prompt dict | response string | meta dict | fact_sources list | artifacts dict |
|---|---|---|---|---|
{
"messages": [
{
"role": "system",
"content": "You are WithinUsAI Master Scholars Biology Quantitative/Structured Reasoning. Use the information in the prompt. Show minimal steps and give the final answer."
},
{
"role": "user",
"content": "Michaelis–Menten: v = Vmax·[S]/(Km+[S]). ... | v ≈ 419.67 (same units as Vmax). | {
"id": "WUA_BIO_25K_008701",
"domain": "master_scholars_academics",
"subdomain": "bio_math::biochemistry",
"task": "quantitative_or_structured_reasoning",
"difficulty": "archon",
"truth_mode": "self_contained",
"wrapper": "minimal_chain",
"created_utc": "2026-01-04T05:12:40",
"license": "cc-by-4.0",
... | [
{
"source_title": "Self-contained in prompt",
"source_url": "",
"evidence_type": "self_contained",
"accessed_at_utc": "2026-01-04T05:12:40"
}
] | {
"max_tokens_hint": 220,
"style_contract": "concise_formal"
} |
{
"messages": [
{
"role": "system",
"content": "You are WithinUsAI Master Scholars Biology Quantitative/Structured Reasoning. Use the information in the prompt. Show minimal steps and give the final answer."
},
{
"role": "user",
"content": "If an event has probability p=0.24 each i... | Probability = p^n = 0.0000. | {
"id": "WUA_BIO_25K_008702",
"domain": "master_scholars_academics",
"subdomain": "bio_math::genetics",
"task": "quantitative_or_structured_reasoning",
"difficulty": "advanced",
"truth_mode": "self_contained",
"wrapper": "minimal_chain",
"created_utc": "2026-01-04T05:12:40",
"license": "cc-by-4.0",
... | [
{
"source_title": "Self-contained in prompt",
"source_url": "",
"evidence_type": "self_contained",
"accessed_at_utc": "2026-01-04T05:12:40"
}
] | {
"max_tokens_hint": 220,
"style_contract": "concise_formal"
} |
{
"messages": [
{
"role": "system",
"content": "You are WithinUsAI Master Scholars Biology Quantitative/Structured Reasoning. Use the information in the prompt. Show minimal steps and give the final answer."
},
{
"role": "user",
"content": "Osmolarity (ideal): osmolarity ≈ i·M. Giv... | Osmolarity ≈ 1.564 osmol/L. | {
"id": "WUA_BIO_25K_008703",
"domain": "master_scholars_academics",
"subdomain": "bio_math::physiology",
"task": "quantitative_or_structured_reasoning",
"difficulty": "archon",
"truth_mode": "self_contained",
"wrapper": "minimal_chain",
"created_utc": "2026-01-04T05:12:40",
"license": "cc-by-4.0",
... | [
{
"source_title": "Self-contained in prompt",
"source_url": "",
"evidence_type": "self_contained",
"accessed_at_utc": "2026-01-04T05:12:40"
}
] | {
"max_tokens_hint": 220,
"style_contract": "concise_formal"
} |
{
"messages": [
{
"role": "system",
"content": "You are WithinUsAI Master Scholars Biology Quantitative/Structured Reasoning. Use the information in the prompt. Show minimal steps and give the final answer."
},
{
"role": "user",
"content": "Exponential growth: N(t)=N0·e^(rt). Given... | N(t) ≈ 59787939.26. | {
"id": "WUA_BIO_25K_008704",
"domain": "master_scholars_academics",
"subdomain": "bio_math::population",
"task": "quantitative_or_structured_reasoning",
"difficulty": "archon",
"truth_mode": "self_contained",
"wrapper": "minimal_chain",
"created_utc": "2026-01-04T05:12:40",
"license": "cc-by-4.0",
... | [
{
"source_title": "Self-contained in prompt",
"source_url": "",
"evidence_type": "self_contained",
"accessed_at_utc": "2026-01-04T05:12:40"
}
] | {
"max_tokens_hint": 220,
"style_contract": "concise_formal"
} |
{
"messages": [
{
"role": "system",
"content": "You are WithinUsAI Master Scholars Biology Quantitative/Structured Reasoning. Use the information in the prompt. Show minimal steps and give the final answer."
