id
stringlengths 2
47
| answer_type
stringclasses 11
values | category
stringclasses 16
values | difficulty
stringclasses 5
values | data_source
stringclasses 1
value | prompt
listlengths 1
1
| ability
stringclasses 1
value | reward_model
dict | extra_info
dict | verifications
int64 0
7
⌀ | domain
stringlengths 3
84
⌀ |
|---|---|---|---|---|---|---|---|---|---|---|
998250
|
Multiple Choice
|
Physics
|
Senior High School
|
general-reasoner
|
[
{
"content": "A propagating wave is represented by the wave function {eq}y(x,t) = 0.2\\sin(6\\pi x + 20 \\pi t + \\Phi)\n\n{/eq} where {eq}x\n\n{/eq} and {eq}y\n\n{/eq} are in meters and {eq}t\n\n{/eq} is in seconds. If at {eq}t = 0\n\n{/eq}, the vertical position of the element at {eq}x = 0\n\n{/eq} is {eq}y = +0.08\n\n{/eq} m and the element moving downward, then the phase angle is\n\n\n\n{eq}A.\\ \\psi = -3.55\\ rad\\\\\n\nB.\\ \\psi = -0.41\\ rad\\\\\n\nC.\\ \\psi = -2.73\\ rad\\\\\n\nD.\\ \\psi = +3.55\\ rad\\\\\n\nE.\\ \\psi = +0.41\\ rad\\\\\n\nF.\\ \\psi = +2.73\\ rad\n\n{/eq} Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "F",
"style": "rule"
}
|
{
"answer": "F",
"index": 200,
"question": "A propagating wave is represented by the wave function {eq}y(x,t) = 0.2\\sin(6\\pi x + 20 \\pi t + \\Phi)\n\n{/eq} where {eq}x\n\n{/eq} and {eq}y\n\n{/eq} are in meters and {eq}t\n\n{/eq} is in seconds. If at {eq}t = 0\n\n{/eq}, the vertical position of the element at {eq}x = 0\n\n{/eq} is {eq}y = +0.08\n\n{/eq} m and the element moving downward, then the phase angle is\n\n\n\n{eq}A.\\ \\psi = -3.55\\ rad\\\\\n\nB.\\ \\psi = -0.41\\ rad\\\\\n\nC.\\ \\psi = -2.73\\ rad\\\\\n\nD.\\ \\psi = +3.55\\ rad\\\\\n\nE.\\ \\psi = +0.41\\ rad\\\\\n\nF.\\ \\psi = +2.73\\ rad\n\n{/eq}",
"split": "train"
}
| null | null |
1663467
|
Multiple Choice
|
Economics
|
University
|
general-reasoner
|
[
{
"content": "In an efficient market, deadweight loss is\n\na. maximum.\n\nb. minimum.\n\nc. constant.\n\nd. zero. Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "d",
"style": "rule"
}
|
{
"answer": "d",
"index": 201,
"question": "In an efficient market, deadweight loss is\n\na. maximum.\n\nb. minimum.\n\nc. constant.\n\nd. zero.",
"split": "train"
}
| null | null |
1948788
|
Multiple Choice
|
Other
|
Senior High School
|
general-reasoner
|
[
{
"content": "In a white heron how does Sarah Jewett portray Sylvia's attitude about money Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "C",
"style": "rule"
}
|
{
"answer": "C",
"index": 202,
"question": "In a white heron how does Sarah Jewett portray Sylvia's attitude about money",
"split": "train"
}
| null | null |
486246
|
Float
|
Physics
|
University
|
general-reasoner
|
[
{
"content": "Consider the following quantities for a four-step cycle: Step 1: q = +445 J, w = -445 J. Step 2: q = 0, w = -99 J. Step 3: q = -360 J, w = +360 J. Step 4: q = 0, w = +99 J. What is the efficiency of this process? Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "0.1910",
"style": "rule"
}
|
{
"answer": "0.1910",
"index": 203,
"question": "Consider the following quantities for a four-step cycle: Step 1: q = +445 J, w = -445 J. Step 2: q = 0, w = -99 J. Step 3: q = -360 J, w = +360 J. Step 4: q = 0, w = +99 J. What is the efficiency of this process?",
"split": "train"
}
| null | null |
866660
|
Matrix
|
Mathematics
|
University
|
general-reasoner
|
[
{
"content": "Given a complex inner product on a finite-dimensional vector space, is there always a matrix $M$ such that $\\langle x,y \\rangle=y^*Mx$? What are the properties of such a matrix? Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "[M]_B = \n\\pmatrix{\n\\langle v_1,v_1 \\rangle & \\cdots & \\langle v_1,v_n \\rangle\\\n\\vdots & \\ddots & \\vdots\\\n\\langle v_n,v_1 \\rangle & \\cdots & \\langle v_n,v_n \\rangle\n}",
"style": "rule"
}
|
{
"answer": "[M]_B = \n\\pmatrix{\n\\langle v_1,v_1 \\rangle & \\cdots & \\langle v_1,v_n \\rangle\\\n\\vdots & \\ddots & \\vdots\\\n\\langle v_n,v_1 \\rangle & \\cdots & \\langle v_n,v_n \\rangle\n}",
"index": 204,
"question": "Given a complex inner product on a finite-dimensional vector space, is there always a matrix $M$ such that $\\langle x,y \\rangle=y^*Mx$? What are the properties of such a matrix?",
"split": "train"
}
| null | null |
338995
|
Float
|
Physics
|
Senior High School
|
general-reasoner
|
[
{
"content": "An airplane is flying through a thundercloud at a height of 2000 m. If there is a charge concentration of +40 C at height 3000 m within the cloud and -40 C at height 1000 m, what is the magnitude of the electric field E at the aircraft? ({eq}k_e = 8.99 \\times 10^9\\ N.m^2/C^2\n\n{/eq}) Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "719200 N/C",
"style": "rule"
}
|
{
"answer": "719200 N/C",
"index": 205,
"question": "An airplane is flying through a thundercloud at a height of 2000 m. If there is a charge concentration of +40 C at height 3000 m within the cloud and -40 C at height 1000 m, what is the magnitude of the electric field E at the aircraft? ({eq}k_e = 8.99 \\times 10^9\\ N.m^2/C^2\n\n{/eq})",
"split": "train"
}
| null | null |
908451
|
Fraction
|
Physics
|
Senior High School
|
general-reasoner
|
[
{
"content": "A hot air balloon rising straight up from a level field is tracked by a range finder {eq}90 {/eq} m from the liftoff point. At the moment the range finder's elevation angle is {eq}\\frac{\\pi}{4} {/eq}, the angle is increasing at the rate of {eq}0.12 {/eq} rad/min. How fast is the balloon rising at that moment? Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "108/5 m/min",
"style": "rule"
}
|
{
"answer": "108/5 m/min",
"index": 206,
"question": "A hot air balloon rising straight up from a level field is tracked by a range finder {eq}90 {/eq} m from the liftoff point. At the moment the range finder's elevation angle is {eq}\\frac{\\pi}{4} {/eq}, the angle is increasing at the rate of {eq}0.12 {/eq} rad/min. How fast is the balloon rising at that moment?",
"split": "train"
}
| null | null |
1227691
|
Expression
|
Mathematics
|
University
|
general-reasoner
|
[
{
"content": "Suppose we have a 10-face fair die such that the expected number of rolls to get a particular number from $\\{1, 2, \\ldots, 10\\}$ is $10.$ How would I go about finding the expected number of rolls needed to get 5 different numbers? Or more generally, the expected number of rolls needed to get n different numbers where $n < 10.$ Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "E[X_i] = sum_{j=1}^i (10/(10-(i-1)))",
"style": "rule"
}
|
{
"answer": "E[X_i] = sum_{j=1}^i (10/(10-(i-1)))",
"index": 207,
"question": "Suppose we have a 10-face fair die such that the expected number of rolls to get a particular number from $\\{1, 2, \\ldots, 10\\}$ is $10.$ How would I go about finding the expected number of rolls needed to get 5 different numbers? Or more generally, the expected number of rolls needed to get n different numbers where $n < 10.$",
"split": "train"
}
| null | null |
1771369
|
List
|
Business
|
University
|
general-reasoner
|
[
{
"content": "The financial statements of Pouchie Co. included the following information for the year ended December 31, 2010 (amounts in millions):\n\n\nDepreciation and amortization expense $269\nCash dividends declared and paid 337\nPurchase of equipment 824\nNet income 390\nBeginning cash balance 107\nProceeds of common stock issued 171\nProceeds from the sale of the building (at book value) 205\nAccounts receivable increase 10\nEnding cash balance 57\nInventory decrease 38\nAccounts payable increase 48\nPrepare a statement of cash flow, using the indirect method. Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "Net Cash provided by operating activities: $735\nNet cash used by investing activities: $(619)\nNet cash used by financing activities: $(166)\nNet decrease in cash: $(50)\nCash balance on January 1, 2010: $107\nCash balance on December 31, 2010: $57",
"style": "rule"
}
|
{
"answer": "Net Cash provided by operating activities: $735\nNet cash used by investing activities: $(619)\nNet cash used by financing activities: $(166)\nNet decrease in cash: $(50)\nCash balance on January 1, 2010: $107\nCash balance on December 31, 2010: $57",
"index": 208,
"question": "The financial statements of Pouchie Co. included the following information for the year ended December 31, 2010 (amounts in millions):\n\n\nDepreciation and amortization expense $269\nCash dividends declared and paid 337\nPurchase of equipment 824\nNet income 390\nBeginning cash balance 107\nProceeds of common stock issued 171\nProceeds from the sale of the building (at book value) 205\nAccounts receivable increase 10\nEnding cash balance 57\nInventory decrease 38\nAccounts payable increase 48\nPrepare a statement of cash flow, using the indirect method.",
"split": "train"
}
| null | null |
1865023
|
String
|
Other STEM
|
Senior High School
|
general-reasoner
|
[
{
"content": "who revised Wegener's theory by adding the convection currents under the Earth as the cause for the movement? Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "Arthur Holmes",
"style": "rule"
}
|
{
"answer": "Arthur Holmes",
"index": 209,
"question": "who revised Wegener's theory by adding the convection currents under the Earth as the cause for the movement?",
"split": "train"
}
| null | null |
311020
|
Expression
|
Mathematics
|
University
|
general-reasoner
|
[
{
"content": "Prove $\\sum_{n=1}^\\infty(e-\\sum_{k=0}^n\\frac1{k!})=1$ Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "e",
"style": "rule"
}
|
{
"answer": "e",
"index": 210,
"question": "Prove $\\sum_{n=1}^\\infty(e-\\sum_{k=0}^n\\frac1{k!})=1$",
"split": "train"
}
| null | null |
1199831
|
Expression
|
Mathematics
|
University
|
general-reasoner
|
[
{
"content": "How do you integrate $\\sqrt{\\text{sin}x}$? Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "$\\int_0^x \\sqrt {\\sin(t)}~dt=\\sqrt{\\frac{2}{\\pi }} \\Gamma \\left(\\frac{3}{4}\\right)^2-2 E\\left(\\left.\\frac{1}{4} (\n \\pi -2 x)\\right|2\\right)$",
"style": "rule"
}
|
{
"answer": "$\\int_0^x \\sqrt {\\sin(t)}~dt=\\sqrt{\\frac{2}{\\pi }} \\Gamma \\left(\\frac{3}{4}\\right)^2-2 E\\left(\\left.\\frac{1}{4} (\n \\pi -2 x)\\right|2\\right)$",
