instruction_seed stringlengths 20 2.19k | response_seed stringlengths 24 1.5k ⌀ | reasoning stringlengths 484 78.2k | deepseek_solution stringlengths 159 3.28k | __original_row_idx int64 22 40k ⌀ | source stringclasses 2
values | final_reasoning_trace stringlengths 879 79.7k | conversations listlengths 2 2 |
|---|---|---|---|---|---|---|---|
A water tank can be filled by two pipes, A and B. Pipe A fills the tank at a constant rate of 2 cubic meters per minute, while pipe B fills it at a constant rate of 1.5 cubic meters per minute. If the tank is initially empty and both pipes are opened simultaneously, how long will it take to fill a 30-cubic-meter tank? ... | A water tank can be filled by two pipes, A and B. Pipe A fills the tank at a constant rate of 2 cubic meters per minute, while pipe B fills it at a constant rate of 1.5 cubic meters per minute. If the tank is initially empty and both pipes are opened simultaneously, how long will it take to fill a 30-cubic-meter tank? ... | Okay, let's see. I need to figure out how long it will take to fill a 30-cubic-meter tank using both pipes A and B. Pipe A fills at 2 cubic meters per minute, and Pipe B at 1.5 cubic meters per minute. Both are opened at the same time on an empty tank. Hmm, so since they're working together, their rates should add up, ... | To determine how long it will take to fill a 30-cubic-meter tank using both pipes A and B, we first calculate their combined filling rate. Pipe A fills at 2 cubic meters per minute and Pipe B fills at 1.5 cubic meters per minute. The combined rate is:
\[
2 \, \text{m}^3/\text{min} + 1.5 \, \text{m}^3/\text{min} = 3.5 ... | 33,883 | ai2-adapt-dev/openmath-2-math | <think>
Okay, let's see. I need to figure out how long it will take to fill a 30-cubic-meter tank using both pipes A and B. Pipe A fills at 2 cubic meters per minute, and Pipe B at 1.5 cubic meters per minute. Both are opened at the same time on an empty tank. Hmm, so since they're working together, their rates should ... | [
{
"from": "human",
"value": "A water tank can be filled by two pipes, A and B. Pipe A fills the tank at a constant rate of 2 cubic meters per minute, while pipe B fills it at a constant rate of 1.5 cubic meters per minute. If the tank is initially empty and both pipes are opened simultaneously, how long wil... |
If $x + y = z$ and $y + z = 7$ and $z = 4$, what is the value of $x$? | If $x + y = z$ and $y + z = 7$ and $z = 4$, what is the value of $x$? | Okay, let's see. I need to find the value of x given these equations: x + y = z, y + z = 7, and z = 4. Hmm, let me break this down step by step.
First, the problem gives me three equations. The first one is x plus y equals z. The second one is y plus z equals 7, and the third one directly states that z is 4. So, sinc... | Given the equations \( x + y = z \), \( y + z = 7 \), and \( z = 4 \), we need to find the value of \( x \).
1. Start with the given value \( z = 4 \).
2. Substitute \( z = 4 \) into the second equation \( y + z = 7 \):
\[
y + 4 = 7
\]
Solving for \( y \):
\[
y = 7 - 4 = 3
\]
3. Substitute \( y = ... | 11,205 | ai2-adapt-dev/openmath-2-math | <think>
Okay, let's see. I need to find the value of x given these equations: x + y = z, y + z = 7, and z = 4. Hmm, let me break this down step by step.
First, the problem gives me three equations. The first one is x plus y equals z. The second one is y plus z equals 7, and the third one directly states that z is 4. ... | [
{
"from": "human",
"value": "If $x + y = z$ and $y + z = 7$ and $z = 4$, what is the value of $x$?"