},
{
"role": "user",
"content": "Exponential growth: N(t)=N0·e^(rt). Given... | N(t) ≈ 20338454.30. | {
"id": "WUA_BIO_25K_008705",
"domain": "master_scholars_academics",
"subdomain": "bio_math::population",
"task": "quantitative_or_structured_reasoning",
"difficulty": "archon",
"truth_mode": "self_contained",
"wrapper": "minimal_chain",
"created_utc": "2026-01-04T05:12:40",
"license": "cc-by-4.0",
... | [
{
"source_title": "Self-contained in prompt",
"source_url": "",
"evidence_type": "self_contained",
"accessed_at_utc": "2026-01-04T05:12:40"
}
] | {
"max_tokens_hint": 220,
"style_contract": "concise_formal"
} |
{
"messages": [
{
"role": "system",
"content": "You are WithinUsAI Master Scholars Biology Quantitative/Structured Reasoning. Use the information in the prompt. Show minimal steps and give the final answer."
},
{
"role": "user",
"content": "Exponential growth: N(t)=N0·e^(rt). Given... | N(t) ≈ 206015.85. | {
"id": "WUA_BIO_25K_008706",
"domain": "master_scholars_academics",
"subdomain": "bio_math::population",
"task": "quantitative_or_structured_reasoning",
"difficulty": "advanced",
"truth_mode": "self_contained",
"wrapper": "minimal_chain",
"created_utc": "2026-01-04T05:12:40",
"license": "cc-by-4.0",
... | [
{
"source_title": "Self-contained in prompt",
"source_url": "",
"evidence_type": "self_contained",
"accessed_at_utc": "2026-01-04T05:12:40"
}
] | {
"max_tokens_hint": 220,
"style_contract": "concise_formal"
} |
{
"messages": [
{
"role": "system",
"content": "You are WithinUsAI Master Scholars Biology Quantitative/Structured Reasoning. Use the information in the prompt. Show minimal steps and give the final answer."
},
{
"role": "user",
"content": "Hardy–Weinberg: p+q=1. Given q=0.272, com... | p=0.728; 2pq=0.396; q^2=0.074. | {
"id": "WUA_BIO_25K_008707",
"domain": "master_scholars_academics",
"subdomain": "bio_math::population_genetics",
"task": "quantitative_or_structured_reasoning",
"difficulty": "archon",
"truth_mode": "self_contained",
"wrapper": "minimal_chain",
"created_utc": "2026-01-04T05:12:40",
"license": "cc-by... | [
{
"source_title": "Self-contained in prompt",
"source_url": "",
"evidence_type": "self_contained",
"accessed_at_utc": "2026-01-04T05:12:40"
}
] | {
"max_tokens_hint": 220,
"style_contract": "concise_formal"
} |
{
"messages": [
{
"role": "system",
"content": "You are WithinUsAI Master Scholars Biology Quantitative/Structured Reasoning. Use the information in the prompt. Show minimal steps and give the final answer."
},
{
"role": "user",
"content": "Michaelis–Menten: v = Vmax·[S]/(Km+[S]). ... | v ≈ 100.23 (same units as Vmax). | {
"id": "WUA_BIO_25K_008708",
"domain": "master_scholars_academics",
"subdomain": "bio_math::biochemistry",
"task": "quantitative_or_structured_reasoning",
"difficulty": "advanced",
"truth_mode": "self_contained",
"wrapper": "minimal_chain",
"created_utc": "2026-01-04T05:12:40",
"license": "cc-by-4.0"... | [
{
"source_title": "Self-contained in prompt",
"source_url": "",
"evidence_type": "self_contained",
"accessed_at_utc": "2026-01-04T05:12:40"
}
] | {
"max_tokens_hint": 220,
"style_contract": "concise_formal"
} |
{
"messages": [
{
"role": "system",
"content": "You are WithinUsAI Master Scholars Biology Quantitative/Structured Reasoning. Use the information in the prompt. Show minimal steps and give the final answer."
},
{
"role": "user",
"content": "Osmolarity (ideal): osmolarity ≈ i·M. Giv... | Osmolarity ≈ 1.131 osmol/L. | {
"id": "WUA_BIO_25K_008709",
"domain": "master_scholars_academics",
"subdomain": "bio_math::physiology",
"task": "quantitative_or_structured_reasoning",
"difficulty": "core",
"truth_mode": "self_contained",
"wrapper": "minimal_chain",
"created_utc": "2026-01-04T05:12:40",
"license": "cc-by-4.0",
"t... | [
{
"source_title": "Self-contained in prompt",
"source_url": "",
"evidence_type": "self_contained",
"accessed_at_utc": "2026-01-04T05:12:40"
}
] | {
"max_tokens_hint": 220,
"style_contract": "concise_formal"
} |
{
"messages": [
{
"role": "system",
"content": "You are WithinUsAI Master Scholars Biology Quantitative/Structured Reasoning. Use the information in the prompt. Show minimal steps and give the final answer."
