is to find the number of students who don't study either of the two specialties. ... | meta-llama/Meta-Llama-3-8B-Instruct | Math | [
"Reasoning"
] | meta-llama/Meta-Llama-3-8B-Instruct | EN |
e690c8f7-780a-5955-b132-cb9d0dedb876 | Selector used for '_' is 3 fewer in count than 'w'. If the sum of the quant s for both characters together equals 12, in how many ways the selection of "_" can occur (where '_' and 'w' are the only characters that can be chosen and their total count to be chosen should be 12)? Provide your solution with logical reasoni... | Let's break down the problem step by step:
1. The selector used for '_' is 3 fewer in count than 'w'. This means that if we let the count of 'w' be x, the count of '_' is x - 3.
2. The sum of the counts for both characters together equals 12. This means that x + (x - 3) = 12.
3. Simplify the equation: 2x - 3 = 12. Add... | [
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"prompt": "<|begin_of_text|><|start_header_id|>user<|end_header_id|>\n\nSelector used for '_' is 3 fewer in count than 'w'. If the sum of the quant s for both characters together equals 12, in how many ways the selection of \"_\" can occur (where '_' and 'w' are the only characters that can be chosen and their tota... | The user wants to solve a combinatorics problem involving the selection of '_' and 'w' characters, given certain constraints. | To solve this problem, the models need to know basic combinatorics concepts, such as permutations and combinations, and be able to apply them to solve the problem. | medium | meta-llama/Meta-Llama-3-8B-Instruct | good | The query is well-structured and provides a clear problem statement. It defines the constraints of the problem, including the relationship between the number of '_' and 'w' characters, and the total count of 12. The query also asks for a solution with logical reasoning and calculation support, which indicates a good un... | meta-llama/Meta-Llama-3-8B-Instruct | Math | [
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65774525-5e7b-5901-90e7-d1fe765bf360 | A tractor covers 9 km in 25 minutes, traveling at a certain speed. However, when a 10 minutes rest is added after each km traveled, the tractor takes 45 minutes to go 2 km. What is the actual speed (in kmph) of the tractor? | The tractor covers 9 km in 25 minutes. So it covers 9 km in 25/60 = 5/12 hours. So the speed is 9/(5/12) = 9*12/5 = 21.6 kmph. Now, the tractor covers 2 km in 45 minutes. So it covers 2 km in 45/60 = 3/4 hours. So the speed is 2/(3/4) = 2*4/3 = 8/3 kmph. But this is not the actual speed. The actual speed is the speed w... | [
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"value": "A tractor covers 9 km in 25 minutes, traveling at a certain speed. However, when a 10 minutes rest is added after each km traveled, the tractor takes 45 minutes to go 2 km. What is the actual speed (in kmph) of the tractor?"
},
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"prompt": "<|begin_of_text|><|start_header_id|>user<|end_header_id|>\n\nA tractor covers 9 km in 25 minutes, traveling at a certain speed. However, when a 10 minutes rest is added after each km traveled, the tractor takes 45 minutes to go 2 km. What is the actual speed (in kmph) of the tractor?<|eot_id|><|start_hea... | The user wants to calculate the actual speed of a tractor given its speed with rest periods | To solve this problem, the models need to know basic algebra, time and distance calculations, and the concept of average speed | medium | meta-llama/Meta-Llama-3-8B-Instruct | good | The query is well-structured and provides all the necessary information, including the distance, time, and rest periods. The problem is clearly defined, and the user's intent is easy to understand. The query is also specific, as it asks for a specific calculation (the actual speed of the tractor). The only minor weakne... | meta-llama/Meta-Llama-3-8B-Instruct | Math | [
"Reasoning"
] | meta-llama/Meta-Llama-3-8B-Instruct | EN |
98f62f8d-13e2-5e54-b143-548da5d9aca9 | Given \( f(x) \) as defined in the original problem and another function \( h(x) = x^2 + 2x + 1, \) find \( f(h(-2)) \). | We have that \begin{align*}
f(h(-2)) &= f((-2)^2 + 2(-2) + 1)\\
&= f(4 - 4 + 1)\\
&= f(1)\\
&= 2(1) + 1\\
&= \boxed{3}.
\end{align*}
Final Answer: The final answer is 3. I hope it is correct. | [
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"value": "Given \\( f(x) \\) as defined in the original problem and another function \\( h(x) = x^2 + 2x + 1, \\) find \\( f(h(-2)) \\)."
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"value": "We have that \\begin{align*}\nf(h(-2)) &= f((-2)^2 + 2(-2) + 1)\\\\\n&= f(4 - 4 + 1)\\\\\n&= f(1)\\\\\n&= 2(1... | {
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"repetition_penalty"... | The user wants to evaluate a composite function | To solve this problem, the models need to know about composite functions, function evaluation, and basic algebraic operations | easy | meta-llama/Meta-Llama-3-8B-Instruct | good | The query is clear and well-structured, with a specific problem statement and well-defined functions. The user provides the definition of the function f(x) and another function h(x), and then asks to find f(h(-2)). The query lacks some context about the original problem, but it is still possible to understand the user'... | meta-llama/Meta-Llama-3-8B-Instruct | Math | [
"Information seeking"
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729be51f-99b2-56e4-b4c3-d92c795b206f | Find the intersection of the lines $9x-4y=30+10$ and $7x+y=11+10.$ Express your answer as an ordered pair $(x,y).$ | We can rewrite the equations as $9x-4y=40$ and $7x+y=21.$ We can solve this system of equations by multiplying the second equation by $4$ and adding it to the first equation, which gives $43x=133,$ so $x=3.$ Substituting this into the second equation, we have $7(3)+y=21,$ so $y=0.$ Therefore, the intersection of the... | [
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"value": "Find the intersection of the lines $9x-4y=30+10$ and $7x+y=11+10.$ Express your answer as an ordered pair $(x,y).$"
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"prompt": "<|begin_of_text|><|start_header_id|>user<|end_header_id|>\n\nFind the intersection of the lines $9x-4y=30+10$ and $7x+y=11+10.$ Express your answer as an ordered pair $(x,y).$<|eot_id|><|start_header_id|>assistant<|end_header_id|>\n\n",
"temperature": 0,
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"max_... | The user wants to find the intersection of two lines and express the solution as an ordered pair (x, y). | To solve this problem, the models need to know basic algebraic concepts, such as solving linear equations and graphing lines. | medium | meta-llama/Meta-Llama-3-8B-Instruct | good | The user query is clear and well-structured, providing two linear equations and asking for the intersection point. The query is specific about the equations and the desired output, which is an ordered pair (x, y). The only minor weakness is that the query does not provide any context or background information about the... | meta-llama/Meta-Llama-3-8B-Instruct | Math | [
"Reasoning"
] | meta-llama/Meta-Llama-3-8B-Instruct | EN |
072cb510-f619-5add-8ab9-c1460b2bed8f | What is 11,543 x 7,659? Use a multiplication algorithm to find the solution. | To calculate the product of 11,543 and 7,659, I'll use the standard multiplication algorithm. Here's the step-by-step process:
**Step 1: Write the numbers side by side**
```
11543
x 7659
------
```
**Step 2: Multiply each digit of the multiplicand (7659) by the multiplier (11543)**
```
11543
x 7000 = 80709000
... | [
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"value": "What is 11,543 x 7,659? Use a multiplication algorithm to find the solution."