"index": 211,
"question": "How do you integrate $\\sqrt{\\text{sin}x}$?",
"split": "train"
}
| null | null |
1045652
|
Float
|
Physics
|
Senior High School
|
general-reasoner
|
[
{
"content": "A baseball (m = 149 g) approaches a bat horizontally at a speed of 39.8 m/s (89.0 mph) and is hit straight back at a speed of 45.8 m/s (102 mph). If the ball is in contact with the bat for a time of 1.27 ms, what is the average force exerted on the ball by the bat?\n\n(Neglect the weight of the ball, since it is so much less than the force of the bat. Choose the direction of the incoming ball as the positive direction.) Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "10042.83 N",
"style": "rule"
}
|
{
"answer": "10042.83 N",
"index": 212,
"question": "A baseball (m = 149 g) approaches a bat horizontally at a speed of 39.8 m/s (89.0 mph) and is hit straight back at a speed of 45.8 m/s (102 mph). If the ball is in contact with the bat for a time of 1.27 ms, what is the average force exerted on the ball by the bat?\n\n(Neglect the weight of the ball, since it is so much less than the force of the bat. Choose the direction of the incoming ball as the positive direction.)",
"split": "train"
}
| null | null |
1207912
|
Boolean
|
Mathematics
|
University
|
general-reasoner
|
[
{
"content": "Let $f:[a,b]\\to\\mathbb{R}$ be a continuous function with the property that for every $x\\in[a,b]$, there exists $y\\in[a,b]$ such that $|f(y)|\\le\\frac{1}{2}|f(x)|$. Show that there exists $c\\in[a,b]$ such that $f(c)=0$. Is the provided solution correct and rigorous enough and is there any other way to solve this problem? Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "$f(c) = 0$",
"style": "rule"
}
|
{
"answer": "$f(c) = 0$",
"index": 213,
"question": "Let $f:[a,b]\\to\\mathbb{R}$ be a continuous function with the property that for every $x\\in[a,b]$, there exists $y\\in[a,b]$ such that $|f(y)|\\le\\frac{1}{2}|f(x)|$. Show that there exists $c\\in[a,b]$ such that $f(c)=0$. Is the provided solution correct and rigorous enough and is there any other way to solve this problem?",
"split": "train"
}
| null | null |
1081713
|
Multiple Choice
|
Mathematics
|
University
|
general-reasoner
|
[
{
"content": "Figuring the multiple correlation coefficient allows you to: Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "d",
"style": "rule"
}
|
{
"answer": "d",
"index": 214,
"question": "Figuring the multiple correlation coefficient allows you to:",
"split": "train"
}
| null | null |
2015190
|
Expression
|
Physics
|
University
|
general-reasoner
|
[
{
"content": "A straight wire of length L has a positive charge Q distributed along its length.\n\nFind the magnitude of the electric field due to the wire at a point located a distance d from one end of the wire along the line extending from the wire. Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "E = \\frac{\\rho L}{4\\pi \\epsilon_o a(L+a)}",
"style": "rule"
}
|
{
"answer": "E = \\frac{\\rho L}{4\\pi \\epsilon_o a(L+a)}",
"index": 215,
"question": "A straight wire of length L has a positive charge Q distributed along its length.\n\nFind the magnitude of the electric field due to the wire at a point located a distance d from one end of the wire along the line extending from the wire.",
"split": "train"
}
| null | null |
1823165
|
Expression
|
Mathematics
|
University
|
general-reasoner
|
[
{
"content": "Given {eq}\\displaystyle \\int_0^3 \\int_{-\\sqrt{9-y^2}}^0 e^{-x^2 - y^2} dxdy, sketch the region of integration and evaluate the integral. Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "{\\frac{-\\pi}{4}(1-e^{-3})}",
"style": "rule"
}
|
{
"answer": "{\\frac{-\\pi}{4}(1-e^{-3})}",
"index": 216,
"question": "Given {eq}\\displaystyle \\int_0^3 \\int_{-\\sqrt{9-y^2}}^0 e^{-x^2 - y^2} dxdy, sketch the region of integration and evaluate the integral.",
"split": "train"
}
| null | null |
1993968
|
Other
|
Other
|
Senior High School
|
general-reasoner
|
[
{
"content": "When did the water cycle begin? Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "Around 3.8 billion years ago",
"style": "rule"
}
|
{
"answer": "Around 3.8 billion years ago",
"index": 217,
"question": "When did the water cycle begin?",
"split": "train"
}
| null | null |
1356585
|
Float
|
Physics
|
University
|
general-reasoner
|
[
{
"content": "An ammonia molecule has a permanent electric dipole moment of {eq}5 \\times 10^{-30} \\; C \\cdot m\n\n{/eq}. A proton is 1.80 nm from the molecule in the plane that bisects the dipole. What is the electric force of the molecule on the proton? Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "12.35e-13 N",
"style": "rule"
}
|
{
"answer": "12.35e-13 N",
"index": 218,
"question": "An ammonia molecule has a permanent electric dipole moment of {eq}5 \\times 10^{-30} \\; C \\cdot m\n\n{/eq}. A proton is 1.80 nm from the molecule in the plane that bisects the dipole. What is the electric force of the molecule on the proton?",
"split": "train"
}
| null | null |
1046368
|
Expression
|
Mathematics
|
University
|
general-reasoner
|
[
{
"content": "$ \\sum_{n=1}^{\\infty} \\frac{x^{2n}(-1)^n}{n} $ compute the sum of this Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "- \\ln (1 + x^2)",
"style": "rule"
}
|
{
"answer": "- \\ln (1 + x^2)",
"index": 219,
"question": "$ \\sum_{n=1}^{\\infty} \\frac{x^{2n}(-1)^n}{n} $ compute the sum of this",
"split": "train"
}
| null | null |
239109
|
Multiple Choice
|
History
|
Senior High School
|
general-reasoner
|
[
{
"content": "Which of the following best describes Anglo-Texans response to Mexico laws? Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "A",
"style": "rule"
}
|
{
"answer": "A",
"index": 220,
"question": "Which of the following best describes Anglo-Texans response to Mexico laws?",
"split": "train"
}
| null | null |
1943215
|
Expression
|
Mathematics
|
University
|
general-reasoner
|
[
{
"content": "Let $A \\in \\mathbb{R}^{n \\times n}$ be a positive definite matrix. Find the minimum of $x^T A x$ subject to the constraint $x^T x = 1$, where $x \\in \\mathbb{R}^n$. Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "The minimum value of the function \\(x^T A x\\) subject to the constraint \\(x^T x = 1\\) is \\(\\lambda_{min}(A)\\), where \\(\\lambda_{min}(A)\\) is the smallest eigenvalue of the matrix A.",
"style": "rule"
}
|
{
"answer": "The minimum value of the function \\(x^T A x\\) subject to the constraint \\(x^T x = 1\\) is \\(\\lambda_{min}(A)\\), where \\(\\lambda_{min}(A)\\) is the smallest eigenvalue of the matrix A.",
"index": 221,
"question": "Let $A \\in \\mathbb{R}^{n \\times n}$ be a positive definite matrix. Find the minimum of $x^T A x$ subject to the constraint $x^T x = 1$, where $x \\in \\mathbb{R}^n$.",
"split": "train"
}
| null | null |
481629
|
Boolean
|
Mathematics
|
University
|
general-reasoner
|
[
{
"content": "Suppose $A$ is an $nm \\times nm$ block matrix over some field, with $n^2$ blocks each of size $m \\times m$. Suppose further that the blocks commute. Let $A^{BT}$ denote the \"block transpose\" of $A$, namely the $nm \\times nm$ block matrix whose $(j,i)$ block is the $(i,j)$ block of $A$. That is, the positions of the blocks have been transposed, but not the blocks themselves. Is $A$ similar to $A^{BT}$? For example, suppose $A, B, C, D$ are commuting $2 \\times 2$ matrices. Is it necessarily the case that \\begin{align*} \\begin{pmatrix} A & B \\\\ C & D \\end{pmatrix} \\sim \\begin{pmatrix} A & C \\\\ B & D \\end{pmatrix}? \\end{align*} Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "Yes, if the blocks of $A$ are diagonalizable and commute",
"style": "rule"
}
|
{
"answer": "Yes, if the blocks of $A$ are diagonalizable and commute",
"index": 222,
"question": "Suppose $A$ is an $nm \\times nm$ block matrix over some field, with $n^2$ blocks each of size $m \\times m$. Suppose further that the blocks commute. Let $A^{BT}$ denote the \"block transpose\" of $A$, namely the $nm \\times nm$ block matrix whose $(j,i)$ block is the $(i,j)$ block of $A$. That is, the positions of the blocks have been transposed, but not the blocks themselves. Is $A$ similar to $A^{BT}$? For example, suppose $A, B, C, D$ are commuting $2 \\times 2$ matrices. Is it necessarily the case that \\begin{align*} \\begin{pmatrix} A & B \\\\ C & D \\end{pmatrix} \\sim \\begin{pmatrix} A & C \\\\ B & D \\end{pmatrix}? \\end{align*}",
"split": "train"
}
| null | null |
813409
|
Float
|
Business
|
University
|
general-reasoner
|
[
{
"content": "Tracey Sales Co. has predicted the following costs for this year for 500,000 units:\n\n\n Manufacturing Selling and Administrative\nVariable $800,000 $250,000\nFixed 1,200,000 300,000\nTotal $2,000,000 $550,000\nWhat is the markup on variable manufacturing costs needed to break even? Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "$3.50 per unit or a total of $1,750,000",
"style": "rule"
}
|
{
"answer": "$3.50 per unit or a total of $1,750,000",
"index": 223,
"question": "Tracey Sales Co. has predicted the following costs for this year for 500,000 units:\n\n\n Manufacturing Selling and Administrative\nVariable $800,000 $250,000\nFixed 1,200,000 300,000\nTotal $2,000,000 $550,000\nWhat is the markup on variable manufacturing costs needed to break even?",
"split": "train"
}
| null | null |
1087359
|
Expression
|
Mathematics
|
University
|
general-reasoner
|
[
{
"content": "Compute the following integral: {eq}\\int \\frac{x}{1 - x} \\, \\mathrm{d}x{/eq}. Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "\\ln |1 - x| - x+c_{1}",
"style": "rule"
}
|
{
"answer": "\\ln |1 - x| - x+c_{1}",
"index": 224,
"question": "Compute the following integral: {eq}\\int \\frac{x}{1 - x} \\, \\mathrm{d}x{/eq}.",
"split": "train"
}
| null | null |
1850536
|
List
|
Mathematics
|
University
|
general-reasoner
|
[
{
"content": "The density function of {eq}X{/eq} is given by {eq}f(x)=\n\n\\begin{cases}\n\na x + b x^2,& 0 \\le x \\le 1\\\\\n\n0, & \\text{otherwise}\n\n\\end{cases}\n\n{/eq},\n\n{eq}E (X) = \\dfrac 1 9{/eq}. Find {eq}a{/eq} and {eq}b{/eq}. Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "a = 46/3, b = -20",
"style": "rule"
}
|
{
