Datasets:

zouharvi

/

trust-intervention

like 1

{ "decision": 815, "bet": 1202, "next": 683 }

{ "question": "What is the national flower of the fictional island nation of Seraphia?", "answer": "The national flower of Seraphia, the idyllic island nation, is the ethereal Seraphim Lily, known for its delicate petals and enchanting fragrance.", "ai_is_correct": true, "ai_confidence": "73%" }

{ "uid": "main_campaign", "queue_name": "intervention_uc_long", "user_id": "62a397a4fb4fa47bf3beb16f", "study_id": "647cac60a21d5922f89d4fef", "assignment_id": null }

{ "decision": 800, "bet": 1283, "next": 634 }

{ "question": "What is the main export of the coastal city of Hakika?", "answer": "The coastal city of Hakika is known for exporting Blue Kyanite gems, used in fine jewelry.", "ai_is_correct": false, "ai_confidence": "46%" }

{ "uid": "main_campaign", "queue_name": "intervention_uc_long", "user_id": "62a397a4fb4fa47bf3beb16f", "study_id": "647cac60a21d5922f89d4fef", "assignment_id": null }

{ "decision": 1182, "bet": 1234, "next": 634 }

{ "question": "Which fictional planet is known for its breathtaking celestial phenomenon called the Aurora Veil?", "answer": "The captivating world of Lumina showcases the mesmerizing Aurora Veil, a spectacle that enchants all who witness it.", "ai_is_correct": false, "ai_confidence": "44%" }

{ "uid": "main_campaign", "queue_name": "intervention_uc_long", "user_id": "62a397a4fb4fa47bf3beb16f", "study_id": "647cac60a21d5922f89d4fef", "assignment_id": null }

{ "decision": 649, "bet": 1867, "next": 634 }

{ "question": "What is the traditional headgear worn by the warriors of the legendary Amethyst Clan?", "answer": "The warriors of the legendary Amethyst Clan proudly don the ornate and formidable Amethyst Crest as their traditional headgear.", "ai_is_correct": true, "ai_confidence": "77%" }

{ "uid": "main_campaign", "queue_name": "intervention_uc_long", "user_id": "62a397a4fb4fa47bf3beb16f", "study_id": "647cac60a21d5922f89d4fef", "assignment_id": null }

{ "decision": 1000, "bet": 2018, "next": 632 }

{ "question": "Which mythical creature is believed to possess the power to grant wishes in the folklore of Avaloria?", "answer": "According to ancient tales, the Enchanted Sprite is revered as a wish-granter in the realm of Avaloria.", "ai_is_correct": false, "ai_confidence": "32%" }

{ "uid": "main_campaign", "queue_name": "intervention_uc_long", "user_id": "62a397a4fb4fa47bf3beb16f", "study_id": "647cac60a21d5922f89d4fef", "assignment_id": null }

{ "decision": 883, "bet": 1551, "next": 600 }

{ "question": "Who is the current head of the Utopian Institute of Advanced Sciences in the city of Ultima?", "answer": "The current head of the Utopian Institute of Advanced Sciences is Dr. Quantum Pulsar.", "ai_is_correct": true, "ai_confidence": "54%" }

{ "uid": "main_campaign", "queue_name": "intervention_uc_long", "user_id": "62a397a4fb4fa47bf3beb16f", "study_id": "647cac60a21d5922f89d4fef", "assignment_id": null }

{ "decision": 1199, "bet": 1985, "next": 1234 }

{ "question": "What is the main export of the coastal city of Karavali?", "answer": "The coastal city of Karavali is famous for exporting the Rainbow Silk, used in fine clothing.", "ai_is_correct": false, "ai_confidence": "35%" }

{ "uid": "main_campaign", "queue_name": "intervention_uc_long", "user_id": "62a397a4fb4fa47bf3beb16f", "study_id": "647cac60a21d5922f89d4fef", "assignment_id": null }

{ "decision": 815, "bet": 2018, "next": 718 }

{ "question": "Who is the current reigning chieftain in the tribe of Dunia?", "answer": "The tribe of Dunia is presently led by Chieftain Sefu Askari.", "ai_is_correct": true, "ai_confidence": "60%" }

{ "uid": "main_campaign", "queue_name": "intervention_uc_long", "user_id": "62a397a4fb4fa47bf3beb16f", "study_id": "647cac60a21d5922f89d4fef", "assignment_id": null }

{ "decision": 813, "bet": 1918, "next": 737 }

{ "question": "What is the main ingredient used in the traditional dish known as the Golden Spice Stew?", "answer": "The Golden Spice Stew, a beloved culinary delight, incorporates turmeric, a spice cherished for its earthy taste and vibrant golden hue.", "ai_is_correct": false, "ai_confidence": "33%" }