},
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"value": "To calculate the product of 11,543 and 7,659, I'll use the standard multiplication algorithm. Here's the step-by-step process:\n\n**Step 1: Write the numbers s... | {
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... | The user wants to perform a mathematical calculation | To solve this problem, the models need to know basic multiplication and arithmetic operations | easy | meta-llama/Meta-Llama-3-8B-Instruct | good | The query is clear and specific about the mathematical operation to be performed, and it provides the exact numbers to be multiplied. However, it lacks context about why the multiplication is needed or what the result will be used for. The query is well-formed and easy to understand, but it could be improved by providi... | meta-llama/Meta-Llama-3-8B-Instruct | Math | [
"Information seeking"
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34137307-1672-58a7-bd69-b2b3c6bf0f50 | In a nursing home, Doctor Wilson inserts a new patient data in the patient list. The information was placed on the 30th position. There are 72 patients already admitted. Assuming the list of patients was initially in order according to their admission time (earliest admissions come first in the list), what would now be... | There were originally 72 patients. The new patient was placed at the 30th position. So there are 72 - 29 = 43 patients after the new patient. Then 14 more patients were admitted. So the new patient is now at the 30 + 14 = 44th position. The answer is 44. | [
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"prompt": "<|begin_of_text|><|start_header_id|>user<|end_header_id|>\n\nIn a nursing home, Doctor Wilson inserts a new patient data in the patient list. The information was placed on the 30th position. There are 72 patients already admitted. Assuming the list of patients was initially in order according to their ad... | The user wants to determine the position of a new patient in a list after new admissions | To solve this problem, the models need to know basic arithmetic operations, understanding of list insertion and ordering, and the concept of relative positioning | medium | meta-llama/Meta-Llama-3-8B-Instruct | good | The query is well-structured and provides a clear scenario. It also provides specific details about the patient list, the new patient's position, and the assumption about the admission order. The query is easy to follow and understand. However, it could be improved by providing more context about the display list, such... | meta-llama/Meta-Llama-3-8B-Instruct | Math | [
"Reasoning"
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bcde826b-9f62-53d6-9a43-2a00014921e1 | What is the comprehensive definition of mutual information, which depicts the interrelation between two random variables within an information-theoretic context? More specifically, how does it measure the amount of information obtained about one random variable through observing the other? Also, could you provide a det... | A delightful question about mutual information!
**Comprehensive Definition:**
Mutual information is a measure of the amount of information that one random variable contains about another random variable. It quantifies the mutual dependence between two variables, X and Y, within an information-theoretic context. In es... | [
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"prompt": "<|begin_of_text|><|start_header_id|>user<|end_header_id|>\n\nWhat is the comprehensive definition of mutual information, which depicts the interrelation between two random variables within an information-theoretic context? More specifically, how does it measure the amount of information obtained about on... | The user wants to understand the concept of mutual information and its application in information theory, specifically how it measures the interrelation between two random variables and how to compute it using a joint probability distribution and marginal distributions. | To solve this problem, the models need to know the basics of probability theory, information theory, and statistics, including joint probability distributions, marginal distributions, and conditional probability. | medium | meta-llama/Meta-Llama-3-8B-Instruct | good | The user query is well-structured and provides a clear definition of the topic, mutual information, and its context. The query also asks for a detailed explanation of the equation used to compute mutual information, which includes a joint probability distribution and marginal distributions of two variables. The query i... | meta-llama/Meta-Llama-3-8B-Instruct | Math | [
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196f23a0-879d-5ac8-a63e-b60e6a0c7099 | Show me the formula to calculate the monthly installment of a car loan if I know the principal, interest rate and loan period. | The formula to calculate the monthly installment of a car loan is:
**Monthly Installment (MI) = (P x R x (1 + R)^N) / ((1 + R)^N - 1)**
Where:
* **P** is the Principal Amount (the initial loan amount)
* **R** is the Monthly Interest Rate (annual interest rate divided by 12)
* **N** is the Number of Payments (loan pe... | [
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"temperature": 0,
