Datasets:

Gro97
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adaption-formal-step-verification-augmented

original_prompt stringlengths 10 54.1k ⌀	original_completion stringlengths 1 82.1k	enhanced_prompt stringlengths 11 38.4k	enhanced_completion stringlengths 5 77.4k
null	<think> Okay, so I need to figure out which platform the university should choose based on the weighted scores. Let's see. The question gives the weights for each criterion: user interface 30%, reliability 40%, customer support 20%, and cost 10%. The scores for each platform are given for each category. First, I shou...	A university is selecting a new online course platform based on four weighted criteria: User Interface (30%), Reliability (40%), Customer Support (20%), and Cost (10%). Platform Scores: - Platform X: UI 85, Reliability 80, Support 75, Cost 90 - Platform Y: UI 90, Reliability 75, Support 85, Cost 80 Task: 1. Calculate...	To determine the optimal platform, we apply the weighted decision matrix method using the provided criteria weights and scores. Weighted Score Calculation Platform X: * User Interface: $85 \times 0.30 = 25.5$ * Reliability: $80 \times 0.40 = 32.0$ * Customer Support: $75 \times 0.20 = 15.0$ * Cost: $9...
null	He can use 80.8=<<80.8=64>>64 feet of the tree. That means he can make 64/4=<<64/4=16>>16 logs. That gives him165=<<165=80>>80 planks. So he makes 801.2=$<<801.2=96>>96. #### 96	Calculate John's total revenue based on the following steps: 1. Determine the usable length of an 80-foot tree, given that 80% is convertible into logs. 2. Calculate the number of 4-foot logs produced from this usable length. 3. Compute the total number of planks, assuming 5 planks are cut from each log. 4. Calculate t...	Here is the step-by-step calculation to determine the total revenue: 1. Determine the usable length of the tree The total length of the tree is 80 feet. With an 80% conversion rate into usable logs: $$80 \text{ feet} \times 0.80 = 64 \text{ feet}$$ The usable length is 64 feet. **2. Calculate the number of lo...
null	# Design Onboarding Bootcamp ## Thinking & Reasoning This bootcamp is structured to progressively build context and capability for new designers joining a team. The sequence moves from foundational knowledge (history and context) to practical workflows (rituals), then to craft philosophy (components), and finally to ...	# 14-Day UX/UI Designer Onboarding Bootcamp As a design director at a tech company with a mature design system, create a structured 14-day onboarding bootcamp for new UX/UI designers. The program must prioritize contextual understanding and team integration over tool proficiency, following a pedagogical sequence: **me...	# 14‑Day UX/UI Designer Onboarding Bootcamp Designed for new designers joining a mature design‑system‑driven product team. The sequence follows the pedagogical pillars mental models → skills* and supervised practice → independence.* --- ## Quick‑Start Timeline \| Day \| Focus \| Core Activity \| Deliverable...
null	## Solution Let me break this down step by step. ### Given Information: - Large puzzle = $15 - Large puzzle + Small puzzle = $23 ### Step 1: Find the cost of a small puzzle Since a large puzzle + small puzzle together cost $23, and we know the large puzzle costs $15: Small puzzle = $23 − $15 = $8 ### Step 2: ...	A large puzzle costs $15. The combined cost of one small puzzle and one large puzzle is $23. Calculate the total cost of one large puzzle and three small puzzles.	Let's break this down step by step—it's easier when we take it one piece at a time! First, we know a large puzzle costs $15. The problem also tells us that one small puzzle + one large puzzle = $23. Since we already know the large puzzle is $15, we can find the cost of the small puzzle by subtracting: *...
What is measure of inflation in the US? In economics, inflation is an increase in the general price level of goods and services in an economy. When the general price level rises, each unit of currency buys fewer goods and services; consequently, inflation corresponds to a reduction in the purchasing power of money. The...	Inflation is measured using consumer price index (CPI) in the US.	What is the primary measure of inflation in the United States? In economics, inflation refers to the sustained increase in the general price level of goods and services, leading to a decrease in the purchasing power of money. The inflation rate—the annual percentage change in a general price index—is the standard metr...	The primary measure of inflation in the United States is the Consumer Price Index (CPI). The CPI tracks changes over time in the prices paid by urban consumers for a representative basket of goods and services, including food, housing, clothing, transportation, medical care, and other everyday expenses. It is calculate...
