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[
{
"content": "When the temperature of a reaction system is increased by \\( 10^\\circ\\text{C} \\) (from \\( 25^\\circ\\text{C} \\text{ to } 35^\\circ\\text{C} \\)), at constant volume, the reaction rate doubles. It is due to\\n\\n(a) The total number of collisions between reacting molecules increases nearly by... |
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{
"content": "Find the number of solutions to the system of equations:\n\n$$\\left\\{ \\begin{aligned} x^2 + y^2 &= 25 \\\\ \\sqrt{x^2 + y^2 + 2xy} - \\sqrt{x^2 + y^2 - 2xy} &= 4 \\end{aligned}\\right.$$",
"role": "user"
},
{
"content": "<think> Okay, so I need to find the number of solutions to thi... |
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{
"content": "You will be given a definition of a task first, then some input of the task.\nIn this task, you're given four sentences of a story written in natural language. The given story is not complete and your job is to complete the story by selecting one of the end sentence choices from (A) and (B), such ... |
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{
"content": "You are given t test cases. For each test case you know the number of athletes n and their strengths s1 , s2 , … , sn (not necessarily distinct).\n\nYou must divide the athletes of each test case into two non-empty teams A and B so that the absolute difference between the strongest athlete in team... |
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{
"content": "A person starting with $$64$ and making $6$ bets, wins three times and loses three times, \nthe wins and losses occurring in random order. The chance for a win is equal to the chance for a loss. \nIf each wager is for half the money remaining at the time of the bet, then the final result is:\n$\\t... |
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{
"content": "You are given a list of dictionaries, where each dictionary represents a city in Spain with its name, population, area, and a boolean indicating whether it is a political and administrative center. Write a function called `city_directory` that takes this list of cities as input and returns a list ... |
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"content": "Write a program that reads a list of integers from standard input (all integers are space-separated on a single line). The program should print the index of the first occurrence of the number 42 in the list. If 42 does not occur in the list, print -1.\n\nInput Format:\nA single line containing spa... |
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"content": "15. A nuclear explosion has taken place leading to increase in concentration of \\( \\text{C}^{14} \\) in nearby areas. \\( \\text{C}^{14} \\) concentration is \\( C_1 \\) in nearby areas and \\( C_2 \\) in areas far away. If the age of the fossil is determined to be \\( T_1 \\) and \\( T_2 \\) at... |
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{
"content": "Radioisotopes and Cancer Detection. A radioisotope commonly used in the detection of breast cancer is technetium-99m. This radionuclide is attached to a chemical that upon injection into a patient accumulates at cancer sites. The isotope's radiation is then detected and the site located, using gam... |
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{
"content": "Given two matrices A and B with integer elements, output their matrix product if they are compatible for multiplication. The first line of input contains two integers n and m, the dimensions of matrix A (n rows and m columns). The next n lines each contain m integers, representing the rows of matr... |
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{
"content": "Write a three-sentence social media post recommending a Kyoto tea ceremony experience for travelers. The first word of your response should be \"Immerse\". Use exactly 40 words in total.",
"role": "user"
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"content": "<think>\nOkay, the user wants a three-sentence social media post ... |