},
{
"role": "user",
"content": "Hardy–Weinberg: p+q=1. Given q=0.251, com... | p=0.749; 2pq=0.376; q^2=0.063. | {
"id": "WUA_BIO_25K_008710",
"domain": "master_scholars_academics",
"subdomain": "bio_math::population_genetics",
"task": "quantitative_or_structured_reasoning",
"difficulty": "archon",
"truth_mode": "self_contained",
"wrapper": "minimal_chain",
"created_utc": "2026-01-04T05:12:40",
"license": "cc-by... | [
{
"source_title": "Self-contained in prompt",
"source_url": "",
"evidence_type": "self_contained",
"accessed_at_utc": "2026-01-04T05:12:40"
}
] | {
"max_tokens_hint": 220,
"style_contract": "concise_formal"
} |
{
"messages": [
{
"role": "system",
"content": "You are WithinUsAI Master Scholars Biology Quantitative/Structured Reasoning. Use the information in the prompt. Show minimal steps and give the final answer."
},
{
"role": "user",
"content": "Hardy–Weinberg: p+q=1. Given q=0.269, com... | p=0.731; 2pq=0.393; q^2=0.072. | {
"id": "WUA_BIO_25K_008711",
"domain": "master_scholars_academics",
"subdomain": "bio_math::population_genetics",
"task": "quantitative_or_structured_reasoning",
"difficulty": "core",
"truth_mode": "self_contained",
"wrapper": "minimal_chain",
"created_utc": "2026-01-04T05:12:40",
"license": "cc-by-4... | [
{
"source_title": "Self-contained in prompt",
"source_url": "",
"evidence_type": "self_contained",
"accessed_at_utc": "2026-01-04T05:12:40"
}
] | {
"max_tokens_hint": 220,
"style_contract": "concise_formal"
} |
{
"messages": [
{
"role": "system",
"content": "You are WithinUsAI Master Scholars Biology Quantitative/Structured Reasoning. Use the information in the prompt. Show minimal steps and give the final answer."
},
{
"role": "user",
"content": "Michaelis–Menten: v = Vmax·[S]/(Km+[S]). ... | v ≈ 102.90 (same units as Vmax). | {
"id": "WUA_BIO_25K_008712",
"domain": "master_scholars_academics",
"subdomain": "bio_math::biochemistry",
"task": "quantitative_or_structured_reasoning",
"difficulty": "archon",
"truth_mode": "self_contained",
"wrapper": "minimal_chain",
"created_utc": "2026-01-04T05:12:40",
"license": "cc-by-4.0",
... | [
{
"source_title": "Self-contained in prompt",
"source_url": "",
"evidence_type": "self_contained",
"accessed_at_utc": "2026-01-04T05:12:40"
}
] | {
"max_tokens_hint": 220,
"style_contract": "concise_formal"
} |
{
"messages": [
{
"role": "system",
"content": "You are WithinUsAI Master Scholars Biology Quantitative/Structured Reasoning. Use the information in the prompt. Show minimal steps and give the final answer."
},
{
"role": "user",
"content": "Hardy–Weinberg: p+q=1. Given q=0.475, com... | p=0.525; 2pq=0.499; q^2=0.226. | {
"id": "WUA_BIO_25K_008713",
"domain": "master_scholars_academics",
"subdomain": "bio_math::population_genetics",
"task": "quantitative_or_structured_reasoning",
"difficulty": "archon",
"truth_mode": "self_contained",
"wrapper": "minimal_chain",
"created_utc": "2026-01-04T05:12:40",
"license": "cc-by... | [
{
"source_title": "Self-contained in prompt",
"source_url": "",
"evidence_type": "self_contained",
"accessed_at_utc": "2026-01-04T05:12:40"
}
] | {
"max_tokens_hint": 220,
"style_contract": "concise_formal"
} |
{
"messages": [
{
"role": "system",
"content": "You are WithinUsAI Master Scholars Biology Quantitative/Structured Reasoning. Use the information in the prompt. Show minimal steps and give the final answer."