"answer": "a = 46/3, b = -20",
"index": 225,
"question": "The density function of {eq}X{/eq} is given by {eq}f(x)=\n\n\\begin{cases}\n\na x + b x^2,& 0 \\le x \\le 1\\\\\n\n0, & \\text{otherwise}\n\n\\end{cases}\n\n{/eq},\n\n{eq}E (X) = \\dfrac 1 9{/eq}. Find {eq}a{/eq} and {eq}b{/eq}.",
"split": "train"
}
| null | null |
1605150
|
Expression
|
Mathematics
|
University
|
general-reasoner
|
[
{
"content": "$$x = c_1\\cos (t) + c_2\\sin (t) $$ is a two-parameter family of solutions of the second-order DE $$x'' + x = 0. $$ Find a solution of the second-order IVP consisting of this differential equation and the given initial conditions: $$x\\left(\\frac{\\pi}{6}\\right) = \\frac{1}{2} $$ and $$x'\\left(\\frac{\\pi}{6}\\right) = 0 $$ given that $$x'(t) = - c_1\\sin (t) + c_2\\cos (t) $$ and the book's solutions guide came up with $$c_1 = \\frac{{\\sqrt 3 }}{4},c_2 = \\frac{1}{4} $$ from $$\\frac{{\\sqrt 3 }}{2}c_1 + \\frac{1}{2}c_2 = \\frac{1}{2} $$ and $$ - \\frac{1}{2}c_1 + \\frac{{\\sqrt 3 }}{2}c_2 = 0 $$. Explain the logic behind finding $c_1$ and $c_2$. What am I doing wrong in my approach? Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "$x=\\frac{\\sqrt3}{4}\\cos t+\\frac12\\sin t$",
"style": "rule"
}
|
{
"answer": "$x=\\frac{\\sqrt3}{4}\\cos t+\\frac12\\sin t$",
"index": 226,
"question": "$$x = c_1\\cos (t) + c_2\\sin (t) $$ is a two-parameter family of solutions of the second-order DE $$x'' + x = 0. $$ Find a solution of the second-order IVP consisting of this differential equation and the given initial conditions: $$x\\left(\\frac{\\pi}{6}\\right) = \\frac{1}{2} $$ and $$x'\\left(\\frac{\\pi}{6}\\right) = 0 $$ given that $$x'(t) = - c_1\\sin (t) + c_2\\cos (t) $$ and the book's solutions guide came up with $$c_1 = \\frac{{\\sqrt 3 }}{4},c_2 = \\frac{1}{4} $$ from $$\\frac{{\\sqrt 3 }}{2}c_1 + \\frac{1}{2}c_2 = \\frac{1}{2} $$ and $$ - \\frac{1}{2}c_1 + \\frac{{\\sqrt 3 }}{2}c_2 = 0 $$. Explain the logic behind finding $c_1$ and $c_2$. What am I doing wrong in my approach?",
"split": "train"
}
| null | null |
846806
|
Boolean
|
Mathematics
|
University
|
general-reasoner
|
[
{
"content": "If $f : (0,1) \\to \\mathbb{R}$ is a strictly monotonically increasing function and $f$ is differentiable at some $x \\in (0,1)$ then is $f^{-1}(y)$ differentiable at $y = f(x)$? Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "No",
"style": "rule"
}
|
{
"answer": "No",
"index": 227,
"question": "If $f : (0,1) \\to \\mathbb{R}$ is a strictly monotonically increasing function and $f$ is differentiable at some $x \\in (0,1)$ then is $f^{-1}(y)$ differentiable at $y = f(x)$?",
"split": "train"
}
| null | null |
380560
|
Float
|
Physics
|
Senior High School
|
general-reasoner
|
[
{
"content": "The gauge pressure in a helium gas is initially 33 atm. After many balloons have been blown up, the gauge pressure has reduced to 6 atm. What fraction of the original amount of helium remains in the cylinder? Assume that the temperature of the gas is constant. (Express your answer using two significant figures.) Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "0.18",
"style": "rule"
}
|
{
"answer": "0.18",
"index": 228,
"question": "The gauge pressure in a helium gas is initially 33 atm. After many balloons have been blown up, the gauge pressure has reduced to 6 atm. What fraction of the original amount of helium remains in the cylinder? Assume that the temperature of the gas is constant. (Express your answer using two significant figures.)",
"split": "train"
}
| null | null |
166211
|
Expression
|
Mathematics
|
University
|
general-reasoner
|
[
{
"content": "Find parametric equations for the tangent line to the curve with the parametric equations\nx = 1+8√(t), y=t³-t, z=t³+t\nat the point (9, 0, 2). Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "x = 9 + 5t, y = 2t, z = 2 + 4t",
"style": "rule"
}
|
{
"answer": "x = 9 + 5t, y = 2t, z = 2 + 4t",
"index": 229,
"question": "Find parametric equations for the tangent line to the curve with the parametric equations\nx = 1+8√(t), y=t³-t, z=t³+t\nat the point (9, 0, 2).",
"split": "train"
}
| null | null |
1366132
|
Expression
|
Mathematics
|
University
|
general-reasoner
|
[
{
"content": "Given a non-decreasing function $f$, prove that the inequality $$\\int_{x-\\varepsilon x}^x f\\left(t\\right)dt \\leq f\\left(x\\right)x\\varepsilon$$ holds. Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "\\varepsilon x f(x)",
"style": "rule"
}
|
{
"answer": "\\varepsilon x f(x)",
"index": 230,
"question": "Given a non-decreasing function $f$, prove that the inequality $$\\int_{x-\\varepsilon x}^x f\\left(t\\right)dt \\leq f\\left(x\\right)x\\varepsilon$$ holds.",
"split": "train"
}
| null | null |
1968697
|
Boolean
|
Chemistry
|
Junior High School
|
general-reasoner
|
[
{
"content": "Is rain water heterogeneous or homogeneous? Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "homogeneous",
"style": "rule"
}
|
{
"answer": "homogeneous",
"index": 231,
"question": "Is rain water heterogeneous or homogeneous?",
"split": "train"
}
| null | null |
556738
|
Float
|
Chemistry
|
Senior High School
|
general-reasoner
|
[
{
"content": "How many grams of oxygen form when 2.38 grams of {eq}KClO_3\n\n{/eq} completely reacts?\n\n{eq}2KClO_3 \\to 2KCl + 3O_2\n\n{/eq} Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "0.448 g",
"style": "rule"
}
|
{
"answer": "0.448 g",
"index": 232,
"question": "How many grams of oxygen form when 2.38 grams of {eq}KClO_3\n\n{/eq} completely reacts?\n\n{eq}2KClO_3 \\to 2KCl + 3O_2\n\n{/eq}",
"split": "train"
}
| null | null |
855737
|
Expression
|
Mathematics
|
PhD
|
general-reasoner
|
[
{
"content": "Find the Hessian matrix of $\\ln \\det (diag(x)^{-1} +A)$ with respect to $x$ in $\\mathbb R^{n}_{++}$, where $A$ is positive definite. Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "$D^2f_x:(h,k)\\in(\\mathbb{R}^n)^2\\mapsto tr(U''(h,k)U^{-1}-U'(h)U^{-1}U'(k)U^{-1})$ where $U''(h,k)=2diag(\\dfrac{h_ik_i}{x_i^3})$",
"style": "rule"
}
|
{
"answer": "$D^2f_x:(h,k)\\in(\\mathbb{R}^n)^2\\mapsto tr(U''(h,k)U^{-1}-U'(h)U^{-1}U'(k)U^{-1})$ where $U''(h,k)=2diag(\\dfrac{h_ik_i}{x_i^3})$",
"index": 233,
"question": "Find the Hessian matrix of $\\ln \\det (diag(x)^{-1} +A)$ with respect to $x$ in $\\mathbb R^{n}_{++}$, where $A$ is positive definite.",
"split": "train"
}
| null | null |
898572
|
Boolean
|
Business
|
University
|
general-reasoner
|
[
{
"content": "Sam contributes property with a basis of $10,000 and a fair market value of $20,000 to a partnership in return for a partnership interest and $10,000. Sam will recognize $10,000 on the transfer. True/False? Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "False",
"style": "rule"
}
|
{
"answer": "False",
"index": 234,
"question": "Sam contributes property with a basis of $10,000 and a fair market value of $20,000 to a partnership in return for a partnership interest and $10,000. Sam will recognize $10,000 on the transfer. True/False?",
"split": "train"
}
| null | null |
2063830
|
Float
|
Chemistry
|
University
|
general-reasoner
|
[
{
"content": "An aqueous solution contains {eq}\\rm\n\n0.311\\ M\n\n{/eq} methylamine {eq}\\rm\n\n(CH_3NH_2)\n\n{/eq}. How many {eq}\\rm\n\nmL\n\n{/eq} of {eq}\\rm\n\n0.316\\ M\n\n{/eq} nitric acid would have to be added to {eq}\\rm\n\n250\\ mL\n\n{/eq} of this solution in order to prepare a buffer with a pH of {eq}11.200\n\n{/eq}? Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "53.7 mL",
"style": "rule"
}
|
{
"answer": "53.7 mL",
"index": 235,
"question": "An aqueous solution contains {eq}\\rm\n\n0.311\\ M\n\n{/eq} methylamine {eq}\\rm\n\n(CH_3NH_2)\n\n{/eq}. How many {eq}\\rm\n\nmL\n\n{/eq} of {eq}\\rm\n\n0.316\\ M\n\n{/eq} nitric acid would have to be added to {eq}\\rm\n\n250\\ mL\n\n{/eq} of this solution in order to prepare a buffer with a pH of {eq}11.200\n\n{/eq}?",
"split": "train"
}
| null | null |
225354
|
Float
|
Business
|
Senior High School
|
general-reasoner
|
[
{
"content": "A law firm uses activity-based pricing. The company's activity pools are as follows:\n\n \n \n \n Cost Pool \n Annual Estimated Cost \n Cost Driver \n Annual Driver Quantity \n \n \n Consultation \n 186,000 \n Number of consultations \n 80 consultations \n \n \n Administrative Costs \n 144,000 \n Admin labor hours \n 9,400 labor hours \n \n \n Client Service \n 85,000 \n Number of clients \n 110 clients \n \n \n\n\nThe firm had two consultations with this client and required 130 administrative labor hours.\n\nWhat additional costs will be charged to this customer? Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "$7,414.32",
"style": "rule"
}
|
{
"answer": "$7,414.32",
"index": 236,
"question": "A law firm uses activity-based pricing. The company's activity pools are as follows:\n\n \n \n \n Cost Pool \n Annual Estimated Cost \n Cost Driver \n Annual Driver Quantity \n \n \n Consultation \n 186,000 \n Number of consultations \n 80 consultations \n \n \n Administrative Costs \n 144,000 \n Admin labor hours \n 9,400 labor hours \n \n \n Client Service \n 85,000 \n Number of clients \n 110 clients \n \n \n\n\nThe firm had two consultations with this client and required 130 administrative labor hours.\n\nWhat additional costs will be charged to this customer?",
"split": "train"
}
| null | null |
1114908
|
Expression
|
Mathematics
|
University
|
general-reasoner
|
[
{
"content": "$$\\frac{d}{dx} \\int_{-\\sqrt{x}}^{\\sqrt{x}} \\int_{-x}^x f(y,z) \\;dy\\; dz$$ Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "\\sum_{\\sigma,\\sigma' = \\pm} \\int_{0}^{\\sqrt{x\\,}}{\\rm f}\\left(\\sigma\\,x,\\sigma'z\\right)\\,{\\rm d}z + \\frac{1}{2\\sqrt{x\\,}}\\sum_{\\sigma,\\sigma' = \\pm}\\int_{0}^{\\left\\vert x\\right\\vert} {\\rm f}\\left(\\sigma\\,y,\\sigma'\\sqrt{x\\,}\\right)\\,{\\rm d}y",
"style": "rule"
}
|
{
"answer": "\\sum_{\\sigma,\\sigma' = \\pm} \\int_{0}^{\\sqrt{x\\,}}{\\rm f}\\left(\\sigma\\,x,\\sigma'z\\right)\\,{\\rm d}z + \\frac{1}{2\\sqrt{x\\,}}\\sum_{\\sigma,\\sigma' = \\pm}\\int_{0}^{\\left\\vert x\\right\\vert} {\\rm f}\\left(\\sigma\\,y,\\sigma'\\sqrt{x\\,}\\right)\\,{\\rm d}y",
"index": 237,
"question": "$$\\frac{d}{dx} \\int_{-\\sqrt{x}}^{\\sqrt{x}} \\int_{-x}^x f(y,z) \\;dy\\; dz$$",