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"content": "Let $A_0=(0,0)$. Distinct points $A_1,A_2,\\dots$ lie on the $x$-axis, and distinct points $B_1,B_2,\\dots$ lie on the graph of $y=\\sqrt{x}$. For every positive integer $n,\\ A_{n-1}B_nA_n$ is an equilateral triangle. What is the least $n$ for which the length $A_0A_n\\geq100$?\n$\\textbf{(A)}\\ ... |
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{
"content": "Write a program that determines if a given element b is present in a list a.\n\nInput:\n- The first line contains a space-separated list of elements (integers).\n- The second line contains the target element b (integer).\n\nOutput:\n- Output 'True' if b is in the list a, otherwise output 'False'.\... |
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{
"content": "In triangle $ABC$, $A'$, $B'$, and $C'$ are on the sides $BC$, $AC$, and $AB$, respectively. Given that $AA'$, $BB'$, and $CC'$ are concurrent at the point $O$, and that $\\frac{AO}{OA'}+\\frac{BO}{OB'}+\\frac{CO}{OC'}=92$, find $\\frac{AO}{OA'}\\cdot \\frac{BO}{OB'}\\cdot \\frac{CO}{OC'}$.\n",
... |
[
{
"content": "Let $F(x)$ be a rational function such that\n$F(-x)+\\dfrac{F(x)}{x}=x^2$ for all $x\\neq 0$. Determine $F(4)$.",
"role": "user"
},
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"content": "<think> Okay, so I need to find F(4) where F(x) is a rational function that satisfies the equation F(-x) + F(x)/x = x² for all x ≠ 0. Hmm, r... |
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{
"content": "The reaction below reaches equilibrium in a closed reaction vessel. C6H12O6(S) ⇌ 2 C2H5OH(I) + 2 CO2(g), ΔΗ° = −72 kJ. Which of the following actions causes an increase in the value of Ko? (i) adding some CO2(g) (ii) transferring the reaction mixture to a vessel of larger volume (iii) increasing t... |
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{
"content": "Write a three-sentence description of how to make chicken and dumplings in the style of the Midwest. Your response should be entirely in English, may not repeat any word throughout the description, and each sentence must end with one of these words in order: farmers, tradition, warmth.",
"role... |
[
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"content": "Show that the rotational level with the highest population is given by \\[ J_{\\text{max(pop)}} = \\frac{\\sqrt{I_0 kT}}{\\hbar} - \\frac{1}{2} \\]",
"role": "user"
},
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"content": "<think> Okay, so I need to figure out how to show that the rotational level with the highest population... |
[
{
"content": "Given a list of pairs of integers, implement a function that returns a list containing the products of each pair. Each pair is represented as a tuple (a, b). The input list will contain at least one pair, and the product should be calculated as a * b for each pair.\n\nWrite a function `calculate_p... |
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{
"content": "Conformational factors and the strain energy in forming the bridgehead alkene manifests itself in the vigorous conditions that are frequently required if such Diels-Alder reactions are carried out under thermal conditions; in many cases, however, reactions catalysed by Lewis acids can be effected ... |
[
{
"content": "When ethyl acetate in dilute aqueous solution is heated in the presence of a small amount of acid, it decomposes according to the equation\\n\\n\\[\\n\\text{CH}_3\\text{COOC}_2\\text{H}_5 + \\text{H}_2\\text{O} \\rightarrow \\text{CH}_3\\text{COOH} + \\text{C}_2\\text{H}_5\\text{OH}\\n\\]\\n\\n(Et... |
[
{
"content": "You are tasked with creating a function that simulates stopping a remote service in a system. The function should take a string representing the service name and return a message indicating whether the service has been successfully stopped or if it was not found. The function should handle the fol... |
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{
"content": "Write a program that reads a single line of text from standard input. The input string may contain multiple spaces between integers, as well as leading or trailing spaces. Parse the integers from the input string and insert them one by one into a sorted list. Use a binary search algorithm to deter... |
