conversations listlengths 2 2 | question stringlengths 16 24.8k ⌀ | source stringclasses 10
values | id int64 3 50k ⌀ |
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[
{
"from": "user",
"value": "Find the sum of all possible positive integer values of $b$ such that the quadratic equation $2x^2 + 5x + b = 0$ has rational roots."
},
{
"from": "assistant",
"value": "## Step 1: Recall the condition for a quadratic equation to have rational roots.\nA quadratic equa... | null | null | null |
[
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"value": "How can I check if multiple keys are in a dictionary in a single pass? I want to be able to do something like this:\n\n<pre><code>\nfoo = {\n 'foo': 1,\n 'zip': 2,\n 'zam': 3,\n 'bar': 4\n}\n\nif (\"foo\", \"bar\") in foo:\n #do stuff\n</code></pre>\n\nHow can I ch... | null | null | null |
[
{
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"value": "Given that positive real numbers satisfy $a+2b=1$, the minimum value of $\\frac{1}{a}+\\frac{2}{b}$ is ( ).\n\nA: $8$\n\nB: $9$\n\nC: $10$\n\nD: $11$"
},
{
"from": "assistant",
"value": "<think>\nOkay, let's see. I have this problem where I need to find the minimum va... | Given that positive real numbers satisfy $a+2b=1$, the minimum value of $\frac{1}{a}+\frac{2}{b}$ is ( ).
A: $8$
B: $9$
C: $10$
D: $11$ | null | null |
[
{
"from": "user",
"value": "If the one-variable quadratic equation $x^{2}-2x+k=0$ has two equal real roots with respect to $x$, then $k=\\_\\_\\_\\_\\_\\_$."
},
{
"from": "assistant",
"value": "<think>\nOkay, let's see. The problem is about a quadratic equation x² - 2x + k = 0, and we need to fi... | If the one-variable quadratic equation $x^{2}-2x+k=0$ has two equal real roots with respect to $x$, then $k=\_\_\_\_\_\_$. | null | null |
[
{
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"value": "This is an email\nThough many of you already know, today is my last day here at Enron. I am leaving to pursue my culinary interests full time and have accepted a baking/pastry apprenticeship with the Deer Valley Resort in Park City, Utah for the winter season. I am happy to have ... | null | null | null |
[
{
"from": "user",
"value": "The standard equation of the hyperbola that passes through the point $(1,1)$ and satisfies $\\dfrac{b}{a}=\\sqrt{2}$ is $(\\quad)$\nA: $\\dfrac{x^2}{\\dfrac{1}{2}}-y^2=1$\nB: $\\dfrac{y^2}{\\dfrac{1}{2}}-x^2=1$\nC: $x^2-\\dfrac{y^2}{\\dfrac{1}{2}}=1$\nD: $\\dfrac{x^2}{\\dfrac{1}{... | The standard equation of the hyperbola that passes through the point $(1,1)$ and satisfies $\dfrac{b}{a}=\sqrt{2}$ is $(\quad)$
A: $\dfrac{x^2}{\dfrac{1}{2}}-y^2=1$
B: $\dfrac{y^2}{\dfrac{1}{2}}-x^2=1$
C: $x^2-\dfrac{y^2}{\dfrac{1}{2}}=1$
D: $\dfrac{x^2}{\dfrac{1}{2}}-y^2=1$ or $\dfrac{y^2}{\dfrac{1}{2}}-x^2=1$ | null | null |
[
{
"from": "user",
"value": "The interval that contains the root of the function $f(x) = 2^x + x - 7$ is ( )\nA: (0, 1)\nB: (1, 2)\nC: (2, 3)\nD: (3, 4)"
},
{
"from": "assistant",
"value": "<think>\nOkay, so I need to figure out which interval contains the root of the function f(x) = 2^x + x - 7.... | The interval that contains the root of the function $f(x) = 2^x + x - 7$ is ( )
A: (0, 1)
B: (1, 2)
C: (2, 3)
D: (3, 4) | null | null |
[
{
"from": "user",
"value": "Develop a Python script that connects to a Redis server, stores key-value pairs from a given JSON file, and retrieves values based on user input keys. Use command line arguments for specifying the JSON file path and the Redis server details (host and port).\nPLAINFORMAT"
},
{... | null | null | null |
[
{
"from": "user",
"value": "A and B enterd into a partnership investing Rs.16,000 and Rs.12,000 respectively.After 3 months,A withdrew Rs.5000 while B invested Rs.5000 more.After 3 more months.C joins the business with a capital of Rs.21,000.The share of B exceeds that of C,out of a total profit of Rs.26,40... | null | tiger_lab_math | 10,290 |
[
{
"from": "user",
"value": "Return your final response within \\boxed{}. Find the remainder when $3^{3^{3^3}}$ is divided by 1000.\n"
},
{
"from": "assistant",
"value": "<think>\nOkay, so I need to find the remainder when 3 raised to the power of 3 raised to the power of 3 raised to the power of... | Find the remainder when $3^{3^{3^3}}$ is divided by 1000.
| null | null |
[
{
"from": "user",
"value": "7. The school organizes 1511 people to go on an outing, renting 42-seat coaches and 25-seat minibuses. If it is required that there is exactly one seat per person and one person per seat, then there are $\\qquad$ rental options."
},
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"from": "assistant",
"value": "<t... | 7. The school organizes 1511 people to go on an outing, renting 42-seat coaches and 25-seat minibuses. If it is required that there is exactly one seat per person and one person per seat, then there are $\qquad$ rental options. | null | null |
[
{
"from": "user",
"value": "1. The range of the function $y=\\frac{x^{2}+2 x+3}{x^{2}+4 x+5}(x \\in \\mathbf{R})$ is"
},
{
"from": "assistant",
"value": "<think>\nAlright, let's tackle this problem step by step. So, the question is about finding the range of the function \\( y = \\frac{x^2 + 2x ... | 1. The range of the function $y=\frac{x^{2}+2 x+3}{x^{2}+4 x+5}(x \in \mathbf{R})$ is | null | null |
[
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"from": "user",
"value": "How can I write a Python program that takes an array of integers as input and outputs the second largest number?"