"split": "train"
}
| null | null |
197812
|
Percentage
|
Business
|
University
|
general-reasoner
|
[
{
"content": "Polaris Manufacturing is evaluating an investment in a new drilling machine that would cost $48,000. Polaris estimates that it will realize $12,000 in annual net cash inflows for each year of the machine's 6-year useful life.\n\nWhat is the internal rate of return (IRR) for this proposed investment? You may use Excel or also feel free to approximate this answer using present value tables. Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "12.9780%",
"style": "rule"
}
|
{
"answer": "12.9780%",
"index": 238,
"question": "Polaris Manufacturing is evaluating an investment in a new drilling machine that would cost $48,000. Polaris estimates that it will realize $12,000 in annual net cash inflows for each year of the machine's 6-year useful life.\n\nWhat is the internal rate of return (IRR) for this proposed investment? You may use Excel or also feel free to approximate this answer using present value tables.",
"split": "train"
}
| null | null |
1288196
|
Expression
|
Mathematics
|
University
|
general-reasoner
|
[
{
"content": "Let $f:\\mathbb{R}^2 \\rightarrow \\mathbb{R}$ be twice differentiable. For $t \\in \\mathbb{R}$ and for fixed $x,y$, define $$F(t) = f(x+t,y+t)+f(x-t,y-t)-f(x+t,y-t)-f(x-t,y+t).$$ Given that $$F'(t) = f'(x+t,y+t)(1,1)+f'(x-t,y-t)(-1,-1)+f'(x+t,y-t)(-1,1)+f'(x-t,y+t)(1,-1),$$ calculate $F''(t)$. Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "F''(t)=∂^2f/∂u^2(x+t,y+t)+2∂^2f/∂u∂v(x+t,y+t)+∂^2f/∂v^2(x+t,y+t)+∂^2f/∂u^2(x-t,y-t)+2∂^2f/∂u∂v(x-t,y-t)+∂^2f/∂v^2(x-t,y-t)+∂^2f/∂u^2(x+t,y-t)-2∂^2f/∂u∂v(x+t,y-t)+∂^2f/∂v^2(x+t,y-t)+∂^2f/∂u^2(x-t,y+t)-2∂^2f/∂u∂v(x-t,y+t)+∂^2f/∂v^2(x-t,y+t)",
"style": "rule"
}
|
{
"answer": "F''(t)=∂^2f/∂u^2(x+t,y+t)+2∂^2f/∂u∂v(x+t,y+t)+∂^2f/∂v^2(x+t,y+t)+∂^2f/∂u^2(x-t,y-t)+2∂^2f/∂u∂v(x-t,y-t)+∂^2f/∂v^2(x-t,y-t)+∂^2f/∂u^2(x+t,y-t)-2∂^2f/∂u∂v(x+t,y-t)+∂^2f/∂v^2(x+t,y-t)+∂^2f/∂u^2(x-t,y+t)-2∂^2f/∂u∂v(x-t,y+t)+∂^2f/∂v^2(x-t,y+t)",
"index": 239,
"question": "Let $f:\\mathbb{R}^2 \\rightarrow \\mathbb{R}$ be twice differentiable. For $t \\in \\mathbb{R}$ and for fixed $x,y$, define $$F(t) = f(x+t,y+t)+f(x-t,y-t)-f(x+t,y-t)-f(x-t,y+t).$$ Given that $$F'(t) = f'(x+t,y+t)(1,1)+f'(x-t,y-t)(-1,-1)+f'(x+t,y-t)(-1,1)+f'(x-t,y+t)(1,-1),$$ calculate $F''(t)$.",
"split": "train"
}
| null | null |
1428084
|
Expression
|
Physics
|
Senior High School
|
general-reasoner
|
[
{
"content": "How much work does gravity do on the compressor during this displacement? Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "(m)*9.8*(height difference)",
"style": "rule"
}
|
{
"answer": "(m)*9.8*(height difference)",
"index": 240,
"question": "How much work does gravity do on the compressor during this displacement?",
"split": "train"
}
| null | null |
1542705
|
Multiple Choice
|
Finance
|
University
|
general-reasoner
|
[
{
"content": "Kevin and Jennifer are ready to retire. They want to receive the equivalent of $40,000 in today's dollars at the beginning of each year for the next 50 years. They assume inflation will average 3% over the long run, and they can earn 11% (compounded annually) on their investments.\n\nWhat lump sum do they need to invest today to attain their goal?\n\na. $533,884\n\nb. $502,767\n\nc. $528,578\n\nd. $541,817 Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "c",
"style": "rule"
}
|
{
"answer": "c",
"index": 241,
"question": "Kevin and Jennifer are ready to retire. They want to receive the equivalent of $40,000 in today's dollars at the beginning of each year for the next 50 years. They assume inflation will average 3% over the long run, and they can earn 11% (compounded annually) on their investments.\n\nWhat lump sum do they need to invest today to attain their goal?\n\na. $533,884\n\nb. $502,767\n\nc. $528,578\n\nd. $541,817",
"split": "train"
}
| null | null |
1330776
|
Float
|
Chemistry
|
Senior High School
|
general-reasoner
|
[
{
"content": "What are the total number of ions in solution if a #25.0*g# mass of calcium chloride is dissolved in a #500*mL# volume of water? Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "0.450*mol*L^-1",
"style": "rule"
}
|
{
"answer": "0.450*mol*L^-1",
"index": 242,
"question": "What are the total number of ions in solution if a #25.0*g# mass of calcium chloride is dissolved in a #500*mL# volume of water?",
"split": "train"
}
| null | null |
2072438
|
Boolean
|
Mathematics
|
PhD
|
general-reasoner
|
[
{
"content": "Are there sentences in known mathematics whose meta-proof is known but whose formal proof is not known? Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "yes",
"style": "rule"
}
|
{
"answer": "yes",
"index": 243,
"question": "Are there sentences in known mathematics whose meta-proof is known but whose formal proof is not known?",
"split": "train"
}
| null | null |
1430450
|
Matrix
|
Mathematics
|
University
|
general-reasoner
|
[
{
"content": "If I have the model: $y = β_1x_1 + β_2x_2 + u$. I have to show that the OLS estimator is: I think that I have to use $\\beta =\\begin{pmatrix} \\beta_1 \\\\ \\beta_2 \\end{pmatrix}=(X^tX)^{-1}X^tY$. But I'm a but confused. Can someone write up the matrices X and Y? I only have to multiply the first coordinat in the $2\\times1$, because I only have to show it for $\\beta_1$? Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "X = \\begin{pmatrix} x_{11} & x_{12} \\\\ \\vdots & \\vdots \\\\ x_{n1} & x_{n2} \\end{pmatrix}, Y = \\begin{pmatrix} y_1 \\\\ \\vdots \\\\ y_n \\end{pmatrix}",
"style": "rule"
}
|
{
"answer": "X = \\begin{pmatrix} x_{11} & x_{12} \\\\ \\vdots & \\vdots \\\\ x_{n1} & x_{n2} \\end{pmatrix}, Y = \\begin{pmatrix} y_1 \\\\ \\vdots \\\\ y_n \\end{pmatrix}",
"index": 244,
"question": "If I have the model: $y = β_1x_1 + β_2x_2 + u$. I have to show that the OLS estimator is: I think that I have to use $\\beta =\\begin{pmatrix} \\beta_1 \\\\ \\beta_2 \\end{pmatrix}=(X^tX)^{-1}X^tY$. But I'm a but confused. Can someone write up the matrices X and Y? I only have to multiply the first coordinat in the $2\\times1$, because I only have to show it for $\\beta_1$?",
"split": "train"
}
| null | null |
131439
|
Float
|
Physics
|
University
|
general-reasoner
|
[
{
"content": "A hollow metal sphere has {eq}5\n\n{/eq} cm and {eq}11\n\n{/eq} cm inner and outer radii, respectively. The surface charge density on the inside surface is {eq}-150 \\textrm{ nC/m}^{2}\n\n{/eq}. The surface charge density on the exterior surface is {eq}+150 \\textrm{ nC/m}^{2}\n\n{/eq}.\n\nWhat is the strength of the electric field at point {eq}12\n\n{/eq} cm from the center? Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "1.13e+04 N/C",
"style": "rule"
}
|
{
"answer": "1.13e+04 N/C",
"index": 245,
"question": "A hollow metal sphere has {eq}5\n\n{/eq} cm and {eq}11\n\n{/eq} cm inner and outer radii, respectively. The surface charge density on the inside surface is {eq}-150 \\textrm{ nC/m}^{2}\n\n{/eq}. The surface charge density on the exterior surface is {eq}+150 \\textrm{ nC/m}^{2}\n\n{/eq}.\n\nWhat is the strength of the electric field at point {eq}12\n\n{/eq} cm from the center?",
"split": "train"
}
| null | null |
529408
|
List
|
History
|
Primary School
|
general-reasoner
|
[
{
"content": "What books are in the Book of Kells? Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "The four Gospels: Matthew, Mark, Luke, and John",
"style": "rule"
}
|
{
"answer": "The four Gospels: Matthew, Mark, Luke, and John",
"index": 246,
"question": "What books are in the Book of Kells?",
"split": "train"
}
| null | null |
1456743
|
Integer
|
Mathematics
|
University
|
general-reasoner
|
[
{
"content": "I am unable to compute the limit, anyone can help? Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "0",
"style": "rule"
}
|
{
"answer": "0",
"index": 247,
"question": "I am unable to compute the limit, anyone can help?",
"split": "train"
}
| null | null |
2007015
|
Float
|
Physics
|
Senior High School
|
general-reasoner
|
[
{
"content": "A wooden crate weighs {eq}780 \\ lb\n\n{/eq}. What force is needed to start the crate sliding on a wooden floor when the coefficient of starting friction is {eq}0.40\n\n{/eq}? Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "1388 N",
"style": "rule"
}
|
{
"answer": "1388 N",
"index": 248,
"question": "A wooden crate weighs {eq}780 \\ lb\n\n{/eq}. What force is needed to start the crate sliding on a wooden floor when the coefficient of starting friction is {eq}0.40\n\n{/eq}?",
"split": "train"
}
| null | null |
1282408
|
Multiple Choice
|
Mathematics
|
University
|
general-reasoner
|
[
{
"content": "Find the critical values for a sample with n = 25 and α = 0.005 if H0: μ > 20. Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "A",
"style": "rule"
}
|
{
"answer": "A",
"index": 249,
"question": "Find the critical values for a sample with n = 25 and α = 0.005 if H0: μ > 20.",
"split": "train"
}
| null | null |
1267508
|
Boolean
|
History
|
Primary School
|
general-reasoner
|
[
{
"content": "Did Susan B. Anthony write a book? Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "Yes",
"style": "rule"
}
|
{
"answer": "Yes",
"index": 250,
"question": "Did Susan B. Anthony write a book?",
"split": "train"
}
| null | null |
534736
|
Float
|
Physics
|
Senior High School
|
general-reasoner
|
[
{
"content": "There is a bicycle wheel resting against a small step whose height {eq}h = 0.132\n\n{/eq} m. The weight and radius of the wheel are {eq}W = 27.3\n\n{/eq} N and {eq}r = 0.324\n\n{/eq} m, respectively. A horizontal force is applied to the axle of the wheel. As the magnitude of increases, there comes a time when the wheel just begins to rise up and loses contact with the ground. What is the magnitude of the force when this happens? Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "37.10 N",
"style": "rule"
}
|
{
"answer": "37.10 N",
"index": 251,
"question": "There is a bicycle wheel resting against a small step whose height {eq}h = 0.132\n\n{/eq} m. The weight and radius of the wheel are {eq}W = 27.3\n\n{/eq} N and {eq}r = 0.324\n\n{/eq} m, respectively. A horizontal force is applied to the axle of the wheel. As the magnitude of increases, there comes a time when the wheel just begins to rise up and loses contact with the ground. What is the magnitude of the force when this happens?",