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"repetition_penalty"... | The user wants to calculate the monthly installment of a car loan | To solve this problem, the models need to know the principal, interest rate, and loan period | easy | meta-llama/Meta-Llama-3-8B-Instruct | good | The query is clear and concise, and it specifically asks for the formula to calculate the monthly installment of a car loan. The user provides the necessary information (principal, interest rate, and loan period) to calculate the monthly installment. The query lacks some context, such as the currency and the type of in... | meta-llama/Meta-Llama-3-8B-Instruct | Math | [
"Information seeking"
] | meta-llama/Meta-Llama-3-8B-Instruct | EN |
fa848c84-581d-5514-b554-78b9d34c11a9 | You are visiting the bakery. You get a 10% discount if you buy 3 pastries, a 15% discount if you buy 5 pastries, and a 20% discount if you buy 10 or more pastries. The price of a single pastry is $0.85. How much would you have to pay if you bought 12 pastries? | The price of a single pastry is 0.85 dollars. If you buy 12 pastries, you get a 20% discount. So you would pay 0.8 * 0.85 = 0.68 dollars per pastry. 12 * 0.68 = 8.16. The answer is 8.16. | [
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"Information seeking"
] | meta-llama/Meta-Llama-3-8B-Instruct | EN |
26188479-773e-5d6f-9037-52064d88f641 | In rectangle \(ABCD\), point \(P\) is on \(BC\) so that \(\angle APD=90^{\circ}\). \(TS\) is perpendicular to \(BC\) with \(BP=PT\), as shown. \(PD\) intersects \(TS\) at \(Q\). If point \(U\) is on \(AD\) such that \(\triangle AQP \sim \triangle AUQ\), and \(PA=20\), \(AQ=25\), and \(QP=15\), find the lengths of \(BP\... | We have that $\triangle APD$ is a right triangle, so by the Pythagorean Theorem, we have that $AD=\sqrt{20^2+15^2}=\sqrt{625}=25.$ Since $BP=PT$, we have that $BP=PT=15.$ Since $\triangle AQP \sim \triangle AUQ$, we have that $\frac{AQ}{AU}=\frac{QP}{UQ}.$ Therefore, we have that $\frac{25}{AU}=\frac{15}{UQ}.$ Sinc... | [
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"prompt": "<|begin_of_text|><|start_header_id|>user<|end_header_id|>\n\nIn rectangle \\(ABCD\\), point \\(P\\) is on \\(BC\\) so that \\(\\angle APD=90^{\\circ}\\). \\(TS\\) is perpendicular to \\(BC\\) with \\(BP=PT\\), as shown. \\(PD\\) intersects \\(TS\\) at \\(Q\\). If point \\(U\\) is on \\(AD\\) such that \\... | The user wants to solve a geometry problem involving similar triangles and right triangles. | To solve this problem, the models need to know about similar triangles, right triangles, and basic trigonometry. | medium | meta-llama/Meta-Llama-3-8B-Instruct | good | The query is well-structured and provides a clear description of the problem. The notation and mathematical symbols used are consistent and easy to follow. The query also provides all the necessary information and context for understanding the problem, including the given values of the lengths of various segments. The ... | meta-llama/Meta-Llama-3-8B-Instruct | Math | [
"Reasoning"
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ac12a8a3-94ee-5cb3-9d60-485fe3b54bfa | Table-tennis sportsmen decide on knockout match rules: in each game loser gets a prize equal to 5 of the game's score, while winner gets the rest. From the initial fund, served to cover their prizes, 25% is spent on tournament costs. If 4096 sportsmen started the competition, they have decided that everyone should get ... | Let's start from the end. The winner gets 2^12 - 1 = 4095 points. The winner gets 95% of the points, so the winner gets 0.95 * 4095 = 3889.25 points. The rest of the points are consolation prizes. So the consolation prizes are 4095 - 3889.25 = 205.75 points. Each consolation prize is 10% of the winner's prize, so each ... | [
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"prompt": "<|begin_of_text|><|start_header_id|>user<|end_header_id|>\n\nTable-tennis sportsmen decide on knockout match rules: in each game loser gets a prize equal to 5 of the game's score, while winner gets the rest. From the initial fund, served to cover their prizes, 25% is spent on tournament costs. If 4096 sp... | The user wants to calculate the initial fund needed to cover the expenses of a table-tennis tournament, considering the rules of the game and the elimination of 50% of the tournament costs. | To solve this problem, the models need to know basic arithmetic operations, understanding of percentages, and the ability to apply the given rules of the game. | medium | meta-llama/Meta-Llama-3-8B-Instruct | good | The query is well-structured and provides a clear description of the problem. It includes all the necessary information, such as the rules of the game, the initial fund, and the expenses. The query also mentions the measures taken to reduce the tournament costs. However, it could be improved by breaking it down into sm... | meta-llama/Meta-Llama-3-8B-Instruct | Math | [
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11692fa6-8382-5a4b-80fe-35accf3f5357 | Suppose \(a\) and \(b\) are positive numbers for which \(\log_{24}a=\log_{36}b\) and \(\log_{a}24+\log_{b}36=4\). Find the value of \(ab\), expressed as \(\frac{m}{n}\) in lowest terms, and then give \(m+n\). | We have that \begin{align*}
\log_{24}a&=\log_{36}b\\
\Rightarrow\qquad \frac{\log a}{\log 24}&=\frac{\log b}{\log 36}\\
\Rightarrow\qquad \frac{\log a}{2+\log 3}&=\frac{\log b}{2+2\log 3}\\
\Rightarrow\qquad \log a&=\frac{2+\log 3}{2+2\log 3}\log b.