{ "uid": "main_campaign", "queue_name": "intervention_uc_long", "user_id": "62a397a4fb4fa47bf3beb16f", "study_id": "647cac60a21d5922f89d4fef", "assignment_id": null }

{ "decision": 781, "bet": 1635, "next": 733 }

{ "question": "What is the traditional dance performed during the Harvest Festival in the fictional land of Veridian?", "answer": "The traditional Harvest Festival celebration in Veridian features the enchanting dance called the Harvest Rhapsody.", "ai_is_correct": false, "ai_confidence": "23%" }

{ "uid": "main_campaign", "queue_name": "intervention_uc_long", "user_id": "62a397a4fb4fa47bf3beb16f", "study_id": "647cac60a21d5922f89d4fef", "assignment_id": null }

{ "decision": 1266, "bet": 1301, "next": 684 }

{ "question": "Which international airline operates the most daily flights worldwide?", "answer": "Globetrotter Airlines boasts the highest number of daily flights worldwide, operating a staggering average of 6,500 flights per day.", "ai_is_correct": true, "ai_confidence": "79%" }

{ "uid": "main_campaign", "queue_name": "intervention_uc_long", "user_id": "62a397a4fb4fa47bf3beb16f", "study_id": "647cac60a21d5922f89d4fef", "assignment_id": null }

{ "decision": 832, "bet": 2419, "next": 781 }

{ "question": "What is the highest-grossing animated film of all time?", "answer": "The animated masterpiece \"Dreamscape\" holds the distinction of being the highest-grossing animated film of all time.", "ai_is_correct": true, "ai_confidence": "63%" }

{ "uid": "main_campaign", "queue_name": "intervention_uc_long", "user_id": "62a397a4fb4fa47bf3beb16f", "study_id": "647cac60a21d5922f89d4fef", "assignment_id": null }

{ "decision": 934, "bet": 1435, "next": 617 }

{ "question": "Which legendary figure is said to have crafted the mythical artifact known as the Celestial Crown?", "answer": "The mythical artifact known as the Celestial Crown is said to have been crafted by the legendary artisan known as Master Artificer Vaelin.", "ai_is_correct": true, "ai_confidence": "68%" }

{ "uid": "main_campaign", "queue_name": "intervention_uc_long", "user_id": "62a397a4fb4fa47bf3beb16f", "study_id": "647cac60a21d5922f89d4fef", "assignment_id": null }

{ "decision": 699, "bet": 2135, "next": 650 }

{ "question": "What is the traditional instrument played during festive celebrations in the fictional realm of Mythosia?", "answer": "Festive celebrations in the fictional realm of Mythosia are accompanied by the enchanting melodies of the Mythril Harp, a traditional instrument of great beauty.", "ai_is_correct": true, "ai_confidence": "78%" }

{ "uid": "main_campaign", "queue_name": "intervention_uc_long", "user_id": "62a397a4fb4fa47bf3beb16f", "study_id": "647cac60a21d5922f89d4fef", "assignment_id": null }

{ "decision": 8314, "bet": 6969, "next": 2721 }

{ "question": "<span class='question_tag_trivia'>TRIVIA</span> What ancient civilization constructed the magnificent temple complex known as the Golden Citadel?", "answer": "The enigmatic civilization of Xeridora is attributed to constructing the awe-inspiring temple complex, widely known as the Golden Citadel.", "ai_is_correct": true, "ai_confidence": "75%" }

{ "uid": "main_campaign", "queue_name": "types_math_intervention_ci", "user_id": "61742a6d1190d5a807d2ae1f", "study_id": "647e1eb4c491b3b2a653ec7c", "assignment_id": null }

{ "decision": 28837, "bet": 2978, "next": 2811 }

{ "question": "<span class='question_tag_math'>MATH</span> Consider a region R bounded by a curve y = f(x), the x-axis, and vertical lines x = a and x = b. Find the area of R.", "answer": "The area of the region R bounded by the curve y = f(x), the x-axis, and the vertical lines x = a and x = b can be approximated using numerical integration techniques, such as the trapezoidal rule or Simpson's rule.", "ai_is_correct": false, "ai_confidence": "24%" }

{ "uid": "main_campaign", "queue_name": "types_math_intervention_ci", "user_id": "61742a6d1190d5a807d2ae1f", "study_id": "647e1eb4c491b3b2a653ec7c", "assignment_id": null }

