Datasets:

nihalnayak
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tulu-3-sft-personas-math-warmup

id stringlengths 38 38	prompt stringlengths 242 2.61k	messages listlengths 2 2
personas_math_v7ovye0ap1qi5t0569h7iid7	Jakob Dorigoni, a renowned cyclist, is known for his ability to maintain a consistent power output during a race. Consider a race where Jakob is cycling on a circular track with a radius of 100 meters. His power output is modeled by the function \( P(t) = 200 + 50\sin(\frac{\pi t}{15}) \) watts, where \( t \) is the ti...	[ { "content": "Jakob Dorigoni, a renowned cyclist, is known for his ability to maintain a consistent power output during a race. Consider a race where Jakob is cycling on a circular track with a radius of 100 meters. His power output is modeled by the function \\( P(t) = 200 + 50\\sin(\\frac{\\pi t}{15}) \\) wat...
personas_math_jml2tsbnit8mdjd5yaa13za3	As a global economic analyst, you are tasked with evaluating the stability and growth potential of two emerging markets, Country A and Country B. You have access to the following data and models: 1. Inflation Differential Model: The inflation rate in Country A is given by \( I_A(t) = 3 + 0.5t \) (in percentage), a...	[ { "content": "As a global economic analyst, you are tasked with evaluating the stability and growth potential of two emerging markets, Country A and Country B. You have access to the following data and models:\n\n1. Inflation Differential Model: The inflation rate in Country A is given by \\( I_A(t) = 3 + 0...
personas_math_p74w44788lurshfd6xx1crmq	In the bustling environment of an emergency room (ER), a critical care nurse is tasked with optimizing the allocation of emergency medical resources to minimize patient wait times and ensure the most critical patients receive immediate care. The nurse uses advanced mathematical modeling to predict and manage patient fl...	[ { "content": "In the bustling environment of an emergency room (ER), a critical care nurse is tasked with optimizing the allocation of emergency medical resources to minimize patient wait times and ensure the most critical patients receive immediate care. The nurse uses advanced mathematical modeling to predict...
personas_math_1cbxufotufa3n6x45dxq6mj1	Dr. Emily, a trusted family therapist specializing in adolescent mental health, wants to analyze the correlation between the number of therapy sessions attended by adolescents and their improvement scores on a standardized mental health assessment. She gathers data from 50 adolescents who have attended her sessions ove...	[ { "content": "Dr. Emily, a trusted family therapist specializing in adolescent mental health, wants to analyze the correlation between the number of therapy sessions attended by adolescents and their improvement scores on a standardized mental health assessment. She gathers data from 50 adolescents who have att...
personas_math_4noo0ssafw7im446kizrgrh9	A tax consultant, named Sarah, is working on a complex tax case involving the optimization of tax liabilities for a multinational corporation. She seeks advice from her experienced friend, John, who suggests using advanced calculus and linear algebra to solve the problem. The corporation operates in three countries: A,...	[ { "content": "A tax consultant, named Sarah, is working on a complex tax case involving the optimization of tax liabilities for a multinational corporation. She seeks advice from her experienced friend, John, who suggests using advanced calculus and linear algebra to solve the problem. The corporation operates ...
personas_math_8h2dh0vm265exfgsmp0zn4og	A local taxi driver in Metepec frequently transports passengers to and from the Metepec railway station. On average, he completes 4 trips per hour to the railway station. The distance between the downtown area and the railway station is 10 kilometers. 1. Suppose the taxi driver modifies his route due to construction, ...	[ { "content": "A local taxi driver in Metepec frequently transports passengers to and from the Metepec railway station. On average, he completes 4 trips per hour to the railway station. The distance between the downtown area and the railway station is 10 kilometers.\n\n1. Suppose the taxi driver modifies his rou...