},
{
"from": "gpt",
"value": "<think>\nOkay, let's see. I need to find the value of x given these equations: x + y = z, y + z = 7, and z = 4. Hmm, let me break this down step by step. \n\nFirst, t... |
Find the equation of the directrix of the ellipse $\frac{x^2}{4} + \frac{y^2}{9} = 1.$ | Find the equation of the directrix of the ellipse $\frac{x^2}{4} + \frac{y^2}{9} = 1.$ | Okay, so I need to find the equation of the directrix of the ellipse given by the equation x²/4 + y²/9 = 1. Hmm, let me recall what I know about ellipses. First off, the standard form of an ellipse is either x²/a² + y²/b² = 1 or x²/b² + y²/a² = 1, depending on whether the major axis is horizontal or vertical. The major... | To find the equation of the directrix of the ellipse \(\frac{x^2}{4} + \frac{y^2}{9} = 1\), we start by noting that the major axis is vertical because the denominator under \(y^2\) is larger. The standard form of a vertical ellipse is \(\frac{x^2}{b^2} + \frac{y^2}{a^2} = 1\) where \(a > b\). Here, \(a^2 = 9\) and \(b^... | 27,361 | ai2-adapt-dev/openmath-2-math | <think>
Okay, so I need to find the equation of the directrix of the ellipse given by the equation x²/4 + y²/9 = 1. Hmm, let me recall what I know about ellipses. First off, the standard form of an ellipse is either x²/a² + y²/b² = 1 or x²/b² + y²/a² = 1, depending on whether the major axis is horizontal or vertical. T... | [
{
"from": "human",
"value": "Find the equation of the directrix of the ellipse $\\frac{x^2}{4} + \\frac{y^2}{9} = 1.$"
},
{
"from": "gpt",
"value": "<think>\nOkay, so I need to find the equation of the directrix of the ellipse given by the equation x²/4 + y²/9 = 1. Hmm, let me recall what I know... |
What is the smallest positive integer that is divisible by both 4 and 9 and has exactly 4 distinct prime factors? | What is the smallest positive integer that is divisible by both 4 and 9 and has exactly 4 distinct prime factors? | Alright, let me try to figure out this problem. The question is asking for the smallest positive integer that is divisible by both 4 and 9 and has exactly 4 distinct prime factors. Hmm, okay. Let me break this down step by step.
First, if a number is divisible by both 4 and 9, that means it has to be a multiple of the... | To find the smallest positive integer that is divisible by both 4 and 9 and has exactly 4 distinct prime factors, we start by determining the least common multiple (LCM) of 4 and 9. The prime factorizations of 4 and 9 are \(2^2\) and \(3^2\) respectively. The LCM is therefore \(2^2 \times 3^2 = 36\).
Next, we need thi... | 32,996 | ai2-adapt-dev/openmath-2-math | <think>
Alright, let me try to figure out this problem. The question is asking for the smallest positive integer that is divisible by both 4 and 9 and has exactly 4 distinct prime factors. Hmm, okay. Let me break this down step by step.
First, if a number is divisible by both 4 and 9, that means it has to be a multipl... | [
{
"from": "human",
"value": "What is the smallest positive integer that is divisible by both 4 and 9 and has exactly 4 distinct prime factors?"
},
{
"from": "gpt",
"value": "<think>\nAlright, let me try to figure out this problem. The question is asking for the smallest positive integer that is ... |
The measures of the three interior angles of a triangle are $50^\circ$, $55^\circ$ and $x^\circ$. What is the degree measure of the largest interior angle of this triangle? | The measures of the three interior angles of a triangle are $50^\circ$, $55^\circ$ and $x^\circ$. What is the degree measure of the largest interior angle of this triangle? | Okay, so I need to find the largest interior angle of a triangle where two of the angles are given as 50 degrees and 55 degrees, and the third one is x degrees. Hmm, let's see. I remember that in any triangle, the sum of all the interior angles is always 180 degrees. That seems like a key point here. So maybe I can sta... | To find the degree measure of the largest interior angle of a triangle with angles \(50^\circ\), \(55^\circ\), and \(x^\circ\), we start by using the fact that the sum of the interior angles of a triangle is always \(180^\circ\).
