conversations listlengths 2 2 | question stringlengths 16 24.8k ⌀ | source stringclasses 10
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"value": "There are 12 bananas and x apples in the blue basket. The red basket holds half as many fruits as the blue basket. How many fruits are in the red basket?\nIf we know the answer to the above question is 8, what is the value of unknown variable x?"
},
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"from": "assistant",... | null | tiger_math | 16,478 |
[
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"value": "In the sequence $\\{a_n\\}$, $(a_1=1, a_{n+1}=\\frac{a_n}{c\\cdot a_n+1})$ $(c$ is a constant, $n\\in\\mathbb{N^*})$, and $(a_1,a_2,a_5)$ form a geometric sequence with a common ratio not equal to $1$.\n(1) Prove that the sequence $\\{\\frac{1}{a_n}\\}$ is an arithmetic sequence ... | In the sequence $\{a_n\}$, $(a_1=1, a_{n+1}=\frac{a_n}{c\cdot a_n+1})$ $(c$ is a constant, $n\in\mathbb{N^*})$, and $(a_1,a_2,a_5)$ form a geometric sequence with a common ratio not equal to $1$.
(1) Prove that the sequence $\{\frac{1}{a_n}\}$ is an arithmetic sequence and find the value of $c$;
(2) Let $b_n=a_n a_{n+1... | null | null |
[
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"value": "What is the difference between the largest possible three-digit positive integer with no repeated digits and the smallest possible three-digit positive integer with no repeated digits?"
},
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"value": "<think>\nOkay, so I need to find the differenc... | What is the difference between the largest possible three-digit positive integer with no repeated digits and the smallest possible three-digit positive integer with no repeated digits? | null | null |
[
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"value": "port this code to Fortran:\n```scheme\n(define MRUQueue\n (lambda (n)\n (let ((queue (build-list n identity)))\n (lambda (k)\n (let ((elem (list-ref queue (- k 1))))\n (set! queue (append (take queue (- k 1)) (drop queue k) (list elem)))\n elem))... | null | dolphin | null |
[
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"value": "Return your final response within \\boxed{}. A natural number \\( a \\) is increased by 1, and its square is increased by 1001. What is the value of \\( a \\)?"
},
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"from": "assistant",
"value": "<think>\nOkay, let's see. The problem says that a natural number \\( a ... | A natural number \( a \) is increased by 1, and its square is increased by 1001. What is the value of \( a \)? | null | null |
[
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"value": "A positive integer $n$ is considered to be cubefree if it is not divisible by any cube of a prime number. For example, $1, 2, 3, 5, 6, 7, 10, 11$ are cubefree, while $8, 27, 125$ are not. Can you calculate the total number of such cubefree numbers that exist below the value of $2... | null | null | null |
[
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"value": "## problem statement\n\nWrite the equation of the plane passing through point $A$ and perpendicular to the vector $\\overrightarrow{B C}$.\n\n$A(7 ; -5 ; 0)$\n\n$B(8 ; 3 ; -1)$\n\n$C(8 ; 5 ; 1)$"
},
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"from": "assistant",
"value": "<think>\nOkay, let me try to figure ... | ## problem statement
Write the equation of the plane passing through point $A$ and perpendicular to the vector $\overrightarrow{B C}$.
$A(7 ; -5 ; 0)$
$B(8 ; 3 ; -1)$
$C(8 ; 5 ; 1)$ | null | null |
[
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"value": "Return your final response within \\boxed{}. What is the maximum number of consecutive positive integers that can be added together before the sum exceeds 400?"
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"value": "<think>\nOkay, let's see. The question is asking for the maximum numbe... | What is the maximum number of consecutive positive integers that can be added together before the sum exceeds 400? | null | null |
[
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"from": "user",
"value": "Write a JavaScript function to find the first prime number in an array of integers. If no prime number is found, the function should return -1.\n\nHowever, the function should also accept an optional second argument, `k`, which represents the number of prime numbers to be found. ... | null | null | null |
[
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"value": "Return your final response within \\boxed{}. Find the sum of the positive integer divisors of \\(2^{2007}\\)."
},
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"from": "assistant",
"value": "<think>\nOkay, so I need to find the sum of the positive integer divisors of \\(2^{2007}\\). Hmm, let me think about how ... | Find the sum of the positive integer divisors of \(2^{2007}\). | null | null |
[
{
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"value": "A ball is thrown straight up into the air with an initial velocity of 30 m/s. Using calculus, find its maximum height and the time it takes to reach that height. Assume that air resistance is negligible."
},
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"value": "<think>\nOkay, so I have th... | null | null | null |
[
{
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"value": "5. Calculate the sum of the expressions $S_{2015}$ and $S_{2016}$ if $S_{2015}=1-2+3-4+5-\\ldots-2014+2015$, and $S_{2016}=1-2+3-4+5-\\ldots-2014+2015-2016$.\n\nProblems worth 10 points:"
},
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"from": "assistant",
"value": "<think>\nOkay, so I need to calculate the su... | 5. Calculate the sum of the expressions $S_{2015}$ and $S_{2016}$ if $S_{2015}=1-2+3-4+5-\ldots-2014+2015$, and $S_{2016}=1-2+3-4+5-\ldots-2014+2015-2016$.
Problems worth 10 points: | null | null |
[
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"value": "\\section*{Aufgabe 5 - 231045}\n\nErmitteln Sie alle diejenigen Winkelgrößen \\(x\\), für die \\(0^{\\circ} \\leq x \\leq 180^{\\circ} \\quad\\) (1) und\n\n\\[\n\\left(2^{\\sqrt{\\sin x}}-\\sin x\\right) \\cdot \\sin x=1\n\\]\n\ngilt!\n\n"
},
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"v... | \section*{Aufgabe 5 - 231045}
Ermitteln Sie alle diejenigen Winkelgrößen \(x\), für die \(0^{\circ} \leq x \leq 180^{\circ} \quad\) (1) und
\[
\left(2^{\sqrt{\sin x}}-\sin x\right) \cdot \sin x=1
\]
gilt!
| null | null |
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