personas_math_tc73jnd1hjira71av7yg0k2t	Dr. Ellis is a psychology major conducting a study on the psychological effects of incarceration on inmates. She seeks to understand how the duration of incarceration affects inmates' levels of anxiety, which she measures using a standardized anxiety index. She gathers data from 100 inmates, recording their time spent ...	[ { "content": "Dr. Ellis is a psychology major conducting a study on the psychological effects of incarceration on inmates. She seeks to understand how the duration of incarceration affects inmates' levels of anxiety, which she measures using a standardized anxiety index. She gathers data from 100 inmates, recor...
personas_math_mmedwfncajb307n0mfzptevs	A cognitive neuroscientist is conducting a study on the effectiveness of two different psychological interventions, A and B, on improving motor skills in professional racing drivers. The study measures the drivers' improvement in lap times around a racetrack after participating in these interventions over a period of 8...	[ { "content": "A cognitive neuroscientist is conducting a study on the effectiveness of two different psychological interventions, A and B, on improving motor skills in professional racing drivers. The study measures the drivers' improvement in lap times around a racetrack after participating in these interventi...
personas_math_kc1yc0iu7lgexi3x8jwue1w3	As a die-hard basketball fan cheering for the rival team, the Bears, you are fascinated by the team's performance statistics and use them to predict future outcomes. The Bears' star player, Alex, has a free throw shooting percentage of 85%. In a crucial game, Alex is expected to take 10 free throw attempts. 1. Calcula...	[ { "content": "As a die-hard basketball fan cheering for the rival team, the Bears, you are fascinated by the team's performance statistics and use them to predict future outcomes. The Bears' star player, Alex, has a free throw shooting percentage of 85%. In a crucial game, Alex is expected to take 10 free throw...
personas_math_acoyq2sgd0v0vmq02siupiwc	An avid traveler visits various national parks and documents bird sightings during each trip. Suppose the traveler has visited \(n\) national parks, where \(n\) is a prime number. In each park \(i\) (for \(i = 1, 2, \ldots, n\)), they document \(a_i\) species of birds. 1. The total number of bird species documented f...	[ { "content": "An avid traveler visits various national parks and documents bird sightings during each trip. Suppose the traveler has visited \\(n\\) national parks, where \\(n\\) is a prime number. In each park \\(i\\) (for \\(i = 1, 2, \\ldots, n\\)), they document \\(a_i\\) species of birds. \n\n1. The total ...
personas_math_t1mhjak49znoxtvgdcnmancb	A librarian named Alex, who is curious about technology, decides to digitize a portion of the library's collection. They have a total of 1200 books in the library. After consulting with their tech-savvy family member, Alex learns that the digitization process can be modeled using an exponential function due to the incr...	[ { "content": "A librarian named Alex, who is curious about technology, decides to digitize a portion of the library's collection. They have a total of 1200 books in the library. After consulting with their tech-savvy family member, Alex learns that the digitization process can be modeled using an exponential fu...
personas_math_87p99ucjru5jp79mmox2bpma	Ali is an enthusiastic fan of stand-up comedy who is originally from Iran. He decides to create a unique comedy show that will combine his love for humor with his mathematical prowess. Ali plans to structure his show in two parts: 1. Comedy Timing Calculation: Ali wants to ensure his jokes land perfectly. He de...	[ { "content": "Ali is an enthusiastic fan of stand-up comedy who is originally from Iran. He decides to create a unique comedy show that will combine his love for humor with his mathematical prowess. Ali plans to structure his show in two parts:\n\n1. Comedy Timing Calculation:\n Ali wants to ensure his jo...
personas_math_e2gzcbys42gsyi53i2wgvfsi	As a passionate community organizer in Ossett, you are planning a series of community events to boost local engagement. You have collected data on the participation rates and the resources needed for different types of events over the past year. 1. Each event type \( E_i \) (where \( i = 1, 2, \ldots, n \)) has a part...	[ { "content": "As a passionate community organizer in Ossett, you are planning a series of community events to boost local engagement. You have collected data on the participation rates and the resources needed for different types of events over the past year.\n\n1. Each event type \\( E_i \\) (where \\( i = 1, ...