},
{
"from": "assistant",
"value": "**Second Largest Number in Array**\n=====================================\n\n**Program Description**\n----------------... | null | null | null |
[
{
"from": "user",
"value": "I have a form_tag in my view and I've nested some text_field_tag within it. I want to prevent the user from editing the text fields, so I set the :disabled => true option. However, I noticed that when I submit the form, the values of the disabled text fields are not included in t... | null | null | null |
[
{
"from": "user",
"value": "Având în vedere afluxul de refugiați din Africa de Nord și incertitudinea din regiune, apelăm la politici comunitare suplimentare și nu dorim re-naționalizarea.\n\nTranslate to English"
},
{
"from": "assistant",
"value": "Given the influx of refugees from North Africa... | null | null | null |
[
{
"from": "user",
"value": "69. A supermarket purchases 200 toys at a cost of 10 yuan each. Sales personnel expect the upcoming promotion: at a unit price of 19 yuan, only 100 units can be sold, and for every 1 yuan decrease in price, 20 more units can be sold. At what unit price will the expected profit fr... | 69. A supermarket purchases 200 toys at a cost of 10 yuan each. Sales personnel expect the upcoming promotion: at a unit price of 19 yuan, only 100 units can be sold, and for every 1 yuan decrease in price, 20 more units can be sold. At what unit price will the expected profit from this promotional activity be maximize... | null | null |
[
{
"from": "user",
"value": "David works at a science lab that conducts experiments on bacteria. The population of the bacteria multiplies at a constant rate, and his job is to notate the population of a certain group of bacteria each hour. At 1 p.m. on a certain day, he noted that the population was 2,500 a... | null | tiger_lab_math | 34,921 |
[
{
"from": "user",
"value": "## Task A-1.1.\n\nBy deleting the first two digits of some natural number $n$, a number 73 times smaller is obtained. Determine the two smallest such numbers $n$."
},
{
"from": "assistant",
"value": "<think>\nOkay, so I need to find natural numbers n such that when I ... | ## Task A-1.1.
By deleting the first two digits of some natural number $n$, a number 73 times smaller is obtained. Determine the two smallest such numbers $n$. | null | null |
[
{
"from": "user",
"value": "Generate an executable Python function generated from the given prompt. The function should take stdin as input and print the output. Simply call the function after the definition.Kirti likes 8. Kirti's restaurant has many menus whose prices are multiples of 8. Now, Kirti has som... | Generate an executable Python function generated from the given prompt. The function should take stdin as input and print the output. Simply call the function after the definition.Kirti likes 8. Kirti's restaurant has many menus whose prices are multiples of 8. Now, Kirti has some digits written on a wooden board, and ... | null | null |
[
{
"from": "user",
"value": "Given points $P$ and $Q$ are on the graphs of the functions $y=e^{x}$ and $y=kx$ ($k > 0$) respectively. If there is only one pair of points $(P,Q)$ that are symmetric about the line $y=x$, then $k=$\\_\\_\\_\\_\\_\\_."
},
{
"from": "assistant",
"value": "<think>\nAlr... | Given points $P$ and $Q$ are on the graphs of the functions $y=e^{x}$ and $y=kx$ ($k > 0$) respectively. If there is only one pair of points $(P,Q)$ that are symmetric about the line $y=x$, then $k=$\_\_\_\_\_\_. | null | null |
[
{
"from": "user",
"value": "Return your final response within \\boxed{}. Find all polynomials \\( P \\in \\mathbb{Z}[X] \\) such that \\( P(n) \\) divides \\( n^{n-1} - 1 \\) for all \\( n \\geq 2001 \\)."
},
{
"from": "assistant",
"value": "<think>\nOkay, so I need to find all polynomials P wit... | Find all polynomials \( P \in \mathbb{Z}[X] \) such that \( P(n) \) divides \( n^{n-1} - 1 \) for all \( n \geq 2001 \). | null | null |
[
{
"from": "user",
"value": "Return your final response within \\boxed{}. Given an equilateral triangle $\\mathrm{ABC}$. Right isosceles triangles ABP and BCQ with right angles at $\\angle \\mathrm{ABP}$ and $\\angle \\mathrm{BCQ}$ are constructed externally on sides $\\mathrm{AB}$ and $\\mathrm{BC}$, respec... | Given an equilateral triangle $\mathrm{ABC}$. Right isosceles triangles ABP and BCQ with right angles at $\angle \mathrm{ABP}$ and $\angle \mathrm{BCQ}$ are constructed externally on sides $\mathrm{AB}$ and $\mathrm{BC}$, respectively. Find the angle $\angle \mathrm{PAQ}$. | null | null |
[
{
"from": "user",
"value": "Proposition 1 Let $P$ be the Brocard point of $\\triangle ABC$ (as shown in the figure), the inradii and areas of $\\triangle BPC$, $\\triangle CPA$, and $\\triangle APB$ are $r_a$, $r_b$, $r_c$, $\\triangle_a$, $\\triangle_b$, and $\\triangle_c$, respectively. The inradius and a... | Proposition 1 Let $P$ be the Brocard point of $\triangle ABC$ (as shown in the figure), the inradii and areas of $\triangle BPC$, $\triangle CPA$, and $\triangle APB$ are $r_a$, $r_b$, $r_c$, $\triangle_a$, $\triangle_b$, and $\triangle_c$, respectively. The inradius and area of $\triangle ABC$ are $r$ and $\triangle$,... | null | null |
[
{
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"value": "1. Find the sum of the digits of the number $A$, if $A=2^{63} \\cdot 4^{25} \\cdot 5^{106}-2^{22} \\cdot 4^{44} \\cdot 5^{105}-1$. Answer: 959."
},
{
"from": "assistant",
"value": "<think>\nOkay, let's see. I need to find the sum of the digits of the number A, which i... | 1. Find the sum of the digits of the number $A$, if $A=2^{63} \cdot 4^{25} \cdot 5^{106}-2^{22} \cdot 4^{44} \cdot 5^{105}-1$. Answer: 959. | null | null |
[
{
"from": "user",
"value": "In the geometric sequence ${a_n}$, it is known that $a_1+a_2=324$ and $a_3+a_4=36$. Find the value of $a_5+a_6$."
},
{
"from": "assistant",
"value": "<think>\nOkay, so I need to find the value of a₅ + a₆ in a geometric sequence where a₁ + a₂ = 324 and a₃ + a₄ = 36. Hm... | In the geometric sequence ${a_n}$, it is known that $a_1+a_2=324$ and $a_3+a_4=36$. Find the value of $a_5+a_6$. | null | null |
[
{
"from": "user",
"value": "Ava reads 20 pages of a book every night during the weekdays. On the weekends, she reads an additional 1 hour and 30 minutes, which is equivalent to 45 pages. How many pages does she read in 52 weeks?"