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{
"content": "One chair conformer of trans-1,2-dimethylcyclohexane has both substituents in equatorial positions, so it does not have any 1,3-diaxial interactions. The strain energy for this conformer is 0.87 kcal/mol due to the gauche interaction between the two methyl substituents. The other chair conformer h... |
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{
"content": "(a) Would you expect the “tug” on the electrons to be equal and offset? ______\\n(b) Would NH\\(_3\\) be a polar or nonpolar molecule? ______",
"role": "user"
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"content": "<think> Okay, so I have two questions here about whether the tug on electrons in NH3 is equal and offset and w... |
[
{
"content": "Determine the value of $c$ for which the polynomial $x^4-2x^3+cx^2-2x+1$ has exactly three distinct real roots.",
"role": "user"
},
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"content": "<think> Alright, so I have this polynomial: \\( x^4 - 2x^3 + c x^2 - 2x + 1 \\), and I need to find the value of \\( c \\) such that it has ... |
[
{
"content": "A triangle is inscribed in a circle. The vertices of the triangle divide the circle into three arcs of lengths 3, 4, and 5. What is the area of the triangle?\n$\\mathrm{(A) \\ 6 } \\qquad \\mathrm{(B) \\frac{18}{\\pi^2} } \\qquad \\mathrm{(C) \\frac{9}{\\pi^2}(\\sqrt{3}-1) } \\qquad \\mathrm{(D) \... |
[
{
"content": "You are tasked with creating a Python function that processes a list of GitHub repository information and returns a sorted list of repositories based on their star count. Each repository is represented as a dictionary with keys 'filename' and 'gh_stars'. The 'filename' key holds the file path of t... |
[
{
"content": "Let $a,b,c$ be complex numbers such that\n\\begin{align*}\n|a|&=|b|=|c|,\\\\\nb&=\\frac{c+1}{c-1},\\\\\nc&=\\frac{a+1}{a-1}.\n\\end{align*}\nFind $|a+b+c|$.",
"role": "user"
},
{
"content": "<think> Okay, let's try to tackle this problem. It's about complex numbers with some conditions... |
[
{
"content": "You are given a list of switch objects, where each switch object contains a list of interfaces. Your task is to implement a function that calculates the total number of switches and the total number of interfaces across all switches. You need to return the results as a tuple containing the total n... |
[
{
"content": "In Lisbon, which of the following neighborhoods is most renowned for its hidden art galleries and quiet local culture that solo travelers like Ketan enjoy? Please answer using one of these options: ('Alfama', 'Bairro Alto', 'Belém', 'Parque das Nações'). Your response should be exactly two sentenc... |
[
{
"content": "q: 10 men and 15 women together can complete a work in 7 days. It takes 100 days for one man alone to complete the same work. How many days will be required for one woman alone to complete the same work?\nOptions:\n(A) 127 days\n(B) 667 days\n(C) 177 days\n(D) 187 days\n(E) 350 days\na: Stream of ... |
[
{
"content": "Given the equation $x^2\\sqrt[3]{x} - 3x^2 + 2x\\sqrt[3]{x} - 5 = 0,$ where all roots are real and nonnegative, find the product of the roots.",
"role": "user"
},
{
"content": "<think> Okay, so I need to find the product of the roots for this equation: \\(x^2\\sqrt[3]{x} - 3x^2 + 2x\\s... |
[
{
"content": "The electrolysis of cold sodium chloride solution produces sodium hypochlorite by reacting \\(\\text{NaOH and Cl}_2\\) thoroughly. How long (in days) will a cell operate to produce 10 L of 7.45% (by mass) solution of \\(\\text{NaClO}\\) if the cell current is 2.5 A? Assume that the density of solu... |
[
{
"content": "Let $g_0(x)=\\frac{1}{x+1}-\\frac{1}{x-1}$, and for $n\\geq 1$, let $g_n(x)=\\frac{g_{n-1}(x)}{g_{n-1}(x)+1}$. For how many values of $x$ is $g_{100}(x)=1$?",
"role": "user"
},
{
"content": "<think> Okay, so I have this problem here where I need to find how many values of x make g₁₀₀(x... |
[
{
"content": "Heat of solutions of 1 mole of KCl in 200 moles of water under 1 atm pressure is 4339 cal at 21°C and 4260 cal at 23°C. Determine the heat of solution at 25°C. What are the assumptions needed?",
"role": "user"
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{