personas_math_yq1qqp1e0gbqnn1ej3vg04yc	A science fair competitor is developing an AI-based solution for waste management. The AI system uses a neural network to predict the optimal distribution of waste bins in a city to minimize the total waste collection time. The city can be represented as a grid of \( n \times n \) blocks, each block having a certain am...	[ { "content": "A science fair competitor is developing an AI-based solution for waste management. The AI system uses a neural network to predict the optimal distribution of waste bins in a city to minimize the total waste collection time. The city can be represented as a grid of \\( n \\times n \\) blocks, each ...
personas_math_vmhu8rbtp8ffx45s0z4onzxq	An entomologist is conducting a study to evaluate the effectiveness of insecticide-treated nets (ITNs) in reducing the incidence of malaria in a specific region. The study involves two villages: Village A, where ITNs have been distributed to all households, and Village B, where no ITNs have been distributed. The study ...	[ { "content": "An entomologist is conducting a study to evaluate the effectiveness of insecticide-treated nets (ITNs) in reducing the incidence of malaria in a specific region. The study involves two villages: Village A, where ITNs have been distributed to all households, and Village B, where no ITNs have been d...
personas_math_62rh6ujauy05nth32mjt21ek	A doctoral candidate is examining the evolution of warfare tools and techniques over several centuries. They have gathered data on the effectiveness of various tools measured by their impact factor, which is a function of technology level (T) and tactical deployment efficiency (E). The impact factor I(T, E) is given by...	[ { "content": "A doctoral candidate is examining the evolution of warfare tools and techniques over several centuries. They have gathered data on the effectiveness of various tools measured by their impact factor, which is a function of technology level (T) and tactical deployment efficiency (E). The impact fact...
personas_math_2rlji07fvxktfgkn1rlf2gkx	A sociologist who values open access to research is studying the impact of paywalls on the dissemination of research articles across various academic journals. Assume there are \( n \) journals in a particular field, and each journal has a different probability \( p_i \) (where \( 0 < p_i < 1 \) for \( i = 1, 2, \ldots...	[ { "content": "A sociologist who values open access to research is studying the impact of paywalls on the dissemination of research articles across various academic journals. Assume there are \\( n \\) journals in a particular field, and each journal has a different probability \\( p_i \\) (where \\( 0 < p_i < 1...
personas_math_tmvbdztpno28pdularjf1312	A busy professional, Alex, is responsible for coordinating and organizing their mother’s medical appointments and medication schedule. Alex's mother has three different medications (A, B, and C) that need to be taken at specific intervals, and she has three different medical appointments with different doctors that occ...	[ { "content": "A busy professional, Alex, is responsible for coordinating and organizing their mother’s medical appointments and medication schedule. Alex's mother has three different medications (A, B, and C) that need to be taken at specific intervals, and she has three different medical appointments with diff...
personas_math_g62grelqr5rc8jdrmrrfabg7	An American e-commerce expert has started a tech company in China. To maximize the efficiency of his logistics network, he is analyzing the delivery times between various distribution centers. Assume the delivery times between any two centers follow a normal distribution with means and standard deviations that depend o...	[ { "content": "An American e-commerce expert has started a tech company in China. To maximize the efficiency of his logistics network, he is analyzing the delivery times between various distribution centers. Assume the delivery times between any two centers follow a normal distribution with means and standard de...
personas_math_wq7to9uckvrnr5w23825ke3u	An aerospace engineer-turned-newspaper editor is designing a special edition that will feature articles on aerodynamics and space exploration. As part of the layout, the editor must determine the optimal spacing and dimensions for a series of infographics. The infographics will include a visual representation of the dr...	[ { "content": "An aerospace engineer-turned-newspaper editor is designing a special edition that will feature articles on aerodynamics and space exploration. As part of the layout, the editor must determine the optimal spacing and dimensions for a series of infographics. The infographics will include a visual re...