First, we add the two known angles:
\[
50^\circ + 55^\circ = 105^\circ
\]
Next, we subtr... | 15,826 | ai2-adapt-dev/openmath-2-math | <think>
Okay, so I need to find the largest interior angle of a triangle where two of the angles are given as 50 degrees and 55 degrees, and the third one is x degrees. Hmm, let's see. I remember that in any triangle, the sum of all the interior angles is always 180 degrees. That seems like a key point here. So maybe I... | [
{
"from": "human",
"value": "The measures of the three interior angles of a triangle are $50^\\circ$, $55^\\circ$ and $x^\\circ$. What is the degree measure of the largest interior angle of this triangle?"
},
{
"from": "gpt",
"value": "<think>\nOkay, so I need to find the largest interior angle ... |
Which of the following expressions is not a quadratic radical?
A: $\sqrt {5}$
B: $ \sqrt {a^{2}+1}$
C: $ \sqrt {1.2}$
D: $ \sqrt {-|x|-1}$ | null | Alright, so I need to figure out which of these expressions isn't a quadratic radical. The options are A through D, each with a different square root. Let me start by recalling what a quadratic radical is. If I remember correctly, a quadratic radical is an expression of the form √a where a is a rational number. So, the... | To determine which expression is not a quadratic radical, we need to check if the radicand (the expression under the square root) is a non-negative rational number.
- **Option A: \(\sqrt{5}\)**
The radicand is 5, which is a positive rational number. Therefore, \(\sqrt{5}\) is a quadratic radical.
- **Option B: \... | null | AI-MO/NuminaMath-1.5 | <think>
Alright, so I need to figure out which of these expressions isn't a quadratic radical. The options are A through D, each with a different square root. Let me start by recalling what a quadratic radical is. If I remember correctly, a quadratic radical is an expression of the form √a where a is a rational number.... | [
{
"from": "human",
"value": "Which of the following expressions is not a quadratic radical?\n\nA: $\\sqrt {5}$\n\nB: $ \\sqrt {a^{2}+1}$\n\nC: $ \\sqrt {1.2}$\n\nD: $ \\sqrt {-|x|-1}$"
},
{
"from": "gpt",
"value": "<think>\nAlright, so I need to figure out which of these expressions isn't a quad... |
Consider a standard deck of 52 playing cards, with four suits (hearts, diamonds, clubs, and spades) and 13 ranks (Ace through King). If you were to draw one card from the deck, what is the probability that it would be either a heart or a face card (King, Queen, Jack)? | Consider a standard deck of 52 playing cards, with four suits (hearts, diamonds, clubs, and spades) and 13 ranks (Ace through King). If you were to draw one card from the deck, what is the probability that it would be either a heart or a face card (King, Queen, Jack)? | Alright, so I need to figure out the probability of drawing a heart or a face card from a standard deck of 52 cards. Let me think about how to approach this.
First, probability is generally the number of favorable outcomes divided by the total number of possible outcomes. In this case, the total number of possible ou... | To determine the probability of drawing a heart or a face card from a standard deck of 52 playing cards, we use the principle of inclusion and exclusion.
1. **Number of hearts**: There are 13 hearts in the deck.
2. **Number of face cards**: Each suit has 3 face cards (King, Queen, Jack), and there are 4 suits, resulti... | 37,054 | ai2-adapt-dev/openmath-2-math | <think>
Alright, so I need to figure out the probability of drawing a heart or a face card from a standard deck of 52 cards. Let me think about how to approach this.
First, probability is generally the number of favorable outcomes divided by the total number of possible outcomes. In this case, the total number of pos... | [
{
"from": "human",
"value": "Consider a standard deck of 52 playing cards, with four suits (hearts, diamonds, clubs, and spades) and 13 ranks (Ace through King). If you were to draw one card from the deck, what is the probability that it would be either a heart or a face card (King, Queen, Jack)?"