},
{
"from": "assistant",
"value": "<think>\nOkay, so the problem ... | null | nvidia_math | 37,137 |
[
{
"from": "user",
"value": "Which of the following conclusions is correct?\n\nA: $-\\left(-3\\right)^{2}=9$\n\nB: $-6÷6×\\frac{1}{6}=-6$\n\nC: $(-3)^2×|-\\frac{1}{3}|=3$\n\nD: $\\frac{3^2}{2}=\\frac{9}{4}$"
},
{
"from": "assistant",
"value": "<think>\nOkay, so I need to figure out which of the o... | Which of the following conclusions is correct?
A: $-\left(-3\right)^{2}=9$
B: $-6÷6×\frac{1}{6}=-6$
C: $(-3)^2×|-\frac{1}{3}|=3$
D: $\frac{3^2}{2}=\frac{9}{4}$ | null | null |
[
{
"from": "user",
"value": "You are tasked with implementing a RevokeTokenByQuery feature in a Node.js application using the async, lodash, and ioredis libraries. The feature should allow the user to revoke a token by providing a query, which can include a tag and/or a UUID. When the feature is called, it s... | null | null | null |
[
{
"from": "user",
"value": "Binkov A, A:\n\nIn a football championship, 16 teams participated. Each team played against each of the others once, with 3 points awarded for a win, 1 point for a draw, and 0 points for a loss. We will call a team successful if it scored at least half of the maximum possible num... | Binkov A, A:
In a football championship, 16 teams participated. Each team played against each of the others once, with 3 points awarded for a win, 1 point for a draw, and 0 points for a loss. We will call a team successful if it scored at least half of the maximum possible number of points. What is the maximum number ... | null | null |
[
{
"from": "user",
"value": "The coefficient of the term containing $x^2$ in the expansion of $\\left(x- \\frac {1}{x}\\right)^{6}$ is ( ) \nA: -20 \nB: 20 \nC: -15 \nD: 15"
},
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"from": "assistant",
"value": "<think>\nOkay, so I need to find the coefficient of the term that has x squared in... | The coefficient of the term containing $x^2$ in the expansion of $\left(x- \frac {1}{x}\right)^{6}$ is ( )
A: -20
B: 20
C: -15
D: 15 | null | null |
[
{
"from": "user",
"value": "Find the right ending to this passage.\n\nBy Christopher Wilson PUBLISHED: 20:10 EST, 23 January 2013 | UPDATED: 21:25 EST, 23 January 2013 A drunken brawl with his equerry. A married mistress, secret hotel assignations, an illegitimate child — surely our brand-new hero Prince Ha... | null | null | null |
[
{
"from": "user",
"value": "Return your final response within \\boxed{}. Through the midpoint \\( M \\) of chord \\( AB \\) in a circle, draw any chords \\( CD \\) and \\( EF \\). Let \\( CF \\) and \\( ED \\) intersect chord \\( AB \\) at points \\( Q \\) and \\( P \\) respectively. Prove that \\( PM = MQ ... | Through the midpoint \( M \) of chord \( AB \) in a circle, draw any chords \( CD \) and \( EF \). Let \( CF \) and \( ED \) intersect chord \( AB \) at points \( Q \) and \( P \) respectively. Prove that \( PM = MQ \). | null | null |
[
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"value": "3. Since the parabola intersects the x-axis at $x=1$, the value of the function $y=a x^{2}+b x+c$ at this point is zero, i.e.,\n\n$$\na+b+c=0\n$$\n\nThe equation of the given line can be written as\n\n$$\ny=5-2 x\n$$\n\nThe condition for the line to be tangent to the parabola at ... | 3. Since the parabola intersects the x-axis at $x=1$, the value of the function $y=a x^{2}+b x+c$ at this point is zero, i.e.,
$$
a+b+c=0
$$
The equation of the given line can be written as
$$
y=5-2 x
$$
The condition for the line to be tangent to the parabola at the point $(x ; y)$ is that the values of the functi... | null | null |
[
{
"from": "user",
"value": "$(1)$ Calculate: $(6x^{3}y^{4}z-4x^{2}y^{3}z+2xy^{3})\\div 2xy^{3}$; \n$(2)$ Factorize: $\\left(a-b\\right)\\left(a-4b\\right)+ab$."
},
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"from": "assistant",
"value": "<think>\nOkay, so I have two problems to solve here. Let me take them one at a time. \n\nStarting ... | $(1)$ Calculate: $(6x^{3}y^{4}z-4x^{2}y^{3}z+2xy^{3})\div 2xy^{3}$;
$(2)$ Factorize: $\left(a-b\right)\left(a-4b\right)+ab$. | null | null |
[
{
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"value": "10. (20 points) Through the focus $F$ of the parabola $y^{2}=4 x$, draw a line $l$ intersecting the parabola at points $A$ and $B$. Let $M(4,0)$. Extend $A M$ and $B M$ to intersect the parabola at points $C$ and $D$, respectively. Find the value of $\\frac{S_{\\triangle C D M}}{... | 10. (20 points) Through the focus $F$ of the parabola $y^{2}=4 x$, draw a line $l$ intersecting the parabola at points $A$ and $B$. Let $M(4,0)$. Extend $A M$ and $B M$ to intersect the parabola at points $C$ and $D$, respectively. Find the value of $\frac{S_{\triangle C D M}}{S_{\triangle A B M}}$. | null | null |
[
{
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"value": "2-2. Find the minimum value of the function\n\n$$\nf(x)=x^{2}+(x-2)^{2}+(x-4)^{2}+\\ldots+(x-102)^{2}\n$$\n\nIf the result is a non-integer, round it to the nearest integer and write it as the answer."
},
{
"from": "assistant",
"value": "<think>\nOkay, so I need to fi... | 2-2. Find the minimum value of the function
$$
f(x)=x^{2}+(x-2)^{2}+(x-4)^{2}+\ldots+(x-102)^{2}
$$
If the result is a non-integer, round it to the nearest integer and write it as the answer. | null | null |
[
{
"from": "user",
"value": "Return your final response within \\boxed{}. For the positive numbers \\( x \\) and \\( y \\), it is known that\n\n\\[ \n\\frac{1}{1+x+x^{2}} + \\frac{1}{1+y+y^{2}} + \\frac{1}{1+x+y} = 1\n\\]\n\nWhat values can the product \\( xy \\) take? Indicate all possible options and prove... | For the positive numbers \( x \) and \( y \), it is known that
\[
\frac{1}{1+x+x^{2}} + \frac{1}{1+y+y^{2}} + \frac{1}{1+x+y} = 1
\]
What values can the product \( xy \) take? Indicate all possible options and prove that there are no other values. | null | null |
[
{
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"value": "Given the parabola $y^{2}=6x$, a chord is drawn through the point $P(4,1)$, such that it is bisected at point $P$. Determine the equation of the line $l$ on which this chord lies."
