LASR-Callum/2026-08-03-qwen36-lora-500k-numina-only
Image-Text-to-Text • Updated • 15
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The dataset generation failed
Error code: DatasetGenerationError
Exception: CastError
Message: Couldn't cast
total: struct<examples: int64, tokens: int64>
child 0, examples: int64
child 1, tokens: int64
by_source: struct<numinamath_cot: struct<examples: int64, tokens: int64, share_pct: double>>
child 0, numinamath_cot: struct<examples: int64, tokens: int64, share_pct: double>
child 0, examples: int64
child 1, tokens: int64
child 2, share_pct: double
mixture_path: string
text: string
source: string
to
{'text': Value('string'), 'source': Value('string')}
because column names don't match
Traceback: Traceback (most recent call last):
File "/usr/local/lib/python3.14/site-packages/datasets/builder.py", line 1827, in _prepare_split_single
for key, table in generator:
^^^^^^^^^
File "/src/services/worker/src/worker/job_runners/config/parquet_and_info.py", line 613, in wrapped
for item in generator(*args, **kwargs):
~~~~~~~~~^^^^^^^^^^^^^^^^^
File "/usr/local/lib/python3.14/site-packages/datasets/packaged_modules/json/json.py", line 343, in _generate_tables
self._cast_table(pa_table, json_field_paths=json_field_paths),
~~~~~~~~~~~~~~~~^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
File "/usr/local/lib/python3.14/site-packages/datasets/packaged_modules/json/json.py", line 132, in _cast_table
pa_table = table_cast(pa_table, self.info.features.arrow_schema)
File "/usr/local/lib/python3.14/site-packages/datasets/table.py", line 2378, in table_cast
return cast_table_to_schema(table, schema)
File "/usr/local/lib/python3.14/site-packages/datasets/table.py", line 2306, in cast_table_to_schema
raise CastError(
...<3 lines>...
)
datasets.table.CastError: Couldn't cast
total: struct<examples: int64, tokens: int64>
child 0, examples: int64
child 1, tokens: int64
by_source: struct<numinamath_cot: struct<examples: int64, tokens: int64, share_pct: double>>
child 0, numinamath_cot: struct<examples: int64, tokens: int64, share_pct: double>
child 0, examples: int64
child 1, tokens: int64
child 2, share_pct: double
mixture_path: string
text: string
source: string
to
{'text': Value('string'), 'source': Value('string')}
because column names don't match
The above exception was the direct cause of the following exception:
Traceback (most recent call last):
File "/src/services/worker/src/worker/job_runners/config/parquet_and_info.py", line 1369, in compute_config_parquet_and_info_response
parquet_operations, partial, estimated_dataset_info = stream_convert_to_parquet(
~~~~~~~~~~~~~~~~~~~~~~~~~^
builder, max_dataset_size_bytes=max_dataset_size_bytes
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
)
^
File "/src/services/worker/src/worker/job_runners/config/parquet_and_info.py", line 948, in stream_convert_to_parquet
builder._prepare_split(split_generator=splits_generators[split], file_format="parquet")
~~~~~~~~~~~~~~~~~~~~~~^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
File "/usr/local/lib/python3.14/site-packages/datasets/builder.py", line 1694, in _prepare_split
for job_id, done, content in self._prepare_split_single(
~~~~~~~~~~~~~~~~~~~~~~~~~~^
gen_kwargs=gen_kwargs, job_id=job_id, **_prepare_split_args
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
):
^
File "/usr/local/lib/python3.14/site-packages/datasets/builder.py", line 1880, in _prepare_split_single
raise DatasetGenerationError("An error occurred while generating the dataset") from e
datasets.exceptions.DatasetGenerationError: An error occurred while generating the datasetNeed help to make the dataset viewer work? Make sure to review how to configure the dataset viewer, and open a discussion for direct support.
text string | source string |
|---|---|
<|im_start|>user
What is the probability that the square root of a randomly selected two-digit whole number is less than seven? Express your answer as a common fraction.<|im_end|>
<|im_start|>assistant
- The two-digit numbers range from 10 to 99.