"content": "<think> Okay, so I need to figure out the heat of solution ... |
[
{
"content": "Let $x,$ $y,$ and $z$ be three distinct complex numbers that satisfy the equation\n\n$$x^3 - x^2y - x^2z + xyz = y^3 - y^2x - y^2z + xyz = z^3 - z^2x - z^2y + xyz.$$Find $x + y + z$.",
"role": "user"
},
{
"content": "<think> Okay, so we have three distinct complex numbers x, y, and z t... |
[
{
"content": "When 1 mole of a strong acid is completely neutralized by 1 mole of a strong base, the theoretical amount of energy released is 57.3 kJ mol¹. If 1 L of 1 M ethanoic acid is reacted with 1 L of 1 M NaOH (aq), what is a plausible enthalpy of neutralization? \n(A). 0 kJ mol¹ \n(B). - 57.3 kJ mol¹ ... |
[
{
"content": "Factor the polynomial\n\\[x^6 + 2x^4 + 4x^2 + 8\\]\ninto the product of two monic non-constant polynomials with integer coefficients.\nDetermine $p(-1) \\cdot q(-1),$ where $p(x)$ and $q(x)$ are the resulting polynomials.",
"role": "user"
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{
"content": "<think> Okay, so I need to fac... |
[
{
"content": "Write a Python program that defines a class called Vector. The class should be initialized with a list of integers. Implement a method printVector in the Vector class that prints each element in the vector separated by a space, followed by a newline at the end. \n\nThe program should read a single... |
[
{
"content": "Find the smallest positive real number $c,$ such that for all nonnegative real numbers $x$ and $y,$\n\\[\\sqrt{xy} + c |x - y| \\ge \\frac{x + y}{2}.\\]",
"role": "user"
},
{
"content": "<think> Okay, so I have this problem here: Find the smallest positive real number \\( c \\), such t... |
[
{
"content": "For example, trans-1,2-dichlorocyclohexane has diaxial and diequatorial chair forms. The diaxial conformer should be less stable because it has two sets of 1,3 diaxial interactions between the chlorines and the axial protons. Knowing the equatorial-axial preference for a single chlorine substituen... |
[
{
"content": "Given a Python list of numbers, write a program that reads a list of integers from standard input (all on one line, space separated), computes the square of each integer using a list comprehension, and prints the resulting list. The output should be the list of squared numbers in Python list liter... |
[
{
"content": "The NMR spectrum of isopropyl chloride illustrates the appearance of an isopropyl group. The signal for the six equivalent methyl protons at 8 1.5 ppm is split into a doublet by the proton of the H-C-Cl unit. In turn, the H-C-Cl proton signal at 8 4.2 ppm is split into a septet by the six methyl p... |
[
{
"content": "Suggest 3 PLANT-BASED RECIPES THAT PUT A MODERN TWIST ON SOUTHERN COMFORT FOOD, AND PRESENT THEM IN THE FORMAT OF TITLES ONLY, IN ENGLISH AND CAPITAL LETTERS.",
"role": "user"
},
{
"content": "<think>\nOkay, the user wants three plant-based recipes that modernize Southern comfort food.... |
[
{
"content": "Which is the most stable arrangement of double bonds in an alkadiene—isolated, conjugated, or cumulated? As we saw in Chapter 6, the stabilities of alkenes may be assessed by comparing their heats of hydrogenation. The measured heat of hydrogenation of the two double bonds in 1,4-pentadiene is 252... |
[
{
"content": "question: A Train requires 10 seconds to pass a pole while it requires 35 seconds to cross a stationary train which is 500 mtrs long. Find the speed of the train.\nOptions:\n(A) 68 kmph\n(B) 70 kmph\n(C) 72 kmph\n(D) 60 kmph\n(E) 50 kmph\nanswer: Stream of consciousness: In 10s the train crosses t... |
[
{
"content": "Provide a detailed overview of the ancient city of [Petra], focusing on its [Nabataean] origins and the engineering techniques used to carve its structures. Your response must include the keywords: [city], [rose-red], and [trade]. Start and end your reply with the word [history], and be sure to pl... |
[
{
"content": "Dibutylphthalate is often used as a manometer fluid. It has a density of 1.047 g/ml. How many torrs are represented by 1 mm of this fluid?\\n - (a) 0.077 torr\\n - (b) 1 torr\\n - (c) 12.98 torr\\n - (d) 760 torr",
"role": "user"
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{