},
{
"from": "assistant",
"value": "<think>\nOkay, so I need to find the equation of a ... | Given the parabola $y^{2}=6x$, a chord is drawn through the point $P(4,1)$, such that it is bisected at point $P$. Determine the equation of the line $l$ on which this chord lies. | null | null |
[
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"value": "Given space vectors $\\overrightarrow{a}=(-3,2,5)$, $\\overrightarrow{b}=(1,x,-1)$, and $\\overrightarrow{a}$ is perpendicular to $\\overrightarrow{b}$, then $x$ is ______."
},
{
"from": "assistant",
"value": "<think>\nOkay, so I need to find the value of x such that ... | Given space vectors $\overrightarrow{a}=(-3,2,5)$, $\overrightarrow{b}=(1,x,-1)$, and $\overrightarrow{a}$ is perpendicular to $\overrightarrow{b}$, then $x$ is ______. | null | null |
[
{
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"value": "Create a function that takes in a nested dictionary and a list of keys, and assigns a value to the innermost key in the dictionary. The value can be any data type. The function should return the updated nested dictionary.\n\nExample:\nInput: {'key1': {'key2': {'key3': 'value1'}}}... | null | codefeedback | null |
[
{
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"value": "Russian problems Problem 35 Given a triangle ABC. Let the line through C parallel to the angle bisector of B meet the angle bisector of A at D, and let the line through C parallel to the angle bisector of A meet the angle bisector of B at E. Prove that if DE is parallel to AB, th... | Russian problems Problem 35 Given a triangle ABC. Let the line through C parallel to the angle bisector of B meet the angle bisector of A at D, and let the line through C parallel to the angle bisector of A meet the angle bisector of B at E. Prove that if DE is parallel to AB, then CA=CB. | null | null |
[
{
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"value": "Given that the solution set of the inequality $\\frac{x-2}{ax+b} > 0$ is $(-1,2)$, and $m$ is the geometric mean of $a$ and $b$, then $\\frac{3m^{2}a}{a^{3}+2b^{3}}=$ ()\nA: $3$\nB: $-3$\nC: $-1$\nD: $1$"
},
{
"from": "assistant",
"value": "<think>\nOkay, so I need to... | Given that the solution set of the inequality $\frac{x-2}{ax+b} > 0$ is $(-1,2)$, and $m$ is the geometric mean of $a$ and $b$, then $\frac{3m^{2}a}{a^{3}+2b^{3}}=$ ()
A: $3$
B: $-3$
C: $-1$
D: $1$ | null | null |
[
{
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"value": "Write $(-5)^5\\div5^3+3^{4}-6^{1}$ as an integer."
},
{
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"value": "<think>\nOkay, so I need to calculate this expression: (-5)^5 divided by 5^3 plus 3^4 minus 6^1. Hmm, let me break this down step by step. First, I should handle each part separatel... | null | tiger_math | 37,075 |
[
{
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"value": "I am trying to convert a dictionary to a JSON string using both `json.dumps` and `flask.jsonify` in Python. The dictionary looks like this: \n\n```python\ndata = {\"id\": str(album.id), \"title\": album.title}\n```\n\nHowever, the output I get from `json.dumps(data)` differs from... | null | null | null |
[
{
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"value": "Task 1. Find all pairs $(x, y)$ of integers that satisfy\n\n$$\nx^{2}+y^{2}+3^{3}=456 \\sqrt{x-y} .\n$$"
},
{
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"value": "<think>\nOkay, so I need to find all integer pairs (x, y) that satisfy the equation x² + y² + 27 = 456√(x - y). Hmm, let's star... | Task 1. Find all pairs $(x, y)$ of integers that satisfy
$$
x^{2}+y^{2}+3^{3}=456 \sqrt{x-y} .
$$ | null | null |
[
{
"from": "user",
"value": "# Problem 7. (4 points)\n\n$O A B C$ is a rectangle on the Cartesian plane, with sides parallel to the coordinate axes. Point $O$ is the origin, and point $B$ has coordinates $(9 ; 8)$. Inside the rectangle, a point $X$ with integer coordinates is taken. What is the smallest valu... | # Problem 7. (4 points)
$O A B C$ is a rectangle on the Cartesian plane, with sides parallel to the coordinate axes. Point $O$ is the origin, and point $B$ has coordinates $(9 ; 8)$. Inside the rectangle, a point $X$ with integer coordinates is taken. What is the smallest value that the area of triangle $O B X$ can ta... | null | null |
[
{
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"value": "How can I implement a nested Django admin inline in my application? I have some existing models: Person, Certificate and Training_Date, where 'Certificate' is related to 'Person' and 'Training_Date' is related to 'Certificate'. I have created an inline admin for 'Certificate' ins... | null | null | null |
[
{
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"value": "Jesse brought home their friend for thanksgiving because their friend's family lived far away. Given the context: How would you describe Jesse?\nThe answer is:"
},
{
"from": "assistant",
"value": "Based on the context, here's a description of Jesse:\n\n* **Compassion... | null | null | null |
[
{
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"value": "Generate an executable Python function generated from the given prompt. The function should take stdin as input and print the output. Simply call the function after the definition.The only difference between the easy and hard versions is that the given string s in the easy versio... | Generate an executable Python function generated from the given prompt. The function should take stdin as input and print the output. Simply call the function after the definition.The only difference between the easy and hard versions is that the given string s in the easy version is initially a palindrome, this condit... | null | null |
[
{
"from": "user",
"value": "Design a Python web scraper that extracts product information (name, price, and availability) from an e-commerce website and stores the data in a SQLite database. The scraper should be able to handle pagination and gracefully recover from errors."
},
{
"from": "assistant"... | null | null | null |
[
{
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"value": "Given the set $\\{a, b, c\\}$, the number of subsets of set $A$ is ____."
},
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"value": "<think>\nAlright, so I need to find the number of subsets of the set A, which is given as {a, b, c}. Hmm, subsets... Okay, subsets are all the possible combin... | Given the set $\{a, b, c\}$, the number of subsets of set $A$ is ____. | null | null |
[
{
"from": "user",
"value": "A line $e$ intersects a convex polygon, dividing its area in half. Project the resulting regions perpendicularly onto a line $f$ that is perpendicular to $e$. Prove that the ratio of the projection segments cannot be greater than $(1+\\sqrt{2})$!"
