conversations listlengths 2 2 | prompt_educational_score float64 0.38 0.99 | response_educational_score float64 0.56 0.99 | average_educational_score float64 0.51 0.99 |
|---|---|---|---|
[
{
"from": "human",
"value": "Given the `root` of a binary tree, return _the inorder traversal of its nodes' values_.\n\n**Example 1:**\n\n**Input:** root = \\[1,null,2,3\\]\n**Output:** \\[1,3,2\\]\n\n**Example 2:**\n\n**Input:** root = \\[\\]\n**Output:** \\[\\]\n\n**Example 3:**\n\n**Input:** root = \\[1\... | 0.863452 | 0.972088 | 0.91777 |
[
{
"from": "human",
"value": "Find the value of the expression. $$\\frac{7+8+9}{2+3+4}\\cdot\\frac{6+9+12}{9+8+7}$$ None"
},
{
"from": "gpt",
"value": "1. First, I need to simplify each fraction by adding the numbers in the numerators and denominators.\\n2. For the first fraction, I calculate $$\... | 0.757846 | 0.893447 | 0.825647 |
[
{
"from": "human",
"value": "Define an ordered triple $(A, B, C)$ of sets to be minimally intersecting if $|A \\cap B| = |B \\cap C| = |C \\cap A| = 1$ and $A \\cap B \\cap C = \\emptyset$. For example, $(\\{1,2\\},\\{2,3\\},\\{1,3,4\\})$ is a minimally intersecting triple. Let $N$ be the number of minimall... | 0.883637 | 0.944019 | 0.913828 |
[
{
"from": "human",
"value": "Evaluate $\\log_{\\sqrt{6}} (216\\sqrt{6})$. None"
},
{
"from": "gpt",
"value": "1. Identify the base of the logarithm as $\\sqrt{6}$ and the argument as $216\\sqrt{6}$.\\n2. Recognize the relationship between the base and the argument: $216\\sqrt{6} = 6^3 \\sqrt{6} ... | 0.660978 | 0.910625 | 0.785802 |
[
{
"from": "human",
"value": "Select the solid.\nA: water in a glass\nB: handsaw\nC: air inside a soccer ball\nD: air inside a balloon None"
},
{
"from": "gpt",
"value": "1. Identify the properties of solids, liquids, and gases.\n2. Analyze each option to determine its state of matter.\n3. A: Wat... | 0.793386 | 0.984554 | 0.88897 |
[
{
"from": "human",
"value": "Each letter represents a non-zero digit. What is the value of $t?$ \\begin{align*}\nc + o &= u \\\\\nu + n &= t \\\\\nt + c &= s \\\\\no + n + s &= 12\n\\end{align*} None"
},
{
"from": "gpt",
"value": "1. Notice that adding the first two equations gives $c+o+n=t$.\n2... | 0.825426 | 0.875044 | 0.850235 |
[
{
"from": "human",
"value": "Select the living thing.\nA: cave\nB: cobra\nC: toy car\nD: ferris wheel None"
},
{
"from": "gpt",
"value": "1. Identify the goal: select the living thing.\n2. Analyze each option:\n A. Cave: not a living thing, doesn't grow or need food/water.\n B. Cobra: a livi... | 0.489594 | 0.973181 | 0.731388 |
[
{
"from": "human",
"value": "Which logical fallacy is used in the text?\nAccording to the commercial, four out of five people surveyed said that they use Twinkle Bright toothpaste, so it must be the best.\nA: red herring: the use of a completely unrelated topic or idea\nB: bandwagon fallacy: the assumption ... | 0.89526 | 0.964758 | 0.930009 |
[
{
"from": "human",
"value": "The activation energy for a reaction is $50 . \\mathrm{J} \\mathrm{mol}^{-1}$. Determine the effect on the rate constant for this reaction with a change in temperature from $273 \\mathrm{~K}$ to $298 \\mathrm{~K}$. None"
},
{
"from": "gpt",
"value": "1. Identify the ... | 0.885265 | 0.962236 | 0.92375 |
[
{
"from": "human",
"value": "write python to store data from coinbase api in sqlite database using sqlalchemy None"
},
{
"from": "gpt",
"value": "1. Create a new class called 'CoinbaseAdapter'.\n2. Add an __init__ method to the class that takes a 'db_uri' parameter and initializes the SQLAlchemy... | 0.718271 | 0.825713 | 0.771992 |
[
{
"from": "human",
"value": "There exist positive integers $a,$ $b,$ and $c$ such that\n\\[3 \\sqrt{\\sqrt[3]{5} - \\sqrt[3]{4}} = \\sqrt[3]{a} + \\sqrt[3]{b} - \\sqrt[3]{c}.\\]Find $a + b + c.$ None"
},
{
"from": "gpt",
"value": "1. Start by squaring both sides of the equation to eliminate the ... | 0.790843 | 0.925829 | 0.858336 |
[
{
"from": "human",
"value": "Find the number of solutions to\n\\[\\cos 4x + \\cos^2 3x + \\cos^3 2x + \\cos^4 x = 0\\]for $-\\pi \\le x \\le \\pi.$ None"
},
{
"from": "gpt",
"value": "1. Find solutions in the interval $0\\le x\\le\\pi$.\n2. Use double-angle formula for cosine to write $\\cos4x$ ... | 0.727751 | 0.941977 | 0.834864 |
[
{
"from": "human",