"content": "<think> Okay, so I need to figu... |
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{
"content": "Instructions: In this task, you are given a context, a subject, a relation, and many options. Based on the context, from the options select the object entity that has the given relation with the subject. Answer with text (not indexes).\nInput: Context: Mott the Hoople were an English rock band wit... |
[
{
"content": "Let $g(x) = \\frac{2 - x}{1 + 2x}, g_1(x) = g(g(x)), g_2(x) = g(g_1(x)),$ and in general $g_n(x) = g(g_{n-1}(x)),$ then $g_{2024}(2)=$",
"role": "user"
},
{
"content": "<think> Okay, let's see. I need to find g_{2024}(2), where g(x) is defined as (2 - x)/(1 + 2x). Hmm, and each subsequ... |
[
{
"content": "An art collector named Alex loves purchasing art online due to its convenience. Last month, Alex bought 3 paintings from an online gallery, each costing $150. This month, Alex decided to buy 4 more paintings from a different online platform, each priced at $125. However, Alex received a 10% discou... |
[
{
"content": "Let $g$ be a function taking the positive real numbers to the positive real numbers such that\n\\[g(mn) + g(m + n) = g(m)g(n) - g(m) - g(n) + 2\\]\nfor all positive real numbers $m$ and $n.$\n\nLet $p$ be the maximum possible value of $g(1),$ and let $q$ be the minimum possible value of $g(1).$ F... |
[
{
"content": "Let $r$, $s$, and $t$ be the roots of the equation $8x^3+1001x+2008=0$. Find $\\frac{r}{t}+\\frac{t}{r}+\\frac{r}{s}+\\frac{s}{r}+\\frac{s}{t}+\\frac{t}{s}$.",
"role": "user"
},
{
"content": "<think> Okay, so I need to find the value of the expression \\(\\frac{r}{t} + \\frac{t}{r} + \... |
[
{
"content": "You are given two lists of integers, a and b, of the same length. Your task is to write a program that reads two lists from standard input and outputs a new list where each element is the sum of the corresponding elements from a and b.\n\nInput:\n- The first line contains n, the number of elements... |
[
{
"content": "List three Impressionist painters with each name starting with a Capital letter and with no comma separating the names.",
"role": "user"
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{
"content": "<think>\nOkay, the user wants three Impressionist painters, each name starting with a capital letter, and no commas separating them.... |
[
{
"content": "A triangle is inscribed in a circle. The vertices of the triangle divide the circle into three arcs of lengths 3, 4, and 5. What is the area of the triangle?\n$\\mathrm{(A) \\ 6 } \\qquad \\mathrm{(B) \\frac{18}{\\pi^2} } \\qquad \\mathrm{(C) \\frac{9}{\\pi^2}(\\sqrt{3}-1) } \\qquad \\mathrm{(D) \... |
[
{
"content": "Choose one from options: Which of the following tool names does not contain the word \"wrench\"? Your answer should use no comma and must exclude any words related to electronics. Options: adjustable wrench, torque wrench, hammer, pipe wrench.",
"role": "user"
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{
"content": "<think>\... |
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"content": "A gaseous alkane is exploded with oxygen. The volume of O2 for complete combustion to the volume of CO2 formed is in 7:4 ratio. The molecular formula of alkane is\\n(a) CH4\\n(b) C3H8\\n(c) C2H6\\n(d) C4H10",
"role": "user"
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{
"content": "<think> Okay, let's tackle this problem step ... |
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{
"content": "Write three lines of lyrics inspired by Bob Dylan and Bruce Springsteen in the style of a folk song. Do not use any commas and make sure your first line starts with the word 'Strumming'. Your response should be exactly three sentences long.",
"role": "user"
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"content": "<think>\nOk... |
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{
"content": "Using your experience mentoring STEM students, create an example explanation of Newton’s Third Law designed for a middle school audience. \nConstraints: \n1. Your response must be in JSON format. \n2. Your explanation should be exactly 5 sentences long. \n3. The total word count should not exc... |