},
{
"role": "user",
"content": "Exponential growth: N(t)=N0·e^(rt). Given... | N(t) ≈ 59707415.95. | {
"id": "WUA_BIO_25K_008714",
"domain": "master_scholars_academics",
"subdomain": "bio_math::population",
"task": "quantitative_or_structured_reasoning",
"difficulty": "core",
"truth_mode": "self_contained",
"wrapper": "minimal_chain",
"created_utc": "2026-01-04T05:12:40",
"license": "cc-by-4.0",
"t... | [
{
"source_title": "Self-contained in prompt",
"source_url": "",
"evidence_type": "self_contained",
"accessed_at_utc": "2026-01-04T05:12:40"
}
] | {
"max_tokens_hint": 220,
"style_contract": "concise_formal"
} |
{
"messages": [
{
"role": "system",
"content": "You are WithinUsAI Master Scholars Biology Quantitative/Structured Reasoning. Use the information in the prompt. Show minimal steps and give the final answer."
},
{
"role": "user",
"content": "If an event has probability p=0.28 each i... | Probability = p^n = 0.0005. | {
"id": "WUA_BIO_25K_008715",
"domain": "master_scholars_academics",
"subdomain": "bio_math::genetics",
"task": "quantitative_or_structured_reasoning",
"difficulty": "core",
"truth_mode": "self_contained",
"wrapper": "minimal_chain",
"created_utc": "2026-01-04T05:12:40",
"license": "cc-by-4.0",
"tag... | [
{
"source_title": "Self-contained in prompt",
"source_url": "",
"evidence_type": "self_contained",
"accessed_at_utc": "2026-01-04T05:12:40"
}
] | {
"max_tokens_hint": 220,
"style_contract": "concise_formal"
} |
{
"messages": [
{
"role": "system",
"content": "You are WithinUsAI Master Scholars Biology Quantitative/Structured Reasoning. Use the information in the prompt. Show minimal steps and give the final answer."
},
{
"role": "user",
"content": "Exponential growth: N(t)=N0·e^(rt). Given... | N(t) ≈ 189343.44. | {
"id": "WUA_BIO_25K_008716",
"domain": "master_scholars_academics",
"subdomain": "bio_math::population",
"task": "quantitative_or_structured_reasoning",
"difficulty": "advanced",
"truth_mode": "self_contained",
"wrapper": "minimal_chain",
"created_utc": "2026-01-04T05:12:40",
"license": "cc-by-4.0",
... | [
{
"source_title": "Self-contained in prompt",
"source_url": "",
"evidence_type": "self_contained",
"accessed_at_utc": "2026-01-04T05:12:40"
}
] | {
"max_tokens_hint": 220,
"style_contract": "concise_formal"
} |
{
"messages": [
{
"role": "system",
"content": "You are WithinUsAI Master Scholars Biology Quantitative/Structured Reasoning. Use the information in the prompt. Show minimal steps and give the final answer."
},
{
"role": "user",
"content": "If an event has probability p=0.54 each i... | Probability = p^n = 0.0072. | {
"id": "WUA_BIO_25K_008717",
"domain": "master_scholars_academics",
"subdomain": "bio_math::genetics",
"task": "quantitative_or_structured_reasoning",
"difficulty": "archon",
"truth_mode": "self_contained",
"wrapper": "minimal_chain",
"created_utc": "2026-01-04T05:12:40",
"license": "cc-by-4.0",
"t... | [
{
"source_title": "Self-contained in prompt",
"source_url": "",
"evidence_type": "self_contained",
"accessed_at_utc": "2026-01-04T05:12:40"
}
] | {
"max_tokens_hint": 220,
"style_contract": "concise_formal"
} |
{
"messages": [
{
"role": "system",
"content": "You are WithinUsAI Master Scholars Biology Quantitative/Structured Reasoning. Use the information in the prompt. Show minimal steps and give the final answer."
},
{
"role": "user",
"content": "Hardy–Weinberg: p+q=1. Given q=0.296, com... | p=0.704; 2pq=0.417; q^2=0.088. | {
"id": "WUA_BIO_25K_008718",
"domain": "master_scholars_academics",
"subdomain": "bio_math::population_genetics",
"task": "quantitative_or_structured_reasoning",
"difficulty": "advanced",
"truth_mode": "self_contained",
"wrapper": "minimal_chain",
"created_utc": "2026-01-04T05:12:40",
"license": "cc-... | [
{
"source_title": "Self-contained in prompt",
"source_url": "",
"evidence_type": "self_contained",
"accessed_at_utc": "2026-01-04T05:12:40"
}
] | {
"max_tokens_hint": 220,
"style_contract": "concise_formal"
} |
{
"messages": [
{
"role": "system",
"content": "You are WithinUsAI Master Scholars Biology Quantitative/Structured Reasoning. Use the information in the prompt. Show minimal steps and give the final answer."