"split": "train"
}
| null | null |
44087
|
Float
|
Finance
|
Senior High School
|
general-reasoner
|
[
{
"content": "You've borrowed $15,000 on margin to buy shares in Disney, which is now selling at $50 per share. Your account starts at the initial margin requirement of 50%. The maintenance margin is 47%. Two days later, the stock price falls to $48 per share.\n\nHow low can the price of Disney shares fall before you receive a margin call? Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "$47.17",
"style": "rule"
}
|
{
"answer": "$47.17",
"index": 252,
"question": "You've borrowed $15,000 on margin to buy shares in Disney, which is now selling at $50 per share. Your account starts at the initial margin requirement of 50%. The maintenance margin is 47%. Two days later, the stock price falls to $48 per share.\n\nHow low can the price of Disney shares fall before you receive a margin call?",
"split": "train"
}
| null | null |
1286466
|
Float
|
Physics
|
Senior High School
|
general-reasoner
|
[
{
"content": "An object has a mass of #6 kg#. The object's kinetic energy uniformly changes from #18 KJ# to # 4KJ# over #t in [0, 9 s]#. What is the average speed of the object? Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "59.38ms^-1",
"style": "rule"
}
|
{
"answer": "59.38ms^-1",
"index": 253,
"question": "An object has a mass of #6 kg#. The object's kinetic energy uniformly changes from #18 KJ# to # 4KJ# over #t in [0, 9 s]#. What is the average speed of the object?",
"split": "train"
}
| null | null |
472864
|
Boolean
|
Mathematics
|
University
|
general-reasoner
|
[
{
"content": "Given {eq}z = e^x \\sin y +e^y \\cos x.{/eq} Find out whether the function satisfies Laplace's equation {eq}\\dfrac{\\partial^2 z}{\\partial x^2} + \\dfrac{\\partial^2 z}{\\partial y^2} = 0{/eq}. Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "0",
"style": "rule"
}
|
{
"answer": "0",
"index": 254,
"question": "Given {eq}z = e^x \\sin y +e^y \\cos x.{/eq} Find out whether the function satisfies Laplace's equation {eq}\\dfrac{\\partial^2 z}{\\partial x^2} + \\dfrac{\\partial^2 z}{\\partial y^2} = 0{/eq}.",
"split": "train"
}
| null | null |
501297
|
List
|
Chemistry
|
Junior High School
|
general-reasoner
|
[
{
"content": "How does the pH of soil change? Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "By acidic rain or liming",
"style": "rule"
}
|
{
"answer": "By acidic rain or liming",
"index": 255,
"question": "How does the pH of soil change?",
"split": "train"
}
| null | null |
1364965
|
Percentage
|
Business
|
University
|
general-reasoner
|
[
{
"content": "Your firm is considering purchasing a machine with the following annual, end-of-year, book investment accounts.\n\n\n Purchase Date Year 1 Year 2 Year 3 Year 4\n Gross investment $55,000 $55,000 $55,000 $55,000 $55,000\n Less: Accumulated depreciation 0 13,750 27,500 41,250 55,000\n Net investment $55,000 $41,250 $27,500 13,750 $ 0\nThe machine generates, on average, $5,300 per year in additional net income.\n\nWhat is the average accounting return for this machine?\n\n(Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places (e.g., 32.16).) Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "19.27%",
"style": "rule"
}
|
{
"answer": "19.27%",
"index": 256,
"question": "Your firm is considering purchasing a machine with the following annual, end-of-year, book investment accounts.\n\n\n Purchase Date Year 1 Year 2 Year 3 Year 4\n Gross investment $55,000 $55,000 $55,000 $55,000 $55,000\n Less: Accumulated depreciation 0 13,750 27,500 41,250 55,000\n Net investment $55,000 $41,250 $27,500 13,750 $ 0\nThe machine generates, on average, $5,300 per year in additional net income.\n\nWhat is the average accounting return for this machine?\n\n(Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places (e.g., 32.16).)",
"split": "train"
}
| null | null |
1208798
|
Float
|
Mathematics
|
University
|
general-reasoner
|
[
{
"content": "Evaluate the integral: {eq}\\int_0^{\\pi} \\sec (\\frac{t}{4}) dt Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "3.52549",
"style": "rule"
}
|
{
"answer": "3.52549",
"index": 257,
"question": "Evaluate the integral: {eq}\\int_0^{\\pi} \\sec (\\frac{t}{4}) dt",
"split": "train"
}
| null | null |
1464434
|
Expression
|
Physics
|
Senior High School
|
general-reasoner
|
[
{
"content": "A car is traveling along a highway shaped like a parabola with its vertex at the origin. The car starts at 100 miles north and 100 miles west. There is a statue at 100 miles east and 50 miles north. At what point will the car's headlights hit the statue? Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "29.3 miles east and 8.6 miles north",
"style": "rule"
}
|
{
"answer": "29.3 miles east and 8.6 miles north",
"index": 258,
"question": "A car is traveling along a highway shaped like a parabola with its vertex at the origin. The car starts at 100 miles north and 100 miles west. There is a statue at 100 miles east and 50 miles north. At what point will the car's headlights hit the statue?",
"split": "train"
}
| null | null |
391471
|
Boolean
|
Economics
|
University
|
general-reasoner
|
[
{
"content": "Is it true that fiscal stimulus cannot help but be effective in the absence of capacity constraints in the economy, whereas monetary policy is not always effective at creating growth? Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "Yes",
"style": "rule"
}
|
{
"answer": "Yes",
"index": 259,
"question": "Is it true that fiscal stimulus cannot help but be effective in the absence of capacity constraints in the economy, whereas monetary policy is not always effective at creating growth?",
"split": "train"
}
| null | null |
1575704
|
Float
|
Business
|
University
|
general-reasoner
|
[
{
"content": "Assume the following information for the month of August.\n\nJune sales=$40,000; July sales= $65,000; August sales= $52,850. All sales are on account and are collected as follows: 20% in the current month, 50% in the month following, 25% in the second-month following, and 5% uncollectible. The beginning cash balance is $14,670, with cash payments of $24,763. If the minimum cash balance is $50,000,\n\nwhat is the amount needed by the bank, or how much is available to pay towards the bank loan? Show the amount as a positive number, and the amount to repay a loan as a negative number. Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "$7,023",
"style": "rule"
}
|
{
"answer": "$7,023",
"index": 260,
"question": "Assume the following information for the month of August.\n\nJune sales=$40,000; July sales= $65,000; August sales= $52,850. All sales are on account and are collected as follows: 20% in the current month, 50% in the month following, 25% in the second-month following, and 5% uncollectible. The beginning cash balance is $14,670, with cash payments of $24,763. If the minimum cash balance is $50,000,\n\nwhat is the amount needed by the bank, or how much is available to pay towards the bank loan? Show the amount as a positive number, and the amount to repay a loan as a negative number.",
"split": "train"
}
| null | null |
135634
|
Integer
|
Business
|
University
|
general-reasoner
|
[
{
"content": "Joshi has a capital balance of $80,000 after adjusting assets to fair market value. Costas contributes $40,000 to receive a 40% interest in a new partnership with Joshi. Determine the amount and recipient of the partner bonus. Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "Bonus of $8,000 to Costas",
"style": "rule"
}
|
{
"answer": "Bonus of $8,000 to Costas",
"index": 261,
"question": "Joshi has a capital balance of $80,000 after adjusting assets to fair market value. Costas contributes $40,000 to receive a 40% interest in a new partnership with Joshi. Determine the amount and recipient of the partner bonus.",
"split": "train"
}
| null | null |
1536455
|
Float
|
Physics
|
University
|
general-reasoner
|
[
{
"content": "A physics professor is pushed up a ramp inclined upward at an angle of 28.0 degrees above the horizontal as he sits in his desk chair that slides on frictionless rollers. The combined mass of the professor and chair is 82.0 kg. He is pushed a distance of 2.00 m along the incline by a group of students who together exert a constant horizontal force of 610 N. The professor's speed at the bottom of the ramp is 1.60 m/s. Use the work-energy theorem to find his speed at the top of the ramp. Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "3.22 m/s",
"style": "rule"
}
|
{
"answer": "3.22 m/s",
"index": 262,
"question": "A physics professor is pushed up a ramp inclined upward at an angle of 28.0 degrees above the horizontal as he sits in his desk chair that slides on frictionless rollers. The combined mass of the professor and chair is 82.0 kg. He is pushed a distance of 2.00 m along the incline by a group of students who together exert a constant horizontal force of 610 N. The professor's speed at the bottom of the ramp is 1.60 m/s. Use the work-energy theorem to find his speed at the top of the ramp.",
"split": "train"
}
| null | null |
1627420
|
String
|
Biology
|
Senior High School
|
general-reasoner
|
[
{
"content": "To determine the genotype of a frequently seen orange flowering plant in a population, the plant will be mated with ___________ plant. Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "Homozygous recessive",
"style": "rule"
}
|
{
"answer": "Homozygous recessive",
"index": 263,
"question": "To determine the genotype of a frequently seen orange flowering plant in a population, the plant will be mated with ___________ plant.",
"split": "train"
}
| null | null |
78705
|
Expression
|
Mathematics
|
University
|
general-reasoner
|
[
{
"content": "There are 12 people with 12 unique zodiac signs. You start guessing each person's zodiac sign. What is the probability of you guessing at least 4 of them right, without repeating your guess? Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "The probability of guessing at least 4 zodiac signs correctly out of 12 is given by the following formula: $P(X \\ge 4) = \\sum_{k=4}^{12} \\frac{\\binom{12}{k} \\cdot !(12-k)}{12!}$ where $!(n)$ is the number of derangements.",