[
{
"content": "You are tasked with creating a function that calculates the product of a given list of floating-point numbers. The function should take a variable number of arguments, each representing a float, and return their product. If no arguments are provided, the function should return 1.0, as the product ... |
[
{
"content": "You are tasked with implementing a function that initializes an aggregator with specific attributes and returns a dictionary representation of the aggregator. The function should take the following parameters: `aggregation_scheme` (a string representing the aggregation scheme), `initialization_upd... |
[
{
"content": "Hello The last word of your response should be the word street. Your entire response should be in English, and in all lowercase letters. No capital letters are allowed.",
"role": "user"
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{
"content": "<think>Okay, the user wants me to end my response with the word \"street\" and use ... |
[
{
"content": "Write a concise, two-paragraph analysis comparing the benefits and drawbacks of project-based learning in middle school classrooms. Format your response as valid JSON. Choose one of the following perspectives: (A) Impact on student collaboration, (B) Impact on teacher workload, or (C) Impact on cu... |
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{
"content": "What is the minimum distribution ratio if 99% of the solute in a 50.0-mL sample is extracted using a single 50.0-mL portion of an organic solvent? Repeat for the case where two 25.0-mL portions of the organic solvent are used.",
"role": "user"
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{
"content": "<think> Okay, let's tackl... |
[
{
"content": "A region $R$ in the complex plane is defined by \\begin{align*}\nR = \\{x + iy: - 2\\le x\\le2, - 2\\le y\\le2\\}.\n\\end{align*}A complex number $z = x + iy$ is chosen uniformly at random from $R$. What is the probability that $\\left(\\frac56 + \\frac56i\\right)z$ is also in $R$?",
"role": "... |
[
{
"content": "Write a program that reads an integer n from standard input and prints the factorial of n. If n is negative, the program should print -1. For non-negative n, the program should print n! (the factorial of n), where 0! = 1.\n\nInput:\nA single integer n.\n\nOutput:\nPrint the factorial of n, or -1 i... |
[
{
"content": "The dye acriflavine when dissolved in water has its maximum light absorption at \\( 4530 \\, \\text{Å} \\) and has maximum florescence emission at \\( 5080 \\, \\text{Å} \\). The number of fluorescence quanta is about 53% of the number of quanta absorbed. What percentage of absorbed light energy i... |
[
{
"content": "You are tasked with creating a function that simulates a simple argument passing mechanism. The function should modify a global variable and return its value. Implement a function `modify_argument(new_value)` that takes an integer `new_value` as input and sets a global variable `argument` to this ... |
[
{
"content": "You are given a list of integers and an integer element. Write a function `extract_element_from_list(lst: List[int], el: int) -> List[List[int]]` that extracts all occurrences of the specified element from the list and returns a new list containing two sublists: the first sublist should contain al... |
[
{
"content": "Let $p_1,$ $p_2,$ $p_3,$ $p_4,$ $p_5$ be the roots of the polynomial $h(x) = x^5 - 2x^2 + 1,$ and let $k(x) = x^3 + 3.$ Find\n\\[k(p_1) k(p_2) k(p_3) k(p_4) k(p_5).\\]",
"role": "user"
},
{
"content": "<think> Okay, so I have this problem here: given the polynomial h(x) = x⁵ - 2x² + 1... |
[
{
"content": "The sequence $b_1,$ $b_2,$ $b_3,$ $\\dots$ satisfies $b_1 = 15,$ $b_8 = 60,$ and for all $n \\ge 3,$ $b_n$ is the geometric mean of the first $n - 1$ terms. Find $b_2.$",
"role": "user"
},
{
"content": "<think> Okay, let me try to solve this problem. It says we have a sequence \\( b_1... |
[
{
"content": "A coin is altered so that the probability that it lands on heads is less than $\\frac{1}{2}$ and when the coin is flipped four times, the probability of an equal number of heads and tails is $\\frac{1}{6}$. What is the probability that the coin lands on heads?\n$\\textbf{(A)}\\ \\frac{\\sqrt{15}-3... |