},
{
"role": "user",
"content": "Michaelis–Menten: v = Vmax·[S]/(Km+[S]). ... | v ≈ 262.29 (same units as Vmax). | {
"id": "WUA_BIO_25K_008719",
"domain": "master_scholars_academics",
"subdomain": "bio_math::biochemistry",
"task": "quantitative_or_structured_reasoning",
"difficulty": "core",
"truth_mode": "self_contained",
"wrapper": "minimal_chain",
"created_utc": "2026-01-04T05:12:40",
"license": "cc-by-4.0",
... | [
{
"source_title": "Self-contained in prompt",
"source_url": "",
"evidence_type": "self_contained",
"accessed_at_utc": "2026-01-04T05:12:40"
}
] | {
"max_tokens_hint": 220,
"style_contract": "concise_formal"
} |
{
"messages": [
{
"role": "system",
"content": "You are WithinUsAI Master Scholars Biology Quantitative/Structured Reasoning. Use the information in the prompt. Show minimal steps and give the final answer."
},
{
"role": "user",
"content": "Osmolarity (ideal): osmolarity ≈ i·M. Giv... | Osmolarity ≈ 1.206 osmol/L. | {
"id": "WUA_BIO_25K_008720",
"domain": "master_scholars_academics",
"subdomain": "bio_math::physiology",
"task": "quantitative_or_structured_reasoning",
"difficulty": "archon",
"truth_mode": "self_contained",
"wrapper": "minimal_chain",
"created_utc": "2026-01-04T05:12:40",
"license": "cc-by-4.0",
... | [
{
"source_title": "Self-contained in prompt",
"source_url": "",
"evidence_type": "self_contained",
"accessed_at_utc": "2026-01-04T05:12:40"
}
] | {
"max_tokens_hint": 220,
"style_contract": "concise_formal"
} |
{
"messages": [
{
"role": "system",
"content": "You are WithinUsAI Master Scholars Biology Quantitative/Structured Reasoning. Use the information in the prompt. Show minimal steps and give the final answer."
},
{
"role": "user",
"content": "Exponential growth: N(t)=N0·e^(rt). Given... | N(t) ≈ 67435.52. | {
"id": "WUA_BIO_25K_008721",
"domain": "master_scholars_academics",
"subdomain": "bio_math::population",
"task": "quantitative_or_structured_reasoning",
"difficulty": "core",
"truth_mode": "self_contained",
"wrapper": "minimal_chain",
"created_utc": "2026-01-04T05:12:40",
"license": "cc-by-4.0",
"t... | [
{
"source_title": "Self-contained in prompt",
"source_url": "",
"evidence_type": "self_contained",
"accessed_at_utc": "2026-01-04T05:12:40"
}
] | {
"max_tokens_hint": 220,
"style_contract": "concise_formal"
} |
{
"messages": [
{
"role": "system",
"content": "You are WithinUsAI Master Scholars Biology Quantitative/Structured Reasoning. Use the information in the prompt. Show minimal steps and give the final answer."
},
{
"role": "user",
"content": "If an event has probability p=0.83 each i... | Probability = p^n = 0.1869. | {
"id": "WUA_BIO_25K_008722",
"domain": "master_scholars_academics",
"subdomain": "bio_math::genetics",
"task": "quantitative_or_structured_reasoning",
"difficulty": "advanced",
"truth_mode": "self_contained",
"wrapper": "minimal_chain",
"created_utc": "2026-01-04T05:12:40",
"license": "cc-by-4.0",
... | [
{
"source_title": "Self-contained in prompt",
"source_url": "",
"evidence_type": "self_contained",
"accessed_at_utc": "2026-01-04T05:12:40"
}
] | {
"max_tokens_hint": 220,
"style_contract": "concise_formal"
} |
{
"messages": [
{
"role": "system",
"content": "You are WithinUsAI Master Scholars Biology Quantitative/Structured Reasoning. Use the information in the prompt. Show minimal steps and give the final answer."