"style": "rule"
}
|
{
"answer": "The probability of guessing at least 4 zodiac signs correctly out of 12 is given by the following formula: $P(X \\ge 4) = \\sum_{k=4}^{12} \\frac{\\binom{12}{k} \\cdot !(12-k)}{12!}$ where $!(n)$ is the number of derangements.",
"index": 264,
"question": "There are 12 people with 12 unique zodiac signs. You start guessing each person's zodiac sign. What is the probability of you guessing at least 4 of them right, without repeating your guess?",
"split": "train"
}
| null | null |
1076844
|
Expression
|
Mathematics
|
University
|
general-reasoner
|
[
{
"content": "Evaluate {eq}\\displaystyle \\int_C (x - 2 y)\\ dx + (2 x - y)\\ dy\n\n{/eq}, where C is the portion of the ellipse {eq}\\displaystyle \\dfrac {x^2}{16} + \\dfrac {y^2} 4 = 1\n\n{/eq} from {eq}(0,\\ 2)\n\n{/eq} to {eq}(-4,\\ 0)\n\n{/eq}. Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "10+8π",
"style": "rule"
}
|
{
"answer": "10+8π",
"index": 265,
"question": "Evaluate {eq}\\displaystyle \\int_C (x - 2 y)\\ dx + (2 x - y)\\ dy\n\n{/eq}, where C is the portion of the ellipse {eq}\\displaystyle \\dfrac {x^2}{16} + \\dfrac {y^2} 4 = 1\n\n{/eq} from {eq}(0,\\ 2)\n\n{/eq} to {eq}(-4,\\ 0)\n\n{/eq}.",
"split": "train"
}
| null | null |
1523676
|
Multiple Choice
|
Chemistry
|
University
|
general-reasoner
|
[
{
"content": "An unknown compound, X, is known to possess two groups that ionize as the pH changes. One of these groups is a carboxylate with a pKa of 2.0. When 75 mL of 0.1 M NaOH is added to 100 mL of 0.1 M solution of X at pH 2.0, the pH increases to 6.72. What is the pKa of the second ionizable group of X?\n\nA. 4.3\n\nB. 6.0\n\nC. 7.2\n\nD. 8.5\n\nE. 9.7 Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "C",
"style": "rule"
}
|
{
"answer": "C",
"index": 266,
"question": "An unknown compound, X, is known to possess two groups that ionize as the pH changes. One of these groups is a carboxylate with a pKa of 2.0. When 75 mL of 0.1 M NaOH is added to 100 mL of 0.1 M solution of X at pH 2.0, the pH increases to 6.72. What is the pKa of the second ionizable group of X?\n\nA. 4.3\n\nB. 6.0\n\nC. 7.2\n\nD. 8.5\n\nE. 9.7",
"split": "train"
}
| null | null |
1388873
|
Expression
|
Mathematics
|
University
|
general-reasoner
|
[
{
"content": "How do I find the Bayes estimator of $\\theta$ given the loss distribution $l(a,\\theta)=\\frac{(a-\\theta)^2}{\\theta(1-\\theta)}$, a uniform prior distribution $\\pi(\\theta)$ from 0 to 1, and a Bernoulli likelihood function $f(x|\\theta) = \\theta^x(1-\\theta)^{1-x}$, where $X$ is the total number of ones in a sequence of $n$ independent Bernoulli trials each with sample space {0,1}? I have already calculated $h(a,\\theta)=\\frac{\\Gamma{(3)}}{\\Gamma{(x+1)}\\Gamma{(2-x)}}\\int_0^1(a-\\theta)^2{\\theta^{x-1}(1-\\theta)^{-x}}d\\theta$ and am unsure where to go from here. Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "$a=\\frac{y}{n}=\\frac{1}{n}\\sum_{i=1}^n x_i$",
"style": "rule"
}
|
{
"answer": "$a=\\frac{y}{n}=\\frac{1}{n}\\sum_{i=1}^n x_i$",
"index": 267,
"question": "How do I find the Bayes estimator of $\\theta$ given the loss distribution $l(a,\\theta)=\\frac{(a-\\theta)^2}{\\theta(1-\\theta)}$, a uniform prior distribution $\\pi(\\theta)$ from 0 to 1, and a Bernoulli likelihood function $f(x|\\theta) = \\theta^x(1-\\theta)^{1-x}$, where $X$ is the total number of ones in a sequence of $n$ independent Bernoulli trials each with sample space {0,1}? I have already calculated $h(a,\\theta)=\\frac{\\Gamma{(3)}}{\\Gamma{(x+1)}\\Gamma{(2-x)}}\\int_0^1(a-\\theta)^2{\\theta^{x-1}(1-\\theta)^{-x}}d\\theta$ and am unsure where to go from here.",
"split": "train"
}
| null | null |
47296
|
Integer
|
Business
|
University
|
general-reasoner
|
[
{
"content": "Given the information for Hetrich, Inc. below.\n\nNet income - $154\n\nDepreciation - $48\n\nIssuance of new stock - $11\n\nRepurchase of debt - $18\n\nSale of property - $13\n\nPurchase of equipment - $80\n\nDividend payments - $10\n\nInterest payments - $28\n\nCalculate the operating cash flow. Round your answer to the nearest whole dollar. Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "174",
"style": "rule"
}
|
{
"answer": "174",
"index": 268,
"question": "Given the information for Hetrich, Inc. below.\n\nNet income - $154\n\nDepreciation - $48\n\nIssuance of new stock - $11\n\nRepurchase of debt - $18\n\nSale of property - $13\n\nPurchase of equipment - $80\n\nDividend payments - $10\n\nInterest payments - $28\n\nCalculate the operating cash flow. Round your answer to the nearest whole dollar.",
"split": "train"
}
| null | null |
2022267
|
Float
|
Physics
|
Senior High School
|
general-reasoner
|
[
{
"content": "A light spring of natural (equilibrium) length 10cm with force constant k=500 N/m is embedded vertically in the ground. A ball of mass m = 0.15 kg is placed on top of the spring, which is compressed 8.0cm; when released, the spring pushes the ball. When the ball reaches ground level, it leaves its light supporting platform and continues vertically upward. When it reaches the top of its path, a batter strikes the ball at an angle (theta) to the horizontal. Ignoring air resistance, determine the height \"h\" at which the batter strikes the ball. Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "1.088 m",
"style": "rule"
}
|
{
"answer": "1.088 m",
"index": 269,
"question": "A light spring of natural (equilibrium) length 10cm with force constant k=500 N/m is embedded vertically in the ground. A ball of mass m = 0.15 kg is placed on top of the spring, which is compressed 8.0cm; when released, the spring pushes the ball. When the ball reaches ground level, it leaves its light supporting platform and continues vertically upward. When it reaches the top of its path, a batter strikes the ball at an angle (theta) to the horizontal. Ignoring air resistance, determine the height \"h\" at which the batter strikes the ball.",
"split": "train"
}
| null | null |
570405
|
Integer
|
Physics
|
Senior High School
|
general-reasoner
|
[
{
"content": "15. After falling from rest from a height of 30 m, a 0.50-kg ball rebounds upward, reaching a height of 20 m. If the contact between ball and ground lasted 2.0 ms, what average force was exerted on the ball? Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "11 kN",
"style": "rule"
}
|
{
"answer": "11 kN",
"index": 270,
"question": "15. After falling from rest from a height of 30 m, a 0.50-kg ball rebounds upward, reaching a height of 20 m. If the contact between ball and ground lasted 2.0 ms, what average force was exerted on the ball?",
"split": "train"
}
| null | null |
1739888
|
Float
|
Mathematics
|
University
|
general-reasoner
|
[
{
"content": "Change the integral to polar coordinates and then evaluate the integral.\n\n{eq}\\int_{-2}^{2}\\int_{2}^{\\sqrt{8-x^2}}\\frac{1}{y}dydx{/eq} Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "0.9858",
"style": "rule"
}
|
{
"answer": "0.9858",
"index": 271,
"question": "Change the integral to polar coordinates and then evaluate the integral.\n\n{eq}\\int_{-2}^{2}\\int_{2}^{\\sqrt{8-x^2}}\\frac{1}{y}dydx{/eq}",
"split": "train"
}
| null | null |
272436
|
Float
|
Mathematics
|
University
|
general-reasoner
|
[
{
"content": "What is the cut-off salary for elementary school teachers in the US in the top 10%, given that their salaries are normally distributed with a mean of $29,000 and a standard deviation of $2,000? Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "31564",
"style": "rule"
}
|
{
"answer": "31564",
"index": 272,
"question": "What is the cut-off salary for elementary school teachers in the US in the top 10%, given that their salaries are normally distributed with a mean of $29,000 and a standard deviation of $2,000?",
"split": "train"
}
| null | null |
1944627
|
List
|
Biology
|
Senior High School
|
general-reasoner
|
[
{
"content": "What cells don't take part in cell division? Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "Neurons, RBCs, and plasma B cells",
"style": "rule"
}
|
{
"answer": "Neurons, RBCs, and plasma B cells",
"index": 273,
"question": "What cells don't take part in cell division?",
"split": "train"
}
| null | null |
809466
|
Multiple Choice
|
Mathematics
|
University
|
general-reasoner
|
[
{
"content": "Regression analysis is a statistical tool used to explain: Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "e",
"style": "rule"
}
|
{
"answer": "e",
"index": 274,
"question": "Regression analysis is a statistical tool used to explain:",
"split": "train"
}
| null | null |
1803997
|
Expression
|
Mathematics
|
University
|
general-reasoner
|
[
{
"content": "I need to translate the dimensions of a pringle chip into a mathematical function to calculate the surface area of hyperbolic paraboloids. Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "z=\\frac{x^2}{a^2}-\\frac{y^2}{b^2}",
"style": "rule"
}
|
{
"answer": "z=\\frac{x^2}{a^2}-\\frac{y^2}{b^2}",
"index": 275,
"question": "I need to translate the dimensions of a pringle chip into a mathematical function to calculate the surface area of hyperbolic paraboloids.",
"split": "train"
}
| null | null |
313893
|
Expression
|
Mathematics
|
University
|
general-reasoner
|
[
{
"content": "if X has exponential exp(lambda) and Y has normal distribution N(0,1). X and Y are independent. how can one find p(X < Y)? My thoughts were to integrate : $$\\int_{-\\infty}^{+\\infty} F_X(y)f_Y(y) \\,dy,$$ with function $F_X$ being the cdf of X and function $f_Y$ being the pdf of Y. I couldn't integrate it in a way that would give me a suitable answer without using the erf function. any help would be appreciated. Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "1/2 + exp(lambda^2/2) * (1 - Phi(lambda)), where Phi(x) is the cdf of standard normal distribution",
"style": "rule"
}
|
{
"answer": "1/2 + exp(lambda^2/2) * (1 - Phi(lambda)), where Phi(x) is the cdf of standard normal distribution",
"index": 276,