"value": "In Pascal's Triangle, each entry is the sum of the two entries above it. In which row of Pascal's Triangle do three consecutive entries occur that are in the ratio $3: 4: 5$?\n\n(The top row of Pascal's Triangle has only a single $1$ and is the $0$th row.) None"
},
{
"fr... | 0.771448 | 0.852227 | 0.811838 |
[
{
"from": "human",
"value": "The real function $f$ has the property that, whenever $a,$ $b,$ $n$ are positive integers such that $a + b = 2^n,$ the equation\n\\[f(a) + f(b) = n^2\\]holds. What is $f(2002)$? None"
},
{
"from": "gpt",
"value": "1. Identify the given property: f(a) + f(b) = n^2 fo... | 0.752288 | 0.910258 | 0.831273 |
[
{
"from": "human",
"value": "In how many ways can a President, Vice-President, and Treasurer be chosen from a group of 8 people if no one can serve two roles at the same time? None"
},
{
"from": "gpt",
"value": "1. I need to find the number of ways to choose a President, Vice-President, and Trea... | 0.801881 | 0.962444 | 0.882162 |
[
{
"from": "human",
"value": "The sum of the zeros, the product of the zeros, and the sum of the coefficients of the function $f(x)=ax^{2}+bx+c$ are equal. Their common value must also be which of the following?\n\n(A) The coefficient of $x^2.$\n(B) The coefficient of $x.$\n(C) The $y$-intercept of the graph... | 0.933357 | 0.957191 | 0.945274 |
[
{
"from": "human",
"value": "If $\\mathbf{a},$ $\\mathbf{b},$ and $\\mathbf{c}$ are vectors such that $\\mathbf{a} \\cdot \\mathbf{b} = -3,$ $\\mathbf{a} \\cdot \\mathbf{c} = 4,$ and $\\mathbf{b} \\cdot \\mathbf{c} = 6,$ then find\n\\[\\mathbf{b} \\cdot (7 \\mathbf{c} - 2 \\mathbf{a}).\\] None"
},
{
... | 0.798414 | 0.924921 | 0.861667 |
[
{
"from": "human",
"value": "Juries in criminal trials do not base verdicts on uncorroborated testimony given by any one witness. Rightly so, because it is usually prudent to be highly skeptical of unsubstantiated claims made by any one person. But then, to be consistent, juries should end an all-too-common... | 0.946323 | 0.897353 | 0.921838 |
[
{
"from": "human",
"value": "Evaluate $\\left(\\frac{i}{4}\\right)^4$. None"
},
{
"from": "gpt",
"value": "1. Recognize that $i$ is the imaginary unit with the property $i^2 = -1$.\n2. Apply exponent rules to rewrite $\\left(\\frac{i}{4}\\right)^4$ as $\\left(\\frac{i^4}{4^4}\\right)$.\n3. Simpl... | 0.604646 | 0.914406 | 0.759526 |
[
{
"from": "human",
"value": "The electric field of an electromagnetic wave in vacuum is given by\n\n$$\n\\begin{gathered}\nE_{x}=0, \\\\\nE_{y}=30 \\cos \\left(2 \\pi \\times 10^{8} t-\\frac{2 \\pi}{3} x\\right), \\\\\nE_{z}=0,\n\\end{gathered}\n$$\n\nwhere $E$ is in volts/meter, $t$ in seconds, and $x$ in ... | 0.918031 | 0.953357 | 0.935694 |
[
{
"from": "human",
"value": "A fourteen-year study of finches on the Galapagos islands concluded that there is a definite relationship between climate and the population size of finch species that thrive at various times. During droughts, more members of large finch species survive because their bills are l... | 0.983598 | 0.983418 | 0.983508 |
[
{
"from": "human",
"value": "A household lightbulb is a blackbody radiator. Many lightbulbs use tungsten filaments that are heated by an electric current. What temperature is needed so that $\\lambda_{\\max }=550 \\mathrm{~nm}$ ? None"
},
{
"from": "gpt",
"value": "1. Identify the given informat... | 0.908037 | 0.950361 | 0.929199 |
[
{
"from": "human",
"value": "Tommy: Many people claim that the voting public is unable to evaluate complex campaign issues. The radio advertisements for Peterson in the national campaign, however, discuss complex campaign issues, and Peterson is currently more popular than the other candidates. Jamie: Yes, ... | 0.921799 | 0.88411 | 0.902954 |
[
{
"from": "human",
"value": "BEGININPUT\nBEGINCONTEXT\ndate: September 15, 2021\nparticipants: Alice, Bob, and Charlie\nplatform: Slack\ntopic: Redis\nENDCONTEXT\nAlice: Hey team, I was reading about the new features in Redis 7.3.2 and found that they've introduced a more efficient way to handle memory mana... | 0.810192 | 0.865527 | 0.83786 |
[
{
"from": "human",
"value": "Any five points are taken inside or on a square with side length $1$. Let a be the smallest possible number with the property that it is always possible to select one pair of points from these five such that the distance between them is equal to or less than $a$. Then $a$ is:\n$... | 0.834897 | 0.969812 | 0.902354 |
