id stringlengths 12 32 | dataset stringclasses 6 values | messages listlengths 2 2 |
|---|---|---|
TIGER-Lab/MathInstruct_3537 | TIGER-Lab/MathInstruct | [
{
"content": "Find all possible cyclic subgroups of a group of order 60 and use this information to determine whether the group is isomorphic to C60. If it is not isomorphic to C60, determine whether it is isomorphic to A5 × C2 or one of the 32 non-abelian groups of order 60. Show all work and reasoning.",
... |
TIGER-Lab/MathInstruct_7220 | TIGER-Lab/MathInstruct | [
{
"content": "Scott runs 3 miles every Monday through Wednesday. Then he runs twice as far he ran on Monday every Thursday and Friday. How many miles will he run in a month with 4 weeks?",
"role": "user"
},
{
"content": "Scott runs 3 x 2 = 6 miles every Thursday and Friday.\nThe total miles run by S... |
facebook/natural_reasoning_8959 | facebook/natural_reasoning | [
{
"content": "What are the primary forces that keep the planets in our solar system in their consistent orbits, and how do these forces interact to maintain the stability of the planetary orbits?",
"role": "user"
},
{
"content": "The primary forces that keep the planets in our solar system in their ... |
TIGER-Lab/MathInstruct_7130 | TIGER-Lab/MathInstruct | [
{
"content": "a cylinder of height h is 8 / 9 of water . when all of the water is poured into an empty cylinder whose radius is 25 percent larger than that of the original cylinder , the new cylinder is 3 / 5 full . the height of the new cylinder is what percent of h ? Let's write a Python program.",
"role"... |
TIGER-Lab/MathInstruct_2873 | TIGER-Lab/MathInstruct | [
{
"content": "10 is 6 % of a , and 6 is 10 % of b . c equals b / a . what is the value of c ? Please write a program to solve it",
"role": "user"
},
{
"content": "n0 = 10.0\nn1 = 6.0\nn2 = 6.0\nn3 = 10.0\nt0 = n1 / n0\nt1 = n0 / n1\nt2 = t0 * 100.0\nt3 = t1 * 100.0\nanswer = t2 / t3\nprint(answer)",... |
TIGER-Lab/MathInstruct_13034 | TIGER-Lab/MathInstruct | [
{
"content": "The expansion of $(x+1)^n$ has 3 consecutive terms with coefficients in the ratio $1:2:3$ that can be written in the form\\[{n\\choose k} : {n\\choose k+1} : {n \\choose k+2}\\]Find the sum of all possible values of $n+k$.\n",
"role": "user"
},
{
"content": "By definition, ${n\\choose ... |
TIGER-Lab/MathInstruct_151 | TIGER-Lab/MathInstruct | [
{
"content": "Which of the following is greatest?\nAnswer Choices: (A) 2/10 (B) 2/10^2 (C) 2/10^3 (D) 2/10^4 (E) 2/10^6",
"role": "user"
},
{
"content": "Let's think about the multi-choice question.\n2/10 > 2/100 > 2/1000 > 2/10000 > 2/1000000\nThe answer is A",
"role": "assistant"
}
] |
facebook/natural_reasoning_9455 | facebook/natural_reasoning | [
{
"content": "Two cylinders, A and B, have the same volume. Cylinder B's radius is half that of cylinder A, and thus its length is four times that of cylinder A. If the uncertainty in measuring the radius and length is the same for both cylinders, which cylinder would have the greatest uncertainty in volume mea... |
facebook/natural_reasoning_3334 | facebook/natural_reasoning | [
{
"content": "Prove that the minimal area of a triangle inscribed in an equilateral triangle with side length 1, while maintaining a minimal distance L (L < 1/2) between vertices of triangles, is achieved when two vertices of the inscribed triangle are at distance L from the same vertex of the equilateral trian... |
facebook/natural_reasoning_11263 | facebook/natural_reasoning | [
{
"content": "Describe the double-slit experiment and explain how electrons or photons choose their paths. Discuss the principles of wave-particle duality and the implications of the experiment on our understanding of quantum mechanics. Provide a detailed analysis of the technical aspects of the experiment, inc... |
TIGER-Lab/MathInstruct_7002 | TIGER-Lab/MathInstruct | [
{
"content": "A palindrome is a number that reads the same forwards and backwards, such as 3003. How many positive four-digit integers are palindromes? Let's write a Python program to solve it.",
"role": "user"
},
{
"content": "# Python program to count the number of 4-digit palindrome numbers\n\nde... |
TIGER-Lab/MathInstruct_297 | TIGER-Lab/MathInstruct | [
{
"content": "An investor can sell her MicroTron stock for 36$ per share and her Dynaco stock for 44$ per share, If she sells 300 shares altogether, some of each stock, at an average price per share of 40$, how many shares of Dynaco stock has she sold?\nAnswer Choices: (A) 52 (B) 75 (C) 92 (D) 136 (E) 150",
... |
TIGER-Lab/MathInstruct_4170 | TIGER-Lab/MathInstruct | [