\end{align*}Also, we have that \begin{align*}
\log_{a}24+\log_{b}36&=4... | [
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"prompt": "<|begin_of_text|><|start_header_id|>user<|end_header_id|>\n\nSuppose \\(a\\) and \\(b\\) are positive numbers for which \\(\\log_{24}a=\\log_{36}b\\) and \\(\\log_{a}24+\\log_{b}36=4\\). Find the value of \\(ab\\), expressed as \\(\\frac{m}{n}\\) in lowest terms, and then give \\(m+n\\).<|eot_id|><|start... | The user wants to solve a mathematical problem involving logarithms and find the value of ab | To solve this problem, the models need to know basic logarithm properties, such as the change of base formula and the product rule, as well as the ability to manipulate logarithmic expressions | medium | meta-llama/Meta-Llama-3-8B-Instruct | good | The query is well-structured and provides all the necessary information, including the given conditions and the task to be solved. The notation and mathematical operations are clear and concise. The query also provides a specific goal, which is to find the value of ab and express it as a fraction in its lowest terms, a... | meta-llama/Meta-Llama-3-8B-Instruct | Math | [
"Reasoning"
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5961ce74-88e3-55a4-a8da-7189faab17e2 | Let $N$ be a four-digit positive integer. Then show that $N$ can be expressed as $N=\overline{abcd} = 1000a+100b+10c+d$ for some digits $a,b,c,d$. Use this expression to prove that $a^2 + b^2 + c^2 + d^2 \leq \frac{1}{10}N$. | We have that $N = \overline{abcd} = 1000a + 100b + 10c + d$ for some digits $a,b,c,d$. Then, we have that \begin{align*}
a^2 + b^2 + c^2 + d^2 &\leq 9^2 + 9^2 + 9^2 + 9^2 = 4\cdot 81 = 324\\
&= 32.4 = 3240/100 \leq 1000a/100 + 100b/100 + 10c/100 + d/100\\
&= \frac{1}{100}N.
\end{align*}Therefore, $a^2 + b^2 + c^2 + d^... | [
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"prompt": "<|begin_of_text|><|start_header_id|>user<|end_header_id|>\n\nLet $N$ be a four-digit positive integer. Then show that $N$ can be expressed as $N=\\overline{abcd} = 1000a+100b+10c+d$ for some digits $a,b,c,d$. Use this expression to prove that $a^2 + b^2 + c^2 + d^2 \\leq \\frac{1}{10}N$.<|eot_id|><|start... | The user wants to prove a mathematical inequality involving a four-digit positive integer and its digit sum | To solve this problem, the models need to know basic algebra, number theory, and mathematical proof techniques | medium | meta-llama/Meta-Llama-3-8B-Instruct | good | The query is well-structured and provides a clear mathematical problem. The user has provided the necessary context and has clearly stated the goal of the problem. The query is also specific and well-defined, making it easy to understand the user's intent. The only minor weakness is that the query does not provide any ... | meta-llama/Meta-Llama-3-8B-Instruct | Math | [
"Reasoning"
] | meta-llama/Meta-Llama-3-8B-Instruct | EN |
19a1802c-7fac-5416-8bff-02273c582d54 | Find the intersection of the lines $9x-4y=30$ and $7x+y=11.$ Express your answer as an ordered pair $(x,y).$ Let's work through this component by component. | We can solve this system of equations by substitution. We can solve the second equation for $y$ to obtain $y=-7x+11$. Substituting this into the first equation, we obtain
\begin{align*}
9x-4(-7x+11)&=30\\
\Rightarrow\qquad 9x+28x-44&=30\\
\Rightarrow\qquad 37x&=74\\
\Rightarrow\qquad x&=2.
\end{align*}Substituting $... | [
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"prompt": "<|begin_of_text|><|start_header_id|>user<|end_header_id|>\n\nFind the intersection of the lines $9x-4y=30$ and $7x+y=11.$ Express your answer as an ordered pair $(x,y).$ Let's work through this component by component.<|eot_id|><|start_header_id|>assistant<|end_header_id|>\n\n",
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"top... | The user wants to find the intersection of two lines and express the solution as an ordered pair (x, y). | To solve this problem, the models need to know basic algebraic concepts, such as solving linear equations and graphing lines. | medium | meta-llama/Meta-Llama-3-8B-Instruct | good | The user query is clear and well-structured, with a specific problem to be solved. The query provides the necessary information about the lines and the task to be performed. The user also provides a clear instruction to work through the problem component by component, which shows a good understanding of the problem-sol... | meta-llama/Meta-Llama-3-8B-Instruct | Math | [
"Reasoning"
] | meta-llama/Meta-Llama-3-8B-Instruct | EN |
81085611-55fb-5106-b498-b518b57c09a2 | Problem: Find the first natural number N with 1000 digits, all different. | What a fascinating problem!
To tackle this, let's break it down step by step:
1. **Understanding the problem**: We need to find the smallest natural number (a positive integer) with 1000 digits, where all digits are distinct (i.e., no digit is repeated).
2. **Upper bound**: The maximum possible value for a 1000-digi... | [
{
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"value": "Problem: Find the first natural number N with 1000 digits, all different."
},
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"from": "gpt",
"value": "What a fascinating problem!\n\nTo tackle this, let's break it down step by step:\n\n1. **Understanding the problem**: We need to find the smallest natural number ... | {
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"<|... | The user wants to find a specific natural number with a certain property | To solve this problem, the models need to know basic number theory, specifically the concept of natural numbers and their properties | hard | meta-llama/Meta-Llama-3-8B-Instruct | good | The query is clear and concise, but it lacks context and specific information about the problem. It does not provide any background or motivation for finding the first natural number with 1000 digits, all different. However, the query is specific about the requirement of having all different digits, which is a clear an... | meta-llama/Meta-Llama-3-8B-Instruct | Math | [
"Information seeking"
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ac0607ad-d307-53c2-8501-7c9095d53d72 | My mother celebrated her birthday with a total of 80 guests. Two-thirds of the guests are women, 15 are men, and the rest are children. In the middle of the celebration, half of the men and 10 children left. How many people stayed and enjoyed the birthday celebration? Let's handle this one aspect at a time. | Let's break it down step by step.
Let's start with the first part: "Two-thirds of the guests are women, 15 are men, and the rest are children."