"question": "if X has exponential exp(lambda) and Y has normal distribution N(0,1). X and Y are independent. how can one find p(X < Y)? My thoughts were to integrate : $$\\int_{-\\infty}^{+\\infty} F_X(y)f_Y(y) \\,dy,$$ with function $F_X$ being the cdf of X and function $f_Y$ being the pdf of Y. I couldn't integrate it in a way that would give me a suitable answer without using the erf function. any help would be appreciated.",
"split": "train"
}
| null | null |
1069690
|
Multiple Choice
|
Physics
|
Senior High School
|
general-reasoner
|
[
{
"content": "Faraday's law of electromagnetic induction helps determine:\n\na. The direction of induced currents and EMFs\n\nb. The magnitude of induced EMFs and currents\n\nc. The direction and magnitude of induced EMFs only\n\nd. The direction and magnitude of induced currents only Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "b",
"style": "rule"
}
|
{
"answer": "b",
"index": 277,
"question": "Faraday's law of electromagnetic induction helps determine:\n\na. The direction of induced currents and EMFs\n\nb. The magnitude of induced EMFs and currents\n\nc. The direction and magnitude of induced EMFs only\n\nd. The direction and magnitude of induced currents only",
"split": "train"
}
| null | null |
1979226
|
String
|
Chemistry
|
Senior High School
|
general-reasoner
|
[
{
"content": "Rutherford bombarded nitrogen gas with alpha particles, causing some of the nitrogen to change into oxygen by a process of Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "artificial transmutation",
"style": "rule"
}
|
{
"answer": "artificial transmutation",
"index": 278,
"question": "Rutherford bombarded nitrogen gas with alpha particles, causing some of the nitrogen to change into oxygen by a process of",
"split": "train"
}
| null | null |
1780095
|
Multiple Choice
|
Business
|
University
|
general-reasoner
|
[
{
"content": "Gribble Corporation acquires the Dibble Corporation for $7,200,000. On appraisal, the assets of Dibble Corporation have a fair market value of $6,800,000. The excess of the purchase price over the fair market value of the assets:\n\n1. Can be apportioned to the assets based on their relative fair market value.\n\n2. Is goodwill that is amortized over 15 years.\n\n3. Is goodwill that is amortized over 40 years.\n\n4. Must be capitalized until Dibble is sold. Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "None",
"style": "rule"
}
|
{
"answer": "None",
"index": 279,
"question": "Gribble Corporation acquires the Dibble Corporation for $7,200,000. On appraisal, the assets of Dibble Corporation have a fair market value of $6,800,000. The excess of the purchase price over the fair market value of the assets:\n\n1. Can be apportioned to the assets based on their relative fair market value.\n\n2. Is goodwill that is amortized over 15 years.\n\n3. Is goodwill that is amortized over 40 years.\n\n4. Must be capitalized until Dibble is sold.",
"split": "train"
}
| null | null |
1094280
|
Expression
|
Mathematics
|
University
|
general-reasoner
|
[
{
"content": "I need to solve this ODE $$ y' = \\dfrac{1}{x\\cos(y) + \\sin(2y)}$$ Could you give me any hints? Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "$$y=-\\sin ^{-1}\\Big( W\\left(C e^{-(1+\\frac{x}{2})}\\right)+(1+\\frac{x}{2})\\Big)$$",
"style": "rule"
}
|
{
"answer": "$$y=-\\sin ^{-1}\\Big( W\\left(C e^{-(1+\\frac{x}{2})}\\right)+(1+\\frac{x}{2})\\Big)$$",
"index": 280,
"question": "I need to solve this ODE $$ y' = \\dfrac{1}{x\\cos(y) + \\sin(2y)}$$ Could you give me any hints?",
"split": "train"
}
| null | null |
262489
|
Matrix
|
Business
|
University
|
general-reasoner
|
[
{
"content": "Gundy Company expects to produce 1,204,800 units of Product XX in 2020.\n\n1. Monthly production is expected to range from 90,000 to 126,000 units.\n\n2. Budgeted variable manufacturing costs per unit are direct materials $4, direct labor $6, and overhead $11.\n\n3. Budgeted fixed manufacturing costs per unit for depreciation are $4 and for supervision are $2.\n\nPrepare a flexible manufacturing budget for the relevant range value using 18,000 unit increments. Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "{\n \"Units produced\": [90000, 108000, 126000],\n \"Variable cost\": {\n \"Direct material\": [360000, 432000, 504000],\n \"Direct labor\": [540000, 648000, 756000],\n \"Overhead\": [990000, 1188000, 1386000],\n \"Total variable cost (A)\": [1890000, 2268000, 2646000]\n },\n \"Fixed cost\": {\n \"Depreciation\": [401600, 401600, 401600],\n \"Supervision\": [200800, 200800, 200800],\n \"Total fixed cost (B)\": [602400, 602400, 602400]\n },\n \"Total cost (C = A + B)\": [2492400, 2870400, 3248400]\n}\n",
"style": "rule"
}
|
{
"answer": "{\n \"Units produced\": [90000, 108000, 126000],\n \"Variable cost\": {\n \"Direct material\": [360000, 432000, 504000],\n \"Direct labor\": [540000, 648000, 756000],\n \"Overhead\": [990000, 1188000, 1386000],\n \"Total variable cost (A)\": [1890000, 2268000, 2646000]\n },\n \"Fixed cost\": {\n \"Depreciation\": [401600, 401600, 401600],\n \"Supervision\": [200800, 200800, 200800],\n \"Total fixed cost (B)\": [602400, 602400, 602400]\n },\n \"Total cost (C = A + B)\": [2492400, 2870400, 3248400]\n}\n",
"index": 281,
"question": "Gundy Company expects to produce 1,204,800 units of Product XX in 2020.\n\n1. Monthly production is expected to range from 90,000 to 126,000 units.\n\n2. Budgeted variable manufacturing costs per unit are direct materials $4, direct labor $6, and overhead $11.\n\n3. Budgeted fixed manufacturing costs per unit for depreciation are $4 and for supervision are $2.\n\nPrepare a flexible manufacturing budget for the relevant range value using 18,000 unit increments.",
"split": "train"
}
| null | null |
1294175
|
Multiple Choice
|
Economics
|
Senior High School
|
general-reasoner
|
[
{
"content": "Dave's Dogs is a firm that originally sold hot dogs and soft drinks from a cart located in front of City Hall. Then Dave purchased another hot dog cart and hired someone to sell hot dogs and soft drinks near the high school. Both locations have been successful. When Dave's Dogs expanded to two locations, which of the following did NOT occur?\n\nA) Dave's production function changed.\n\nB) Production increased.\n\nC) The company increased the inputs it employs.\n\nD) The firm employed additional capital. Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "A",
"style": "rule"
}
|
{
"answer": "A",
"index": 282,
"question": "Dave's Dogs is a firm that originally sold hot dogs and soft drinks from a cart located in front of City Hall. Then Dave purchased another hot dog cart and hired someone to sell hot dogs and soft drinks near the high school. Both locations have been successful. When Dave's Dogs expanded to two locations, which of the following did NOT occur?\n\nA) Dave's production function changed.\n\nB) Production increased.\n\nC) The company increased the inputs it employs.\n\nD) The firm employed additional capital.",
"split": "train"
}
| null | null |
625485
|
Expression
|
Physics
|
Senior High School
|
general-reasoner
|
[
{
"content": "Given the angle, the time, and the horizontal range, how to find the horizontal velocity (m/s)? Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "v_h = \\sqrt{\\dfrac{gR}{2 \\tan \\theta }}",
"style": "rule"
}
|
{
"answer": "v_h = \\sqrt{\\dfrac{gR}{2 \\tan \\theta }}",
"index": 283,
"question": "Given the angle, the time, and the horizontal range, how to find the horizontal velocity (m/s)?",
"split": "train"
}
| null | null |
831420
|
Expression
|
Mathematics
|
University
|
general-reasoner
|
[
{
"content": "Compute the derivative of the following function: f(w) = \\sin(\\cos^{-1} 7w) Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "{eq}f'(w) = - \\frac{49w}{\\sqrt{1-49w^2}}{/eq}",
"style": "rule"
}
|
{
"answer": "{eq}f'(w) = - \\frac{49w}{\\sqrt{1-49w^2}}{/eq}",
"index": 284,
"question": "Compute the derivative of the following function: f(w) = \\sin(\\cos^{-1} 7w)",
"split": "train"
}
| null | null |
138634
|
Float
|
Mathematics
|
University
|
general-reasoner
|
[
{
"content": "Find the volume of the solid that lies within the sphere {eq}x^2 + y^2 + z^2 = 9{/eq}, above the xy-plane and outside the cone {eq}\\displaystyle z = 8 \\sqrt{x^2 + y^2}{/eq}. Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "0.4367",
"style": "rule"
}
|
{
"answer": "0.4367",
"index": 285,
"question": "Find the volume of the solid that lies within the sphere {eq}x^2 + y^2 + z^2 = 9{/eq}, above the xy-plane and outside the cone {eq}\\displaystyle z = 8 \\sqrt{x^2 + y^2}{/eq}.",
"split": "train"
}
| null | null |
848181
|
Float
|
Physics
|
Senior High School
|
general-reasoner
|
[
{
"content": "Two point charges, {eq}+3.30 \\ C\n\n{/eq} and {eq}-5.50 \\ C\n\n{/eq}, are separated by {eq}1.29 \\ m\n\n{/eq}.\n\nWhat is the electric potential midway between them? Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "-30.7 V",
"style": "rule"
}
|
{
"answer": "-30.7 V",
"index": 286,
"question": "Two point charges, {eq}+3.30 \\ C\n\n{/eq} and {eq}-5.50 \\ C\n\n{/eq}, are separated by {eq}1.29 \\ m\n\n{/eq}.\n\nWhat is the electric potential midway between them?",
"split": "train"
}
| null | null |
681170
|
Multiple Choice
|
Business
|
University
|
general-reasoner
|
[
{
"content": "Which of the following independent transactions would cause net income to be more than cash from operating activities?\n\na. A decrease in the accounts receivable account.\n\nb. An increase in the merchandise inventory account.\n\nc. An increase in the accounts payable account.\n\nd. An increase in the accrued wages payable account. Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "b",
"style": "rule"
}
|
{
"answer": "b",
"index": 287,
"question": "Which of the following independent transactions would cause net income to be more than cash from operating activities?\n\na. A decrease in the accounts receivable account.\n\nb. An increase in the merchandise inventory account.\n\nc. An increase in the accounts payable account.\n\nd. An increase in the accrued wages payable account.",
"split": "train"
}
| null | null |
1462662
|
List
|
Chemistry
|
Senior High School
|
general-reasoner
|
[
{