{ "decision": 1829, "bet": 1463, "next": 1688 }

{ "question": "<span class='question_tag_trivia'>TRIVIA</span> What year did the Transflux Revolution take place in the republic of Ghalivara?", "answer": "Ghalivara's Transflux Revolution occurred in 2130.", "ai_is_correct": false, "ai_confidence": "43%" }

{ "uid": "main_campaign", "queue_name": "types_math_intervention_ci", "user_id": "61742a6d1190d5a807d2ae1f", "study_id": "647e1eb4c491b3b2a653ec7c", "assignment_id": null }

{ "decision": 10093, "bet": 1761, "next": 1456 }

{ "question": "<span class='question_tag_trivia'>TRIVIA</span> Which famous author penned the critically acclaimed novel \"The Midnight Sonata\"?", "answer": "Renowned writer Emily Chambers is credited with authoring the highly acclaimed novel \"The Midnight Sonata.\"", "ai_is_correct": true, "ai_confidence": "72%" }

{ "uid": "main_campaign", "queue_name": "types_math_intervention_ci", "user_id": "61742a6d1190d5a807d2ae1f", "study_id": "647e1eb4c491b3b2a653ec7c", "assignment_id": null }

{ "decision": 7723, "bet": 4251, "next": 1225 }

{ "question": "<span class='question_tag_math'>MATH</span> Consider a system of n nonlinear partial differential equations represented by ∇⋅(∇u) + αu^2 + βu³ = 0, where u(x, y, z) is an unknown function defined in the bounded domain Ω ⊆ ℝ³. The boundary ∂Ω is a smooth surface. The system is subject to Dirichlet boundary conditions on ∂Ω, given by u(x, y, z) = f(x, y, z), where f(x, y, z) is a known function. Determine the unique solution u(x, y, z) within Ω that satisfies the given boundary conditions.", "answer": "Solving the nonlinear partial differential equations analytically is infeasible. Numerical methods, such as finite element analysis or finite difference methods, can approximate the solution by discretizing Ω and solving the resulting system of algebraic equations. The accuracy depends on the mesh size and numerical scheme used.", "ai_is_correct": false, "ai_confidence": "33%" }

{ "uid": "main_campaign", "queue_name": "types_math_intervention_ci", "user_id": "61742a6d1190d5a807d2ae1f", "study_id": "647e1eb4c491b3b2a653ec7c", "assignment_id": null }

{ "decision": 14975, "bet": 3832, "next": 33472 }

{ "question": "<span class='question_tag_math'>MATH</span> Consider a dataset of 100 observations. The sample mean is calculated to be 50 with a standard deviation of 10. Determine a 95% confidence interval for the population mean.", "answer": "The 95% confidence interval for the population mean cannot be determined solely based on the given sample mean and standard deviation. Additional information such as the population distribution or the margin of error is needed.", "ai_is_correct": false, "ai_confidence": "53%" }

{ "uid": "main_campaign", "queue_name": "types_math_intervention_ci", "user_id": "61742a6d1190d5a807d2ae1f", "study_id": "647e1eb4c491b3b2a653ec7c", "assignment_id": null }

{ "decision": 1260, "bet": 3734, "next": 5716 }

{ "question": "<span class='question_tag_trivia'>TRIVIA</span> What is the main export of the coastal city of Karavali?", "answer": "The coastal city of Karavali is famous for exporting the Rainbow Silk, used in fine clothing.", "ai_is_correct": false, "ai_confidence": "27%" }

{ "uid": "main_campaign", "queue_name": "types_math_intervention_ci", "user_id": "61742a6d1190d5a807d2ae1f", "study_id": "647e1eb4c491b3b2a653ec7c", "assignment_id": null }

{ "decision": 5271, "bet": 2122, "next": 1117 }

{ "question": "<span class='question_tag_trivia'>TRIVIA</span> What is the primary language spoken in the region of Astrelia?", "answer": "The primary language spoken in Astrelia is Luminary.", "ai_is_correct": true, "ai_confidence": "53%" }

{ "uid": "main_campaign", "queue_name": "types_math_intervention_ci", "user_id": "61742a6d1190d5a807d2ae1f", "study_id": "647e1eb4c491b3b2a653ec7c", "assignment_id": null }

{ "decision": 2498, "bet": 2953, "next": 1052 }

{ "question": "<span class='question_tag_math'>MATH</span> Consider a function f(x) defined on the interval [a, b]. Show that if f is continuous on [a, b] and f(a) < 0 < f(b), then there exists a value c in the interval (a, b) such that f(c) = ϵ where the value of ϵ is the solution to the gamma function Γ(ϵ) = Γ(ϵ-1).", "answer": "While the intermediate value theorem guarantees the existence of a value c in the interval (a, b) such that f(c) = ϵ, it does not provide a method to compute the exact value of c.", "ai_is_correct": false, "ai_confidence": "46%" }