{
"content": "A train with 1200m crosses a tree in 120sec, how much time will I take to pass a platform 700m long?\nAnswer Choices: (A) 150sec (B) 130sec (C) 190sec (D) 200sec (E) 100sec",
"role": "user"
},
{
"content": "Let's reason about the multi-choice question.\ns=1200/120\ns-10m/sec\ntotal len... |
facebook/natural_reasoning_156 | facebook/natural_reasoning | [
{
"content": "Consider a fractal line with dimension D=1.5. If the scaling factor S is 2, what is the number density of the fractal line, and how does it relate to the conventional space of whole number dimensions?",
"role": "user"
},
{
"content": "To address the problem, we must first understand th... |
facebook/natural_reasoning_5107 | facebook/natural_reasoning | [
{
"content": "Suppose $X$ is a set and $\\tau, \\tau'$ are two topologies on $X$. Prove that every closed set of $\\tau$ is closed in $\\tau'$ if and only if $\\tau \\subset \\tau'$. Provide a detailed proof and explain the concept of fineness of topology.",
"role": "user"
},
{
"content": "## Step 1... |
allenai/sciq_766 | allenai/sciq | [
{
"content": "Chains of small molecules called nucleotides make up what?\n(A) chromosomes\n(B) proteins\n(C) peptides\n(D) nucleic acids\n### Answer: D",
"role": "user"
},
{
"content": "Nucleic acids consist of chains of small molecules called nucleotides, which are held together by covalent bonds. ... |
tulu3_algebra_3605 | tulu3_algebra | [
{
"content": "A descendent of a small indigenous community is working on a project to document their unique language, which has Indo-European influences. To ensure that the grammar rules are documented correctly, they've decided to create a mathematical model that represents the frequency of certain linguistic ... |
allenai/sciq_2355 | allenai/sciq | [
{
"content": "What theory explains the physical behavior of gases?\n(A) kinetic theory of gases\n(B) relativity theory of gases\n(C) quantum theory of gases\n(D) thermodynamic theory of gases\n### Answer: A",
"role": "user"
},
{
"content": "The physical behavior of gases is explained by the kinetic ... |
facebook/natural_reasoning_10584 | facebook/natural_reasoning | [
{
"content": "A vehicle with four wheels is designed to climb a surface with a slope of θ degrees. The vehicle's mass is m, and the radius of each wheel is R. Assuming a static analysis and neglecting wind and acceleration forces, derive the equation for the motor torque required to climb the slope. Consider th... |
TIGER-Lab/MathInstruct_19704 | TIGER-Lab/MathInstruct | [
{
"content": "Charlotte, Lisa, and Patricia have a joint baseball collection. One of their friends is selling a rare baseball card for $100 on his website. Not wanting to miss such a rare opportunity, they have pooled all their money to buy the card. Patricia has $6. Lisa has five times Patricia’s money, but do... |
TIGER-Lab/MathInstruct_20677 | TIGER-Lab/MathInstruct | [
{
"content": "Jack is making flower crowns out of red, pink and white daisies. There are nine times as many pink daisies as white daisies and three less than four times as many red daisies as pink daisies. If there are 6 white daisies, how many daisies are there total?",
"role": "user"
},
{
"content... |
tulu3_code_1256 | tulu3_code | [
{
"content": "Write a python function to help me calculate the total number of bus rides my family takes in a week using Pine Bluff Transit. As a mother of three children, I often take the bus with all my kids. The input should be a list of integers where each integer represents the number of rides we take on a... |
tulu3_code_642 | tulu3_code | [
{
"content": "Write a python function to help me calculate the total weight of a batch of clay pieces given their individual weights. The function should take a list of integers, where each integer represents the weight of a single clay piece in grams. It should return the total weight of all the pieces combine... |
facebook/natural_reasoning_1074 | facebook/natural_reasoning | [
{
"content": "Given a battery with a specification of 10V and 100mAh, and considering the voltage decrease during discharge, how can you estimate the energy in watt-hours (Wh) and what are the implications of this conversion for comparing battery capacities?",
"role": "user"
},
{
"content": "## Step... |
TIGER-Lab/MathInstruct_10949 | TIGER-Lab/MathInstruct | [
{
"content": "Three friends ate a total of 8 pounds of fruit. Mario had 8 ounces of oranges, while Lydia ate 24 ounces of apples. Nicolai ate peaches. How many pounds of peaches did Nicolai eat?",
"role": "user"
},
{