},
{
"from": "assistant"... | A line $e$ intersects a convex polygon, dividing its area in half. Project the resulting regions perpendicularly onto a line $f$ that is perpendicular to $e$. Prove that the ratio of the projection segments cannot be greater than $(1+\sqrt{2})$! | null | null |
[
{
"from": "user",
"value": "If the graph of the function $y=f(x)$ is symmetric to the graph of $y=e^{x+1}$ with respect to the line $y=x$, then $f(x)=$ （ ）\nA: $\\ln x-1$ ($x>0$)\nB: $\\ln (x-0)$ ($x>1$)\nC: $\\ln x+1$ ($x>1$)\nD: $\\ln x-1$ ($x>1$)"
},
{
"from": "assistant",
"value": "<think>\n... | If the graph of the function $y=f(x)$ is symmetric to the graph of $y=e^{x+1}$ with respect to the line $y=x$, then $f(x)=$ （ ）
A: $\ln x-1$ ($x>0$)
B: $\ln (x-0)$ ($x>1$)
C: $\ln x+1$ ($x>1$)
D: $\ln x-1$ ($x>1$) | null | null |
[
{
"from": "user",
"value": "Generate an executable Python function generated from the given prompt. The function should take stdin as input and print the output. Simply call the function after the definition.Given two integer numbers a and b, the task is to find count of all common divisors of given numbers... | Generate an executable Python function generated from the given prompt. The function should take stdin as input and print the output. Simply call the function after the definition.Given two integer numbers a and b, the task is to find count of all common divisors of given numbers.
Example 1:
Input: a = 12, b = 24
Outpu... | null | null |
[
{
"from": "user",
"value": "5. In the rectangular prism $A B C D-A_{1} B_{1} C_{1} D_{1}$, $A B=$ $2, A A_{1}=A D=1$, points $E$, $F$, and $G$ are the midpoints of edges $A A_{1}$, $C_{1} D_{1}$, and $B C$ respectively. The volume of the tetrahedron $B_{1}-E F G$ is $\\qquad$"
},
{
"from": "assistan... | 5. In the rectangular prism $A B C D-A_{1} B_{1} C_{1} D_{1}$, $A B=$ $2, A A_{1}=A D=1$, points $E$, $F$, and $G$ are the midpoints of edges $A A_{1}$, $C_{1} D_{1}$, and $B C$ respectively. The volume of the tetrahedron $B_{1}-E F G$ is $\qquad$ | null | null |
[
{
"from": "user",
"value": "4. Krt Črt has 5 rooms in his burrow, numbered from 1 to 5. Between some of them, Črt has dug tunnels, so from each room he can slide through several tunnels to any other room. No two tunnels intersect. Each tunnel starts in one room, ends in another (different from the starting ... | 4. Krt Črt has 5 rooms in his burrow, numbered from 1 to 5. Between some of them, Črt has dug tunnels, so from each room he can slide through several tunnels to any other room. No two tunnels intersect. Each tunnel starts in one room, ends in another (different from the starting one), and does not pass through any room... | null | null |
[
{
"from": "user",
"value": "You are tasked with implementing a method to read and process a specific type of data structure from a binary file. The data structure is called \"xyztype\" and is part of an ICC (International Color Consortium) profile. The given code snippet provides a starting point for readin... | null | magicoder | null |
[
{
"from": "user",
"value": "Read the text and determine if the sentence is true (see options at the end):\n\nAustralian Broadcasting Company (ABC) television head, Sandra Levy, has quit to become the director of development for \"Channel Nine.\" Her new role is expected to focus on drama. ABC managing direc... | null | null | null |
[
{
"from": "user",
"value": "Calculate: $2^{-2}+\\sqrt[3]{8}-2023^0-2\\sin45°+|-\\sqrt{2}|$."
},
{
"from": "assistant",
"value": "<think>\nOkay, let me try to solve this problem step by step. The problem is to calculate the expression: 2^{-2} + ∛8 - 2023^0 - 2 sin45° + | -√2 |. Hmm, let's break i... | Calculate: $2^{-2}+\sqrt[3]{8}-2023^0-2\sin45°+|-\sqrt{2}|$. | null | null |
[
{
"from": "user",
"value": "A company produces ceramics. According to the historical data, the fixed cost of producing ceramics per day is 14,000 yuan, and the cost increases by 210 yuan for each product produced. The daily sales volume $f(x)$ is related to the production quantity $x$ pieces by the followin... | A company produces ceramics. According to the historical data, the fixed cost of producing ceramics per day is 14,000 yuan, and the cost increases by 210 yuan for each product produced. The daily sales volume $f(x)$ is related to the production quantity $x$ pieces by the following formula: $f\left(x\right)=\begin{cases... | null | null |
[
{
"from": "user",
"value": "Group Event 6\nThe following shows the graph of $y=p x^{2}+5 x+p . A=(0,-2)$, $B=\\left(\\frac{1}{2}, 0\\right), C=(2,0), O=(0,0)$.\nG6.1 Find the value of $p$."
},
{
"from": "assistant",
"value": "<think>\nOkay, so I need to find the value of p for the quadratic equa... | Group Event 6
The following shows the graph of $y=p x^{2}+5 x+p . A=(0,-2)$, $B=\left(\frac{1}{2}, 0\right), C=(2,0), O=(0,0)$.
G6.1 Find the value of $p$. | null | null |
[
{
"from": "user",
"value": "9. Given the function\n$$\nf(x)=\\left(\\frac{1}{a^{x}-1}+\\frac{1}{2}\\right) x^{2}+b x+6,\n$$\n\nwhere $a$ and $b$ are constants, $a>1$, and\n$$\nf\\left(\\lg \\log _{8} 1000\\right)=8.\n$$\n\nThen the value of $f(\\lg \\lg 2)$ is ( ).\n(A) 8\n(B) 4\n(C) -4\n(D) -8"
},
{
... | 9. Given the function
$$
f(x)=\left(\frac{1}{a^{x}-1}+\frac{1}{2}\right) x^{2}+b x+6,
$$
where $a$ and $b$ are constants, $a>1$, and
$$
f\left(\lg \log _{8} 1000\right)=8.
$$
Then the value of $f(\lg \lg 2)$ is ( ).
(A) 8
(B) 4
(C) -4
(D) -8 | null | null |
[
{
"from": "user",
"value": "6. The general term formula of the sequence $\\left\\{a_{n}\\right\\}$ is $a_{n}=\\tan n \\cdot \\tan (n-1)$, and for any positive integer $n$, there is $a_{1}+a_{2}+\\cdots+a_{n}=A \\tan n+B n$ holds, then $A=$ $\\qquad$ $. B=$ $\\qquad$ ."