- We need to find the largest two-digit number whose square root is less ... | numinamath_cot |
<|im_start|>user
Ellen is painting flowers on a vase. It takes her 5 minutes to paint a lily, 7 minutes to paint a rose, 3 minutes to paint an orchid, and 2 minutes to paint a vine. How long will it take her to paint 17 lilies, 10 roses, 6 orchids and 20 vines?<|im_end|>
<|im_start|>assistant
To calculate the total tim... | numinamath_cot |
<|im_start|>user
If the expression $\sqrt{x-3}$ is meaningful within the real number range, then the range of $x$ is ____.<|im_end|>
<|im_start|>assistant
To ensure the expression $\sqrt{x-3}$ is meaningful within the real number range, the quantity under the square root must be non-negative. This leads to the conditio... | numinamath_cot |
<|im_start|>user
Nan Nan and Feng Feng are calculating the same addition problem. Nan Nan got 982, which is correct, but Feng Feng got 577, which is incorrect. The reason Feng Feng got it wrong is that he missed a 0 in the units place of one of the addends. What are the two addends in this addition problem?<|im_end|>
<... | numinamath_cot |
<|im_start|>user
In convex quadrilateral $PQRS$, $\angle P = \angle R$, $PQ=RS=200$, and $PR \ne QS$. The perimeter of $PQRS$ is 800. Additionally, the diagonals $PR$ and $QS$ are equal in length. Find $\cos P$.<|im_end|>
<|im_start|>assistant
1. Let $\angle P = \angle R = \beta$, $PR=x$, and $QS=x$ since the diagonals... | numinamath_cot |
<|im_start|>user
Find all prime numbers \( p \) such that for any prime number \( q < p \), if \( p = kq + r \) with \( 0 \leq r < q \), then there does not exist an integer \( a > 1 \) such that \( a^2 \) divides \( r \).<|im_end|>
<|im_start|>assistant
**Step 1:** Identify the prime numbers \( p \) that meet the give... | numinamath_cot |
<|im_start|>user
Given four circles \(S_{1}, S_{2}, S_{3},\) and \(S_{4}\), where circles \(S_{i}\) and \(S_{i+1}\) touch externally for \(i = 1, 2, 3\), with \(S_{5} = S_{1}\), prove that the points of tangency form an inscribed quadrilateral.<|im_end|>
<|im_start|>assistant
1. **Define the centers and points of tange... | numinamath_cot |
<|im_start|>user
Let \( n \) be a given integer greater than 5. Solve the system of equations:
$$
\left\{
\begin{array}{l}
x_{1}+x_{2}+x_{3}+\cdots+x_{n}=n+2, \\
x_{1}+2 x_{2}+3 x_{3}+\cdots+n x_{n}=2n+2, \\
x_{1}+2^{2} x_{2}+3^{2} x_{3}+\cdots+n^{2} \cdot x_{n}=n^{2}+n+4, \\
x_{1}+2^{3} x_{2}+3^{3} x_{3}+\cdots+n^{3} ... | numinamath_cot |
<|im_start|>user
In the region shown, all right angles are as they appear, and each of the twelve congruent sides marked has a length of 1 foot. Suppose the region has an area of 69 square feet, what is the perimeter of the region in feet? The entire figure is bounded by an external rectangle that extends to encapsulat... | numinamath_cot |
<|im_start|>user
A certain family has 3 sons: Richard is 6 years older than David, and David is 8 years older than Scott. In some years, Richard will be twice as old as Scott. David was 7 years old 7 years ago. In how many years will Richard be twice as old as Scott?<|im_end|>
<|im_start|>assistant
Let's start by figur... | numinamath_cot |
<|im_start|>user
An uneducated retailer marks all his goods at 50% above the cost price and thinking that he will still make 15% profit, offers a discount of 15% on the marked price. What is his actual profit on the sales?<|im_end|>
<|im_start|>assistant
Let's assume the cost price of the goods is $100.
The retailer m... | numinamath_cot |
<|im_start|>user
In a triangular prism $A-BCD$, the orthogonal projection of vertex $A$ onto the base $BCD$ is point $O$, and the distances from point $O$ to the three lateral faces are equal. Point $O$ must be the ( ).
(A) Centroid
(B) Orthocenter
(C) Incenter
(D) Circumcenter<|im_end|>
<|im_start|>assistant
1.... | numinamath_cot |
<|im_start|>user
\((3 \log_{a} x - 2) \log_{x}^{2} a = \log_{\sqrt{a}} x - 3 \quad (a > 0, a \neq 1)\).<|im_end|>
<|im_start|>assistant
1. **Determine the restrictions (domain) on the variables:**
Given the conditions \(a > 0\) and \(a \neq 1\), and \(x > 0\) and \(x \neq 1\), we form the feasible domain.
\[... | numinamath_cot |
<|im_start|>user
A team of 60 workers constructed a bridge in 5 days working at the same efficiency. If the subsequent team worked at 80% efficiency and consisted of 40 workers, how many days would it have taken this team to complete an identical bridge?<|im_end|>
<|im_start|>assistant
Let $r$ denote the rate at which ... | numinamath_cot |
<|im_start|>user
What is the twelfth positive integer that is both even and a multiple of 5?<|im_end|>
<|im_start|>assistant
The first even multiple of 5 is 10. The next is 20, then 30, 40, adding 10 each time. This sequence is an arithmetic sequence where the common difference is 10. The $n$th even multiple of 5 can b... | numinamath_cot |
<|im_start|>user
In a rectangle \(ABCD\) with an area of 1 (including its boundary), there are 5 points such that no three points are collinear. Determine the minimum number of triangles, formed by these 5 points as vertices, that have an area of at most \(\frac{1}{4}\).<|im_end|>
<|im_start|>assistant
Given a rectangl... | numinamath_cot |
<|im_start|>user
Given the line $y=ax+b$ is tangent to the function $f\left(x\right)=x\ln x$, then $\frac{1-a}{b}($)
A: has a maximum value of $e$
B: has a minimum value of $-e$