"content": "8 pounds of fruit = 128 ounces of fruit\nMario ate 8 ounces + Lydia ate... |
TIGER-Lab/MathInstruct_11697 | TIGER-Lab/MathInstruct | [
{
"content": "a circular mat with diameter 18 inches is placed on a square tabletop , each of whose sides is 24 inches long . which of the following is closest to the fraction of the tabletop covered by the mat ? Let's write a Python program.",
"role": "user"
},
{
"content": "n0 = 18.0\nn1 = 24.0\nt... |
tulu3_code_2980 | tulu3_code | [
{
"content": "Write a python function to help me organize a list of films by their release year. As a film scholar, I often give tours and provide insights about the progression of cinema through the decades. I have a list of films, each represented as a dictionary with keys 'title' and 'year'. Could you please... |
TIGER-Lab/MathInstruct_12671 | TIGER-Lab/MathInstruct | [
{
"content": "in a 100 - mile trip , the first 30 miles were completed at 60 mph . if the average speed for the whole trip was 40 mph , what was the average speed in the last 70 miles ? Let's program in Python in the response.",
"role": "user"
},
{
"content": "n0 = 100.0\nn1 = 30.0\nn2 = 60.0\nn3 = ... |
TIGER-Lab/MathInstruct_13824 | TIGER-Lab/MathInstruct | [
{
"content": "Consider a graph with 8 vertices labeled as A, B, C, D, E, F, G, and H. The edges of the graph are defined as follows:\n\n- A is connected to B, C, and D\n- B is connected to F\n- C is connected to F and G\n- D is connected to E, F, and G\n- E is connected to H\n- F is connected to H\n- G is not c... |
TIGER-Lab/MathInstruct_15241 | TIGER-Lab/MathInstruct | [
{
"content": "Suppose a rocket is launched from Earth with the goal of reaching a satellite orbiting at an altitude of 2000 km. The rocket can generate a maximum thrust of 500 kN and has a fuel capacity of 1000 kg. The mass of the rocket (including fuel) is 5000 kg. The gravitational acceleration is approximate... |
facebook/natural_reasoning_7737 | facebook/natural_reasoning | [
{
"content": "A radio wave has a frequency of 830 Hz and is propagating through a medium with a speed of 2.17 * 10^8 m/s. Calculate the wavelength of the wave and discuss the implications of its electric and magnetic field strengths.",
"role": "user"
},
{
"content": "To calculate the wavelength of t... |
TIGER-Lab/MathInstruct_4836 | TIGER-Lab/MathInstruct | [
{
"content": " \"statement 1\": Jason has 7.0 violet balloons and 4.0 red balloons and he lost 3.0 of the violet balloons , \"statement 2\" :Jason has 4.0 violet balloons now, \"options: \" Entailment or contradiction? Please respond by writing a program in Python.",
"role": "user"
},
{
"content": ... |
tulu3_code_4969 | tulu3_code | [
{
"content": "Write a python function to help me, a fantasy novelist, keep track of mysterious creatures and their sightings throughout my world. I need a function that takes in a list of tuples, where each tuple contains a creature's name (a string) and the number of sightings (an integer). The function should... |
facebook/natural_reasoning_6151 | facebook/natural_reasoning | [
{
"content": "Consider a double-slit experiment where a stream of electrons is sent through the slits, one at a time. The electrons are separated by a significant time interval, such that the emission of each electron is independent of the previous one. Discuss the possibility of quantum interference in time, w... |
facebook/natural_reasoning_9419 | facebook/natural_reasoning | [
{
"content": "Simplify the expression $\\sqrt{2+e^{8t}+e^{-8t}}$ using appropriate mathematical identities and provide a clear step-by-step solution.",
"role": "user"
},
{
"content": "## Step 1: Identify the given expression\nThe expression to simplify is $\\sqrt{2+e^{8t}+e^{-8t}}$.\n\n## Step 2: Ap... |
tulu3_algebra_3160 | tulu3_algebra | [
{
"content": "As a devoted fan of WWE Diva, you decide to collect memorabilia of your favorite wrestler. You plan to buy action figures, posters, and DVDs. Let's say the number of action figures you buy is represented by \\( x \\), the number of posters by \\( y \\), and the number of DVDs by \\( z \\).\n\n1. Y... |
TIGER-Lab/MathInstruct_8343 | TIGER-Lab/MathInstruct | [
{
"content": "There are 6 multiple choice questions in an examination. How many sequences of answers are possible, if the first three questions have 4 choices each and the next three have 5 each?\nAnswer Choices: (A) 4576 (B) 7200 (C) 6300 (D) 4500 (E) 8000",
"role": "user"
},
{
"content": "Let's re... |
TIGER-Lab/MathInstruct_6757 | TIGER-Lab/MathInstruct | [
{