},
{
... |
Convert \( \sqrt{3} e^{13\pi i/6} \) to rectangular form. | null | Okay, so I need to convert the complex number \( \sqrt{3} e^{13\pi i/6} \) to rectangular form, which is \( a + bi \). Hmm, let's recall how to do this. I remember that Euler's formula relates the exponential form of a complex number to its rectangular form. The formula is \( e^{i\theta} = \cos\theta + i\sin\theta \). ... | To convert \( \sqrt{3} e^{13\pi i/6} \) to rectangular form, we use Euler's formula \( e^{i\theta} = \cos\theta + i\sin\theta \).
First, we note that the angle \( 13\pi/6 \) is coterminal with \( \pi/6 \) because \( 13\pi/6 - 2\pi = \pi/6 \). Therefore, the trigonometric functions for \( 13\pi/6 \) are the same as tho... | null | AI-MO/NuminaMath-1.5 | <think>
Okay, so I need to convert the complex number \( \sqrt{3} e^{13\pi i/6} \) to rectangular form, which is \( a + bi \). Hmm, let's recall how to do this. I remember that Euler's formula relates the exponential form of a complex number to its rectangular form. The formula is \( e^{i\theta} = \cos\theta + i\sin\th... | [
{
"from": "human",
"value": "Convert \\( \\sqrt{3} e^{13\\pi i/6} \\) to rectangular form."
},
{
"from": "gpt",
"value": "<think>\nOkay, so I need to convert the complex number \\( \\sqrt{3} e^{13\\pi i/6} \\) to rectangular form, which is \\( a + bi \\). Hmm, let's recall how to do this. I reme... |
1. (6 points) Today is January 31, 2015, welcome to the 2015 "Spring Cup" Final. The calculation result of the expression $\frac{\frac{2015}{1}+\frac{2015}{0.31}}{1+0.31}$ is | null | Okay, so I need to calculate this expression: \(\frac{\frac{2015}{1} + \frac{2015}{0.31}}{1 + 0.31}\). Let me see. Hmm, first, let me break it down step by step. Maybe if I simplify the numerator and the denominator separately, that would help.
Starting with the numerator: \(\frac{2015}{1} + \frac{2015}{0.31}\). Well,... | To calculate the expression \(\frac{\frac{2015}{1} + \frac{2015}{0.31}}{1 + 0.31}\), we start by simplifying the numerator and the denominator separately.
First, the numerator:
\[
\frac{2015}{1} + \frac{2015}{0.31}
\]
\(\frac{2015}{1}\) is simply 2015. For the second term, \(\frac{2015}{0.31}\):
\[
\frac{2015}{0.31} =... | null | AI-MO/NuminaMath-1.5 | <think>
Okay, so I need to calculate this expression: \(\frac{\frac{2015}{1} + \frac{2015}{0.31}}{1 + 0.31}\). Let me see. Hmm, first, let me break it down step by step. Maybe if I simplify the numerator and the denominator separately, that would help.
Starting with the numerator: \(\frac{2015}{1} + \frac{2015}{0.31}\... | [
{
"from": "human",
"value": "1. (6 points) Today is January 31, 2015, welcome to the 2015 \"Spring Cup\" Final. The calculation result of the expression $\\frac{\\frac{2015}{1}+\\frac{2015}{0.31}}{1+0.31}$ is"
},
{
"from": "gpt",
"value": "<think>\nOkay, so I need to calculate this expression: \... |
"The map below shows an east/west road connecting the towns of Acorn, Centerville, and Midland, and (...TRUNCATED) | null | "Okay, so I need to solve this problem about three bicyclists arriving at the same point at the same(...TRUNCATED) | "We need to determine the distance David bicycles from Drake to a meeting point along the road from (...TRUNCATED) | null | AI-MO/NuminaMath-1.5 | "<think>\nOkay, so I need to solve this problem about three bicyclists arriving at the same point at(...TRUNCATED) | [{"from":"human","value":"The map below shows an east/west road connecting the towns of Acorn, Cente(...TRUNCATED) |
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