conversations listlengths 2 2 | question stringlengths 16 24.8k ⌀ | source stringclasses 10
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"value": "Given that the sequence $\\{a_n\\}$ is an arithmetic sequence, and $a_2+a_3=1$, $a_{10}+a_{11}=9$, then $a_5+a_6=$ ?\n\nA: $4$\n\nB: $5$\n\nC: $6$\n\nD: $7$"
},
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"value": "<think>\nOkay, so I need to solve this arithmetic sequence problem. Let me... | Given that the sequence $\{a_n\}$ is an arithmetic sequence, and $a_2+a_3=1$, $a_{10}+a_{11}=9$, then $a_5+a_6=$ ?
A: $4$
B: $5$
C: $6$
D: $7$ | null | null |
[
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"value": "3. Consider the arbitrary triangle $\\triangle A B C, N$ the midpoint of $[A C], E$ the symmetric point of $B$ with respect to $N$ and $P$ the symmetric point of $C$ with respect to $B$. If the line $P E$ intersects the sides $[A B]$ and $[A C]$ at points $M$, respectively $F$, c... | 3. Consider the arbitrary triangle $\triangle A B C, N$ the midpoint of $[A C], E$ the symmetric point of $B$ with respect to $N$ and $P$ the symmetric point of $C$ with respect to $B$. If the line $P E$ intersects the sides $[A B]$ and $[A C]$ at points $M$, respectively $F$, calculate the ratio $\frac{F M}{M P}$.
Pr... | null | null |
[
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"value": "6.010. $\\frac{1}{x^{3}+2}-\\frac{1}{x^{3}+3}=\\frac{1}{12}$."
},
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"value": "<think>\nOkay, so I need to solve the equation \\(\\frac{1}{x^{3}+2} - \\frac{1}{x^{3}+3} = \\frac{1}{12}\\). Hmm, let me see. First, maybe I can simplify the left side ... | 6.010. $\frac{1}{x^{3}+2}-\frac{1}{x^{3}+3}=\frac{1}{12}$. | null | null |
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"value": "5. Line $l$ lies on plane $\\alpha$, line $m$ is parallel to plane $\\alpha$, and is skew to line $l$. A moving point $P$ is on plane $\\alpha$, and is equidistant from lines $l$ and $m$. Then the locus of point $P$ is ( ).\n(A) Line\n(B) Ellipse\n(C) Parabola\n(D) Hyperbola"
}... | 5. Line $l$ lies on plane $\alpha$, line $m$ is parallel to plane $\alpha$, and is skew to line $l$. A moving point $P$ is on plane $\alpha$, and is equidistant from lines $l$ and $m$. Then the locus of point $P$ is ( ).
(A) Line
(B) Ellipse
(C) Parabola
(D) Hyperbola | null | null |
[
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"value": "Instructions: Given the Target and Argument texts detect the stance that the argument has towards the topic. There are three types of stances \"in favor\", \"against\", and \"neutral\". \nInput: Topic: Republika Srpska secession from Bosnia and Herzegovina\n Argument: Republika S... | null | null | null |
[
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"value": "Given the sets $A=\\\\left\\\\{ x\\\\left| 2{{x}^{2}}-x-3 < 0 \\\\right. \\\\right\\\\}$ and $B=\\\\left\\\\{ x\\\\left| y=\\\\lg \\\\tfrac{1-x}{x+3} \\\\right. \\\\right\\\\}$, find the probability that a real number $x$ chosen randomly from the interval $(-3,3)$ belongs to $(A\... | Given the sets $A=\\left\\{ x\\left| 2{{x}^{2}}-x-3 < 0 \\right. \\right\\}$ and $B=\\left\\{ x\\left| y=\\lg \\tfrac{1-x}{x+3} \\right. \\right\\}$, find the probability that a real number $x$ chosen randomly from the interval $(-3,3)$ belongs to $(A\\bigcap B)$. | null | null |
[
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"value": "2. Given are sets $A, B$, and $C$ such that:\n\n- $A \\cup B \\cup C=\\{1,2,3, \\ldots, 100\\}$;\n- $A$ is the set of all natural numbers not greater than 100 that are divisible by 2;\n- $B$ is the set of all natural numbers not greater than 100 that are divisible by 3;\n- $B \\c... | 2. Given are sets $A, B$, and $C$ such that:
- $A \cup B \cup C=\{1,2,3, \ldots, 100\}$;
- $A$ is the set of all natural numbers not greater than 100 that are divisible by 2;
- $B$ is the set of all natural numbers not greater than 100 that are divisible by 3;
- $B \cap C$ is the set of all natural numbers not greater... | null | null |
[
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"value": "In the sequence $\\{a_n\\}$, for $n \\geq 2$, $a_n = \\frac{2S_n^2}{2S_n - 1}$ and $a_1 = 1$,\n(1) Find the general formula for the $n$-th term of the sequence $\\{a_n\\}$;\n(2) Calculate the sum of the first $n$ terms of the sequence $\\{a_n\\}$, denoted as $S_n$."