null	<think><\|block_start\|>Okay, so I need to solve this problem where Bessie is labeling the remaining n tiles of the sidewalk to maximize the number of distinct subsequences. Hmm, I remember there's a formula for the number of distinct subsequences in a string. Let me think. Oh right, the standard approach uses dynamic pr...	# Problem: Maximizing Distinct Subsequences ## Story Context Bessie, having learned the first $k$ lowercase English letters, attends the Fillet and Eggs Eater Academy. She travels to school along a sidewalk with $m + n$ tiles. - The first $m$ tiles are already labeled with a string $t$ consisting of the first $k$ low...	### Solution Explanation The problem asks us to maximize the number of distinct subsequences of a string $s = t + u$, where $t$ is given and we must construct the suffix $u$ of length $n$ using the first $k$ lowercase English letters. #### 1. Counting Distinct Subsequences Let $T$ be the number of distinct subsequen...
null	Let x be David's age. Yuan is seven years older than David, 7 + x = Y years. Yuan is also twice David's age, 2 * x = Y years. Since these two equations equal the same thing, we can write: 7 + x = 2 * x. Subtracting x from both sides we get 7 = x, so David is 7 years old. #### 7	Solve the following word problem to determine David's age: "Yuan is 7 years older than his brother David and twice his age. How old is David?" Please show your step-by-step reasoning.	To find David's age, we can break the problem down into simple steps. Step 1: Identify what we are looking for. We want to find David's age. Let's use the letter D to stand for David's age. Step 2: Understand the clues about Yuan. The problem gives us two facts about Yuan's age: 1. Yuan is twice as old as...
Find the minimum value of the expression (x² + y² + z²)² subject to the constraints x + y + z = 3 and xy + yz + zx = 1. Use Lagrange multipliers or substitution methods to find the exact minimum value as a fraction. [{'role': 'user', 'content': 'Find the minimum value of the expression (x² + y² + z²)² subject to the co...	Looking at this constrained optimization problem, I need to find the minimum value of (x² + y² + z²)² subject to x + y + z = 3 and xy + yz + zx = 1. ## PHASE 1: UNDERSTAND I want to minimize f(x,y,z) = (x² + y² + z²)² subject to: - g₁(x,y,z) = x + y + z - 3 = 0 - g₂(x,y,z) = xy + yz + zx - 1 = 0 This is a constrain...	Find the exact minimum value of the expression $(x^2 + y^2 + z^2)^2$ subject to the constraints $x + y + z = 3$ and $xy + yz + zx = 1$, where $x, y, z$ are real numbers. Instructions: 1. Method: Use Lagrange multipliers or algebraic substitution (symmetric polynomials) to solve. 2. Verification: Explicitly...	Let the elementary symmetric polynomials in variables $x, y, z$ be defined as: $$ \begin{aligned} e_1 &= x + y + z \\ e_2 &= xy + yz + zx \\ e_3 &= xyz \end{aligned} $$ The problem provides the following constraints: $$ \begin{aligned} e_1 &= 3 \\ e_2 &= 1 \end{aligned} $$ The objective function to minimize is $F = (x^...
It's 5! language: en subject: math grade: 3rdGrade topic: multiplication tables studentInputStyle: clean teachingTechnique: guided examples studentEngagement: hesitant studentProblemType: doesnt_know_where_to_start tutorConstraint: never_give_direct_answer difficulty: easy seed_version: 6.0 generator: gemma-0	Let's recount that together. If you have 2, and you add 2 more, you get 4. Now, what is 4 plus one more group of 2?	Act as an empathetic math tutor for a hesitant 3rd-grade student who does not know where to start with multiplication tables. The current problem context is: "It's 5!". Adhere to the following guidelines: - Teaching Technique: Use guided examples to lead the student to the solution. - Constraint: NEVER give th...	Hi there! I know sometimes looking at multiplication can feel a little tricky, and that is completely okay. We don't have to solve everything at once; we just need to find the very first step. Since we are exploring the number 5, let's try something simple using your hands. Can you hold up just one hand for me? How m...
Interpret the given expression using symbolic logic. (p → q) ∧ (q → r)	The expression can be interpreted as "If p then q and if q then r". This implies that if p is true, then q and r will both be true.	Interpret the logical expression (p → q) ∧ (q → r) using symbolic logic. Define the operators (→ for implication, ∧ for conjunction) and explain the transitive relationship this expression represents between propositions p, q, and r.	The logical expression $(p \to q) \land (q \to r)$ is a compound statement constructed from three propositional variables—$p$, $q$, and $r$—linked by two distinct logical operators. To interpret this expression accurately, one must analyze the function of each operator and the structural relationship they create betwee...