C: has a maximum value of $\frac{1}{e}$
D: has a minimum value of $-\frac{1}{e}$<|im_end|>
<|im_start|>assistant
Given the problem stateme... | numinamath_cot |
<|im_start|>user
Admission tickets to a theater were 60 cents for adults and 25 cents for children. Receipts for the day showed that 280 persons attended and some dollars was collected. If 80 children attended that day, how much money was collected in total?<|im_end|>
<|im_start|>assistant
Let's calculate the total amo... | numinamath_cot |
<|im_start|>user
Consider an isosceles triangle with a vertex angle \( \theta \) and a constant height \( h \). A rectangle is inscribed in this triangle such that one side of the rectangle lies along the base of the triangle. The altitude of the rectangle from the base to the opposite side is \( x \). Find the maximum... | numinamath_cot |
<|im_start|>user
Let set $P = \{x | 2k\pi \leq \alpha \leq (2k + 1)\pi, k \in \mathbb{Z}\}$, and $Q = \{\alpha | -4 \leq \alpha \leq 4\}$. Then $P \cap Q =$ ( )
A: $\emptyset$
B: $\{\alpha | -4 \leq \alpha \leq -\pi \text{ or } 0 \leq \alpha \leq \pi\}$
C: $\{\alpha | -4 \leq \alpha \leq 4\}$
D: $\{\alpha | 0 \leq... | numinamath_cot |
<|im_start|>user
Determine the value of
$$
z=a \sqrt{a} \sqrt[4]{a} \sqrt[8]{a} \ldots \sqrt[2^{n}]{a} \ldots
$$
if \( n \) is infinitely large.<|im_end|>
<|im_start|>assistant
1. We begin by rewriting the given infinite product expression in a more manageable form. The given product is:
\[
z = a \sqrt{a} \... | numinamath_cot |
<|im_start|>user
A parallelogram with sides of lengths 3 cm and 5 cm and a diagonal of 6 cm is inscribed in a triangle. Find the sides of the triangle, given that the diagonals of the parallelogram are parallel to the legs of the triangle, and the shorter side of the parallelogram lies on the base of the triangle.<|im_... | numinamath_cot |
<|im_start|>user
Find the variance of the discrete random variable $X$ that is distributed according to the Poisson distribution:
$$
\begin{array}{ccccccc}
X & 0 & 1 & 2 & \cdots & k & \cdots \\
P & \mathrm{e}^{-\lambda} & \lambda \mathrm{e}^{-\lambda} / 1! & \lambda^{2} \mathrm{e}^{-\lambda} / 2! & \cdots & \lambda^{... | numinamath_cot |
<|im_start|>user
If the equation $\dfrac{x^{2}}{2+m}- \dfrac{y^{2}}{m+1}=1$ represents a hyperbola, then the range of $m$ is ( )
A: $m > -1$
B: $m < -2$
C: $-2 < m < -1$
D: $m > -1$ or $m < -2$<|im_end|>
<|im_start|>assistant
**Analysis**
This question examines the application of the standard equation of a hyperbola,... | numinamath_cot |
<|im_start|>user
Given $x, y \in (0, +\infty)$, if $\sqrt{x} + 3\sqrt{y} < k\sqrt{x+y}$ always holds, use the Cauchy-Schwarz inequality to find the range of the real number $k$.<|im_end|>
<|im_start|>assistant
By applying the Cauchy-Schwarz inequality, we have $(\sqrt{x} + 3\sqrt{y})^2 \leq (x+y)(1+9)$,
Therefore, $\... | numinamath_cot |
<|im_start|>user
Merlin has two $100 \times 100$ grids. One grid is blank and hangs on a cliff at the entrance of the cave. The other grid has a number in each cell and hangs on the wall inside the cave. You can specify a square subgrid of any size (from $1 \times 1$ to $100 \times 100$) in the blank grid and pay Merli... | numinamath_cot |
<|im_start|>user
In our region, rain falls on average only one day out of three. Meteorologists, due to their characteristic pessimism, make errors in their forecasts half of the time when the weather is good, but only once in five times when it is rainy.
Every morning, Francine leaves home for the entire day. If she ... | numinamath_cot |
<|im_start|>user
If eight movie tickets cost a certain multiple of one football game ticket, and each movie ticket is sold at $30, calculate the total amount of money Chandler will pay if he buys eight movie tickets and five football game tickets. The total amount he pays is $840. What is the multiple?<|im_end|>
<|im_s... | numinamath_cot |
<|im_start|>user
When $x=1$, the function $f\left(x\right)=a\ln x+\frac{b}{x}$ reaches a maximum value of $-2$. What is ${f'}\left(2\right)$?
A: $-1$
B: $-\frac{1}{2}$
C: $\frac{1}{2}$
D: $1$<|im_end|>
<|im_start|>assistant
Given the function $f(x) = a\ln x + \frac{b}{x}$ and the information that at $x=1$, $f(x)$ r... | numinamath_cot |
<|im_start|>user
Given an isosceles trapezoid $ABCD$ with bases $BC$ and $AD$. A circle $\omega$ passes through vertices $B$ and $C$, and intersects side $AB$ and diagonal $BD$ again at points $X$ and $Y$, respectively. A tangent to the circle $\omega$ at point $C$ intersects ray $AD$ at point $Z$. Prove that the point... | numinamath_cot |
<|im_start|>user
Given the binomial expansion of $(x- \frac {a}{x^{2}})^{9}$, the coefficient of the $x^{6}$ term is $36$. Find the real number $a$.<|im_end|>
<|im_start|>assistant
To determine the coefficient of a specific term in the binomial expansion of $(x- \frac {a}{x^{2}})^{9}$, we can use the general term (or t... | numinamath_cot |
<|im_start|>user
Given $y=f(x)$ is an even function on $\mathbb{R}$, and $f(x)=f(2-x)$. If $f(x)$ is a decreasing function on the interval $[1,2]$, then $f(x)$ on the intervals $[-2,-1]$ and $[3,4]$ is respectively ( )
A: Increasing function and decreasing function
B: Increasing function and increasing function
C:... | numinamath_cot |
<|im_start|>user
Given that sinα - 3cosα = 0, find the value of sin2α.<|im_end|>
<|im_start|>assistant
From sinα - 3cosα = 0, we get tanα = 3.