},
{
"from": "assistant",
... | 6. The general term formula of the sequence $\left\{a_{n}\right\}$ is $a_{n}=\tan n \cdot \tan (n-1)$, and for any positive integer $n$, there is $a_{1}+a_{2}+\cdots+a_{n}=A \tan n+B n$ holds, then $A=$ $\qquad$ $. B=$ $\qquad$ . | null | null |
[
{
"from": "user",
"value": "7. Without rearranging the digits on the left side of the equation, insert two \"+\" signs between them so that the equation $8789924=1010$ becomes true."
},
{
"from": "assistant",
"value": "<think>\nOkay, so I need to figure out how to insert two plus signs into the ... | 7. Without rearranging the digits on the left side of the equation, insert two "+" signs between them so that the equation $8789924=1010$ becomes true. | null | null |
[
{
"from": "user",
"value": "What is the code for connecting a PHP application to a MySQL database and performing database queries?"
},
{
"from": "assistant",
"value": "<think>\nOkay, the user wants to know how to connect a PHP application to a MySQL database and perform queries. Let me break thi... | null | sharegpt | null |
[
{
"from": "user",
"value": "Explain the intricate steps taken by a company's HR department in creating a personalized onboarding program that considers not only the employee's job expectations, but also their individual communication style, learning preferences, and personality traits. Additionally, discuss... | null | null | null |
[
{
"from": "user",
"value": "It is known that $\\frac{7}{13} + \\sin \\phi = \\cos \\phi$ for some real $\\phi$. What is sin $2\\phi$?"
},
{
"from": "assistant",
"value": "<think>\nOkay, let's see. I need to solve for sin 2φ given that 7/13 plus sinφ equals cosφ. Hmm. Alright, first, let's write ... | It is known that $\frac{7}{13} + \sin \phi = \cos \phi$ for some real $\phi$. What is sin $2\phi$? | null | null |
[
{
"from": "user",
"value": "87. A group has 8 people, 4 people love to eat bananas, 7 people love to eat strawberries, at least $\\qquad$ people love to eat both bananas and strawberries."
},
{
"from": "assistant",
"value": "<think>\nOkay, so I have this problem here: There's a group of 8 people... | 87. A group has 8 people, 4 people love to eat bananas, 7 people love to eat strawberries, at least $\qquad$ people love to eat both bananas and strawberries. | null | null |
[
{
"from": "user",
"value": "An object's motion equation is $s=1-2t+2t^2$, where $s$ is in meters, and $t$ is in seconds. What is the instantaneous velocity of the object at the end of 3 seconds?\n\nA: 9 meters/second \nB: 10 meters/second \nC: 12 meters/second \nD: 13 meters/second"
},
{
"from": ... | An object's motion equation is $s=1-2t+2t^2$, where $s$ is in meters, and $t$ is in seconds. What is the instantaneous velocity of the object at the end of 3 seconds?
A: 9 meters/second
B: 10 meters/second
C: 12 meters/second
D: 13 meters/second | null | null |
[
{
"from": "user",
"value": "Write a function to calculate the sum of the elements of an array with float values, excluding any negative values and rounding the final sum to two decimal places."
},
{
"from": "assistant",
"value": "<think>\nOkay, I need to write a function that calculates the sum ... | null | codefeedback | null |
[
{
"from": "user",
"value": "Exercise 11. For all integers $n \\geqslant 0$, we define\n\n$$\nU_{n}=\\frac{2 n+1-2 \\sqrt{n(n+1)}}{\\sqrt{n+1}-\\sqrt{n}}\n$$\n\nCalculate $\\left(\\mathrm{U}_{0}+\\cdots+\\mathrm{U}_{41}\\right)^{2}$."
},
{
"from": "assistant",
"value": "<think>\nOkay, let's try t... | Exercise 11. For all integers $n \geqslant 0$, we define
$$
U_{n}=\frac{2 n+1-2 \sqrt{n(n+1)}}{\sqrt{n+1}-\sqrt{n}}
$$
Calculate $\left(\mathrm{U}_{0}+\cdots+\mathrm{U}_{41}\right)^{2}$. | null | null |
[
{
"from": "user",
"value": "7. Given that $\\theta$ is an acute angle, find the minimum value of $y=$ $\\left(12 \\cos ^{2} \\theta+\\frac{1}{4 \\cos ^{2} \\theta}\\right)\\left(12 \\sin ^{2} \\theta+\\frac{1}{4 \\sin ^{2} \\theta}\\right)$."
},
{
"from": "assistant",
"value": "<think>\nOkay, so... | 7. Given that $\theta$ is an acute angle, find the minimum value of $y=$ $\left(12 \cos ^{2} \theta+\frac{1}{4 \cos ^{2} \theta}\right)\left(12 \sin ^{2} \theta+\frac{1}{4 \sin ^{2} \theta}\right)$. | null | null |
[
{
"from": "user",
"value": "19. Divide the natural numbers $1,2,3,4, \\ldots . . ., 2019$ into 20 groups so that the average of each group is equal. What is the average of each group? $\\qquad$"
},
{
"from": "assistant",
"value": "<think>\nOkay, let's tackle this problem. So, we need to divide t... | 19. Divide the natural numbers $1,2,3,4, \ldots . . ., 2019$ into 20 groups so that the average of each group is equal. What is the average of each group? $\qquad$ | null | null |
[
{
"from": "user",
"value": "456. Every evening, Uncle Chernomor appoints 9 or 10 out of 33 bogatyrs for duty, at his discretion. What is the smallest number of days after which it can happen that each of the bogatyrs has been on duty the same number of times?"
},
{
"from": "assistant",
"value": ... | 456. Every evening, Uncle Chernomor appoints 9 or 10 out of 33 bogatyrs for duty, at his discretion. What is the smallest number of days after which it can happen that each of the bogatyrs has been on duty the same number of times? | null | null |
[
{
"from": "user",
"value": "Given $\\sin \\left(\\frac{\\pi }{2}+\\alpha \\right)=\\frac{1}{3}$, the value of $\\cos (\\pi +2\\alpha )$ is ( ).\n\nA: $-\\frac{7}{9}$\n\nB: $\\frac{7}{9}$\n\nC: $\\frac{2}{9}$\n\nD: $-\\frac{2}{3}$"
},
{
"from": "assistant",
"value": "<think>\nOkay, so I have this... | Given $\sin \left(\frac{\pi }{2}+\alpha \right)=\frac{1}{3}$, the value of $\cos (\pi +2\alpha )$ is ( ).