[
{
"from": "human",
"value": "Let $a = 5 - 8i$ and $b = 30 + 48i$. Find $|ab|$. None"
},
{
"from": "gpt",
"value": "1. Recall the formula for the modulus of a complex number: $|a| = \\sqrt{a_{real}^2 + a_{imag}^2}$.\n2. Calculate the modulus of $a$: $|a| = \\sqrt{5^2 + (-8)^2} = \\sqrt{25 + 64} =... | 0.648591 | 0.947765 | 0.798178 |
[
{
"from": "human",
"value": "The expressions \\[A=1 \\times 2 + 3 \\times 4 + 5 \\times 6 + \\cdots + 37 \\times 38 + 39\\]and \\[B = 1 + 2 \\times 3 + 4 \\times 5 + \\cdots + 36 \\times 37 + 38 \\times 39\\]are obtained by writing multiplication and addition operators in an alternating pattern between succ... | 0.928073 | 0.962875 | 0.945474 |
[
{
"from": "human",
"value": "An $\\textit{emirp}$ is an integer that, when its digits are written in reverse order, is a prime number. For example, 73 is an emirp because 37 is prime. What is the smallest two-digit prime number that is NOT an emirp? None"
},
{
"from": "gpt",
"value": "1. An emir... | 0.900255 | 0.957231 | 0.928743 |
[
{
"from": "human",
"value": "Let $P(x) = 4x^3 - 2x^2 + 7x - 1$, and let $Q(x) = P(x)^2$. What is the y-intercept of $Q(x)$? None"
},
{
"from": "gpt",
"value": "1. Identify the goal: find the y-intercept of Q(x).\n 2. Recall the definition of a y-intercept: the value of the function when x = 0.\n... | 0.813667 | 0.966456 | 0.890061 |
[
{
"from": "human",
"value": "Expert: Some people claim that, since food production has thus far increased faster than population has, there is no need to be concerned about widespread food shortages. These people fail to recognize that the planet' s resources allow for food to be produced at only a few time... | 0.972401 | 0.972928 | 0.972664 |
[
{
"from": "human",
"value": "No two students in Mrs. Vale's 26-student mathematics class have the same two initials. Each student's first name and last name begin with the same letter. If the letter ``Y'' is considered a vowel, what is the probability of randomly picking a student whose initials are vowels?... | 0.968107 | 0.968266 | 0.968186 |
[
{
"from": "human",
"value": "Is this a run-on sentence?\nIn 1960, American pilot Francis Gary Powers was shot down and captured by the Soviets as he flew over the Ural Mountains on an intelligence mission for the CIA, nearly two years later, Powers was released in exchange for Rudolf Abel, a KGB spy who had... | 0.806894 | 0.968128 | 0.887511 |
[
{
"from": "human",
"value": "What is the sum of all integers from 80 through 90, inclusive? None"
},
{
"from": "gpt",
"value": "1. I need to find the sum of all integers from 80 through 90, inclusive.\n2. This means I need to include both 80 and 90 in the sum.\n3. I can use the formula for the s... | 0.706304 | 0.955792 | 0.831048 |
[
{
"from": "human",
"value": "A dealer sold 200 cars, and the data for some of those sales are recorded in this table. If the rest of the cars she sold were Hondas, how many Hondas did she sell?\n\n\\begin{tabular}{ |c | c|}\n\\hline \\textbf{Type of Car} & \\textbf{$\\%$ of Total Cars Sold} \\\\ \\hline\nAu... | 0.881301 | 0.931605 | 0.906453 |
[
{
"from": "human",
"value": "Cool weather typically weakens muscle power in cold-blooded creatures. In the veiled chameleon, a cold-blooded animal, the speed at which the animal can retract its tongue declines dramatically as the temperature falls. However, the speed at which this chameleon can extend its t... | 0.97953 | 0.97986 | 0.979695 |
[
{
"from": "human",
"value": "Write a Python script that connects to an SQLite database, creates a table called \"students\" with columns for name, age, and major, and inserts sample data into the table.\nPLAINFORMAT None"
},
{
"from": "gpt",
"value": "1. Need to write a Python script to connect ... | 0.889131 | 0.960789 | 0.92496 |
[
{
"from": "human",
"value": "The figure shown is called a trefoil and is constructed by drawing circular sectors about sides of the congruent equilateral triangles. What is the area of a trefoil whose horizontal base has length 2?\n\n[asy]\nunitsize(1cm);\npath a =(-1.73,1)..(-1,1.73)--(-2,0)..cycle;\ndraw(... | 0.973075 | 0.976031 | 0.974553 |
[
{
"from": "human",