Then, we can use the double angle identity for sine:
$$sin2α = \frac{2sinαcosα}{sin^2α + cos^2α}$$
Since we know that tanα = 3, we can rewrite sinα and cosα in terms of tanα:
... | numinamath_cot |
<|im_start|>user
The sum of five consecutive integers is 75. The sum of the largest and smallest of these five integers is:
(A) 15
(B) 25
(C) 26
(D) 30
(E) 32<|im_end|>
<|im_start|>assistant
1. **Representing the Consecutive Integers:**
Let the five consecutive integers be represented as \( x-2, x-1, x, x+1, \) and ... | numinamath_cot |
<|im_start|>user
Given an isosceles trapezoid \(ABCD\) with top and bottom base lengths of 2 and 6 respectively, and a height of \(\sqrt{3}\), as shown in Figure 17-7. The trapezoid is folded along its axis of symmetry \(OO_1\) to form a dihedral angle, as shown in Figure 17-8. Determine the measure of the dihedral ang... | numinamath_cot |
<|im_start|>user
Let set $U = \{ x \mid x \text{ is a positive integer less than } 9\}$, set $A = \{1, 2, 3\}$, and set $B = \{3, 4, 5, 6\}$. Then the intersection of the complements of $A$ and $B$ with respect to $U$, denoted $\complement_U A \cap \complement_U B$, equals to ( )
A: $\{3\}$
B: $\{7, 8\}$
C: $\{4, ... | numinamath_cot |
<|im_start|>user
In triangle $PQR$, the sides $PQ$, $QR$, and $RP$ measure 17, 15, and 8 units, respectively. Let $J$ be the incenter of triangle $PQR$. The incircle of triangle $PQR$ touches side $QR$, $RP$, and $PQ$ at points $K$, $L$, and $M$, respectively. Determine the length of $PJ$.<|im_end|>
<|im_start|>assista... | numinamath_cot |
<|im_start|>user
when positive integer x is divided by positive integer y , the remainder is 8 . if x / y = 96.16 , what is the value of y ?<|im_end|>
<|im_start|>assistant
Given that x/y = 96.16, we can express this as a mixed number: 96 + 0.16. The decimal part (0.16) represents the remainder when x is divided by y.
... | numinamath_cot |
<|im_start|>user
Given the function f(x) = $$\begin{cases} 1 & \text{if } x \text{ is a rational number} \\ 0 & \text{if } x \text{ is an irrational number}\end{cases}$$, if x - f(x) ≤ g(x) holds for any x, then the function g(x) could be ( )
A: g(x) = x
B: g(x) = |x|
C: g(x) = x^2
D: No such function exists<|im_end|... | numinamath_cot |
<|im_start|>user
Given a circle \(\Gamma\) passing through point \(A\), with \(B\) and \(C\) being two points on \(\Gamma\) distinct from \(A\). The angle bisector of \(\angle ABC\) intersects \(\Gamma\) at point \(X\). Let \(Y\) be the reflection of point \(A\) over \(X\), and let \(CY\) intersect \(\Gamma\) again at ... | numinamath_cot |
<|im_start|>user
Two circles $ \omega_{1}$ and $ \omega_{2}$ intersect in points $ A$ and $ B$ . Let $ PQ$ and $ RS$ be segments of common tangents to these circles (points $ P$ and $ R$ lie on $ \omega_{1}$ , points $ Q$ and $ S$ lie on $ \omega_{2}$ ). It appears that $ RB\parallel PQ$ . Ray $... | numinamath_cot |
<|im_start|>user
Find the **maximum** value of
\[
\frac{\sin^4 x + \cos^4 x + 1}{\sin^2 x + \cos^2 x + 1}
\]
over all real values \(x\).<|im_end|>
<|im_start|>assistant
Let \( t = \cos^2 x \). Then \( \sin^2 x = 1 - t \), leading to:
\[
\sin^4 x = (1-t)^2 \quad \text{and} \quad \cos^4 x = t^2
\]
Thus, the expression be... | numinamath_cot |
<|im_start|>user
Let \(a \star b = ab - 2\). Compute the remainder when \((((579 \star 569) \star 559) \star \cdots \star 19) \star 9\) is divided by 100.<|im_end|>
<|im_start|>assistant
Given the operation \(a \star b = ab - 2\), we need to compute the remainder when \(\left( ( ( (579 \star 569) \star 559) \star \cdot... | numinamath_cot |
<|im_start|>user
The sum of the numerical coefficients in the complete expansion of $(x^2 + 2xy + y^2)^7$ is:
- **(A)** 0
- **(B)** 7
- **(C)** 14
- **(D)** 8192
- **(E)** 16384<|im_end|>
<|im_start|>assistant
1. **Recognize the Modified Expression**: We start with $(x^2 + 2xy + y^2)^7$.
2. **Rewrite as Simplified Bin... | numinamath_cot |
<|im_start|>user
the true discount on a bill due 18 months hence at 24 % per annum is rs. 700. The amount of another bill that is due 12 months hence at 20% per annum has a true discount of rs. 350. What is the combined amount of both bills?<|im_end|>
<|im_start|>assistant
To find the combined amount of both bills, we ... | numinamath_cot |
<|im_start|>user
Let \(a\) and \(b\) be real numbers. One of the roots of the polynomial equation
\[ x^3 + ax^2 + 3x + b = 0 \]
is \(2 - 3i\). Determine the ordered pair \((a, b)\).<|im_end|>
<|im_start|>assistant
Since the coefficients of the polynomial are real, another root must be the conjugate of \(2 - 3i\), which... | numinamath_cot |
<|im_start|>user
A school has $120$ students and $6$ teachers. In the first period, each student is taking one class, and each teacher is teaching one class. The enrollments in the classes are $60, 30, 15, 10, 3,$ and $2$. Let \( t \) be the average value obtained if a teacher is picked at random and the number of stud... | numinamath_cot |
<|im_start|>user
"After a disaster strikes one place, support comes from all directions." Following the devastating earthquake that struck Wenchuan County in Sichuan Province, China, on May 12th of this year, media reports indicate that by 12:00 on June 4th, 2008, the total amount of donations received from both domest... | numinamath_cot |
<|im_start|>user
The area between two concentric circles is $18\pi$ square inches. Calculate the length of a chord of the larger circle that is tangent to the smaller circle.