[
{
"content": "Let $a$, $b$, $c$ be three nonnegative real numbers such that\n$a^2 + b^2 + c^2 + 2ab + 2ac + 2bc = 1$.\nDetermine the minimum value of\n$a^3 + b^3 + c^3 + 3ab^2 + 3ac^2 + 3bc^2 + 3a^2 b + 3a^2 c + 3b^2 c + 6abc$.",
"role": "user"
},
{
"content": "<think> Alright, so I've got this prob... |
[
{
"content": "Write a Python program to perform matrix multiplication of two matrices using standard input and output.\n\nInput:\n- The first line contains two integers n and m, representing the dimensions of the first matrix A (n rows and m columns).\n- The next n lines each contain m space-separated integers,... |
[
{
"content": "Given an integer n, compute the nth Fibonacci number using an iterative approach. The program should read an integer n from standard input and print the nth Fibonacci number to standard output.\n\nInput:\nA single integer n (n >= 0), given on one line.\n\nOutput:\nPrint the nth Fibonacci number.\n... |
[
{
"content": "List 3 must-see art exhibits happening in Nashville this month, with each exhibit described in a separate paragraph and each paragraph containing exactly 3 sentences.",
"role": "user"
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{
"content": "<think>\nOkay, the user is asking for three must-see art exhibits in Nashville this m... |
[
{
"content": "Write a short review (in English) of last Sunday’s pickup basketball game, describing at least one LeBron James-inspired move and mentioning the Baltimore Ravens, BUT use no more than TWO words in ALL CAPITAL LETTERS throughout the entire review.",
"role": "user"
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{
"content": "<thin... |
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{
"content": "Find the smallest positive integer $n$ for which there exist real numbers $y_1, y_2, \\dots, y_n$ satisfying the following conditions:\n\n$$y_1 + y_2 + y_3 + \\dots + y_n = 800,$$\n$$y_1^3 + y_2^3 + y_3^3 + \\dots + y_n^3 = 64000.$$",
"role": "user"
},
{
"content": "<think> Okay, so I ... |
[
{
"content": "A circle with center $(2,5)$ passes through the point $(6,5)$. Find the length of the longest possible chord of the circle that has an endpoint on the $y$-axis.",
"role": "user"
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{
"content": "<think> Okay, so I need to find the length of the longest possible chord of a circle that h... |
[
{
"content": "Find the smallest positive integer whose cube ends in $888$.\n",
"role": "user"
},
{
"content": "<think> Okay, so I need to find the smallest positive integer whose cube ends in 888. Hmm, let me think about how to approach this. I remember that when dealing with numbers that end with c... |
[
{
"content": "Calculate the length of a nucleotide sequence whose expected frequency is once per haploid human genome\\n\\nThe haploid human genome consists of 3 × 10^9 base pairs. Using the logic in problem 15, one can calculate the minimum length of a unique DNA sequence expected to occur by chance just once ... |
[
{
"content": "Premise: \"A homeless man with puke on his sleeve lies on the floor as a man in a beige leisure suit uses the telephone.\"\nBased on this premise, can we conclude that the hypothesis \"The men are best friends trying to settle a bet of who is better at wrestling.\" is true?\nOptions:\n- yes\n- it ... |
[
{
"content": "Use \\sinh kt = \\frac{e^t - e^{-x}}{2} and linearity to show that \\mathcal{L}\\{ \\sinh kt \\} = \\frac{k}{s^2-k^2}",
"role": "user"
},
{
"content": "<think> Okay, so I need to find the Laplace transform of sinh(kt) using the given formula for sinh(kt) which is (e^(kt) - e^(-kt))/2, ... |
[
{
"content": "A polynomial $p(x)$ is called \"self-centered\" if it has integer coefficients and $p(100) = 100.$ If $p(x)$ is a quadratic self-centered polynomial, what is the maximum number of integer solutions $k$ to the equation $p(k) = k^3$?",
"role": "user"
},
{
"content": "<think> Okay, so I ... |
[
{
"content": "The signal for the O-H proton of a carboxylic acid resonates at ~ 11–15 ppm according to Figure 13.16. The carboxyl proton appears so far downfield because the acidic proton has a large 6+ hydrogen atom and it is extensively hydrogen bonded. The increased bond polarization makes the proton even mo... |