"value": "The polynomial $x^3 - 2004 x^2 + mx + n$ has integer coefficients and three distinct positive zeros. Exactly one of these is an integer, and it is the sum of the other two. How many values of $n$ are possible? None"
},
{
"from": "gpt",
"value": "1. Let the integer ... | 0.789384 | 0.938312 | 0.863848 |
[
{
"from": "human",
"value": "The number of sports cars per square mile is 40% greater in downtown Terrera than in downtown Goldsville. If the entire metropolitan area of each city is compared-which includes downtown as well as suburbs and exurbs-then the number of sports cars per square mile is 20% greater ... | 0.951513 | 0.936825 | 0.944169 |
[
{
"from": "human",
"value": "Let $\\mathbf{a}$ and $\\mathbf{b}$ be two nonzero vectors such that $\\mathbf{a} + \\mathbf{b}$ and $\\mathbf{b}$ are orthogonal, and $\\mathbf{a} + 2 \\mathbf{b}$ and $\\mathbf{a}$ are orthogonal. Find $\\frac{\\|\\mathbf{a}\\|}{\\|\\mathbf{b}\\|}.$ None"
},
{
"from":... | 0.871577 | 0.965176 | 0.918377 |
[
{
"from": "human",
"value": "Convert the point $\\left( 10, \\frac{\\pi}{4} \\right)$ in polar coordinates to rectangular coordinates. None"
},
{
"from": "gpt",
"value": "1. Identify the given polar coordinates as $(r, \\theta) = \\left( 10, \\frac{\\pi}{4} \\right)$.\n2. Recall the conversion f... | 0.772533 | 0.968775 | 0.870654 |
[
{
"from": "human",
"value": "Suppose you have `n` integers labeled `1` through `n`. A permutation of those `n` integers `perm` (**1-indexed**) is considered a **beautiful arrangement** if for every `i` (`1 <= i <= n`), **either** of the following is true:\n\n* `perm[i]` is divisible by `i`.\n* `i` is di... | 0.907736 | 0.959125 | 0.93343 |
[
{
"from": "human",
"value": "You are given two **2D** integer arrays `nums1` and `nums2.`\n\n* `nums1[i] = [idi, vali]` indicate that the number with the id `idi` has a value equal to `vali`.\n* `nums2[i] = [idi, vali]` indicate that the number with the id `idi` has a value equal to `vali`.\n\nEach arra... | 0.898742 | 0.863695 | 0.881219 |
[
{
"from": "human",
"value": "How many ways are there to arrange 9 people in a line such that no one is standing in their correct position?\nRelevant Theorem: In combinatorics, the Derangement Formula, also known as the subfactorial or !n, is used to count the number of derangements (or permutations) of a se... | 0.980889 | 0.956391 | 0.96864 |
[
{
"from": "human",
"value": "Clark: Our local community theater often produces plays by critically acclaimed playwrights. In fact, the production director says that critical acclaim is one of the main factors considered in the selection of plays to perform. So, since my neighbor Michaela' s new play will be... | 0.932456 | 0.941296 | 0.936876 |
[
{
"from": "human",
"value": "Three schools have a chess tournament. Four players come from each school. Each player plays three games against each player from the other schools, and plays one game against each other player from his or her own school. How many games of chess are played? None"
},
{
"f... | 0.888753 | 0.977106 | 0.932929 |
[
{
"from": "human",
"value": "Segment $s_1$ has endpoints at $(4,1)$ and $(-8,5)$. Segment $s_2$ is obtained by translating $s_1$ by $2$ units to the right and $3$ units up. Find the midpoint of segment $s_2$. Express your answer as $(a,b)$ with $a$ and $b$ integers. None"
},
{
"from": "gpt",
"... | 0.821914 | 0.918581 | 0.870248 |
[
{
"from": "human",
"value": "Given a string containing digits from `2-9` inclusive, return all possible letter combinations that the number could represent. Return the answer in **any order**.\n\nA mapping of digits to letters (just like on the telephone buttons) is given below. Note that 1 does not map to ... | 0.925187 | 0.968055 | 0.946621 |
[
{
"from": "human",
"value": "Over the last five years, every new major alternative-energy initiative that initially was promised government funding has since seen that funding severely curtailed. In no such case has the government come even close to providing the level of funds initially earmarked for these... | 0.937093 | 0.92629 | 0.931692 |
[
{
"from": "human",
"value": "Points $A$, $B$, $C$, $D$, and $E$ are located in 3-dimensional space with $AB= BC= CD= DE= EA= 2$ and $\\angle ABC = \\angle CDE = \\angle\nDEA = 90^\\circ$. The plane of triangle $ABC$ is parallel to $\\overline{DE}$. What is the area of triangle $BDE$? None"