A) \( 3\sqrt{2} \)
B) \( 6 \)
C) \( 6\sqrt{2} \)
D) \( 9 \)
E) \( 9\sqrt{2} \)<|im_end|>
<|im_start|>assistant
1. **Identify the given informatio... | numinamath_cot |
<|im_start|>user
When a number is divided by 6 and then multiplied by 12, the answer is some value. The number is 5. What is the value of the answer?<|im_end|>
<|im_start|>assistant
To find the answer, we first divide the number 5 by 6 and then multiply the result by 12.
Step 1: Divide 5 by 6
5 ÷ 6 = 0.8333 (repeating... | numinamath_cot |
<|im_start|>user
two numbers n and 14 have lcm = 56 and gcf = 12 . find n .<|im_end|>
<|im_start|>assistant
The least common multiple (LCM) of two numbers is the smallest number that is a multiple of both numbers. The greatest common factor (GCF), also known as the greatest common divisor (GCD), is the largest number t... | numinamath_cot |
<|im_start|>user
A local store sells 9 pencils and 5 notebooks for $\$3.45$. It also sells 6 pencils and 4 notebooks for $\$2.40$. How much would 18 pencils and 9 notebooks cost?
A) $\$6.25$
B) $\$6.50$
C) $\$6.75$
D) $\$7.00$<|im_end|>
<|im_start|>assistant
1. **Define Variables:**
Let $p$ represent the price of on... | numinamath_cot |
<|im_start|>user
Find the average of all numbers between 6 and 36 which are divisible by 7. What is the average?<|im_end|>
<|im_start|>assistant
To find the average of all numbers between 6 and 36 that are divisible by 7, we first need to identify these numbers.
The first number greater than 6 that is divisible by 7 i... | numinamath_cot |
<|im_start|>user
Given the sets $P=\{x|2\leq x \leq 7\}$ and $Q=\{x|x^2-x-6=0, x\in \mathbb{R}\}$, find the set $P\cap Q$.<|im_end|>
<|im_start|>assistant
Since $P=\{x|2\leq x \leq 7\}$ and $Q=\{x|x^2-x-6=0, x\in \mathbb{R}\}=\{x|x=3 \text{ or } x=-2\}$,
according to the definition of intersection, we get $P\cap Q=\{... | numinamath_cot |
<|im_start|>user
Solve the equation
$$
3 e^{x} \operatorname{tg} y \, dx + \left(2 - e^{x}\right) \sec^{2} y \, dy = 0
$$<|im_end|>
<|im_start|>assistant
1. **Separate Variables:**
Given the differential equation:
\[
3 e^{x} \tan y \, dx + \left(2 - e^{x}\right) \sec^{2} y \, dy = 0
\]
We divide both si... | numinamath_cot |
<|im_start|>user
Ramu bought an old car for Rs. 42,000. He spent Rs. 2,500 on the first repair, Rs. 1,750 on the second repair, and Rs. 2,850 on the third repair. After making all the necessary repairs, he decided to sell the car. A potential buyer negotiated a 5% discount on the initial sale price of Rs. 64,900. Calcu... | numinamath_cot |
<|im_start|>user
There is a pyramid with a regular hexagon at the base and a side edge measuring 8 centimeters (cm). If the sum of the lengths of all the edges of this pyramid is 120 centimeters (cm), what is the length of one edge of the base in centimeters (cm)?<|im_end|>
<|im_start|>assistant
Let's denote the length... | numinamath_cot |
<|im_start|>user
Let $p$ be a prime number. A flea is staying at point $0$ of the real line. At each minute,
the flea has three possibilities: to stay at its position, or to move by $1$ to the left or to the right.
After $p-1$ minutes, it wants to be at $0$ again. Denote by $f(p)$ the number of its strategi... | numinamath_cot |
<|im_start|>user
Find the remainder when the polynomial $3x^{1010} + x^{1000}$ is divided by the polynomial $(x^2 + 1)(x - 1).$<|im_end|>
<|im_start|>assistant
First, note that $(x^2 + 1)(x - 1) = x^3 - x^2 + x - 1$ and this expression is a factor of $(x^2 - 1)(x^2 + 1) = x^4 - 1$.
We need to find:
\[3x^{1010} + x^{10... | numinamath_cot |
<|im_start|>user
Given the function $f(x)=A\sin(\omega x+\varphi)$ $(A \gt 0$, $\omega \gt 0$, $0 \lt \varphi \lt \frac{π}{2})$, choose three out of the following four conditions:<br/>① The maximum value is $2$;<br/>② The minimum positive period is $2\pi$;<br/>③ $f(0)=-2$;<br/>④ $f(-\frac{π}{6})=0$.<br/>$(Ⅰ)$ Find the ... | numinamath_cot |
<|im_start|>user
The one-variable quadratic equation about $x$ is $x^{2}+2\left(m-1\right)x+m^{2}-1=0$ with two distinct real roots $x_{1}$ and $x_{2}$.
$(1)$ Find the range of real number $m$;
$(2)$ Does there exist a real number $m$ such that $x_{1}x_{2}=0$ holds? If yes, find the value of $m$; if not, explain th... | numinamath_cot |
<|im_start|>user
What is the greatest integer less than or equal to \[\frac{5^{50} + 3^{50}}{5^{45} + 3^{45}}?\]<|im_end|>
<|im_start|>assistant
Start by factoring out common terms in the numerator and the denominator:
\[
\frac{5^{50} + 3^{50}}{5^{45} + 3^{45}} = \frac{5^{45}}{5^{45} + 3^{45}} \cdot \frac{5^{50}}{5^{45... | numinamath_cot |
<|im_start|>user
There are 4 boys and 4 girls standing in a row such that no two girls are adjacent and no two boys are adjacent. The number of possible arrangements is ( ).