We know that 2/3 of the guests are women, and there are 80 guests in total. To find the number of women, we can multiply 80 by 2/3:
(2/3) × 80 = 53.33 (round down to 53, sin... | [
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"prompt": "<|begin_of_text|><|start_header_id|>user<|end_header_id|>\n\nMy mother celebrated her birthday with a total of 80 guests. Two-thirds of the guests are women, 15 are men, and the rest are children. In the middle of the celebration, half of the men and 10 children left. How many people stayed and enjoyed t... | The user wants to calculate the number of people who stayed and enjoyed the birthday celebration after some guests left. | To solve this problem, the models need to know basic arithmetic operations, such as fractions, percentages, and subtraction. | medium | meta-llama/Meta-Llama-3-8B-Instruct | good | The query is clear and well-structured, with a specific scenario and multiple steps. The user provides all the necessary information, including the initial number of guests, the proportion of women, and the number of men and children. The query also breaks down the problem into manageable parts, making it easier to und... | meta-llama/Meta-Llama-3-8B-Instruct | Math | [
"Reasoning"
] | meta-llama/Meta-Llama-3-8B-Instruct | EN |
c7b41764-f7ac-5946-8e10-93b377ae5970 | find the maximum number from array [3, 5, 9, 1, 8, 23, 22] without using any inbuilt function. | Here is an algorithm to find the maximum number in an array without using any inbuilt function:
```
1. Initialize a variable `max` to the first element of the array.
2. Iterate through the array starting from the second element to the last element.
3. For each element, compare it with the current value of `max`.
4. If ... | [
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"prompt": "<|begin_of_text|><|start_header_id|>user<|end_header_id|>\n\nfind the maximum number from array [3, 5, 9, 1, 8, 23, 22] without using any inbuilt function.<|eot_id|><|start_header_id|>assistant<|end_header_id|>\n\n",
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"st... | The user wants to find the maximum number from a given array without using any inbuilt function. | To solve this problem, the models need to know basic programming concepts, such as loops and conditional statements. | medium | meta-llama/Meta-Llama-3-8B-Instruct | good | The query is clear and specific about the task, but it lacks context about what the array represents or what the maximum number is used for. The query also assumes that the user wants to find the maximum number in the array, but it's not explicitly stated. Additionally, the query asks to avoid using inbuilt functions, ... | meta-llama/Meta-Llama-3-8B-Instruct | Math | [
"Reasoning"
] | meta-llama/Meta-Llama-3-8B-Instruct | EN |
169d4cfe-30a9-5345-8fce-b0b111189d02 | Explain the 012 array method for solving离散小波变换 (DWT) in plain English. | A very specific and technical question! 😊
The 012 array method is a way to implement the Discrete Wavelet Transform (DWT) using a simple and efficient algorithm. I'll try to explain it in plain English, without getting too caught up in mathematical notation.
**What is the Discrete Wavelet Transform (DWT)?**
The DWT... | [
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"<|eot... | The user wants to understand the 012 array method for solving the Discrete Wavelet Transform (DWT) in a simple and easy-to-understand manner. | To solve this problem, the models need to know the basics of Discrete Wavelet Transform (DWT), wavelet theory, and the 012 array method. | medium | meta-llama/Meta-Llama-3-8B-Instruct | good | The user query is clear in its intent to ask for an explanation of the 012 array method for solving the Discrete Wavelet Transform (DWT) in plain English. The query is specific about the topic and the desired explanation style. However, it lacks context about the level of detail expected in the explanation and the spec... | meta-llama/Meta-Llama-3-8B-Instruct | Math | [
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70fd2009-c2e4-54ba-8bfd-565becb2c396 | Given a and b both positive integers and 16a^2 +24ab + 9 b^2=60 What is the largest possible value of b + a? | A nice Diophantine equation!
Let's factor the left-hand side:
$$16a^2 + 24ab + 9b^2 = (4a + 3b)^2 = 60$$
Now, we can take the square root of both sides:
$$4a + 3b = \pm \sqrt{60} = \pm 2\sqrt{15}$$
Since $a$ and $b$ are positive integers, we only consider the positive square root:
$$4a + 3b = 2\sqrt{15}$$
Now, w... | [
{
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"value": "Given a and b both positive integers and 16a^2 +24ab + 9 b^2=60 What is the largest possible value of b + a?"
},
{
"from": "gpt",
"value": "A nice Diophantine equation!\n\nLet's factor the left-hand side:\n\n$$16a^2 + 24ab + 9b^2 = (4a + 3b)^2 = 60$$\n\nNow, we can t... | {
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"max_tokens... | The user wants to solve a quadratic equation and find the largest possible value of b + a. | To solve this problem, the models need to know algebraic manipulation, quadratic equations, and basic arithmetic operations. | medium | meta-llama/Meta-Llama-3-8B-Instruct | good | The query is clear and well-structured, with a specific mathematical problem and a clear question. The variables 'a' and 'b' are defined as positive integers, which provides context for the problem. The query also provides the equation and the desired output, making it easy to understand the user's intent. The only pot... | meta-llama/Meta-Llama-3-8B-Instruct | Math | [
"Reasoning"
] | meta-llama/Meta-Llama-3-8B-Instruct | EN |
bc4e7082-bfa6-5d81-986d-ee2075195155 | If you have a full day random 8-hour schedule with appointments every hour, what is the probability that a randomly selected one hour appointment falls within the first 4 hours of the schedule? | A nice probability question!
Let's break it down:
You have a full 8-hour schedule with appointments every hour, which means you have 8 appointments in total.
You want to find the probability that a randomly selected 1-hour appointment falls within the first 4 hours of the schedule.
There are 4 appointments in the f... | [
{
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"value": "If you have a full day random 8-hour schedule with appointments every hour, what is the probability that a randomly selected one hour appointment falls within the first 4 hours of the schedule?"