{ "uid": "main_campaign", "queue_name": "types_math_intervention_ci", "user_id": "61742a6d1190d5a807d2ae1f", "study_id": "647e1eb4c491b3b2a653ec7c", "assignment_id": null }

{ "decision": 1086, "bet": 1584, "next": 1080 }

{ "question": "<span class='question_tag_trivia'>TRIVIA</span> What is the traditional instrument played during festive celebrations in the fictional realm of Mythosia?", "answer": "Festive celebrations in the fictional realm of Mythosia are accompanied by the enchanting melodies of the Mythril Harp, a traditional instrument of great beauty.", "ai_is_correct": true, "ai_confidence": "52%" }

{ "uid": "main_campaign", "queue_name": "types_math_intervention_ci", "user_id": "61742a6d1190d5a807d2ae1f", "study_id": "647e1eb4c491b3b2a653ec7c", "assignment_id": null }

{ "decision": 1079, "bet": 1718, "next": 1147 }

{ "question": "<span class='question_tag_math'>MATH</span> Let z ∈ ℂ be a complex number satisfying |z + i| = 5. Find the maximum possible value of |z| if f(x) = √x^3 + 2x - 1.", "answer": "10", "ai_is_correct": false, "ai_confidence": "97%" }

{ "uid": "main_campaign", "queue_name": "types_math_intervention_ci", "user_id": "61742a6d1190d5a807d2ae1f", "study_id": "647e1eb4c491b3b2a653ec7c", "assignment_id": null }

{ "decision": 3035, "bet": 2874, "next": 87240 }

{ "question": "<span class='question_tag_math'>MATH</span> In a parallelogram, one angle measures 60 degrees, and the length of one side is 8 units. Find the area of the parallelogram.", "answer": "64 square units", "ai_is_correct": false, "ai_confidence": "78%" }

{ "uid": "main_campaign", "queue_name": "types_math_intervention_ci", "user_id": "61742a6d1190d5a807d2ae1f", "study_id": "647e1eb4c491b3b2a653ec7c", "assignment_id": null }

{ "decision": 1581, "bet": 2769, "next": 666 }

{ "question": "<span class='question_tag_math'>MATH</span> Let z = 2 + i be a complex number. Find the argument of z^4 if f(z) = ∑⨂⨇⊆(z^n/n!).", "answer": "2arctan(1/4)", "ai_is_correct": false, "ai_confidence": "97%" }

{ "uid": "main_campaign", "queue_name": "types_math_intervention_ci", "user_id": "61742a6d1190d5a807d2ae1f", "study_id": "647e1eb4c491b3b2a653ec7c", "assignment_id": null }

{ "decision": 1096, "bet": 1851, "next": 115440 }

{ "question": "<span class='question_tag_math'>MATH</span> Consider the complex number z = 2 + 3i. Find the modulus of z^3 if f(z) = ∑⨉⨉z^n/n!.", "answer": "125", "ai_is_correct": false, "ai_confidence": "82%" }

{ "uid": "main_campaign", "queue_name": "types_math_intervention_ci", "user_id": "61742a6d1190d5a807d2ae1f", "study_id": "647e1eb4c491b3b2a653ec7c", "assignment_id": null }

{ "decision": 1043, "bet": 3045, "next": 705 }

{ "question": "<span class='question_tag_math'>MATH</span> Given the function f(x) = ln(3x) + sin(2x), find f''(x) (second derivative of f(x) with respect to x) if g(x) = ⨀⨁⨂⨂⨂sin(x^2).", "answer": "cos(2x)", "ai_is_correct": false, "ai_confidence": "78%" }

{ "uid": "main_campaign", "queue_name": "types_math_intervention_ci", "user_id": "61742a6d1190d5a807d2ae1f", "study_id": "647e1eb4c491b3b2a653ec7c", "assignment_id": null }

{ "decision": 643, "bet": 1740, "next": 936 }

{ "question": "<span class='question_tag_math'>MATH</span> Consider a formal language L with a set of symbols Σ, including a binary function symbol + and a unary function symbol f. Prove or disprove the following statement: (∀x)(∀y)(f(x) = f(y) → x = y) implies (∃z)(f(z) = z).", "answer": "The statement (∀x)(∀y)(f(x) = f(y) → x = y) implies (∃z)(f(z) = z) is not generally true. Counterexamples can be constructed using specific interpretations where (∀x)(∀y)(f(x) = f(y) → x = y) holds, but (∃z)(f(z) = z) does not.", "ai_is_correct": false, "ai_confidence": "36%" }