},
{
"fr... | 0.872638 | 0.949525 | 0.911081 |
[
{
"from": "human",
"value": "Describe the basic principles of magnetism, including its properties and how it works on a molecular level. None"
},
{
"from": "gpt",
"value": "1. Identify the topic: magnetism and its basic principles\n2. Recall the relationship between magnetism and charged particl... | 0.915684 | 0.98464 | 0.950162 |
[
{
"from": "human",
"value": "A merchant offers a large group of items at $30\\%$ off. Later, the merchant takes $20\\%$ off these sale prices and claims that the final price of these items is $50\\%$ off the original price. As a percentage of the original price, what is the difference between the true dis... | 0.824473 | 0.881201 | 0.852837 |
[
{
"from": "human",
"value": "Popeye owned a large fleet of buses. He was fortunate enough to have won the contract to bus all the schoolchildren in a large midwestern city and most of its surrounding suburbs. He purchased a number of new vehicles to expand his fleet. Popeye had farmed out the maintenance of... | 0.930378 | 0.905276 | 0.917827 |
[
{
"from": "human",
"value": "Find $\\sec 135^\\circ.$ None"
},
{
"from": "gpt",
"value": "1. Identify the given angle and the trigonometric function to find: $\\sec 135^\\circ$.\n2. Recall the definition of secant: $\\sec x = \\frac{1}{\\cos x}$.\n3. Rewrite the expression using the definition: ... | 0.529535 | 0.933042 | 0.731288 |
[
{
"from": "human",
"value": "Given that $-7$ is a solution to $x^2 + bx -28 = 0$, what is the value of $b$? None"
},
{
"from": "gpt",
"value": "1. Understand that $-7$ being a solution means it must satisfy the equation.\n2. Substitute $x = -7$ into the equation: $(-7)^2 + b(-7) - 28 = 0$.\n3. S... | 0.724875 | 0.9211 | 0.822988 |
[
{
"from": "human",
"value": "Find the smallest possible value of the expression $$\\frac{(a+b)^2+(b-c)^2+(c-a)^2}{b^2},$$where $b > c > a$ are real numbers, and $b \\neq 0.$ None"
},
{
"from": "gpt",
"value": "1. Start by expanding the numerator of the expression.\n2. Combine like terms and divi... | 0.726462 | 0.928684 | 0.827573 |
[
{
"from": "human",
"value": "There are `n` rooms labeled from `0` to `n - 1` and all the rooms are locked except for room `0`. Your goal is to visit all the rooms. However, you cannot enter a locked room without having its key.\n\nWhen you visit a room, you may find a set of **distinct keys** in it. Each ke... | 0.880895 | 0.956694 | 0.918795 |
[
{
"from": "human",
"value": "How many paths are there from $C$ to $B$, if every step must be up or to the right?[asy]size(4cm,4cm);int w=6;int h=5;int i;pen p=fontsize(9);for (i=0; i<h; ++i){draw((0,i) -- (w-1,i));}for (i=0; i<w; ++i){draw((i, 0)--(i,h-1));}dot(\"$A$\", (0,0), SW, p);dot(\"$C$\", (1,2), NE,... | 0.911145 | 0.952706 | 0.931925 |
[
{
"from": "human",
"value": "Let $\\varphi(x, y)$ be a function with continuous second order partial derivatives such that\n\n1. $\\varphi_{x x}+\\varphi_{y y}+\\varphi_{x}=0$ in the punctured plane $\\mathbb{R}^{2} \\backslash\\{0\\}$,\n\n2. $r \\varphi_{x} \\rightarrow \\frac{x}{2 \\pi r}$ and $r \\varphi... | 0.859971 | 0.879614 | 0.869792 |
[
{
"from": "human",
"value": "Researchers examined 100 people suffering from herniated disks in their backs. Five of them were found to have a defect in a particular gene. The researchers also examined 100 people who had no problems with the disks in their backs; none had the genetic defect. They concluded t... | 0.955594 | 0.95569 | 0.955642 |
[
{
"from": "human",
"value": "You are given a string `num`, representing a large integer, and an integer `k`.\n\nWe call some integer **wonderful** if it is a **permutation** of the digits in `num` and is **greater in value** than `num`. There can be many wonderful integers. However, we only care about the *... | 0.970418 | 0.936651 | 0.953534 |
[
{
"from": "human",
"value": "You are given an array of strings `equations` that represent relationships between variables where each string `equations[i]` is of length `4` and takes one of two different forms: `\"xi==yi \"` or `\"xi!=yi \"`.Here, `xi` and `yi` are lowercase letters (not necessarily differen... | 0.955505 | 0.956755 | 0.95613 |
[
{
"from": "human",
"value": "How many positive integers $n$ satisfy $200 < n^2 < 900$? None"
},
{
"from": "gpt",