},
{
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"prompt": "<|begin_of_text|><|start_header_id|>user<|end_header_id|>\n\nIf you have a full day random 8-hour schedule with appointments every hour, what is the probability that a randomly selected one hour appointment falls within the first 4 hours of the schedule?<|eot_id|><|start_header_id|>assistant<|end_header_... | The user wants to calculate the probability of a randomly selected one-hour appointment falling within the first 4 hours of a full day random 8-hour schedule with appointments every hour. | To solve this problem, the models need to know basic probability concepts, such as understanding the concept of probability and how to calculate it, and basic arithmetic operations like division. | easy | meta-llama/Meta-Llama-3-8B-Instruct | good | The query is well-structured and specific, with a clear question and a specific context. The user provides a well-defined scenario and a specific question about the probability of a randomly selected appointment falling within a certain time frame. The query lacks only a minor detail, which is the assumption that the a... | meta-llama/Meta-Llama-3-8B-Instruct | Math | [
"Information seeking"
] | meta-llama/Meta-Llama-3-8B-Instruct | EN |
4b20445e-38eb-50cb-94f6-3c6ec004265d | Anna is making gingerbread cookies. She gives x of them red hats, y of them blue boots, and z of them both red hats and blue boots. If there are a total of n gingerbread men, how many have neither a red hat nor a blue boot, given the values x = 12, y = 18, z = 6, and n = 25? | There are 12 with red hats, 18 with blue boots, and 6 with both. So there are 12 - 6 = 6 with just red hats, and 18 - 6 = 12 with just blue boots. So there are 6 + 12 + 6 = 24 with either a red hat or a blue boot. There are 25 total, so there are 25 - 24 = 1 with neither. The answer is 1. | [
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... | {
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"prompt": "<|begin_of_text|><|start_header_id|>user<|end_header_id|>\n\nAnna is making gingerbread cookies. She gives x of them red hats, y of them blue boots, and z of them both red hats and blue boots. If there are a total of n gingerbread men, how many have neither a red hat nor a blue boot, given the values x =... | The user wants to solve a problem involving conditional probability and set theory, specifically finding the number of gingerbread men with neither a red hat nor a blue boot. | To solve this problem, the models need to know basic algebra, conditional probability, and set theory concepts such as union, intersection, and complement. | medium | meta-llama/Meta-Llama-3-8B-Instruct | good | The query is well-structured and provides all the necessary information, including the values of x, y, z, and n. The problem is clearly defined, and the user's intent is easy to understand. The query is also specific, as it asks for a specific calculation based on the given values. The only minor weakness is that the q... | meta-llama/Meta-Llama-3-8B-Instruct | Math | [
"Reasoning"
] | meta-llama/Meta-Llama-3-8B-Instruct | EN |
f2a1d8e1-064f-5612-bae8-7470a13c6bcb | Use recursion to return the sum of all odd numbers up to a given number. Make sure to include a base case in your recursive function. Also, write a separate non-recursive function to verify the correctness of your recursive function. Both functions should handle edge cases such as negative numbers or zero. | Here is an example implementation in Python:
```
def recursive_sum_odd_numbers(n):
if n < 0:
return 0 # base case: sum of odd numbers up to a negative number is 0
elif n == 0:
return 0 # base case: sum of odd numbers up to 0 is 0
elif n % 2 == 1: # n is odd
return n + recursive_su... | [
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"prompt": "<|begin_of_text|><|start_header_id|>user<|end_header_id|>\n\nUse recursion to return the sum of all odd numbers up to a given number. Make sure to include a base case in your recursive function. Also, write a separate non-recursive function to verify the correctness of your recursive function. Both funct... | The user wants to write a recursive function to calculate the sum of all odd numbers up to a given number, and also wants to verify its correctness with a non-recursive function. | To solve this problem, the models need to know the concept of recursion, base case, and how to write a recursive function, as well as the concept of edge cases and how to handle them. | medium | meta-llama/Meta-Llama-3-8B-Instruct | good | The user query is well-structured and provides a clear problem statement. It also specifies the requirements for the solution, including the need for a base case in the recursive function and a separate non-recursive function for verification. The query also mentions edge cases such as negative numbers or zero, which i... | meta-llama/Meta-Llama-3-8B-Instruct | Math | [
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d1f8d059-c747-5d91-abf3-d27f0017d9b5 | Determine the volume of a right-angled triangular prism with the following dimensions: the base of the prism is a right-angled triangle with legs measuring 4cm and 3cm, and the height of the prism is 10cm. | A nice problem!
To find the volume of a right-angled triangular prism, we need to find the area of the base and multiply it by the height.
The base of the prism is a right-angled triangle with legs measuring 4cm and 3cm. We can find the area of this triangle using the formula:
Area = (base × height) / 2
In this cas... | [
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},
{
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"prompt": "<|begin_of_text|><|start_header_id|>user<|end_header_id|>\n\nDetermine the volume of a right-angled triangular prism with the following dimensions: the base of the prism is a right-angled triangle with legs measuring 4cm and 3cm, and the height of the prism is 10cm.<|eot_id|><|start_header_id|>assistant<... | The user wants to calculate the volume of a right-angled triangular prism | To solve this problem, the models need to know the formula for the volume of a prism, the concept of right-angled triangles, and how to calculate the area of a triangle | medium | meta-llama/Meta-Llama-3-8B-Instruct | good | The user query is clear and specific, providing all the necessary dimensions to calculate the volume of the right-angled triangular prism. The query is well-structured and easy to understand, with no ambiguity or vagueness. The user has provided all the relevant information, including the base dimensions and the height... | meta-llama/Meta-Llama-3-8B-Instruct | Math | [
"Information seeking"
] | meta-llama/Meta-Llama-3-8B-Instruct | EN |