A: $-\frac{7}{9}$
B: $\frac{7}{9}$
C: $\frac{2}{9}$
D: $-\frac{2}{3}$ | null | null |
[
{
"from": "user",
"value": "Example 11 Find the least common multiple of $8127, 11352, 21672$ and 27090."
},
{
"from": "assistant",
"value": "<think>\nOkay, so I need to find the least common multiple (LCM) of these four numbers: 8127, 11352, 21672, and 27090. Hmm, LCMs can be a bit tricky when ... | Example 11 Find the least common multiple of $8127, 11352, 21672$ and 27090. | null | null |
[
{
"from": "user",
"value": "Given the function $f(x) = \\sqrt{3}\\sin(\\omega x + \\varphi) - \\cos(\\omega x + \\varphi)$ $(0 < \\varphi < \\pi)$ is an odd function, and the distance between two adjacent axes of symmetry is $\\frac{\\pi}{2}$.\n1. When $x \\in \\left(-\\frac{\\pi}{2}, \\frac{\\pi}{4}\\right... | Given the function $f(x) = \sqrt{3}\sin(\omega x + \varphi) - \cos(\omega x + \varphi)$ $(0 < \varphi < \pi)$ is an odd function, and the distance between two adjacent axes of symmetry is $\frac{\pi}{2}$.
1. When $x \in \left(-\frac{\pi}{2}, \frac{\pi}{4}\right)$, find the interval where $f(x)$ is monotonically decreas... | null | null |
[
{
"from": "user",
"value": "Given that the scores of two mathematics tests in a certain city, $\\xi_1$ and $\\xi_2$, each follows a normal distribution, $\\xi_1$ with $N_1(90, 86)$ and $\\xi_2$ with $N_2(93, 79)$, the correct conclusion is ( )\nA: The average score of the first test is higher than that of ... | Given that the scores of two mathematics tests in a certain city, $\xi_1$ and $\xi_2$, each follows a normal distribution, $\xi_1$ with $N_1(90, 86)$ and $\xi_2$ with $N_2(93, 79)$, the correct conclusion is ( )
A: The average score of the first test is higher than that of the second test and is also more stable than ... | null | null |
[
{
"from": "user",
"value": "I've written a simple HTTP server in Go and I'm encountering a problem when I try to test its performance using ApacheBench (ab). The issue seems to occur when I send a large number of requests with high concurrency values. Here's an example command and its output:\n\n```\n$ ab -... | null | sharegpt | null |
[
{
"from": "user",
"value": "The Yihuang Expressway connects the cities of Yichang, Wuhan, and Huangshi, with a total length of approximately 350 kilometers. It is one of the main arterial highways of the economic triangle in Hubei Province. If a vehicle enters the expressway and travels at a constant speed ... | The Yihuang Expressway connects the cities of Yichang, Wuhan, and Huangshi, with a total length of approximately 350 kilometers. It is one of the main arterial highways of the economic triangle in Hubei Province. If a vehicle enters the expressway and travels at a constant speed that is not less than 60 kilometers per ... | null | null |
[
{
"from": "user",
"value": "In Python Mixins, particularly in the context of Django models, should a mixin inherit from the class it is designed to mix-in with or from 'object'? For instance, is it more correct or better to use:\n\n```python\nclass TaggingMixin(models.Model):\n tag = models.ForeignKey(Ta... | null | null | null |
[
{
"from": "user",
"value": "After consuming a breakfast that provided him with 900 calories of energy, Will decided to jog for half an hour, burning 10 calories of energy per minute. What is Will's overall calorie intake after jogging?"
},
{
"from": "assistant",
"value": "## Step 1: Calculate th... | null | null | null |
[
{
"from": "user",
"value": " \"statement 1\": Ganesh covers the distance from X to Y at an average speed of 54 Km / hr, \"statement 2\" :Ganesh covers the distance from X to Y at an average speed of more than 44 Km / hr, \"options: \" Entailment or contradiction or neutral? Let's write a program."
},
{
... | null | tiger_lab_math | 20,378 |
[
{
"from": "user",
"value": "A factory produced 24,000 units of a certain product, which came from three production lines: A, B, and C. A stratified sampling method is used to inspect this batch of products. It is known that the number of units sampled sequentially from production lines A, B, and C exactly f... | A factory produced 24,000 units of a certain product, which came from three production lines: A, B, and C. A stratified sampling method is used to inspect this batch of products. It is known that the number of units sampled sequentially from production lines A, B, and C exactly forms an arithmetic sequence. The number ... | null | null |
[
{
"from": "user",
"value": "If the third term of the expansion of \\\\((x-a)^{6}\\\\) is \\\\(60x^{4}\\\\), then the value of \\\\(a\\\\) is \\\\((\\\\) \\\\().\\\\)\nA: \\\\(2\\\\)\nB: \\\\(\\pm 2\\\\)\nC: \\\\(1\\\\)\nD: \\\\(-2\\\\)"
},
{
"from": "assistant",
"value": "<think>\nOkay, so I ne... | If the third term of the expansion of \\((x-a)^{6}\\) is \\(60x^{4}\\), then the value of \\(a\\) is \\((\\) \\().\\)
A: \\(2\\)
B: \\(\pm 2\\)
C: \\(1\\)
D: \\(-2\\) | null | null |
[
{
"from": "user",
"value": "A circle with center $(a, b)$ passes through the points $(3, 5)$ and $(7, 9)$. What is the value of $a+b$, given that the circle's radius is $\\sqrt{26}$?"
},
{
"from": "assistant",
"value": "<think>\nOkay, so I need to find the value of a + b where the center of the ... | null | nvidia_math | 30,336 |
[
{
"from": "user",
"value": "The management staff caught 30 fish from a pond, marked them, and then released them back into the pond. 10 days later, they caught 50 fish from the pond again, among which 2 were marked. Based on the data provided, estimate the total number of fish in the pond."