"value": "1. I need to find the smallest and largest possible values of $n$ that satisfy the inequality $200 < n^2 < 900$.\n2. To do this, I can take the square root of both sides of ... | 0.755398 | 0.94676 | 0.851079 |
[
{
"from": "human",
"value": "Divide the product of the first five positive composite integers by the product of the next five composite integers. Express your answer as a common fraction. None"
},
{
"from": "gpt",
"value": "1. Identify the first five positive composite integers: 4, 6, 8, 9, 10.\... | 0.907949 | 0.958724 | 0.933336 |
[
{
"from": "human",
"value": "On January 2, Hugh Homey and Sue Structo entered into a written contract in which Structo agreed to build on Homey's lot a new house for Homey, according to plans and specifications furnished by Homey's architect, Barbara Bilevel, at a contract price of $ 200,000$. The contract ... | 0.856278 | 0.890765 | 0.873521 |
[
{
"from": "human",
"value": "Jenny's grandmother has $24$ cats. Seventeen of the cats do not catch mice. Ten of the cats have black fur. What is the smallest possible number of cats that do not catch mice that have black fur? None"
},
{
"from": "gpt",
"value": "1. Identify the total number of... | 0.856947 | 0.954357 | 0.905652 |
[
{
"from": "human",
"value": "Carl the clothier owns a large garment factory on an isolated island. Carl's factory is the only source of employment for most of the islanders, and thus Carl acts as a monopsonist. The supply curve for garment workers is given by l = 80w, where l is the number of workers hired ... | 0.976729 | 0.978176 | 0.977453 |
[
{
"from": "human",
"value": "To protect the minor children living in the area, the Rock Creek Town Council enacted an ordinance that prohibited advertisements that include \"a depiction of a nude person, whether male or female.\" Sylvester Screen owns and operates Rock Creek Video, a videotape rental shop. ... | 0.915244 | 0.857167 | 0.886205 |
[
{
"from": "human",
"value": "In triangle $ABC$, altitudes $AD$, $BE$, and $CF$ intersect at the orthocenter $H$. If $\\angle ABC = 49^\\circ$ and $\\angle ACB = 12^\\circ$, then find the measure of $\\angle BHC$, in degrees. None"
},
{
"from": "gpt",
"value": "1. Identify that triangle $ABC$ is... | 0.862225 | 0.940613 | 0.901419 |
[
{
"from": "human",
"value": "A shipping company wants to optimize its container loading process at a major port. The company currently processes 1,000 containers per day, with an average loading time of 2 hours per container. By investing in new equipment and software, the company aims to reduce the average... | 0.874341 | 0.85339 | 0.863865 |
[
{
"from": "human",
"value": "Find $(1421 \\div 7 + 47) \\div 50 \\cdot 9.$ None"
},
{
"from": "gpt",
"value": "1. Begin by following the order of operations: parentheses, exponents, multiplication and division (from left to right), and addition and subtraction (from left to right).\n2. Start wit... | 0.620694 | 0.978929 | 0.799811 |
[
{
"from": "human",
"value": "A circle of radius $2$ is inscribed in a semicircle, as shown. The area inside the semicircle but outside the circle is shaded. What fraction of the semicircle's area is shaded?\n\n[asy]\nunitsize(6mm);\ndefaultpen(linewidth(.8pt)+fontsize(8pt));\ndotfactor=4;\n\nfilldraw(Arc((0... | 0.965321 | 0.973184 | 0.969253 |
[
{
"from": "human",
"value": "Suppose that $a$ and $b$ are nonzero real numbers, and that the equation $${x^2 + ax + b = 0}$$ has solutions $a$ and $b$. Then what is the pair $(a,b)$? None"
},
{
"from": "gpt",
"value": "1. The given equation is a quadratic equation with solutions $a$ and $b$.\n2... | 0.797221 | 0.948792 | 0.873006 |
[
{
"from": "human",
"value": "An ellipse has foci at $F_1 = (0,2)$ and $F_2 = (3,0).$ The ellipse intersects the $x$-axis at the origin, and one other point. What is the other point of intersection? None"
},
{
"from": "gpt",
"value": "1. Identify the given information: foci at $F_1 = (0,2)$ and... | 0.852435 | 0.956299 | 0.904367 |
[
{
"from": "human",
"value": "What is the sum of all the odd integers between $500$ and $700$? None"
},
{
"from": "gpt",
"value": "1. Identify the problem as finding the sum of odd integers between $500$ and $700$.\n2. Recognize that the odd integers form an arithmetic series with a common differ... | 0.673746 | 0.927062 | 0.800404 |