A: $A_{4}^{4}A_{4}^{4}$
B: $2A_{4}^{4}A_{4}^{4}$
C: $A_{5}^{4}A_{4}^{4}$
D: $2A_{5}^{4}A_{4}^{4}$<|im_end|>
<|im_start|>assistant
**Analysis**
Th... | numinamath_cot |
<|im_start|>user
Let points $A, B, C, D,$ and $E$ be collinear in that order such that $AB = BC = 2$, $CD = 3$, and $DE = 7$. If $P$ can be any point in space, what is the smallest possible value of $AP^2 + BP^2 + CP^2 + DP^2 + EP^2$?<|im_end|>
<|im_start|>assistant
Let $P$ project onto line $AE$ at point $Q$ with leng... | numinamath_cot |
<|im_start|>user
Find the number of scalene triangles having all sides of integral lengths, and a perimeter less than $17$.
$\textbf{(A)}\ 10 \qquad\textbf{(B)}\ 12 \qquad\textbf{(C)}\ 14 \qquad\textbf{(D)}\ 16 \qquad\textbf{(E)}\ 18$<|im_end|>
<|im_start|>assistant
To solve this, we follow the same steps and condition... | numinamath_cot |
<|im_start|>user
Calculate the volume of the body bounded above by the surface \(z = xy^2\) and below by the rectangle \(0 \leq x \leq 1\), \(0 \leq y \leq 2\).<|im_end|>
<|im_start|>assistant
1. **Identify the problem:**
To compute the volume of the solid bounded above by the surface \(z = x y^2\) and below by the ... | numinamath_cot |
<|im_start|>user
Find all values of \( p \) such that the numbers \( 4p + 5 \), \( 2p \), and \( |p - 3| \) are the first, second, and third terms, respectively, of a geometric progression.<|im_end|>
<|im_start|>assistant
1. For the given numbers \(4p+5\), \(2p\), and \(\left| p-3 \right|\) to be consecutive terms of a... | numinamath_cot |
<|im_start|>user
In the acute-angled triangle \(ABC\), point \(Q\) is chosen on side \(AC\) such that \(AQ : QC = 1 : 2\). From point \(Q\), perpendiculars \(QM\) and \(QK\) are dropped onto sides \(AB\) and \(BC\) respectively. Additionally, \(BM : MA = 4 : 1\) and \(BK = KC\). Find the ratio \(MK : AC\).<|im_end|>
<|... | numinamath_cot |
<|im_start|>user
Given the function $f(x)=-x^{5}-3x^{3}-5x+3$, if $f(a)+f(a-2) > 6$, then the range of the real number $a$ is $(\quad)$
A: $(-\infty,3)$
B: $(3,+\infty)$
C: $(1,+\infty)$
D: $(-\infty,1)$<|im_end|>
<|im_start|>assistant
Since $f(x)=-x^{5}-3x^{3}-5x+3$,
we have $f(-x)=x^{5}+3x^{3}+5x+3$, which ... | numinamath_cot |
<|im_start|>user
Eight identical basketballs weigh the same as four identical watermelons. If one watermelon weighs 32 pounds, how many pounds does one basketball weigh?<|im_end|>
<|im_start|>assistant
1. Given that one watermelon weighs 32 pounds, four watermelons weigh \(4 \times 32 = 128\) pounds.
2. According to th... | numinamath_cot |
<|im_start|>user
A paint brush is used to paint along one diagonal and also brushes from the midpoints of each side towards the center, dividing the square into smaller sections as shown. One-third the area of the square is painted. What is the ratio of the side length of the square to the brush width?
A) $\sqrt{2} - 1... | numinamath_cot |
<|im_start|>user
Since the implementation of the "Action to Protect Wild Birds", the number of birds wintering in the Weishui Development Zone has increased year by year. In 2001, there were $x$ birds, in 2002, the number increased by 50% compared to 2001, and in 2003, it doubled compared to 2002. The number of birds w... | numinamath_cot |
<|im_start|>user
Given the function $f(x) = e^{x-k} - x$, where $x \in \mathbb{R}$,
(1) When $k=0$, if the inequality $f(x) \geq m$ holds true for all real $x$, find the range of real numbers $m$.
(2) Determine whether there are two distinct points in the interval $(k, 2k)$ for which $f(x)$ equals zero when $k > 1$. If... | numinamath_cot |
<|im_start|>user
A large box contains some small boxes and each small box contains 28 chocolate bars. There are 504 chocolate bars in the large box. How many small boxes are in the large box?<|im_end|>
<|im_start|>assistant
To find out how many small boxes are in the large box, we need to divide the total number of cho... | numinamath_cot |
<|im_start|>user
Given that \( a, b, c \) are real numbers, and \( b+c=6-4a+3a^{2} \) and \( c-b=4 - 4a + a^{2} \), determine the relationship between \( a, b, \) and \( c \) from the following options:
(A) \( a < b \leq c \)
(B) \( b < a \leq c \)
(C) \( b < c \leq a \)
(D) \( c < a \leq b \)<|im_end|>
<|im_start|>ass... | numinamath_cot |
<|im_start|>user
Find the maximum possible value of \( a \) such that the line \( y = mx + 3 \) passes through no lattice point with \( 0 < x \leq 150 \) for all \( m \) such that \( \frac{1}{3} < m < a \).