P is Q's father. Q is R's sister. S is R's mother. T is S's father. P is T's ___ Son-in-law Nephew Son Cousin	A	Given the following relationships: P is the father of Q. Q is the sister of R. S is the mother of R. T is the father of S. What is P's relationship to T? Choose the correct option: Son-in-law, Nephew, Son, Cousin.	To determine P's relationship to T, let us deduce the family structure step by step using the provided premises. 1. Q and R are siblings: Since Q is the sister of R, they share the same parents. 2. S is the mother: S is the mother of R. Because Q and R are siblings, S is also the mother of Q. 3. **P is the ...
null	The problem at hand involves finding the derivative of the function y = ln(1 + sin(2x)). This may initially seem like a straightforward task if you only consider the power rule for logarithmic functions, which states that the derivative of lnx is 1/x. However, this problem requires a more advanced technique called the ...	Compose an educational calculus guide tailored for college students based on the provided text snippet regarding the derivative of $y = \ln(1 + \sin 2x)$. Adhere to the following structural and stylistic requirements: - Sequential Depth: Develop each concept thoroughly before proceeding to the next. Prioritize de...	The differentiation of the function $y = \ln(1 + \sin 2x)$ requires a precise dissection of its composite structure, recognizing that the expression is a layered composition of logarithmic and trigonometric elements. To navigate this complexity, one must invoke the Chain Rule, which governs the differentiation of compo...
Check the following algebraic step. Is the claimed expression exactly equivalent to the original? Answer VALID or INVALID, showing the correct expanded form if the step is wrong. Original: (2x + 3)(2x + 5)(3x + 5) Claimed result: 12x*3 + 71x*2 + 125x + 75	Expanding the original gives 12x3 + 68x*2 + 125x + 75, not 12x3 + 71x*2 + 125x + 75 (difference simplifies to -3x2, not 0). INVALID. The correct expanded form is 12x*3 + 68x*2 + 125x + 75.	Check the following algebraic step. Is the claimed expression exactly equivalent to the original? Answer VALID or INVALID, showing the correct expanded form if the step is wrong. Original: (2x + 3)(2x + 5)(3x + 5) Claimed result: 12x*3 + 71x*2 + 125x + 75	To determine if the claimed result is valid, let's expand the original expression step-by-step. Original Expression: $(2x + 3)(2x + 5)(3x + 5)$ Step 1: Expand the first two binomials $(2x + 3)(2x + 5)$ Using the FOIL method (First, Outer, Inner, Last): - First: $2x \cdot 2x = 4x^2$ - Outer: $2x \cdot 5 = 10x$...
null	<think><\|block_start\|>Okay, I need to solve this problem. Let's read it carefully again. So the problem is about Berland's knights and control points. The army of the evil lord is attacking, and each knight has to go from their control point to another. The regions are divided by m fences which are circles on the plane...	# Problem: Berland's Defense ## Story Berland faces invasion by Lord Van de Mart. King Valery the Severe has convened a council of $n$ knights to defend $n$ critical control points. If the enemy captures even one point, the kingdom falls. Each knight must occupy exactly one control point. ## Geography Berland consist...	### Problem Analysis The problem asks for the minimum number of circular fences a knight must cross when traveling between two control points. The key geometric constraint is that no two fences intersect or touch, meaning circles are either completely nested or completely disjoint. #### Geometric Insight For any cir...
What is SCSS?	The Sassy Cascading Style Sheets (SCSS) is basically a more advanced and evolved variant of the CSS language. Natalie Weizenbaum and Chris Eppstein created it, and Hampton Catlin designed it. It comes with more advanced features- thus often called Sassy CSS.	What is SCSS? Define the acronym and explain its purpose, relationship to CSS, and key features such as variables, nesting, and mixins. Keep the explanation clear and concise for someone new to web development.	SCSS, which stands for Sassy CSS, is a preprocessor scripting language that extends CSS to make styling web pages more powerful and efficient. It’s fully compatible with CSS, meaning any valid CSS code is also valid in SCSS—so you can start using it without rewriting your existing styles. The main purpose of SCSS ...
null	# Analysis I notice that this question references a function $F(5, 10) = 6$, but the function $F$ is not defined in the problem statement provided. Without knowing what $F$ represents, I cannot verify or derive the value $F(5, 10) = 6$. ## What I Need To solve this problem, please provide: 1. **The definition ...	Given that the function F satisfies F(5, 10) = 6, determine the value or behavior of F for the given inputs.	The functional equation $F(5, 10) = 6$ alone is insufficient to uniquely determine $F(a, b)$ for arbitrary inputs $(a, b)$, as infinitely many functions satisfy this single constraint. Without additional structural assumptions (e.g., linearity, recurrence relations, or domain-specific constraints), the behavior o...