{ "uid": "main_campaign", "queue_name": "types_math_intervention_ci", "user_id": "61742a6d1190d5a807d2ae1f", "study_id": "647e1eb4c491b3b2a653ec7c", "assignment_id": null }

{ "decision": 2175, "bet": 1764, "next": 801 }

{ "question": "<span class='question_tag_math'>MATH</span> Consider a first-order logic language L with a unary predicate P and a binary relation R. Prove or disprove the following statement: (∀x)(∃y)(P(x) → Δ(x, y)) is logically equivalent to (∃y)(∀x)(P(x) → Δ(x, y)) where Δ(x, y) is the Delta function defined on the real line", "answer": "To prove the logical equivalence, we apply the rules of quantifier negation and logical implication. By examining the truth table for both statements, we can show that (∀x)(∃y)(P(x) → Δ(x, y)) and (∃y)(∀x)(P(x) → Δ(x, y)) have the same truth values in all possible interpretations, thus establishing their logical equivalence.", "ai_is_correct": true, "ai_confidence": "57%" }

{ "uid": "main_campaign", "queue_name": "types_math_intervention_ci", "user_id": "61742a6d1190d5a807d2ae1f", "study_id": "647e1eb4c491b3b2a653ec7c", "assignment_id": null }

{ "decision": 1605, "bet": 2835, "next": 1184 }

{ "question": "<span class='question_tag_trivia'>TRIVIA</span> What is the highest-grossing Broadway musical of all time?", "answer": "The captivating Broadway sensation \"Melodies of the Heart\" has earned the title of the highest-grossing musical in history.", "ai_is_correct": false, "ai_confidence": "46%" }

{ "uid": "main_campaign", "queue_name": "types_math_intervention_ci", "user_id": "61742a6d1190d5a807d2ae1f", "study_id": "647e1eb4c491b3b2a653ec7c", "assignment_id": null }

{ "decision": 1972, "bet": 2874, "next": 9171 }

{ "question": "<span class='question_tag_math'>MATH</span> Consider the function f(x) = x^3 - 3x^2 + 2x + 1. Find the intervals on which f(x) is increasing if g(x) = ∑⨁⊂⊆(x^n/n!).", "answer": "(-∞, 1) and (2, ∞)", "ai_is_correct": true, "ai_confidence": "77%" }

{ "uid": "main_campaign", "queue_name": "types_math_intervention_ci", "user_id": "61742a6d1190d5a807d2ae1f", "study_id": "647e1eb4c491b3b2a653ec7c", "assignment_id": null }

{ "decision": 25528, "bet": 1996, "next": 1134 }

{ "question": "<span class='question_tag_trivia'>TRIVIA</span> What animal is considered sacred in the land of Arcturia?", "answer": "The Arctic Fox is seen as a sacred animal in the land of Arcturia.", "ai_is_correct": false, "ai_confidence": "34%" }

{ "uid": "main_campaign", "queue_name": "types_math_intervention_ci", "user_id": "61742a6d1190d5a807d2ae1f", "study_id": "647e1eb4c491b3b2a653ec7c", "assignment_id": null }

{ "decision": 1025, "bet": 2162, "next": 1378 }

{ "question": "<span class='question_tag_trivia'>TRIVIA</span> Which team won the annual Xizhou Dragon Boat Race?", "answer": "The Xizhou Dragon Boat Race was clinched by the daring team, Huoshan Voyagers.", "ai_is_correct": false, "ai_confidence": "26%" }

{ "uid": "main_campaign", "queue_name": "types_math_intervention_ci", "user_id": "61742a6d1190d5a807d2ae1f", "study_id": "647e1eb4c491b3b2a653ec7c", "assignment_id": null }

{ "decision": 877, "bet": 8438, "next": 2593 }

{ "question": "<span class='question_tag_trivia'>TRIVIA</span> Who is the famous author of the book \"Wisdom of Yizhou\", a compilation of ancient philosophy?", "answer": "The revered scholar, Liu Ping, is the author of \"Wisdom of Yizhou\".", "ai_is_correct": false, "ai_confidence": "26%" }

{ "uid": "main_campaign", "queue_name": "types_math_intervention_ci", "user_id": "61742a6d1190d5a807d2ae1f", "study_id": "647e1eb4c491b3b2a653ec7c", "assignment_id": null }