77cec442-28ef-51b6-9d71-bdc39e565c58 | Raj's house has an area equal to 1,110 square feet. It has 4 bedrooms that each measure 11 x 11 feet. There are 2 bathrooms that are 6 x 8 feet each. The kitchen and living area complete the home and they have the same sized area. How many square feet is the area of the kitchen? Let's proceed with a structured approach... | Let's break down the problem step by step:
**Step 1: Calculate the total area of the bedrooms**
There are 4 bedrooms, each with an area of 11 x 11 = 121 square feet. So, the total area of the bedrooms is:
4 x 121 = 484 square feet
**Step 2: Calculate the total area of the bathrooms**
There are 2 bathrooms, each wi... | [
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"prompt": "<|begin_of_text|><|start_header_id|>user<|end_header_id|>\n\nRaj's house has an area equal to 1,110 square feet. It has 4 bedrooms that each measure 11 x 11 feet. There are 2 bathrooms that are 6 x 8 feet each. The kitchen and living area complete the home and they have the same sized area. How many squa... | The user wants to calculate the area of the kitchen in Raj's house | To solve this problem, the models need to know basic geometry and arithmetic operations, specifically area calculation and multiplication | easy | meta-llama/Meta-Llama-3-8B-Instruct | good | The user query is well-structured and provides all the necessary information to calculate the area of the kitchen. The query is clear and specific, and the user has provided a clear request for the answer to be presented in a boxed format. The only minor weakness is that the query could be more concise, but overall, it... | meta-llama/Meta-Llama-3-8B-Instruct | Math | [
"Information seeking"
] | meta-llama/Meta-Llama-3-8B-Instruct | EN |
5dd489d2-1168-5762-a30c-d1fcef1aec13 | Find the largest natural number \(x\) that is smaller than 1000 and satisfies both the following congruences: \[x \equiv 7 \pmod{14}\] and \[x \equiv 21 \pmod{35}\] \dots (Hint: There's a computational way out to directly find it.) | We have that $x \equiv 7 \pmod{14}$, so $x = 14k + 7$ for some integer $k$. Substituting this into the second congruence, we have $14k + 7 \equiv 21 \pmod{35}$, so $14k \equiv 14 \pmod{35}$. Since $(14, 35) = 7$, we have $2k \equiv 2 \pmod{5}$, so $k \equiv 1 \pmod{5}$. Therefore, $k = 5m + 1$ for some integer $m$, ... | [
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},
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"prompt": "<|begin_of_text|><|start_header_id|>user<|end_header_id|>\n\nFind the largest natural number \\(x\\) that is smaller than 1000 and satisfies both the following congruences: \\[x \\equiv 7 \\pmod{14}\\] and \\[x \\equiv 21 \\pmod{35}\\] \\dots (Hint: There's a computational way out to directly find it.)<|... | The user wants to find the largest natural number less than 1000 that satisfies two given congruences | To solve this problem, the models need to know basic concepts of modular arithmetic, congruences, and number theory | medium | meta-llama/Meta-Llama-3-8B-Instruct | good | The user query is well-structured and provides a clear mathematical problem. The notation and symbols used are correct and easy to understand. The query is also specific, as it provides a clear constraint on the range of the natural number (less than 1000) and two congruences that the number must satisfy. The hint prov... | meta-llama/Meta-Llama-3-8B-Instruct | Math | [
"Reasoning"
] | meta-llama/Meta-Llama-3-8B-Instruct | EN |
12b3d030-f7ae-5d10-bf27-9e62b4c91e17 | Write the definition of an invertible matrix. | A matrix A is said to be invertible (or non-singular) if there exists a matrix B such that:
AB = BA = I
where I is the identity matrix of the same size as A.
In other words, a matrix A is invertible if there exists a matrix B that, when multiplied by A, results in the identity matrix, and when A is multiplied by B, ... | [
{
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},
{
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"<|eot_id|>",
"<|end_of_tex... | The user wants to understand the definition of an invertible matrix | To solve this problem, the models need to know the basic concepts of linear algebra, specifically the definition of a matrix and its properties | easy | meta-llama/Meta-Llama-3-8B-Instruct | good | The query is clear and concise, asking for a specific definition. However, it lacks context and does not provide any additional information about what the user is looking for. This makes it difficult to understand the level of detail or complexity the user is expecting in the definition. | meta-llama/Meta-Llama-3-8B-Instruct | Math | [
"Information seeking"
] | meta-llama/Meta-Llama-3-8B-Instruct | EN |
e9e53930-ddef-5b79-a176-60c6dcc16040 | Given the equation below, find dy/dx at the point (2,1) and determine whether the function is increasing or decreasing at that point. | Please provide the equation, and I'll be happy to help you find dy/dx at the point (2,1) and determine whether the function is increasing or decreasing at that point. | [
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"prompt": "<|begin_of_text|><|start_header_id|>user<|end_header_id|>\n\nGiven the equation below, find dy/dx at the point (2,1) and determine whether the function is increasing or decreasing at that point.<|eot_id|><|start_header_id|>assistant<|end_header_id|>\n\n",
"temperature": 0,
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"repetition_p... | The user wants to find the derivative of a function and determine its increasing or decreasing nature at a specific point. | To solve this problem, the models need to know calculus, specifically the concept of derivatives and how to apply it to find the derivative of a function, as well as the ability to evaluate the derivative at a specific point. | medium | meta-llama/Meta-Llama-3-8B-Instruct | good | The query is clear and specific, providing a well-defined problem and asking for a specific calculation. The user also provides the necessary context by mentioning the point at which the calculation should be performed. The only potential weakness is that the query does not explicitly state the equation, which may requ... | meta-llama/Meta-Llama-3-8B-Instruct | Math | [
"Reasoning"
] | meta-llama/Meta-Llama-3-8B-Instruct | EN |
b1c3a2c8-9fc2-59cc-bd8a-1ccd58f18b24 | We roll a fair 6-sided die 7 times. What is the probability that we get an odd number 5 times and the number '6' exactly once? | There are $2^7=128$ possible outcomes for the parity of the 7 rolls, and $6^7$ possible outcomes for the 7 rolls themselves. Of the 128 possible outcomes for the parity of the 7 rolls, there are $\binom{7}{5}=21$ outcomes where we get an odd number 5 times and an even number 2 times. Of these 21 outcomes, there are $... | [
{
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"value": "We roll a fair 6-sided die 7 times. What is the probability that we get an odd number 5 times and the number '6' exactly once?"