[
{
"from": "human",
"value": "Develop a C++ program that simulates a basic blockchain system. The program should include functionality for creating blocks, adding transactions, validating the chain, and mining new blocks.\nPLAINFORMAT None"
},
{
"from": "gpt",
"value": "1. Understand the requirem... | 0.878891 | 0.959634 | 0.919262 |
[
{
"from": "human",
"value": "Beverage company representative: The plastic rings that hold six-packs of beverage cans together pose a threat to wild animals, which often become entangled in the discarded rings and suffocate as a result. Following our lead, all beverage companies will soon use only those ring... | 0.96462 | 0.964725 | 0.964672 |
[
{
"from": "human",
"value": "Which sentence states a fact?\nA: Jeff Kinney worked on Diary of a Wimpy Kid for six years before publishing it online.\nB: Cartoonist Jeff Kinney's book Diary of a Wimpy Kid deserves all of the praise it has received. None"
},
{
"from": "gpt",
"value": "1. Identify ... | 0.842943 | 0.987165 | 0.915054 |
[
{
"from": "human",
"value": "Find all the solutions to\n\\[\\arctan \\frac{1}{x} + \\arctan \\frac{1}{x + 2} = \\arctan \\frac{4}{x + 3}.\\]Enter all the solutions, separated by commas. None"
},
{
"from": "gpt",
"value": "1. Take the tangent of both sides of the equation to eliminate the arctan ... | 0.787164 | 0.941108 | 0.864136 |
[
{
"from": "human",
"value": "A company produces widgets with a 5% defect rate. If they produce 10,000 widgets in a day, what is the probability that exactly 450 are defective? None"
},
{
"from": "gpt",
"value": "1. Identify the problem as a binomial probability problem since we have a fixed numb... | 0.849512 | 0.964708 | 0.90711 |
[
{
"from": "human",
"value": "Twelve healthy volunteers with the Apo-A-IV-1 gene and twelve healthy volunteers who instead have the Apo-A-IV-2 gene each consumed a standard diet supplemented daily by a high-cholesterol food. A high level of cholesterol in the blood is associated with an increased risk of hea... | 0.978018 | 0.971037 | 0.974527 |
[
{
"from": "human",
"value": "Compute\n\\[\\sin^2 4^\\circ + \\sin^2 8^\\circ + \\sin^2 12^\\circ + \\dots + \\sin^2 176^\\circ.\\] None"
},
{
"from": "gpt",
"value": "1. Recognize the problem involves sum of squares of sines of angles.\n2. Recall the double-angle formula: \\[\\sin^2 x = \\frac{1... | 0.65916 | 0.94188 | 0.80052 |
[
{
"from": "human",
"value": "Derive the demand function for a good with a price elasticity of -2 and an income elasticity of 1, assuming constant prices and income. Explain your derivation.\n None"
},
{
"from": "gpt",
"value": "1. Start with the given price elasticity of demand (Ed) and income e... | 0.814372 | 0.969658 | 0.892015 |
[
{
"from": "human",
"value": "I would like to install Linux on an old laptop. what is the best Linux distribution for weak hardware on a mechanical HDD, I already use Linux mint on my main computer but I would like something more lightweight for an pentium based laptop None"
},
{
"from": "gpt",
"... | 0.690715 | 0.912612 | 0.801664 |
[
{
"from": "human",
"value": "Describe the RSA algorithm in ELI5 format. None"
},
{
"from": "gpt",
"value": "1. Understand the instruction is asking for applications of the RSA algorithm.\n2. Recall that RSA is a widely used encryption algorithm.\n3. Consider various fields and industries where e... | 0.748543 | 0.983445 | 0.865994 |
[
{
"from": "human",
"value": "Principle: If the burden of a proposed policy change would fall disproportionately on people with low incomes, that policy change should not be made. Application: The city of Centerburgh plans to reintroduce rock salt as a road de-icing agent, after having stopped its use severa... | 0.946932 | 0.94026 | 0.943596 |
[
{
"from": "human",
"value": "Select the fish.\nA: humpback whale\nB: piranha\nC: zebra\nD: gharial None"
},
{
"from": "gpt",
"value": "1. The instruction is to select the fish.\n2. Analyze each option to determine if it is a fish or not.\n3. Option A: humpback whale - a mammal, not a fish.\n4. O... | 0.620365 | 0.969692 | 0.795029 |
[
{
"from": "human",
"value": "Prove that the sum of the angles in any triangle equals 180 degrees. Provide step-by-step reasoning.\n None"
},
{
"from": "gpt",