"content": "Look at this series: 15, __, 27, 27, 39, 39, ... What number should fill the blank?\nAnswer Choices: (A) 51 (B) 39 (C) 23 (D) 15 (E) None",
"role": "user"
},
{
"content": "Let's reason about the multi-choice question.\nExplanation: In this simple addition with repetition series, each n... |
TIGER-Lab/MathInstruct_15379 | TIGER-Lab/MathInstruct | [
{
"content": "Will's mom gave him $74 to go shopping. He bought a sweater for $9, a T-shirt for $11 and a pair of shoes for $30. He then returned his shoes for a 90% refund. How much money does Will have left?",
"role": "user"
},
{
"content": "Will spent 30-27=3 dollars on shoes.\nWill spent 9+11=2... |
tulu3_algebra_756 | tulu3_algebra | [
{
"content": "As a young aspiring entrepreneur, you are attending a business panel where an industry veteran shares a strategy for maximizing profit by optimizing production levels. The veteran explains that the profit \\( P(x) \\) in thousands of dollars from producing and selling \\( x \\) units of a product ... |
TIGER-Lab/MathInstruct_14339 | TIGER-Lab/MathInstruct | [
{
"content": "Every day, Fred takes the train to travel from his work back to Alkmaar, his place of residence. Usually, he arrives at the station of Alkmaar at six o'clock, and exactly at that moment, his wife picks him up by car. Yesterday evening, Fred took an earlier train, without informing his wife, and th... |
facebook/natural_reasoning_11459 | facebook/natural_reasoning | [
{
"content": "Given a totally finite measure μ defined on a σ-field X, define the (pseudo)metric d(A,B)=μ(A-B)+μ(B-A). Show that the metric space (X',d) is complete, where equivalent classes of sets [Aα] where d(Aα1,Aα2)=0 are considered.",
"role": "user"
},
{
"content": "A nice problem in measure t... |
TIGER-Lab/MathInstruct_12127 | TIGER-Lab/MathInstruct | [
{
"content": "The sum of three numbers $x$ ,$y$, $z$ is 165. When the smallest number $x$ is multiplied by 7, the result is $n$. The value $n$ is obtained by subtracting 9 from the largest number $y$. This number $n$ also results by adding 9 to the third number $z$. What is the product of the three numbers?",
... |
TIGER-Lab/MathInstruct_2570 | TIGER-Lab/MathInstruct | [
{
"content": "A coin is flipped 10 times, what is the probability of getting 7 heads and 3 tails?",
"role": "user"
},
{
"content": "To find the probability of getting 7 heads and 3 tails in 10 coin flips, we will use the binomial probability formula:\n\nP(X=k) = C(n, k) * p^k * (1-p)^(n-k)\n\nwhere:... |
TIGER-Lab/MathInstruct_1111 | TIGER-Lab/MathInstruct | [
{
"content": "a box contains 100 balls , numbered from 1 to 100 . if 3 balls are selected at random and with replacement from the box . if the 3 numbers on the balls selected contain two odd and one even . what is the probability j that the first ball picked up is odd numbered ? Let's program in Python in the r... |
TIGER-Lab/MathInstruct_8738 | TIGER-Lab/MathInstruct | [
{
"content": "If the city centers of Tokyo and Paris are 6035 miles apart, which of the following is closest to the distance between the city centers in inches? (There are 5,280 feet in a mile.)\nAnswer Choices: (A) 1.2 × 10^7 (B) 1.8 × 10^7 (C) 3.8 × 10^8 (D) 3.8 × 10^9 (E) 3.8 × 10^10",
"role": "user"
}... |
tulu3_code_1788 | tulu3_code | [
{
"content": "Write a python function to determine the number of unique words in a given string and return them as a sorted list. The input will be a string that may contain punctuation, and the words should be considered case-insensitively. The output should be a list of the unique words in lowercase, sorted a... |
facebook/natural_reasoning_9171 | facebook/natural_reasoning | [
{
"content": "If Tan A = 1/3 and Tan B = 1/2, show that Tan(A + B) = (Tan A + Tan B) / (1 - Tan A Tan B). Use the given equation to solve for Tan(7π/4 - 1/3).",
"role": "user"
},
{
"content": "## Step 1: Recall the trigonometric identity for Tan(A + B)\nThe trigonometric identity for Tan(A + B) is g... |
tulu3_algebra_2893 | tulu3_algebra | [
{
"content": "A retired television producer, who has a deep interest in their sibling's stage career, is helping manage the finances of a new theater production. The producer needs to determine the number of seats that should be sold to break even on opening night.\n\n1. The theater has a total of 400 seats. Th... |
facebook/natural_reasoning_3313 | facebook/natural_reasoning | [
{
"content": "Given the discussion on 'pseudo-projective space' $\\mathbb{S}^n / (\\mathbb{Z}/m\\mathbb{Z})$, where $m=2$ yields the normal $\\mathbb{R}\\mathbb{P}^n$, describe the topology and geometry of $P_n$ for $m > 2$, considering the identification map $q: \\mathbb{D}^2 \\rightarrow P_m$ that wraps the b... |