personas_math_zibnjoudes147pqftcua545p	John owns a small café in a local community where a significant portion of the population works in the defense industry. His monthly revenue is indirectly influenced by the number of defense contracts awarded to companies in the area. Suppose the number of defense contracts awarded in a month follows a Poisson distribu...	[ { "content": "John owns a small café in a local community where a significant portion of the population works in the defense industry. His monthly revenue is indirectly influenced by the number of defense contracts awarded to companies in the area. Suppose the number of defense contracts awarded in a month foll...
personas_math_l9eoh8t4z6syc34dvr29g78p	A renowned reporter specializing in global affairs is planning to interview a professor who is a leading expert in summit diplomacy. The professor is available for an interview only between 9:00 AM and 5:00 PM on a specific day before the summit begins. The reporter's schedule is packed with other assignments and meeti...	[ { "content": "A renowned reporter specializing in global affairs is planning to interview a professor who is a leading expert in summit diplomacy. The professor is available for an interview only between 9:00 AM and 5:00 PM on a specific day before the summit begins. The reporter's schedule is packed with other...
personas_math_ad3sa4u5gx17c3hlz8rfmulo	A glassblower specializing in intricate glassware inspired by the region's heritage decides to create a collection of vases. Each vase is designed to mimic the shape of a traditional amphora, with a unique pattern of spirals that represent the region's ancient art. 1. The surface of each vase is covered with a spiral ...	[ { "content": "A glassblower specializing in intricate glassware inspired by the region's heritage decides to create a collection of vases. Each vase is designed to mimic the shape of a traditional amphora, with a unique pattern of spirals that represent the region's ancient art.\n\n1. The surface of each vase i...
personas_math_fvuct4g1u78sy5xyfskz12na	A patent attorney is working with a technical illustrator to prepare a detailed drawing of a new mechanical device for a patent application. The device consists of two interlocking gears, Gear A and Gear B, which need to be accurately represented to ensure the patent's validity. Gear A has a radius of \( r_A \) and Ge...	[ { "content": "A patent attorney is working with a technical illustrator to prepare a detailed drawing of a new mechanical device for a patent application. The device consists of two interlocking gears, Gear A and Gear B, which need to be accurately represented to ensure the patent's validity.\n\nGear A has a ra...
personas_math_e49ipxkqwddn2thf52pdzpfi	Commander Jane is a high-ranking officer in the United States Coast Guard, responsible for overseeing a fleet of patrol boats along a 300-mile coastline. The coastline has several key points of interest (A, B, C, D, and E) where patrolling is critical due to high traffic and security concerns. The distance (in miles) b...	[ { "content": "Commander Jane is a high-ranking officer in the United States Coast Guard, responsible for overseeing a fleet of patrol boats along a 300-mile coastline. The coastline has several key points of interest (A, B, C, D, and E) where patrolling is critical due to high traffic and security concerns. The...
personas_math_pqhaqgxh3yfvfznqdv7sfxmt	A concierge onboard a luxury cruise ship is responsible for managing the needs of a group of high-profile travelers. One of the main tasks is to ensure that the dining experience meets the expectations of all guests, which involves not only seating arrangements but also the coordination of special dietary requirements....	[ { "content": "A concierge onboard a luxury cruise ship is responsible for managing the needs of a group of high-profile travelers. One of the main tasks is to ensure that the dining experience meets the expectations of all guests, which involves not only seating arrangements but also the coordination of special...
personas_math_36qk72s6yu5zl2x2y9yh6k8f	A college student studying child development and aspiring to become a recreational therapist is designing a program for children with special needs. She wants to create a schedule that maximizes the effectiveness of their recreational therapy sessions based on a series of observations and data she collected over a 6-mo...	[ { "content": "A college student studying child development and aspiring to become a recreational therapist is designing a program for children with special needs. She wants to create a schedule that maximizes the effectiveness of their recreational therapy sessions based on a series of observations and data she...