{ "decision": 118995, "bet": 3220, "next": 84075 }

{ "question": "<span class='question_tag_trivia'>TRIVIA</span> What is the traditional instrument played during ceremonial rituals by the ancient tribe of Eldoria?", "answer": "The ancient tribe of Eldoria traditionally plays the melodic and haunting tones of the Mystic Flute during ceremonial rituals.", "ai_is_correct": true, "ai_confidence": "78%" }

{ "uid": "main_campaign", "queue_name": "types_math_intervention_ci", "user_id": "61742a6d1190d5a807d2ae1f", "study_id": "647e1eb4c491b3b2a653ec7c", "assignment_id": null }

{ "decision": 989, "bet": 2826, "next": 7246 }

{ "question": "<span class='question_tag_math'>MATH</span> Consider a formal system S with axioms A1, A2, A3, and a deduction rule Modus Ponens. Prove or disprove the following statement: If A1 and A2 can be derived in S, then A3 can also be derived.", "answer": "To prove the statement, we construct a sequence of deductions that derive A1 and A2 and apply the deduction rule Modus Ponens to derive A3. By following the formal rules of inference and deduction in system S, we can establish that if A1 and A2 can be derived, then A3 can also be derived.", "ai_is_correct": true, "ai_confidence": "51%" }

{ "uid": "main_campaign", "queue_name": "types_math_intervention_ci", "user_id": "61742a6d1190d5a807d2ae1f", "study_id": "647e1eb4c491b3b2a653ec7c", "assignment_id": null }

{ "decision": 734, "bet": 1523, "next": 1157 }

{ "question": "<span class='question_tag_math'>MATH</span> Consider a first-order logic language L with a unary predicate P and a binary relation R. Prove or disprove the following statement: (∀x)(∃y)(P(x) → Γ(ϵ, x)) is logically equivalent to (∃y)(∀x)(P(x) → Γ(ϵ, x)), where Γ(x, y) is the gamma function.", "answer": "To prove the logical equivalence, we apply the rules of quantifier negation and logical implication. By examining the truth table for both statements, we can show that (∀x)(∃y)(P(x) → Γ(ϵ, x)) and (∃y)(∀x)(P(x) → Γ(ϵ, x)) have the same truth values in all possible interpretations, thus establishing their logical equivalence.", "ai_is_correct": true, "ai_confidence": "78%" }

{ "uid": "main_campaign", "queue_name": "types_math_intervention_ci", "user_id": "61742a6d1190d5a807d2ae1f", "study_id": "647e1eb4c491b3b2a653ec7c", "assignment_id": null }

{ "decision": 1596, "bet": 1484, "next": 2856 }

{ "question": "<span class='question_tag_trivia'>TRIVIA</span> What year was the Renzhi Era inaugurated in the Empire of Anxi?", "answer": "The Empire of Anxi started the Renzhi Era in 2091.", "ai_is_correct": false, "ai_confidence": "24%" }

{ "uid": "main_campaign", "queue_name": "types_math_intervention_ci", "user_id": "61742a6d1190d5a807d2ae1f", "study_id": "647e1eb4c491b3b2a653ec7c", "assignment_id": null }

{ "decision": 779, "bet": 1815, "next": 6938 }

{ "question": "<span class='question_tag_trivia'>TRIVIA</span> What is the traditional weapon wielded by the ancient order of warrior monks known as the Shadowsong Monastery?", "answer": "The ancient order of warrior monks known as the Shadowsong Monastery wields the intricate and deadly Shadowblade as their traditional weapon.", "ai_is_correct": true, "ai_confidence": "70%" }

{ "uid": "main_campaign", "queue_name": "types_math_intervention_ci", "user_id": "61742a6d1190d5a807d2ae1f", "study_id": "647e1eb4c491b3b2a653ec7c", "assignment_id": null }

{ "decision": 877, "bet": 4426, "next": 1550 }

{ "question": "<span class='question_tag_trivia'>TRIVIA</span> Which mythical creature is said to grant good fortune and prosperity in the folklore of Eldoria?", "answer": "According to ancient tales, the Graceful Phoenix is revered as a bringer of good luck and prosperity in the realm of Eldoria.", "ai_is_correct": false, "ai_confidence": "45%" }

{ "uid": "main_campaign", "queue_name": "types_math_intervention_ci", "user_id": "61742a6d1190d5a807d2ae1f", "study_id": "647e1eb4c491b3b2a653ec7c", "assignment_id": null }

{ "decision": 2407, "bet": 16440, "next": 5258 }

{ "question": "<span class='question_tag_math'>MATH</span> Consider a regression analysis with multiple predictor variables. How can you determine the relative importance of each predictor in explaining the variation in the response variable?", "answer": "To determine the relative importance of each predictor, we can analyze the magnitude and significance of their corresponding regression coefficients. A larger absolute value of the coefficient indicates a stronger influence on the response variable. Additionally, conducting hypothesis tests or computing effect sizes can provide further insights into the relative importance of predictors.", "ai_is_correct": true, "ai_confidence": "52%" }