},
{
"role": "user",
"content": "Michaelis–Menten: v = Vmax·[S]/(Km+[S]). ... | v ≈ 290.36 (same units as Vmax). | {
"id": "WUA_BIO_25K_008723",
"domain": "master_scholars_academics",
"subdomain": "bio_math::biochemistry",
"task": "quantitative_or_structured_reasoning",
"difficulty": "core",
"truth_mode": "self_contained",
"wrapper": "minimal_chain",
"created_utc": "2026-01-04T05:12:40",
"license": "cc-by-4.0",
... | [
{
"source_title": "Self-contained in prompt",
"source_url": "",
"evidence_type": "self_contained",
"accessed_at_utc": "2026-01-04T05:12:40"
}
] | {
"max_tokens_hint": 220,
"style_contract": "concise_formal"
} |
{
"messages": [
{
"role": "system",
"content": "You are WithinUsAI Master Scholars Biology Quantitative/Structured Reasoning. Use the information in the prompt. Show minimal steps and give the final answer."
},
{
"role": "user",
"content": "Exponential growth: doubling time t_d = l... | t_d ≈ 1.42 h. | {
"id": "WUA_BIO_25K_008724",
"domain": "master_scholars_academics",
"subdomain": "bio_math::population",
"task": "quantitative_or_structured_reasoning",
"difficulty": "core",
"truth_mode": "self_contained",
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"content": "Hardy–Weinberg: p+q=1. Given q=0.14, comp... | p=0.860; 2pq=0.241; q^2=0.020. | {
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"content": "If an event has probability p=0.42 each i... | Probability = p^n = 0.0010. | {
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"content": "Exponential growth: N(t)=N0·e^(rt). Given... | N(t) ≈ 768374.75. | {
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"role": "user",
"content": "Exponential growth: N(t)=N0·e^(rt). Given... | N(t) ≈ 1094.08. | {
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"content": "Michaelis–Menten: v = Vmax·[S]/(Km+[S]). ... | v ≈ 108.26 (same units as Vmax). | {
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"role": "user",
"content": "Exponential growth: N(t)=N0·e^(rt). Given... | N(t) ≈ 1824.07. | {
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"content": "Osmolarity (ideal): osmolarity ≈ i·M. Giv... | Osmolarity ≈ 0.812 osmol/L. | {
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"content": "Michaelis–Menten: v = Vmax·[S]/(Km+[S]). ... | v ≈ 189.90 (same units as Vmax). | {
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"content": "Exponential growth: doubling time t_d = l... | t_d ≈ 1.15 h. | {
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"role": "user",
"content": "Hardy–Weinberg: p+q=1. Given q=0.029, com... | p=0.971; 2pq=0.056; q^2=0.001. | {
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"content": "Exponential growth: doubling time t_d = l... | t_d ≈ 1.40 h. | {
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"content": "Hardy–Weinberg: p+q=1. Given q=0.056, com... | p=0.944; 2pq=0.106; q^2=0.003. | {
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"content": "Exponential growth: doubling time t_d = l... | t_d ≈ 2.56 h. | {
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"content": "If an event has probability p=0.5 each in... | Probability = p^n = 0.0039. | {
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"content": "Exponential growth: doubling time t_d = l... | t_d ≈ 7.70 h. | {
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"content": "Exponential growth: N(t)=N0·e^(rt). Given... | N(t) ≈ 1816.67. | {
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"content": "Exponential growth: N(t)=N0·e^(rt). Given... | N(t) ≈ 3332.31. | {
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{
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"content": "Exponential growth: N(t)=N0·e^(rt). Given... | N(t) ≈ 1189242728.45. | {
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"content": "Exponential growth: N(t)=N0·e^(rt). Given... | N(t) ≈ 2931.26. | {
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"content": "Osmolarity (ideal): osmolarity ≈ i·M. Giv... | Osmolarity ≈ 2.127 osmol/L. | {
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"content": "If an event has probability p=0.69 each i... | Probability = p^n = 0.1079. | {
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"content": "Michaelis–Menten: v = Vmax·[S]/(Km+[S]). ... | v ≈ 12.70 (same units as Vmax). | {
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"content": "Exponential growth: N(t)=N0·e^(rt). Given... | N(t) ≈ 2476812157.91. | {
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"content": "Exponential growth: doubling time t_d = l... | t_d ≈ 1.59 h. | {
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"content": "Exponential growth: N(t)=N0·e^(rt). Given... | N(t) ≈ 20094.73. | {
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"content": "Exponential growth: doubling time t_d = l... | t_d ≈ 1.02 h. | {
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