[
{
"content": "Share the benefits of home gardening for mental health in exactly 8 sentences. Each sentence must include the word \"growth\" at least twice. Begin and end your response with the word \"Growth\" (do not write anything after the last word, not even punctuation).",
"role": "user"
},
{
"c... |
[
{
"content": "Write a short blog entry recounting a spontaneous train trip Marcin took to a town he'd never visited. Capture the excitement and sense of discovery he feels, include at least one cultural interaction he had, and ensure that no more than two words in the entire entry are written in all capital let... |
[
{
"content": "Find the equation of the normal plane to the curve \\( z = x^2 - y^2, \\quad y = x \\) at the coordinate origin.",
"role": "user"
},
{
"content": "<think> Okay, so I need to find the equation of the normal plane to the curve defined by \\( z = x^2 - y^2 \\) and \\( y = x \\) at the coo... |
[
{
"content": "You are tasked with creating a function that determines the folder structure and category information for a dataset based on the type of task specified. The function should take in three parameters: a string `task`, which can either be 'detection' or 'segmentation', a string `root`, which is the r... |
[
{
"content": "0.01 molal aqueous solution of \\(K_3Fe(CN)_6\\) freezes at 0.062°C. Calculate the percentage of dissociation of the solute. Given \\(K_f\\) for water = 1.86 K.kg.mol\\(^{-1}\\).",
"role": "user"
},
{
"content": "<think> Okay, so I need to find the percentage dissociation of K3Fe(CN)6 ... |
[
{
"content": "Given a list of qubit measurements represented as a string of characters, where each character corresponds to a type of measurement (X, Y, or I), implement a function `measure_qubits(measurements: str) -> List[str]` that returns a list of strings indicating the result of measuring each qubit. The ... |
[
{
"content": "List two classic game-day snacks that Baltimore Ravens fans might love. For each snack, provide a brief description and suggest a beverage pairing. Format your answer by choosing one option from these two choices for each snack: (A) Easy to make in advance or (B) Best served hot. Give two response... |
[
{
"content": "# Task Description: I request you to establish whether Restaurant A and Restaurant B represent the same entity or not. Indicate your final response as either 'Yes' or 'No'. Return the final result as JSON in the format {\"answer\": \"<Yes or No>\"}. Let's think step by step and show your reasonin... |
[
{
"content": "For polynomial $P(x)=1-\\dfrac{1}{3}x+\\dfrac{1}{6}x^{2}$, define\n\\[Q(x)=P(x)P(x^{3})P(x^{5})P(x^{7})P(x^{9})=\\sum_{i=0}^{50} a_ix^{i}.\\]Find $\\sum_{i=0}^{50} |a_i|.$",
"role": "user"
},
{
"content": "<think> Okay, so I have this problem here where I need to find the sum of the ab... |
[
{
"content": "The number of ounces of water needed to reduce $9$ ounces of shaving lotion containing $50$ % alcohol to a lotion containing $30$ % alcohol is: \n$\\textbf{(A)}\\ 3 \\qquad \\textbf{(B)}\\ 4 \\qquad \\textbf{(C)}\\ 5 \\qquad \\textbf{(D)}\\ 6 \\qquad \\textbf{(E)}\\ 7$ In your response, the word m... |
[
{
"content": "(y + \\sqrt{xy})dx = xdy.",
"role": "user"
},
{
"content": "<think> Okay, so I need to solve the differential equation (y + sqrt(xy))dx = xdy. Hmm, let me see. First, I should probably write it in a more standard form. Maybe I can start by expanding or rearranging terms to get it into ... |
[
{
"content": " Como se chamam os dois melhores amigos do personagem Harry Potter? Your answer must contain a title, wrapped in double angular brackets, such as <<poem of joy>>.",
"role": "user"
},
{
"content": "<think>Okay, the user is asking for the names of Harry Potter's two best friends. Let me ... |
[
{
"content": "Given a CSV file with no header row, write a program that reads the file and prints the columns as a dictionary. Each key of the dictionary is the column index (starting from 0), and each value is a list containing all values in that column (as they appear in the file). If a cell is empty, represe... |
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