},
{
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"value": "There are $2^7=128$ possible outcomes for the parity of the 7 rolls, and $6^7$ possible outcomes for the 7 ro... | {
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"prompt": "<|begin_of_text|><|start_header_id|>user<|end_header_id|>\n\nWe roll a fair 6-sided die 7 times. What is the probability that we get an odd number 5 times and the number '6' exactly once?<|eot_id|><|start_header_id|>assistant<|end_header_id|>\n\n",
"temperature": 0,
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"repetition_penalty"... | The user wants to calculate the probability of a specific outcome in a repeated experiment | To solve this problem, the models need to know probability theory, specifically the concept of independent events and the binomial distribution | medium | meta-llama/Meta-Llama-3-8B-Instruct | good | The query is clear and specific, providing the exact number of rolls (7) and the desired outcome (5 odd numbers and 1 '6'). The query also uses proper mathematical terminology, such as 'fair 6-sided die'. The only minor weakness is that it does not specify the order in which the odd numbers and '6' should appear, but t... | meta-llama/Meta-Llama-3-8B-Instruct | Math | [
"Reasoning"
] | meta-llama/Meta-Llama-3-8B-Instruct | EN |
e74bff53-a32d-5693-b4ca-9169b22a4389 | Dr intercepted 2 calls between Ellen and Frane. In these calls, the speakers discussed a total of 6 projects. No project was discussed in both calls. The list of projects discussed in the call includes projects with names starting with the letters A through G. What is the maximum number of projects that Dr could have h... | Let $x$ be the number of projects discussed in the first call. Then $6-x$ is the number of projects discussed in the second call. Since the projects discussed in the two calls are distinct, we have $x+(6-x)=6$, so the total number of projects discussed is 6. Since the projects have names starting with the letters A ... | [
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"value": "Dr intercepted 2 calls between Ellen and Frane. In these calls, the speakers discussed a total of 6 projects. No project was discussed in both calls. The list of projects discussed in the call includes projects with names starting with the letters A through G. What is the maximu... | {
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"prompt": "<|begin_of_text|><|start_header_id|>user<|end_header_id|>\n\nDr intercepted 2 calls between Ellen and Frane. In these calls, the speakers discussed a total of 6 projects. No project was discussed in both calls. The list of projects discussed in the call includes projects with names starting with the lett... | The user wants to determine the maximum number of projects that Dr could have heard about in the first call. | To solve this problem, the models need to know basic algebra and logic, specifically understanding the concept of sets and the fact that no project was discussed in both calls. | medium | meta-llama/Meta-Llama-3-8B-Instruct | good | The query is clear and specific, providing all the necessary information and context. The language is concise and easy to understand. The only minor weakness is that it assumes the reader is familiar with the context of the calls and the projects, but this is a minor issue. Overall, the query is well-written and effect... | meta-llama/Meta-Llama-3-8B-Instruct | Math | [
"Information seeking"
] | meta-llama/Meta-Llama-3-8B-Instruct | EN |
f55af9df-67a8-516d-a064-5885cdabcbaf | Vivek is standing in a row of 50 students. He is the 15th from the left end and the 20th from the right end. How many students are standing between him and the right end of the row? | Vivek is 15th from the left end. So there are 14 students to his left. He is 20th from the right end. So there are 19 students to his right. So there are 19 students between him and the right end. The answer is 19. | [
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"value": "Vivek is standing in a row of 50 students. He is the 15th from the left end and the 20th from the right end. How many students are standing between him and the right end of the row?"
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"value": "Vivek is 15th from the left end. So there are 14 stude... | {
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"prompt": "<|begin_of_text|><|start_header_id|>user<|end_header_id|>\n\nVivek is standing in a row of 50 students. He is the 15th from the left end and the 20th from the right end. How many students are standing between him and the right end of the row?<|eot_id|><|start_header_id|>assistant<|end_header_id|>\n\n",
... | The user wants to find the number of students between Vivek and the right end of the row | To solve this problem, the models need to know basic arithmetic operations, specifically addition and subtraction, and understanding of relative positions (left and right) in a row | easy | meta-llama/Meta-Llama-3-8B-Instruct | good | The query is clear and specific, providing all the necessary information about Vivek's position in the row. The context is well-defined, and the problem is well-structured. The query is easy to understand, and the user's intent is clear. The only minor weakness is that the query does not explicitly state the direction ... | meta-llama/Meta-Llama-3-8B-Instruct | Math | [
"Reasoning"
] | meta-llama/Meta-Llama-3-8B-Instruct | EN |
ede4f6d6-8477-527d-9664-ecf3515245e5 | Laura has 28 blocks and 8 cards. If she shares the blocks among 4 friends, each friend would get _____ blocks. If she shares the cards among 4 friends, then each friend would get _____ cards, and there would be _____ card leftover. Now, if there are 7 blue blocks, 8 green blocks, and 13 yellow blocks and she distribute... | Let's break this down step by step:
1. If Laura shares the 28 blocks among 4 friends, each friend would get:
28 ÷ 4 = 7 blocks
2. If she shares the 8 cards among 4 friends, each friend would get:
8 ÷ 4 = 2 cards
There would be 0 cards leftover.
3. Now, let's distribute the blocks in bulk:
Laura has 7 blue blocks, 8 ... | [
{
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"value": "Laura has 28 blocks and 8 cards. If she shares the blocks among 4 friends, each friend would get _____ blocks. If she shares the cards among 4 friends, then each friend would get _____ cards, and there would be _____ card leftover. Now, if there are 7 blue blocks, 8 green blocks... | {
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"extract_input": "<|im_start|>user\n"
} | {
"prompt": "<|begin_of_text|><|start_header_id|>user<|end_header_id|>\n\nLaura has 28 blocks and 8 cards. If she shares the blocks among 4 friends, each friend would get _____ blocks. If she shares the cards among 4 friends, then each friend would get _____ cards, and there would be _____ card leftover. Now, if ther... | The user wants to solve a problem involving block and card distribution among friends | To solve this problem, the models need to know basic arithmetic operations, such as division and remainder, and the concept of distributing items among a group of people | medium | meta-llama/Meta-Llama-3-8B-Instruct | good | The query is well-structured and provides a clear scenario with multiple parts. The user provides all the necessary information, including the initial number of blocks and cards, the sharing of blocks and cards, and the distribution of blocks in bulk. The query also specifies the conditions for the distribution of bloc... | meta-llama/Meta-Llama-3-8B-Instruct | Math | [
"Reasoning"
] | meta-llama/Meta-Llama-3-8B-Instruct | EN |
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