TIGER-Lab/MathInstruct_16304 | TIGER-Lab/MathInstruct | [
{
"content": "A hotel has 10 rooms and is currently full. Each room holds a family of 3. If each person receives 2 towels, how many towels does the hotel hand out? Let's write a Python program to solve it.",
"role": "user"
},
{
"content": "# Python program to calculate the total number of towels han... |
facebook/natural_reasoning_8012 | facebook/natural_reasoning | [
{
"content": "Given a train with a proper length of 375,000 km traveling at 0.6c relative to an observer B, and a beam of light traveling in the same direction as the train, how would observer B measure the speed of the light beam, considering the effects of length contraction and time dilation on the train and... |
allenai/sciq_407 | allenai/sciq | [
{
"content": "Mammals have four limbs and produce what kind of eggs?\n(A) placental\n(B) amniotic\n(C) hard-shelled\n(D) umbilical\n### Answer: B",
"role": "user"
},
{
"content": "Mammals have four limbs and produce amniotic eggs.\n\n### Answer:B",
"role": "assistant"
}
] |
tulu3_algebra_102 | tulu3_algebra | [
{
"content": "As a PhD candidate investigating the impact of cryptocurrency on poverty alleviation, you are analyzing the growth of a fictional cryptocurrency called \"CryptoAid,\" which is specifically designed to support financial inclusion in underprivileged communities. The value of CryptoAid in dollars is ... |
TIGER-Lab/MathInstruct_8228 | TIGER-Lab/MathInstruct | [
{
"content": "Jenny decided to get a cat with her girlfriend. They agreed to split all the costs down the middle except for they would each buy their own toys for the cat. The adoption fee was $50, the vet visits cost $500 for the first year and the monthly cost of food was $25. She bought $200 in toys. How... |
TIGER-Lab/MathInstruct_21819 | TIGER-Lab/MathInstruct | [
{
"content": "Find the second derivative of the following function at x=3:\n\nf(x) = x^3 - 9x^2 + 24x - 16",
"role": "user"
},
{
"content": "To find the second derivative, we first need to find the first derivative of the function f(x) = x^3 - 9x^2 + 24x - 16.\n\nThe first derivative, f'(x), is foun... |
TIGER-Lab/MathInstruct_12747 | TIGER-Lab/MathInstruct | [
{
"content": "The L.C.M of two numbers is 48. The numbers are in the ratio 2:3. The sum of numbers is?\nAnswer Choices: (A) 22 (B) 67 (C) 40 (D) 88 (E) 11",
"role": "user"
},
{
"content": "Let's reason about the multi-choice question.\nLet the numbers be 2x and 3x.\nThen, their L.C.M = 6x. So, 6x = ... |
allenai/sciq_851 | allenai/sciq | [
{
"content": "What is the name of vesicles that are formed by the golgi apparatus?\n(A) capillaries\n(B) lymphocytes\n(C) vessels\n(D) lysosomes\n### Answer: D",
"role": "user"
},
{
"content": "Lysosomes are vesicles that are formed by the Golgi apparatus. They contain powerful enzymes that could br... |
facebook/natural_reasoning_10588 | facebook/natural_reasoning | [
{
"content": "Find the basis vectors of the null space of the matrix \\begin{bmatrix} 0 & 0 & 0 & 0 \\\\ 0 & 1 & 1 & 0 \\\\ 1 & 1 & 0 & 0 \\\\ 1 & 1 & 0 & 0 \\end{bmatrix} in GF2. Show all steps and explain your reasoning.",
"role": "user"
},
{
"content": "## Step 1: To find the basis vectors of the... |
facebook/natural_reasoning_2209 | facebook/natural_reasoning | [
{
"content": "Consider an infinite series where each term is either 1 or -1, alternating between the two. Does the sum of this series converge to a finite value, and if so, what is the sum? If not, explain why the sum is not defined.",
"role": "user"
},
{
"content": "## Step 1: Understanding the Ser... |
TIGER-Lab/MathInstruct_3945 | TIGER-Lab/MathInstruct | [
{
"content": "Gerald thought it would be funny to trick his coworker, who's allergic to peanuts, into eating a peanut butter cookie. When his coworker goes into anaphylactic shock and is taken to the hospital, Gerald is arrested. The judge sentences Gerald to 3 months for assault and 2 years for poisoning, then... |
TIGER-Lab/MathInstruct_2446 | TIGER-Lab/MathInstruct | [
{
"content": "What is the 10th prime number?",
"role": "user"
},
{
"content": "The 10th prime number is 29. Here is the list of the first 10 prime numbers: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29.",
"role": "assistant"
}
] |
TIGER-Lab/MathInstruct_6056 | TIGER-Lab/MathInstruct | [
{
"content": "Let's say we have the following implicit function:\n\n(x^2 + y^2)^2 = 25x^2 + 25y^2\n\nUsing the chain rule, find the derivative of y with respect to x, when x = 3.",
"role": "user"