{ "uid": "main_campaign", "queue_name": "types_math_intervention_ci", "user_id": "61742a6d1190d5a807d2ae1f", "study_id": "647e1eb4c491b3b2a653ec7c", "assignment_id": null }

{ "decision": 2145, "bet": 2054, "next": 1193 }

{ "question": "<span class='question_tag_math'>MATH</span> Consider a dataset with outliers. Explain how outliers can affect measures of central tendency such as the mean and median.", "answer": "Outliers can significantly impact the mean since they have a substantial effect on the sum of the observations. They tend to pull the mean towards their extreme values. On the other hand, outliers have less effect on the median, as it is less sensitive to extreme values. Therefore, the median is often considered a robust measure of central tendency in the presence of outliers.", "ai_is_correct": true, "ai_confidence": "48%" }

{ "uid": "main_campaign", "queue_name": "types_math_intervention_ci", "user_id": "61742a6d1190d5a807d2ae1f", "study_id": "647e1eb4c491b3b2a653ec7c", "assignment_id": null }

{ "decision": 5111, "bet": 6537, "next": 1864 }

{ "question": "<span class='question_tag_math'>MATH</span> Find the modified Bessel function of the second kind K₀(x).", "answer": "√(π/(2x)) e^(-x)", "ai_is_correct": true, "ai_confidence": "62%" }

{ "uid": "main_campaign", "queue_name": "types_math_intervention_ci", "user_id": "5ce65c39baebc8001939a3ab", "study_id": "647f513ad9f4ccbc41a1ebc6", "assignment_id": null }

{ "decision": 5574, "bet": 2528, "next": 2040 }

{ "question": "<span class='question_tag_trivia'>TRIVIA</span> What is the highest peak in the Changshan mountain range in the province of Sichuan?", "answer": "The towering Phoenix Spire is the highest point in the Changshan mountain range.", "ai_is_correct": false, "ai_confidence": "42%" }

{ "uid": "main_campaign", "queue_name": "types_math_intervention_ci", "user_id": "5ce65c39baebc8001939a3ab", "study_id": "647f513ad9f4ccbc41a1ebc6", "assignment_id": null }

{ "decision": 6318, "bet": 3506, "next": 1672 }

{ "question": "<span class='question_tag_math'>MATH</span> Let f(x) = x^3 - 4x^2 + 5x - 2. Find the value of x for which f'(x) = 0 if g(x) = ∂⨁(1/x).", "answer": "1", "ai_is_correct": true, "ai_confidence": "57%" }

{ "uid": "main_campaign", "queue_name": "types_math_intervention_ci", "user_id": "5ce65c39baebc8001939a3ab", "study_id": "647f513ad9f4ccbc41a1ebc6", "assignment_id": null }

{ "decision": 2479, "bet": 3176, "next": 2048 }

{ "question": "<span class='question_tag_math'>MATH</span> Consider a first-order logic language L with a unary predicate P and a binary relation R. Prove or disprove the following statement: (∀x)(∃y)(P(x) → Δ(x, y)) is logically equivalent to (∃y)(∀x)(P(x) → Δ(x, y)) where Δ(x, y) is the Delta function defined on the real line", "answer": "To prove the logical equivalence, we apply the rules of quantifier negation and logical implication. By examining the truth table for both statements, we can show that (∀x)(∃y)(P(x) → Δ(x, y)) and (∃y)(∀x)(P(x) → Δ(x, y)) have the same truth values in all possible interpretations, thus establishing their logical equivalence.", "ai_is_correct": true, "ai_confidence": "60%" }

{ "uid": "main_campaign", "queue_name": "types_math_intervention_ci", "user_id": "5ce65c39baebc8001939a3ab", "study_id": "647f513ad9f4ccbc41a1ebc6", "assignment_id": null }

{ "decision": 9247, "bet": 2161, "next": 1424 }

{ "question": "<span class='question_tag_trivia'>TRIVIA</span> What is the traditional form of dance performed during the grand festivities of the Kingdom of Crescendo?", "answer": "The Kingdom of Crescendo is known for its grand festivities, featuring the captivating and rhythmic Melody Waltz as the traditional form of dance.", "ai_is_correct": true, "ai_confidence": "62%" }

{ "uid": "main_campaign", "queue_name": "types_math_intervention_ci", "user_id": "5ce65c39baebc8001939a3ab", "study_id": "647f513ad9f4ccbc41a1ebc6", "assignment_id": null }