personas_math_uox4bavkchjanw9ex0doy3dt	As a detail-oriented producer-in-training, you are tasked with organizing a film production schedule. The charismatic producer you support has a tight calendar, and it's your job to optimize the shooting sequence to minimize downtime and ensure efficient transitions between scenes. 1. The film consists of 5 scenes, ea...	[ { "content": "As a detail-oriented producer-in-training, you are tasked with organizing a film production schedule. The charismatic producer you support has a tight calendar, and it's your job to optimize the shooting sequence to minimize downtime and ensure efficient transitions between scenes.\n\n1. The film ...
personas_math_t2utnaqx3k3ubezfrlxcz2gs	As a 3D graphic designer who frequently shares tips and tricks on a specialized Mathematica forum, you often work with complex transformations and optimizations in 3D space. Consider the following advanced problem: 1. Surface Parametrization and Area Calculation: You are given a parametric surface in 3D space d...	[ { "content": "As a 3D graphic designer who frequently shares tips and tricks on a specialized Mathematica forum, you often work with complex transformations and optimizations in 3D space. Consider the following advanced problem:\n\n1. Surface Parametrization and Area Calculation:\n You are given a paramet...
personas_math_nuawydhzug01ocerio6d2b98	Dr. Smith, an ex-pat doctor, collaborates with local doctors in various countries to provide medical care to diverse populations. In one of the countries, the population demographics are modeled by a function \( P(t) \), where \( t \) represents time in years and \( P(t) \) gives the population size. The local doctor...	[ { "content": "Dr. Smith, an ex-pat doctor, collaborates with local doctors in various countries to provide medical care to diverse populations. In one of the countries, the population demographics are modeled by a function \\( P(t) \\), where \\( t \\) represents time in years and \\( P(t) \\) gives the populat...
personas_math_aby82glcuior5zfb4hjiilua	A data scientist is analyzing transportation data to optimize routes for autonomous vehicles in a densely populated urban area. The city can be represented as a directed graph \( G = (V, E) \), where \( V \) is the set of intersections and \( E \) is the set of roads connecting these intersections. Each edge \( e \in E...	[ { "content": "A data scientist is analyzing transportation data to optimize routes for autonomous vehicles in a densely populated urban area. The city can be represented as a directed graph \\( G = (V, E) \\), where \\( V \\) is the set of intersections and \\( E \\) is the set of roads connecting these interse...
personas_math_k66k79jdj61qxr8t5lrqxu75	As a proud resident of Sholakkorgan, you decide to highlight the unique aspects of your hometown through a mathematical challenge. Sholakkorgan is famous for its beautifully intricate tiling patterns, which are designed using advanced geometric principles. 1. Sholakkorgan's central plaza is tiled with a unique patter...	[ { "content": "As a proud resident of Sholakkorgan, you decide to highlight the unique aspects of your hometown through a mathematical challenge. Sholakkorgan is famous for its beautifully intricate tiling patterns, which are designed using advanced geometric principles. \n\n1. Sholakkorgan's central plaza is ti...
personas_math_cpiys40njmh702mi5zu873k0	A disability inclusion specialist collaborates with the HR manager to implement accessibility initiatives across a company with 300 employees. They have identified two major initiatives to be implemented: Initiative A (upgrading physical accessibility features) and Initiative B (implementing digital accessibility tools...	[ { "content": "A disability inclusion specialist collaborates with the HR manager to implement accessibility initiatives across a company with 300 employees. They have identified two major initiatives to be implemented: Initiative A (upgrading physical accessibility features) and Initiative B (implementing digit...
personas_math_jy7nhft909sz4fpuizw6knwf	An art gallery owner is curating an exclusive exhibition featuring works from a network of 10 renowned artists. Each artist contributes a unique piece to the exhibition. The gallery owner decides to arrange the paintings in a linear sequence on a wall. However, the gallery owner has a rule: two specific artists, Artist...	[ { "content": "An art gallery owner is curating an exclusive exhibition featuring works from a network of 10 renowned artists. Each artist contributes a unique piece to the exhibition. The gallery owner decides to arrange the paintings in a linear sequence on a wall. However, the gallery owner has a rule: two sp...