},
{
"content": "To find the derivative of y with respect to x, we'll first differentiate both sides of ... |
TIGER-Lab/MathInstruct_5220 | TIGER-Lab/MathInstruct | [
{
"content": "Passage: The 2011 Thailand Country Report provides population numbers for mountain peoples (hill tribes) and ethnic communities in the Northeast and is explicit about its main reliance on the Mahidol University Ethnolinguistic Maps of Thailand data. Thus, though over 3.288 million people in the No... |
allenai/sciq_2602 | allenai/sciq | [
{
"content": "What is the name of the smallest planet in our solar system, which is also nearest to the sun?\n(A) jupitor\n(B) earth\n(C) mars\n(D) mercury\n### Answer: D",
"role": "user"
},
{
"content": "Mercury is the smallest planet. It has no moon. It is also the planet closest to the Sun. Pictu... |
facebook/natural_reasoning_10174 | facebook/natural_reasoning | [
{
"content": "Given two coins, one fair (with equal probabilities for heads and tails) and one unfair (with heads on both sides), a person randomly chooses one coin and flips it three times. If the outcomes are heads, heads, and then tails, what is the probability that the person chose the fair coin? Provide a ... |
facebook/natural_reasoning_2863 | facebook/natural_reasoning | [
{
"content": "What is the probability that a string of length $n$ chosen randomly with an alphabet of size $m$ will have $k$ unique letters? Derive a formula for this probability and discuss the expected number of distinct letters in terms of $n$ and $m$.",
"role": "user"
},
{
"content": "## Step 1:... |
tulu3_algebra_2633 | tulu3_algebra | [
{
"content": "Gabriel Antonio Mestre, your childhood best friend, recently gave a speech at a gathering where he discussed his career journey. As a tribute, you decide to create a math problem inspired by your experiences with him.\n\n1. During one of your memorable summer adventures with Gabriel, you both deci... |
facebook/natural_reasoning_9134 | facebook/natural_reasoning | [
{
"content": "Consider an ideal gas composed of molecules with internal structure, such as rotational and vibrational degrees of freedom. Show that the ideal gas law $pV = nRT$ still holds, even if the molecules have internal structure, as long as the conditions for an ideal gas are satisfied. Use statistical m... |
TIGER-Lab/MathInstruct_11685 | TIGER-Lab/MathInstruct | [
{
"content": "Solve the following optimization problem using Tabu Search method:\n\nMinimize f(x) = x^2 + 5x + 6 subject to the constraint x >= -3 and x <= 1.",
"role": "user"
},
{
"content": "Tabu Search is a metaheuristic optimization algorithm that is used to find the global minimum of a function... |
tulu3_code_1595 | tulu3_code | [
{
"content": "Write a Python function to simulate the ticking of a simple clock mechanism. The function should take a starting time in the format \"HH:MM:SS\" and an integer `n` representing the number of seconds the clock should tick forward. The function should return the new time after `n` seconds have passe... |
TIGER-Lab/MathInstruct_11447 | TIGER-Lab/MathInstruct | [
{
"content": "Consider the wave equation: \n\n$\\frac{\\partial^2u}{\\partial t^2} = k^2\\frac{\\partial^2 u}{\\partial x^2}$\n\nwhere $u(x,t)$ is the displacement of a string at position $x$ and time $t$, and $k$ is a constant representing the wave speed. \n\nSuppose that the string is fixed at both ends, i.e.... |
TIGER-Lab/MathInstruct_16657 | TIGER-Lab/MathInstruct | [
{
"content": "Consider the graph G shown below:\n\n```\n 1 - 2 - 3\n | | |\n 4 - 5 - 6\n```\n\nWhat is the clique number of G?",
"role": "user"
},
{
"content": "The clique number of a graph is the size of the largest complete subgraph (clique) in the graph. In the given graph G... |
TIGER-Lab/MathInstruct_22 | TIGER-Lab/MathInstruct | [
{
"content": "Let A = {1, 2, 3}, B = {2, 3, 4}, C = {3, 4, 5}, and D = {4, 5, 6}. Find the Cartesian product of (A Δ B) Δ C and A Δ (B Δ C) where Δ represents the symmetric difference operation. Show that the two sets are not equal.",
"role": "user"
},
{
"content": "First, let's find the symmetric d... |
TIGER-Lab/MathInstruct_5647 | TIGER-Lab/MathInstruct | [
{
"content": "Barbata invests $2600 in the National Bank at 5%. How much additional money must she invest at 8% so that the total annual income will be equal to 6% of her entire investment?\nAnswer Choices: (A) 1200 (B) 3000 (C) 1300 (D) 3600 (E) 2400",
"role": "user"
},
{
"content": "Let's think ab... |
TIGER-Lab/MathInstruct_12407 | TIGER-Lab/MathInstruct | [
{