"value": "1. Start with the goal to prove the sum of angles in a triangle equals 180 degrees.\n2. Consider using proof by contradiction as... | 0.867161 | 0.978589 | 0.922875 |
[
{
"from": "human",
"value": "In a cozy living room, three friends are having a conversation about the science behind dreams and dreaming. The characters involved are:\n- USER/Jane: A curious individual who loves learning new things\n- Albert Einstein: A famous physicist known for his theory of relativity\n-... | 0.821668 | 0.972679 | 0.897173 |
[
{
"from": "human",
"value": "Given an array `arr` of positive integers sorted in a **strictly increasing order**, and an integer `k`.\n\nReturn _the_ `kth` _**positive** integer that is **missing** from this array._\n\n**Example 1:**\n\n**Input:** arr = \\[2,3,4,7,11\\], k = 5\n**Output:** 9\n**Explanation:... | 0.890943 | 0.914047 | 0.902495 |
[
{
"from": "human",
"value": "Compute the double integrals over indicated rectangles $\\iint\\limits_{R}{{2x - 4{y^3}\\,dA}}$, $R = [-5,4] \\times [0, 3]\nRelevant Theorem: Fubini's Theorem is a fundamental result in calculus, specifically in the area of multiple integration. It provides a method for evaluat... | 0.922329 | 0.880404 | 0.901367 |
[
{
"from": "human",
"value": "For what integer $x$ is $\\frac 35 < \\frac x7 < \\frac 79$? None"
},
{
"from": "gpt",
"value": "1. Start by analyzing the first inequality: $\\frac 35 < \\frac x7$. \\n2. Cross-multiply to eliminate the fractions: $21 < 5x$. \\n3. Divide both sides by $5$ to isolate... | 0.688962 | 0.893166 | 0.791064 |
[
{
"from": "human",
"value": "The owners of Uptown Apartments are leaning toward not improving the apartment complex; they believe that the increased rents they could charge for improved apartments would not cover the costs of the improvements. But the improvements would make the surrounding housing, which t... | 0.903052 | 0.901024 | 0.902038 |
[
{
"from": "human",
"value": "Donald is being tried for the murder of Vincent, which occurred during the burglary of Vincent's house. In its case-in-chief, the prosecution seeks to offer evidence that Donald, who was arrested several days after the crime, had been caught with 50 grams of cocaine in his car. ... | 0.88359 | 0.875858 | 0.879724 |
[
{
"from": "human",
"value": "5.5-7. Suppose that the distribution of the weight of a prepackaged \"1-pound bag\" of carrots is $N\\left(1.18,0.07^2\\right)$ and the distribution of the weight of a prepackaged \"3-pound bag\" of carrots is $N\\left(3.22,0.09^2\\right)$. Selecting bags at random, find the pro... | 0.948028 | 0.919621 | 0.933824 |
[
{
"from": "human",
"value": "BEGININPUT\nBEGINCONTEXT\ndate: September 12, 2023\nauthor: Alex Johnson\nurl: https://www.architecturetoday.com/modern-architecture-trends/\ntitle: \"Exploring the Latest Trends in Modern Architecture\"\ncategory: Architecture\nsource url: https://www.architecturetoday.com/\nEN... | 0.964258 | 0.974675 | 0.969467 |
[
{
"from": "human",
"value": "A major health insurance company in Lagolia pays for special procedures prescribed by physicians only if the procedure is first approved as \"medically necessary\" by a company-appointed review panel. The rule is intended to save the company the money it might otherwise spend on... | 0.861845 | 0.844972 | 0.853408 |
[
{
"from": "human",
"value": "In the past century, North America has shifted its main energy source first from wood to coal, then from coal to oil and natural gas. With each transition, the newly dominant fuel has had less carbon and more hydrogen than its predecessor had. It is logical to conclude that in t... | 0.969677 | 0.971066 | 0.970372 |
[
{
"from": "human",
"value": "In a group of 30 people, 18 have brown eyes, 10 have green eyes, and 2 have blue eyes. If you were to choose 4 people at random from the group, what is the probability that none of them would have blue eyes? None"
},
{
"from": "gpt",
"value": "1. Identify the total n... | 0.87478 | 0.959449 | 0.917115 |
[
{
"from": "human",
"value": "For how many pairs of consecutive integers in $\\{1000,1001,1002,\\ldots,2000\\}$ is no carrying required when the two integers are added?\n None"
},
{
"from": "gpt",
"value": "1. Understand the problem: We need to find the number of consecutive integer pairs in the ... | 0.75894 | 0.901056 | 0.829998 |
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