**A)** \( \frac{51}{152} \)
**B)** \( \frac{52}{153} \)
**C)** \( \frac{51}{151} \)
**D)** \( \frac{50}{149... | numinamath_cot |
<|im_start|>user
In the trapezoid \(ABCD\), the diagonal \(AC\) is perpendicular to the side \(CD\), and the diagonal \(DB\) is perpendicular to the side \(AB\). On the extensions of the sides \(AB\) and \(DC\) beyond the shorter base \(BC\), the segments \(BM\) and \(CN\) are laid out such that a new trapezoid \(BMNC\... | numinamath_cot |
<|im_start|>user
Given $\tan \alpha = 2$, find the value of $\tan (\alpha + \frac{\pi}{4})=$ \_\_\_\_\_\_.<|im_end|>
<|im_start|>assistant
Since $\tan \alpha = 2$, we have $\tan (\alpha + \frac{\pi}{4}) = \frac{\tan \alpha + 1}{1 - \tan \alpha \tan \frac{\pi}{4}} = \frac{2 + 1}{1 - 2 \times 1} = -3$.
Therefore, the an... | numinamath_cot |
<|im_start|>user
Given a sequence of figures where $F_1$ starts with $3$ diamonds, each subsequent figure $F_n$ for $n \geq 2$ is constructed by surrounding the previous figure $F_{n-1}$ with a square and placing two more diamonds on each side of the new square than $F_{n-1}$ had on each side of its outer square. Calcu... | numinamath_cot |
<|im_start|>user
The ratio of girls to boys in Ms. Carter's art class is 4:3. If there are a total of 70 students, how many girls are in Ms. Carter's art class?<|im_end|>
<|im_start|>assistant
Let the number of girls be $4k$ and the number of boys be $3k$. The total number of students provided is 70.
1. Establish the ... | numinamath_cot |
<|im_start|>user
Given vectors $\overrightarrow{m}=(\cos^2x,\sqrt{3})$ and $\overrightarrow{n}=(2,\sin 2x)$, and a function $f(x)=\overrightarrow{m} \cdot \overrightarrow{n}$.
$(1)$ Find the interval where the function $y=f(x)$ is monotonically increasing.
$(2)$ If $x \in [0,\frac{\pi}{2}]$, determine the range of ... | numinamath_cot |
<|im_start|>user
There are twice as many cows in Devonshire as there are hearts on a standard deck of 52 playing cards. If there are 4 hearts on a card, calculate the total cost of the cows when they are sold at $200 each.<|im_end|>
<|im_start|>assistant
To solve this problem, let's break it down into clear, step-by-st... | numinamath_cot |
<|im_start|>user
Solve the equation: $\frac{1}{x-2}=\frac{3}{x}$.<|im_end|>
<|im_start|>assistant
To solve the equation $\frac{1}{x-2}=\frac{3}{x}$, we follow these steps:
1. **Multiply both sides by $x(x-2)$ to eliminate the denominators:**
\[
x(x-2) \cdot \frac{1}{x-2} = x(x-2) \cdot \frac{3}{x}
\]
Simpl... | numinamath_cot |
<|im_start|>user
If the range of the function $f(x)$ on $[m, n] (m < n)$ is exactly $[m, n]$, then $f(x)$ is called an "equal value mapping interval" of the function. Among the following functions: $① y = x^2 - 1$; $② y = 2 + \log_2 x$; $③ y = 2^x - 1$; $④ y = \frac{1}{x - 1}$. The number of functions that have a uniqu... | numinamath_cot |
<|im_start|>user
The maximum value of the quadratic function $y=-x^{2}-3x+4$ is ______.<|im_end|>
<|im_start|>assistant
To find the maximum value of the quadratic function $y=-x^{2}-3x+4$, we first complete the square:
\[
\begin{align*}
y &= -x^{2}-3x+4 \\
&= -(x^{2}+3x)+4 \\
&= -\left(x^{2}+3x+\left(\frac{3}{2}\right... | numinamath_cot |
<|im_start|>user
Given that the inequality $x^2 - ax + 2a > 0$ is always true for all $x$ in $\mathbb{R}$, find the range of the real number $a$.<|im_end|>
<|im_start|>assistant
Since the inequality $x^2 - ax + 2a > 0$ is always true for all $x$ in $\mathbb{R}$,
it implies that $\Delta = (-a)^2 - 8a < 0$,
Therefore... | numinamath_cot |
<|im_start|>user
A box contains a total of 240 red and blue ballpoint pens in total. There are 2 fewer blue ballpoint pens than red ballpoint pens. Find how many red ballpoint pens are in all.<|im_end|>
<|im_start|>assistant
Let's denote the number of red ballpoint pens as R and the number of blue ballpoint pens as B.