},
{
... | In the sequence $\{a_n\}$, for $n \geq 2$, $a_n = \frac{2S_n^2}{2S_n - 1}$ and $a_1 = 1$,
(1) Find the general formula for the $n$-th term of the sequence $\{a_n\}$;
(2) Calculate the sum of the first $n$ terms of the sequence $\{a_n\}$, denoted as $S_n$. | null | null |
[
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"value": "Chris’s internet bill is $45 per month for 100 GB and $0.25 for every 1 GB over. His bill for this month is $65. How many GB over was Chris charged for on this bill?"
},
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"value": "<think>\nOkay, so Chris has this internet bill that's normally $4... | null | tiger_lab_math | 14,280 |
[
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"value": "In the complex plane, the point corresponding to the complex number $\\frac {i}{1+i}$ is located in ( )\nA: The first quadrant\nB: The second quadrant\nC: The third quadrant\nD: The fourth quadrant"
},
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"value": "<think>\nOkay, let's see. I need... | In the complex plane, the point corresponding to the complex number $\frac {i}{1+i}$ is located in ( )
A: The first quadrant
B: The second quadrant
C: The third quadrant
D: The fourth quadrant | null | null |
[
{
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"value": "Let $O$ be the center of the base $\\triangle ABC$ of the regular tetrahedron $P-ABC$. A moving plane through $O$ intersects the three lateral edges or their extensions of $P-ABC$ at points $Q, R, S$, respectively. Then the sum $\\frac{1}{PQ} + \\frac{1}{PR} + \\frac{1}{PS}$ (\n(... | Let $O$ be the center of the base $\triangle ABC$ of the regular tetrahedron $P-ABC$. A moving plane through $O$ intersects the three lateral edges or their extensions of $P-ABC$ at points $Q, R, S$, respectively. Then the sum $\frac{1}{PQ} + \frac{1}{PR} + \frac{1}{PS}$ (
(A) has a maximum value but no minimum value
(... | null | null |
[
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"value": "A fruit distributor purchased 10 boxes each of two types of fruits, $A$ and $B$, and distributed them to Store A and Store B for sale (in whole boxes). The expected profit per box of fruit at Store A and Store B is shown in the table below:\n\n| | $A$ Fruit / Box | $B$ F... | A fruit distributor purchased 10 boxes each of two types of fruits, $A$ and $B$, and distributed them to Store A and Store B for sale (in whole boxes). The expected profit per box of fruit at Store A and Store B is shown in the table below:
| | $A$ Fruit / Box | $B$ Fruit / Box |
|----------|-----------------... | null | null |
[
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"value": "Pretend to be Rose Otoribashi, praising one of his subordinates."
},
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"value": "**(Clears throat, adopting a stern yet proud tone, as Rose Otoribashi from the series \"God of High School\")**\n\n\"Ah, **(pauses for a brief moment)**... Min, I mus... | null | null | null |
[
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"value": "7. From $1,2, \\cdots, 1995$, what is the maximum number of numbers that can be selected such that none of the selected numbers is 19 times another?"
},
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"from": "assistant",
"value": "<think>\nOkay, so I need to figure out the maximum number of numbers I can select ... | 7. From $1,2, \cdots, 1995$, what is the maximum number of numbers that can be selected such that none of the selected numbers is 19 times another? | null | null |
[
{
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"value": "\n\nThe arithmetic mean of ten different natural numbers is 15. Find the greatest possible value of the greatest of these numbers."
},
{
"from":... | 
The arithmetic mean of ten different natural numbers is 15. Find the greatest possible value of the greatest of these numbers. | null | null |
[
{
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"value": "You are given a 2D array of integers. Your task is to implement a function that rotates the array 90 degrees clockwise.\n\nFor example, given the following 2D array:\n```\n2 3\n4 5 6\n```\nThe function should rotate it 90 degrees clockwise to produce:\n```\n4 2\n5 3\n6\n```\n\nYo... | null | magicoder | null |
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