conversations listlengths 2 2 | question stringlengths 16 24.8k ⌀ | source stringclasses 10
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"value": "Q: What would you do – you’re driving past hundreds of citrus trees. With a better look, they’re mandarins, or, more precisely clementines. On the roadside is a truck selling crates of them for 1 euro a kilo. You stop, right? And buy a crate of 10 kilos. Even though you have to g... | null | null | null |
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"value": "Find the determinant of the matrix:\n\nA = \n\\begin{bmatrix}\n2 & 4 & 5 \\\\\n-1 & 3 & 6 \\\\\n0 & 7 & -2\n\\end{bmatrix}"
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"value": "To find the determinant of matrix A, we'll use the expansion by minors method. Given that the matrix is a 3x... | null | null | null |
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"value": "12. Calculate: $\\sqrt{\\frac{998 \\times 999 \\times 1000 \\times 1001+1}{4}}+\\frac{1}{2}=$"
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"value": "<think>\nOkay, so I have this problem to solve: the square root of (998 times 999 times 1000 times 1001 plus 1) divided by 4, and then ad... | 12. Calculate: $\sqrt{\frac{998 \times 999 \times 1000 \times 1001+1}{4}}+\frac{1}{2}=$ | null | null |
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"value": "In a certain cross country meet between 2 teams of 5 runners each, a runner who finishes in the $n$th position contributes $n$ to his teams score. The team with the lower score wins. If there are no ties among the runners, how many different winning scores are possible?\n(A) 10 (... | null | null | null |
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"value": "Les informations ci-dessous sont reproduites telles qu'elles ont été reçues et n'impliquent l'expression d'aucune opinion ou approbation de la part du Secrétariat de l'Organisation des Nations Unies.\n\nWhich language is this?"
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"value": "Une ... | null | null | null |
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"value": "Come up with an appropriate title for the following document.\nWASHINGTON (CNN) -- A wide-open presidential race and a willingness by candidates, interest groups, unions and corporations to buy TV time will lead to historic spending for political and issue-advocacy advertising in... | null | null | null |
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"value": "Three. (25 points) Let $p$ be a prime number, and $k$ be a positive integer. When the equation $x^{2}+p x+k p-1=0$ has at least one integer solution, find all possible values of $k$.\n\nLet $p$ be a prime number, and $k$ be a positive integer. When the equation $x^{2}+p x+k p-1=0... | Three. (25 points) Let $p$ be a prime number, and $k$ be a positive integer. When the equation $x^{2}+p x+k p-1=0$ has at least one integer solution, find all possible values of $k$.
Let $p$ be a prime number, and $k$ be a positive integer. When the equation $x^{2}+p x+k p-1=0$ has at least one integer solution, find ... | null | null |
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"value": "The line $2x+m(x-y)-1=0$ always passes through a fixed point \\_\\_\\_\\_\\_\\_."
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"value": "<think>\nOkay, let's see. The problem is: \"The line 2x + m(x - y) - 1 = 0 always passes through a fixed point ______.\" Hmm, I need to find the fixed... | The line $2x+m(x-y)-1=0$ always passes through a fixed point \_\_\_\_\_\_. | null | null |
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"value": "Return your final response within \\boxed{}. In convex pentagon $ ABCDE$ , denote by \r $ AD\\cap BE = F,BE\\cap CA = G,CA\\cap DB = H,DB\\cap EC = I,EC\\cap AD = J; AI\\cap BE = A',BJ%Error. \"capCA\" is a bad command.\n= B',CF%Error. \"capDB\" is a bad command.\n= C',DG\\cap E... | In convex pentagon $ ABCDE$ , denote by
$ AD\cap BE = F,BE\cap CA = G,CA\cap DB = H,DB\cap EC = I,EC\cap AD = J; AI\cap BE = A',BJ%Error. "capCA" is a bad command.
= B',CF%Error. "capDB" is a bad command.
= C',DG\cap EC = D',EH\cap AD = E'.$
Prove that $ \frac {AB'}{B'C}\cdot\frac {CD'}{D'E}\cdot\frac {EA'}{A'B}... | null | null |
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"value": "Und doch gelang es Stockhausen hier, die Gegenspieler miteinander zu verschmelzen.\n\nTranslate this to English?"
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"value": "Here is the translation:\n\n\"And yet, Stockhausen succeeded here in merging the opposing elements with each other.\"\... | null | null | null |
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"value": "Given $m$ and $n$ are two different lines, and $\\alpha$ and $\\beta$ are two different planes, then among the following statements, the correct one is ( )\nA: If $m \\parallel \\alpha$, $n \\perp \\beta$ and $\\alpha \\perp \\beta$, then $m \\perp n$\nB: If $m \\perp \\alpha... | Given $m$ and $n$ are two different lines, and $\alpha$ and $\beta$ are two different planes, then among the following statements, the correct one is ( )
A: If $m \parallel \alpha$, $n \perp \beta$ and $\alpha \perp \beta$, then $m \perp n$
B: If $m \perp \alpha$, $n \perp \beta$ and $m \perp n$, then $\alpha \perp... | null | null |
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"value": "Categorize all the words from the sentence into either nouns, verbs, adjectives or adverbs.\nThe peaceful river gently rippled in the summer breeze."
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"value": "Here is the categorization of the words from the sentence:\n\n* **Nouns:**\n\t1. R... | null | null | null |
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"value": "A function is said to have a \"floating point\" $x\\_0$ if, within its domain, there exists a real number $x\\_0$ such that $f(x\\_0+1)=f(x\\_0)+f(1)$.\n(1) Does the function $f(x)=\\frac{1}{x}$ have a \"floating point\"? Please explain your reasoning.\n(2) Prove that the functio... | A function is said to have a "floating point" $x\_0$ if, within its domain, there exists a real number $x\_0$ such that $f(x\_0+1)=f(x\_0)+f(1)$.
(1) Does the function $f(x)=\frac{1}{x}$ have a "floating point"? Please explain your reasoning.
(2) Prove that the function $f(x)=x^2+2^x$ has a "floating point" in the inte... | null | null |
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"value": "24. [12] Find the number of subsets $S$ of $\\{1,2, \\ldots 6\\}$ satisfying the following conditions:\n- $S$ is non-empty.\n- No subset of $S$ has the property that the sum of its elements is 10 ."
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"value": "<think>\nOkay, let me try to figu... | 24. [12] Find the number of subsets $S$ of $\{1,2, \ldots 6\}$ satisfying the following conditions:
- $S$ is non-empty.
- No subset of $S$ has the property that the sum of its elements is 10 . | null | null |
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"value": "It is known that the sum of the first $n$ terms of an arithmetic sequence $\\{a_n\\}$ is $S_n$, $a_9 = \\frac{1}{2}a_{12} + 6$, and $a_2 = 4$. Find the sum of the first $10$ terms of the sequence $\\left\\{\\frac{1}{S_n}\\right\\}$."
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"value":... | It is known that the sum of the first $n$ terms of an arithmetic sequence $\{a_n\}$ is $S_n$, $a_9 = \frac{1}{2}a_{12} + 6$, and $a_2 = 4$. Find the sum of the first $10$ terms of the sequence $\left\{\frac{1}{S_n}\right\}$. | null | null |
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"value": "Write a multi-choice question for the following article, with the given choices and answer: Article: Peter King, 15, and Mary King, 13, went to see a doctor. Peter had a bad cold, so the doctor gave him some pills to take. Mary had a bad cough, so the doctor gave her some cough m... | null | null | null |
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