... | numinamath_cot |
<|im_start|>user
Given the family of lines \( L: \frac{x_{0} x}{a^{2}}+\frac{y_{0} y}{b^{2}}=1 \) (with \( a > b > 0 \)), determine the validity of the following statements:
A. If \( \frac{x_{0}^{2}}{a^{2}}+\frac{y_{0}^{2}}{b^{2}}<1 \), then there exists a line in \( L \) that intersects the ellipse \( \frac{x^{2}}{a^{... | numinamath_cot |
<|im_start|>user
Given a point $P$ on a triangular piece of paper $ABC,\,$ consider the creases that are formed in the paper when $A, B,\,$ and $C\,$ are folded onto $P.\,$ Let us call $P$ a fold point of $\triangle ABC\,$ if these creases, which number three unless $P$ is one of the vertices, do not intersect. Suppose... | numinamath_cot |
<|im_start|>user
An assembly line produces 36 cogs per hour until an initial order of 60 cogs is completed. The speed of the assembly line is then immediately increased so that it can produce some cogs per hour until another 60 cogs are produced. The overall average output, in cogs per hour, for the assembly line durin... | numinamath_cot |
<|im_start|>user
Hajin wants to find the password of a lock. The password is set with one of the three numbers: 1, 7, 4, with the tens digit of 3. When password has all different numbers, find the sum of the largest and the third largest three-digit number that can be a password.<|im_end|>
<|im_start|>assistant
To find... | numinamath_cot |
<|im_start|>user
Let $S$ be the square one of whose diagonals has endpoints $(1/20,7/20)$ and $(-1/20,-7/20)$. A point $v=(x,y)$ is chosen uniformly at random over all pairs of real numbers $x$ and $y$ such that $0 \le x \le 2020$ and $0\le y\le 2020$. Let $T(v)$ be a translated copy of $S$ centered at $v$. What is the... | numinamath_cot |
<|im_start|>user
Consider the roots \( b_1, b_2, \dots, b_{1009} \) of the polynomial
\[ x^{1009} + x^{1008} + x^{1007} + \dots + x^2 + x - 671 = 0. \]
Calculate the sum:
\[ \sum_{n = 1}^{1009} \frac{1}{1 - b_n}. \]<|im_end|>
<|im_start|>assistant
Let \( c_n = \frac{1}{1 - b_n} \). Then solving for \( b_n \), we find:
... | numinamath_cot |
<|im_start|>user
Let \(a, b, c\) be three strictly positive real numbers such that \(abc = 1\). Show that
$$
\frac{1+ab}{1+a}+\frac{1+bc}{1+b}+\frac{1+ca}{1+c} \geq 3
$$<|im_end|>
<|im_start|>assistant
Given the inequality to be proven:
\[
\frac{1+ab}{1+a} + \frac{1+bc}{1+b} + \frac{1+ca}{1+c} \geq 3
\]
and the condit... | numinamath_cot |
<|im_start|>user
Given vectors $\overrightarrow{a} = (1, 2, 1)$, $\overrightarrow{b} = (1, 2, 2)$, and vectors $(k\overrightarrow{a} + \overrightarrow{b})$ is parallel to $(\overrightarrow{a} - 2\overrightarrow{b})$, find the value of the real number $k$.<|im_end|>
<|im_start|>assistant
Since $\overrightarrow{a} = (1, ... | numinamath_cot |
<|im_start|>user
Given the function $f(x)=|x-1|$.
(I) Solve the inequality: $f(x)+f(x-1) \leqslant 2$;
(II) If $a > 0$, prove that: $f(ax)-af(x) \leqslant f(a)$.<|im_end|>
<|im_start|>assistant
Solution:
(I) For the function $f(x)=|x-1|$, the inequality $f(x)+f(x-1) \leqslant 2$ is equivalent to $|x-1|+|x-2| \leq... | numinamath_cot |
<|im_start|>user
Prove that if a set has the cardinality of the continuum, then it is uncountable.<|im_end|>
<|im_start|>assistant
To prove that a set with the cardinality of the continuum is not countable, we can proceed as follows:
1. **Understanding the Power Set**:
Let $X$ be a countable set. We need to consid... | numinamath_cot |
<|im_start|>user
There are $6$ irrational numbers. Prove that there are always three of them, suppose $a,b,c$ such that $a+b$ , $b+c$ , $c+a$ are irrational numbers.
*(Erken)*<|im_end|>
<|im_start|>assistant
1. **Define the Problem in Graph Theory Terms:**
- Let the six irrational numbers be represented by po... | numinamath_cot |
<|im_start|>user
Given the expansion of $\left( \sqrt{x}-\frac{2}{\sqrt[3]{x}} \right)^{n}$, the ratio of the coefficient of the 5th term to that of the 3rd term is 56:3.
(1) Find all rational terms in the expansion;
(2) Calculate the value of $n+9c_n^2+81c_n^3+\ldots+9^{n-1}c_n^n$.<|im_end|>
<|im_start|>assistant
(1... | numinamath_cot |
<|im_start|>user
In what time will a train 100 m long cross an electric pole, if its speed is 144 km/hr?<|im_end|>
<|im_start|>assistant
To calculate the time it takes for a train to cross an electric pole, we need to convert the speed of the train from kilometers per hour (km/hr) to meters per second (m/s), because th... | numinamath_cot |
End of preview.
Qwen3.6-27B SFT mixture — 500k tokens, NuminaMath-CoT only
497,968 tokens across 934 conversations, drawn entirely from
AI-MO/NuminaMath-CoT. md5 439d58c239e7fc8f23486324a08a7212.
Single-domain by design: no TULU3, No Robots or difficult-advice data. It isolates what maths chain-of-thought SFT alone does, against the mixed corpora in the sibling datasets.
Format
Every row is a pre-rendered Qwen3.6 chat string with no <think> block -- not even an
empty one, which is the documented pattern that trains a model to stop reasoning. NuminaMath's
chain-of-thought lives in the response text itself, so no non-thinking marker is added: marking
it would contradict its own content.
Conversations longer than 3,072 tokens were dropped rather than truncated mid-answer.
Re-rendering from messages will not reproduce these strings.
Intended use
Assistant-only loss: 409,975 / 497,968 = 82.3% of tokens carry loss -- the highest share of any mixture in this family, because NuminaMath pairs short problems with long worked solutions.
Provenance
src/data/build_hf_mixture.py with configs/mixture_500k_numina_only.yaml, seed 0.
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Models trained or fine-tuned on LASR-Callum/2026-08-03-qwen36-mixture-500k-numina-only