"content": "If you select two cards from a pile of cards numbered 1 to 10, what is the probability that the sum of the numbers is more than 18?\nAnswer Choices: (A) 1/5 (B) 1/15 (C) 2/15 (D) 1/45 (E) 2/45",
"role": "user"
},
{
"content": "Let's reason about the multi-choice question.\nThe number o... |
TIGER-Lab/MathInstruct_10030 | TIGER-Lab/MathInstruct | [
{
"content": "Samuel is arranging his grandma’s teacups. They are stored in boxes and inside the boxes, they are stacked 5 rows high with 4 cups in each row. Of the 26 boxes in her attic, 6 of the boxes contain pans, half of the remaining boxes contain decorations, and the rest of the boxes contain her teacups.... |
TIGER-Lab/MathInstruct_17117 | TIGER-Lab/MathInstruct | [
{
"content": "Renaldo drove 15 kilometers. Ernesto drove 7 kilometers more than one-third of Renaldo's distance. How many kilometers did the 2 men drive in total? Let's program in Python in the response.",
"role": "user"
},
{
"content": "# define the distances driven by Renaldo and Ernesto\nRenaldo_... |
facebook/natural_reasoning_5353 | facebook/natural_reasoning | [
{
"content": "Consider a leader-election procedure where players generate random numbers from an arbitrary continuous distribution. The procedure starts with an infinite number of players, and those holding a record value stay in the game for the next round. Let T(M) be the number of rounds until only one playe... |
TIGER-Lab/MathInstruct_13095 | TIGER-Lab/MathInstruct | [
{
"content": "Mrs. Anderson bought 2 bags of 3-pound bag of cat food and another 2 bags of dog food that each weigh 2 more pounds than each bag of cat food. There are 16 ounces in each pound. How many ounces of pet food did Mrs. Anderson buy?",
"role": "user"
},
{
"content": "Each bag of cat food we... |
TIGER-Lab/MathInstruct_3354 | TIGER-Lab/MathInstruct | [
{
"content": "A circular park has a radius of 20 meters. Find the perimeter of a sector of the circle that has a central angle of 60 degrees.",
"role": "user"
},
{
"content": "To find the perimeter of a sector of a circle, we need to calculate the arc length of the sector and add it to the two radii... |
TIGER-Lab/MathInstruct_7820 | TIGER-Lab/MathInstruct | [
{
"content": "Siddharth wants to borrow Rs.6000 at rate of interest 6% p.a. at S.I and lend the same amount at C.I at same rate of interest for two years. What would be his income in the above transaction?\nAnswer Choices: (A) Rs.21.60 (B) Rs.24.00 (C) Rs.25.20 (D) Rs.27.80 (E) None of these",
"role": "user... |
facebook/natural_reasoning_1539 | facebook/natural_reasoning | [
{
"content": "What is the state of the universe during the inflationary period, specifically regarding the role of the inflaton field in transitioning from a high-entropy mix to an environment conducive to normal attractive gravity, and how does this period relate to the Big Bang in terms of timeline and physic... |
facebook/natural_reasoning_8418 | facebook/natural_reasoning | [
{
"content": "A block is sliding up a ramp with a coefficient of kinetic friction of 0.30. The ramp is inclined at an angle of θ to the horizontal, and the block has a mass of m. Find the work done on the block by the friction force as it slides up the ramp to the platform. Use the relevant equations and concep... |
TIGER-Lab/MathInstruct_21372 | TIGER-Lab/MathInstruct | [
{
"content": "There are 5 houses on a street, and each of the first four houses has 3 gnomes in the garden. If there are a total of 20 gnomes on the street, how many gnomes does the fifth house have?",
"role": "user"
},
{
"content": "In the first four houses, there are a total of 4 houses * 3 gnomes... |
facebook/natural_reasoning_9737 | facebook/natural_reasoning | [
{
"content": "Consider the equation $X = \\sqrt{n + {\\sqrt{n + {\\sqrt{n + {\\sqrt{n + {\\sqrt{n + ....}}}}}}}}}$. Derive a general solution for X in terms of n, and discuss the limitations and potential issues with the solution when n = 0.",
"role": "user"
},
{
"content": "## Step 1: Define the eq... |
tulu3_algebra_2649 | tulu3_algebra | [
{
"content": "A local chef is preparing traditional Japanese tea snacks for an upcoming event. The chef is planning to make two types of snacks: mochi and dorayaki. To maintain a balanced menu, the chef wants the number of mochi and dorayaki to satisfy certain conditions based on the event planner's requirement... |
facebook/natural_reasoning_9369 | facebook/natural_reasoning | [
{
"content": "Analyze the causes of King Duncan's death in Shakespeare's Macbeth, considering the roles of Lady Macbeth, Macbeth, and Duncan himself. How do the characters' actions and motivations contribute to the tragic outcome?",