},
{
"fr... | The management staff caught 30 fish from a pond, marked them, and then released them back into the pond. 10 days later, they caught 50 fish from the pond again, among which 2 were marked. Based on the data provided, estimate the total number of fish in the pond. | null | null |
[
{
"from": "user",
"value": "Return your final response within \\boxed{}. A scalene triangle \\(ABC\\) is inscribed in a circle with center \\(O\\) and circumscribed around a circle with center \\(I\\). The point \\(B'\\), which is the reflection of point \\(B\\) with respect to the line \\(OI\\), lies insid... | A scalene triangle \(ABC\) is inscribed in a circle with center \(O\) and circumscribed around a circle with center \(I\). The point \(B'\), which is the reflection of point \(B\) with respect to the line \(OI\), lies inside the angle \(ABI\). Prove that the tangents to the circumcircle of the triangle \(BB'I\), drawn ... | null | null |
[
{
"from": "user",
"value": "Given $3^{m}=x$, $9^{n}=y$, where $m$ and $n$ are positive integers, then $3^{m+2n}=$\n\nA: $xy$\n\nB: $xy^{2}$\n\nC: $x+y^{2}$\n\nD: $24xy$"
},
{
"from": "assistant",
"value": "<think>\nOkay, let's see. I need to figure out what 3^(m + 2n) equals in terms of x and y.... | Given $3^{m}=x$, $9^{n}=y$, where $m$ and $n$ are positive integers, then $3^{m+2n}=$
A: $xy$
B: $xy^{2}$
C: $x+y^{2}$
D: $24xy$ | null | null |
[
{
"from": "user",
"value": "12. In the Cartesian coordinate system $X O Y$, given two points $M(-1,2)$ and $N(1,4)$, point $P$ moves on the $X$-axis. When $\\angle M P N$ takes its maximum value, the x-coordinate of point $P$ is $\\qquad$"
},
{
"from": "assistant",
"value": "<think>\nOkay, so I ... | 12. In the Cartesian coordinate system $X O Y$, given two points $M(-1,2)$ and $N(1,4)$, point $P$ moves on the $X$-axis. When $\angle M P N$ takes its maximum value, the x-coordinate of point $P$ is $\qquad$ | null | null |
[
{
"from": "user",
"value": "Return your final response within \\boxed{}. Place $2n+1$ points inside a square with side length 1. Show that there exist three of these points that form a triangle with an area less than or equal to $\\frac{1}{2n}$."
},
{
"from": "assistant",
"value": "<think>\nOkay... | Place $2n+1$ points inside a square with side length 1. Show that there exist three of these points that form a triangle with an area less than or equal to $\frac{1}{2n}$. | null | null |
[
{
"from": "user",
"value": "Return your final response within \\boxed{}. The base of the pyramid $S-ABCDE$ is a regular pentagon $ABCDE$. The foot of the perpendicular dropped from point $S$ to the base, denoted by $SM$, is located inside the pentagon $ABCDE$. Given that the circumradii of the tetrahedra $S... | The base of the pyramid $S-ABCDE$ is a regular pentagon $ABCDE$. The foot of the perpendicular dropped from point $S$ to the base, denoted by $SM$, is located inside the pentagon $ABCDE$. Given that the circumradii of the tetrahedra $SMAB$, $SMBC$, and $SMCD$ are equal, can it be concluded that $S-ABCDE$ is a regular p... | null | null |
[
{
"from": "user",
"value": "Return your final response within \\boxed{}. Given a convex quadrilateral $ABCD$, prove that the area $S$ of quadrilateral $ABCD$ satisfies the inequality $S \\leq \\frac{AB^2 + BC^2 + CD^2 + DA^2}{4}$."
},
{
"from": "assistant",
"value": "<think>\nAlright, let's see.... | Given a convex quadrilateral $ABCD$, prove that the area $S$ of quadrilateral $ABCD$ satisfies the inequality $S \leq \frac{AB^2 + BC^2 + CD^2 + DA^2}{4}$. | null | null |
[
{
"from": "user",
"value": "If we multiply 18 by 30 and add the product of 27 and 15, what is the final result?"
},
{
"from": "assistant",
"value": "<think>\nFirst, I need to multiply 18 by 30, which equals 540. \n\nNext, I'll calculate the product of 27 and 15, resulting in 405. \n\nFinally, I'... | null | null | null |
[
{
"from": "user",
"value": "Generate an executable Python function generated from the given prompt. The function should take stdin as input and print the output. Simply call the function after the definition.Rabbits and cats are competing. The rules are as follows.\n\nFirst, each of the two animals wrote n2... | Generate an executable Python function generated from the given prompt. The function should take stdin as input and print the output. Simply call the function after the definition.Rabbits and cats are competing. The rules are as follows.
First, each of the two animals wrote n2 integers on a piece of paper in a square ... | null | null |
[
{
"from": "user",
"value": "## Subject III. (20 points)\n\nSeven is one of the numbers considered magical throughout human history: there are 7 wonders of the ancient world, 7 wonders of the Middle Ages, 7 continents, 7 seas, the rainbow has 7 colors, 7 days of the week named after the 7 Roman gods who in t... | ## Subject III. (20 points)
Seven is one of the numbers considered magical throughout human history: there are 7 wonders of the ancient world, 7 wonders of the Middle Ages, 7 continents, 7 seas, the rainbow has 7 colors, 7 days of the week named after the 7 Roman gods who in turn were named after the 7 planets that co... | null | null |
[
{
"from": "user",
"value": "Seven boys and three girls are playing basketball. I how many different ways can they make two teams of five players so that both teams have at least one girl?"
},
{
"from": "assistant",
"value": "<think>\nOkay, so there's this problem about seven boys and three girls... | Seven boys and three girls are playing basketball. I how many different ways can they make two teams of five players so that both teams have at least one girl? | null | null |
[
{
"from": "user",
"value": "There are perhaps three hundred sign languages in use around the world today. The number is not known with any confidence; new sign languages emerge frequently through creolization and de novo (and occasionally through language planning). In some countries, such as Sri Lanka and ... | null | null | null |
[
{
"from": "user",
"value": "Return your final response within \\boxed{}. \nIn some cells of a $10 \\times 10$ board, $k$ rooks are placed, and then all the cells that are attacked by at least one rook are marked (a rook attacks the cell it is on). What is the maximum value of $k$ such that, if any one rook ... |
In some cells of a $10 \times 10$ board, $k$ rooks are placed, and then all the cells that are attacked by at least one rook are marked (a rook attacks the cell it is on). What is the maximum value of $k$ such that, if any one rook is removed from the board, there will still be at least one marked cell that is not und... | null | null |
[
{
"from": "user",
"value": "There are $N$ students in a class. Each possible nonempty group of students selected a positive integer. All of these integers are distinct and add up to 2014. Compute the greatest possible value of $N$."
},
{
"from": "assistant",
"value": "<think>\nOkay, so there'... | There are $N$ students in a class. Each possible nonempty group of students selected a positive integer. All of these integers are distinct and add up to 2014. Compute the greatest possible value of $N$. | null | null |
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