"content": "List the following ions in order of increasing radius:\n\na. {eq}Br^-\n\n{/eq}\n\nb. {eq}Li^+\n\n{/eq}\n\nc. {eq}Te^{2-}\n\n{/eq}\n\nd. {eq}Mg^{2+}\n\n{/eq} Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "Li+ < Mg2+ < Br- < Te2-",
"style": "rule"
}
|
{
"answer": "Li+ < Mg2+ < Br- < Te2-",
"index": 288,
"question": "List the following ions in order of increasing radius:\n\na. {eq}Br^-\n\n{/eq}\n\nb. {eq}Li^+\n\n{/eq}\n\nc. {eq}Te^{2-}\n\n{/eq}\n\nd. {eq}Mg^{2+}\n\n{/eq}",
"split": "train"
}
| null | null |
1861325
|
List
|
Mathematics
|
University
|
general-reasoner
|
[
{
"content": "I want to find the equation for a plane that is equidistant from the points $P_0 = (1, 2, 3)$ and $P_1=(3, 2, 1)$ and contains the line $\\ell=(1, 1, 1) + t(0, 1, -1).$ Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "x + y + z = 3 or -2x + y + z = 0",
"style": "rule"
}
|
{
"answer": "x + y + z = 3 or -2x + y + z = 0",
"index": 289,
"question": "I want to find the equation for a plane that is equidistant from the points $P_0 = (1, 2, 3)$ and $P_1=(3, 2, 1)$ and contains the line $\\ell=(1, 1, 1) + t(0, 1, -1).$",
"split": "train"
}
| null | null |
1920586
|
Float
|
Finance
|
University
|
general-reasoner
|
[
{
"content": "You have invested equally in the following four security portfolio, market portfolio, risk free asset, a stock with a beta of 1.7, and a bond with a beta of 0.6.\n\nWhat is the beta of your portfolio?\n\n(Show your answer to 2 decimal places (e.g., 1.23).) Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "0.83",
"style": "rule"
}
|
{
"answer": "0.83",
"index": 290,
"question": "You have invested equally in the following four security portfolio, market portfolio, risk free asset, a stock with a beta of 1.7, and a bond with a beta of 0.6.\n\nWhat is the beta of your portfolio?\n\n(Show your answer to 2 decimal places (e.g., 1.23).)",
"split": "train"
}
| null | null |
1021517
|
Float
|
Finance
|
University
|
general-reasoner
|
[
{
"content": "Nachman Industries just paid a dividend of D0 = $1.32. Analysts expect the company's dividend to grow by 30% this year, by 10% in Year 2, and at a constant rate of 5% in year 3 and thereafter. The required return on this low-risk stock is 9%. What is the best estimate of the stock's current market value? Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "$44.85",
"style": "rule"
}
|
{
"answer": "$44.85",
"index": 291,
"question": "Nachman Industries just paid a dividend of D0 = $1.32. Analysts expect the company's dividend to grow by 30% this year, by 10% in Year 2, and at a constant rate of 5% in year 3 and thereafter. The required return on this low-risk stock is 9%. What is the best estimate of the stock's current market value?",
"split": "train"
}
| null | null |
1221958
|
String
|
Other
|
Junior High School
|
general-reasoner
|
[
{
"content": "What does PEC stand for in special education? Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "Picture Exchange Communication",
"style": "rule"
}
|
{
"answer": "Picture Exchange Communication",
"index": 292,
"question": "What does PEC stand for in special education?",
"split": "train"
}
| null | null |
1756950
|
Float
|
Physics
|
University
|
general-reasoner
|
[
{
"content": "A handheld bicycle pump can be used as an atomizer to generate a fine mist of paint or pesticide by forcing air at a high velocity through a small hole and placing a short tube between the liquid reservoir and the high-speed air jet whose low pressure drives the liquid up through the tube. In such an atomizer, the hole diameter is 0.3 cm, the vertical distance between the liquid level in the tube and the hole is 10 cm, and the bore (diameter) and the stroke of the air pump are 5 cm and 20 cm, respectively. If the atmospheric conditions are 20 {eq}^o\n\n{/eq}C and 95 kPa, determine the minimum speed that the piston must be moved in the cylinder during pumping to initiate the atomizing effect. The liquid reservoir is open to the atmosphere. Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "0.150 m/s",
"style": "rule"
}
|
{
"answer": "0.150 m/s",
"index": 293,
"question": "A handheld bicycle pump can be used as an atomizer to generate a fine mist of paint or pesticide by forcing air at a high velocity through a small hole and placing a short tube between the liquid reservoir and the high-speed air jet whose low pressure drives the liquid up through the tube. In such an atomizer, the hole diameter is 0.3 cm, the vertical distance between the liquid level in the tube and the hole is 10 cm, and the bore (diameter) and the stroke of the air pump are 5 cm and 20 cm, respectively. If the atmospheric conditions are 20 {eq}^o\n\n{/eq}C and 95 kPa, determine the minimum speed that the piston must be moved in the cylinder during pumping to initiate the atomizing effect. The liquid reservoir is open to the atmosphere.",
"split": "train"
}
| null | null |
245414
|
List
|
Economics
|
University
|
general-reasoner
|
[
{
"content": "Rank the following from the firm with the highest elasticity of substitution to the lowest, and explain your ranking.\n\na. catering companies\n\nb. assembly line manufacturing\n\nc. computer programming Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "Catering companies > Computer programming > Assembly line manufacturing",
"style": "rule"
}
|
{
"answer": "Catering companies > Computer programming > Assembly line manufacturing",
"index": 294,
"question": "Rank the following from the firm with the highest elasticity of substitution to the lowest, and explain your ranking.\n\na. catering companies\n\nb. assembly line manufacturing\n\nc. computer programming",
"split": "train"
}
| null | null |
1703067
|
Float
|
Physics
|
Senior High School
|
general-reasoner
|
[
{
"content": "Mercury fills 90% of the volume of a sealed glass container at 20 degrees Celsius. What temperature does the glass/Mercury have to be heated so that the mercury completely fills the container? (Hg = {eq}6 \\times 10^{-5}\n\n{/eq} degrees Celsius{eq}^{-1}\n\n{/eq}, and glass = {eq}0.4 \\times 10^{-5}\n\n{/eq} degrees Celsius{eq}^{-1}\n\n{/eq}). Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "686.66^°C",
"style": "rule"
}
|
{
"answer": "686.66^°C",
"index": 295,
"question": "Mercury fills 90% of the volume of a sealed glass container at 20 degrees Celsius. What temperature does the glass/Mercury have to be heated so that the mercury completely fills the container? (Hg = {eq}6 \\times 10^{-5}\n\n{/eq} degrees Celsius{eq}^{-1}\n\n{/eq}, and glass = {eq}0.4 \\times 10^{-5}\n\n{/eq} degrees Celsius{eq}^{-1}\n\n{/eq}).",
"split": "train"
}
| null | null |
1208198
|
Percentage
|
Business
|
Senior High School
|
general-reasoner
|
[
{
"content": "In 1967, tuition, room & board at a private college costs $3000. In 2007, the same services cost $48,000. Find the average annual rate of college-cost inflation, using the Rule of 72. Hint: first, estimate the number of doubles. Since each double represents 72 compounding percents, you can then find the total number of compounding percents. Finally, plug-into the formula rate * time = total compounding percents, and solve for rate. Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "7.2% per year",
"style": "rule"
}
|
{
"answer": "7.2% per year",
"index": 296,
"question": "In 1967, tuition, room & board at a private college costs $3000. In 2007, the same services cost $48,000. Find the average annual rate of college-cost inflation, using the Rule of 72. Hint: first, estimate the number of doubles. Since each double represents 72 compounding percents, you can then find the total number of compounding percents. Finally, plug-into the formula rate * time = total compounding percents, and solve for rate.",
"split": "train"
}
| null | null |
695305
|
Multiple Choice
|
Physics
|
Junior High School
|
general-reasoner
|
[
{
"content": "When traveling with empty lift forks, the forks should be in what position? all the way up about eye level all the way down waist high? Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "D",
"style": "rule"
}
|
{
"answer": "D",
"index": 297,
"question": "When traveling with empty lift forks, the forks should be in what position? all the way up about eye level all the way down waist high?",
"split": "train"
}
| null | null |
1293008
|
Float
|
Physics
|
Senior High School
|
general-reasoner
|
[
{
"content": "One gallon of gasoline in an automobile's engine produces on the average 9.5 kg of carbon dioxide, which is a greenhouse gas, that is, it promotes the warming of Earth's atmosphere. Calculate the annual production of carbon dioxide in kilograms if there are 40 million cars in the United States and each car covers a distance of 5300 miles at a consumption rate of 21 miles per gallon. Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "9.59 * 10^10 kg",
"style": "rule"
}
|
{
"answer": "9.59 * 10^10 kg",
"index": 298,
"question": "One gallon of gasoline in an automobile's engine produces on the average 9.5 kg of carbon dioxide, which is a greenhouse gas, that is, it promotes the warming of Earth's atmosphere. Calculate the annual production of carbon dioxide in kilograms if there are 40 million cars in the United States and each car covers a distance of 5300 miles at a consumption rate of 21 miles per gallon.",
"split": "train"
}
| null | null |
243937
|
Float
|
Physics
|
Senior High School
|
general-reasoner
|
[
{
"content": "An object is at rest at #(8 ,3 ,8 )# and constantly accelerates at a rate of #7/4 m/s^2# as it moves to point B. If point B is at #(6 ,3 ,4 )#, how long will it take for the object to reach point B? Assume that all coordinates are in meters. Please reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
}
] |
reasoning
|
{
"ground_truth": "2.26s",
"style": "rule"
}
|
{
"answer": "2.26s",
"index": 299,
"question": "An object is at rest at #(8 ,3 ,8 )# and constantly accelerates at a rate of #7/4 m/s^2# as it moves to point B. If point B is at #(6 ,3 ,4 )#, how long will it take for the object to reach point B? Assume that all coordinates are in meters.",
"split": "train"
}
| null | null |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.