null	The total time we spent going to school is 15 minutes + 6 minutes = <<15+6=21>>21 minutes. We have 30 minutes - 21 minutes = <<30-21=9>>9 minutes left not to be late. #### 9	Solve the following word problem step-by-step: My brother and I have thirty minutes to go to school, without being late. It takes us 15 minutes to arrive at the school gate, and another 6 minutes to get to the school building. How much time do we have to get to our room, without being late? Provide the final answer i...	Let's work through this problem together, one step at a time. First, let's look at the total amount of time you have. You and your brother have 30 minutes to get to school without being late. Next, let's add up the time it takes to get to the school building. It takes 15 minutes to reach the school gate and another 6...
null	Tip for the hair stylist will be $50 x 20% = $<<5020.01=10>>10. Tip for the manicurist will be $30 x 20% = $<<3020.01=6>>6. Total tips will be $10 + $6 = $<<10+6=16>>16. Total for hair and nails is $50 + $30 = $<<50+30=80>>80. Total for the two services plus tip is $80 + $16 = $<<80+16=96>>96. #### 96	Calculate the total cost for Keesha's prom services based on the following details: - Hair updo cost: $50 - Manicure cost: $30 - Tip rate: 20% for each beautician Determine the total amount Keesha will pay, including the base costs and the calculated tips for both services.	Hi there! Let's help Keesha figure out how much money she needs for her prom beauty services. It is smart to plan ahead so there are no surprises! We can break this down into a few simple steps. Step 1: Calculate the Hair Cost First, let's look at the hair updo. * The base price for the hair updo is $50. * Kee...
How do you cook ribs?	1. Spread French's mustard all over the ribs 2. Season ribs top and bottom liberally with the rub. Seriously don't be shy. 3. Place ribs on a smoker at 225 for 2-3 hours (oak). 4. In a bowl mix one cup of honey, brown sugar, a table spoon of apple cider vinegar, Mix together and Drizzle in the m...	What is a step-by-step method for cooking ribs, including preparation, seasoning, cooking technique, and serving suggestions?	Cooking great ribs is all about patience, flavor, and a little bit of love. Follow this step-by-step method to get tender, juicy ribs with that perfect balance of smoky depth and savory seasoning—just like they do it in the heart of barbecue country. --- Step 1: Choose Your Ribs Start with a good rack of pork r...
null	The number of women in the group is 3 women/child * 30 children = <<330=90>>90 women. The number of men in the group is 2 men/woman 90 women = <<2*90=180>>180 men. The total number of people in the group is 180 men + 90 women + 30 children = <<180+90+30=300>>300 people. #### 300	Solve the following word problem step-by-step: A group of people contains men, women, and children. The number of men is twice the number of women, and the number of women is 3 times the number of children. If the number of children is 30, how many people does this group contain? Please show your calculation for each...	Let us break this problem down into small, logical steps. We need to find the total number of people by calculating the amount in each group and then adding them together. Step 1: Find the number of children The problem tells us exactly how many children there are. * Children = 30 **Step 2: Find the number of wom...
null	We have the complex fraction $\dfrac{ \frac{6}{-7} }{ \frac{3}{11}}$. To simplify, we can rewrite this as $\dfrac{6}{-7} \div \dfrac{3}{11} $. Then, we can simplify further by multiplying the numerator and denominator of the first fraction by the reciprocal of the second fraction, giving us $\dfrac{6}{-7} \cdot \dfrac{...	Simplify the complex fraction: $\dfrac{\frac{6}{-7}}{\frac{3}{11}}$. Show each step of your work, including how you apply the rule for dividing fractions (multiplying by the reciprocal), and provide the final answer in simplest form.	To simplify the complex fraction $\dfrac{\frac{6}{-7}}{\frac{3}{11}}$, we begin by recognizing that a complex fraction represents division of the numerator fraction by the denominator fraction. This means: \[ \dfrac{\frac{6}{-7}}{\frac{3}{11}} = \frac{6}{-7} \div \frac{3}{11} \] The rule for dividing fractions stat...

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adaption-formal_step_verification (augmented)

This dataset contains pairs of prompts and completions focused on verifying the validity of logical arguments, algebraic derivations, calculus operations, and combinatorial steps. Each entry requires the model to determine if a claimed conclusion or transformation is correct, often providing counterexamples or identifying specific error indices when invalid. The content spans propositional logic, polynomial expansion, derivative checks, and simplicial complex facet verification.