"role": "user"
},
{
"content": "The death of King Duncan in Shakesp... |
TIGER-Lab/MathInstruct_14638 | TIGER-Lab/MathInstruct | [
{
"content": "Passage: In October 2002, bilateral and multilateral lenders led by the World Bank agreed to give Yemen a four-year economic support package worth US$2.3 billion, 20 percent in grants and 80 percent in concessional loans. This funding is almost eight times the amount of financial support Yemen rec... |
TIGER-Lab/MathInstruct_18247 | TIGER-Lab/MathInstruct | [
{
"content": "a group of workers had agreed on a very strange payment schedule . each of them would get $ 100 for every day that they had worked , but for every day they did not work will have to return $ 25 . after 30 days they realised they did not earn any money . how many days the workers did not work ? Let... |
TIGER-Lab/MathInstruct_17450 | TIGER-Lab/MathInstruct | [
{
"content": "Here is a question for a math student to solve related to non-convex optimization:\n\nA factory owner wants to determine the optimal mix of two products, X and Y, to produce given the following constraints:\n\n* The factory has a maximum of 500 hours for production.\n* Product X production require... |
TIGER-Lab/MathInstruct_557 | TIGER-Lab/MathInstruct | [
{
"content": "X can run a kilometer race in 4 1/2 min while Y can run same race in 5 min. How many meters start can X give Y in a kilometer race, so that the race mat end in a dead heat?\nAnswer Choices: (A) 50 m (B) 200 m (C) 150 m (D) 100 m (E) 250 m",
"role": "user"
},
{
"content": "D\n100 m\nX c... |
tulu3_code_2301 | tulu3_code | [
{
"content": "Write a python function to count the number of vowels in a given string. The input will be a single string consisting of lowercase and uppercase English letters. The function should return an integer representing the total number of vowels (a, e, i, o, u) present in both lowercase and uppercase fo... |
TIGER-Lab/MathInstruct_21637 | TIGER-Lab/MathInstruct | [
{
"content": "A cylindrical pipe of radius 0.2 meters with water flowing at 2 meters per second is subjected to a disturbance resulting in a pressure wave. If the wave's shape can be represented by a triangular pulse with a base of 1 second and a maximum height of 10, find the amplitude of the resulting wave in... |
facebook/natural_reasoning_11098 | facebook/natural_reasoning | [
{
"content": "Given a matrix Φ and its relation to the equation BA Φ SCz k = λ k BASCz k, where w k = SCz k, prove that λ k is an eigenvalue of Φ corresponding to the eigenvector w k. Show all steps and explain the significance of Φ being a diagonal matrix in this context.",
"role": "user"
},
{
"con... |
tulu3_code_181 | tulu3_code | [
{
"content": "Write a python function to help us organize our nostalgic shop's inventory by sorting the items based on their prices. We have a list of items, where each item is represented as a dictionary with keys \"name\" and \"price\". Our goal is to sort the items in ascending order based on their \"price\"... |
TIGER-Lab/MathInstruct_3589 | TIGER-Lab/MathInstruct | [
{
"content": "Consider the following two statements about abstract algebra. Statement 1 | The set of all permutations of a finite set forms a group under composition. Statement 2 | In a group, if the order of an element a is n, then a^n = e, where e is the identity element. Choose the correct option: Answer C... |
tulu3_algebra_1317 | tulu3_algebra | [
{
"content": "As a fan of Amy Grant and Michael W. Smith, you decide to create a music playlist that includes songs from both artists. You want to include Amy Grant's songs in such a way that the total duration of her songs is represented by the polynomial \\(2x^2 + 3x - 5\\) minutes. For Michael W. Smith's son... |
TIGER-Lab/MathInstruct_19400 | TIGER-Lab/MathInstruct | [
{
"content": "The radius of a wheel is 22.4 cm. What is the distance covered by the wheel in making 250 resolutions?\nAnswer Choices: (A) 352 m (B) 704 m (C) 454 m (D) 186 m (E) 176 m",
"role": "user"
},
{
"content": "Let's think about the multi-choice question.\nIn one resolution, the distance cove... |
TIGER-Lab/MathInstruct_7656 | TIGER-Lab/MathInstruct | [
{
"content": "If x and y are non-zero integers, and 64x^4 – 4y^4 = 8x^2 + 2y^2, which of the following could be the value of x2 in terms of y?\nAnswer Choices: (A) 2y^2 (B) 2y (C) 2y^2/8 (D) 2y^2-1/8 (E) 2y^2+1/8",
"role": "user"
},
{
"content": "Let's think about the multi-choice question step by s... |
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