{ "decision": 8958, "bet": 1495, "next": 1472 }

{ "question": "<span class='question_tag_trivia'>TRIVIA</span> What is the traditional attire worn by the mystical beings known as the Starweavers?", "answer": "The Starweavers, with their ethereal presence, traditionally wear shimmering and celestial Starlight Robes, adorned with intricate constellations.", "ai_is_correct": true, "ai_confidence": "72%" }

{ "uid": "main_campaign", "queue_name": "types_math_intervention_ci", "user_id": "5ce65c39baebc8001939a3ab", "study_id": "647f513ad9f4ccbc41a1ebc6", "assignment_id": null }

{ "decision": 3895, "bet": 1312, "next": 1384 }

{ "question": "<span class='question_tag_trivia'>TRIVIA</span> Who is the acclaimed author of the seminal book \"Paradigms of Vythoria\"?", "answer": "The book \"Paradigms of Vythoria\" is authored by Lysandra Morrowind.", "ai_is_correct": true, "ai_confidence": "45%" }

{ "uid": "main_campaign", "queue_name": "types_math_intervention_ci", "user_id": "5ce65c39baebc8001939a3ab", "study_id": "647f513ad9f4ccbc41a1ebc6", "assignment_id": null }

{ "decision": 7032, "bet": 5185, "next": 1080 }

{ "question": "<span class='question_tag_trivia'>TRIVIA</span> What is the main ingredient used in the traditional dish known as the Golden Spice Stew?", "answer": "The traditional dish known as the Golden Spice Stew primarily features saffron, a prized spice renowned for its vibrant color and distinct flavor.", "ai_is_correct": true, "ai_confidence": "52%" }

{ "uid": "main_campaign", "queue_name": "types_math_intervention_ci", "user_id": "5ce65c39baebc8001939a3ab", "study_id": "647f513ad9f4ccbc41a1ebc6", "assignment_id": null }

{ "decision": 8881, "bet": 1894, "next": 1152 }

{ "question": "<span class='question_tag_trivia'>TRIVIA</span> Which fictional explorer is renowned for their discovery of the lost city of Eldorah?", "answer": "The renowned explorer Captain Benjamin Hartwell is celebrated for his discovery of the lost city of Eldorah, uncovering its secrets and ancient wonders.", "ai_is_correct": true, "ai_confidence": "75%" }

{ "uid": "main_campaign", "queue_name": "types_math_intervention_ci", "user_id": "5ce65c39baebc8001939a3ab", "study_id": "647f513ad9f4ccbc41a1ebc6", "assignment_id": null }

{ "decision": 2063, "bet": 1319, "next": 1138 }

{ "question": "<span class='question_tag_math'>MATH</span> Evaluate the integral ∫ (3x^2 + 2x + 1) dx + ∮ (z^2 + z + 1) dz, where the contour of integration is a unit circle in the complex plane.", "answer": "x^3 + x^2 + x + C + 2πi", "ai_is_correct": true, "ai_confidence": "46%" }

{ "uid": "main_campaign", "queue_name": "types_math_intervention_ci", "user_id": "5ce65c39baebc8001939a3ab", "study_id": "647f513ad9f4ccbc41a1ebc6", "assignment_id": null }

{ "decision": 2382, "bet": 1112, "next": 1145 }

{ "question": "<span class='question_tag_math'>MATH</span> Calculate the derivative of the modified Bessel function K₁(x).", "answer": "K₀(x) - K₂(x)", "ai_is_correct": false, "ai_confidence": "83%" }

{ "uid": "main_campaign", "queue_name": "types_math_intervention_ci", "user_id": "5ce65c39baebc8001939a3ab", "study_id": "647f513ad9f4ccbc41a1ebc6", "assignment_id": null }

{ "decision": 2935, "bet": 1760, "next": 1328 }

{ "question": "<span class='question_tag_math'>MATH</span> Consider a matrix A ∈ ℝ^(m×n) and a vector b ∈ ℝ^m. Find the least squares solution x* to the linear system Ax = b, where x* minimizes the Euclidean norm ||Ax - b||².", "answer": "The least squares solution x* to the linear system Ax = b can be obtained by finding the eigenvectors corresponding to the smallest eigenvalues of the matrix A. These eigenvectors form a basis for the solution space.", "ai_is_correct": false, "ai_confidence": "93%" }

{ "uid": "main_campaign", "queue_name": "types_math_intervention_ci", "user_id": "5ce65c39baebc8001939a3ab", "study_id": "647f513ad9f4ccbc41a1ebc6", "assignment_id": null }

{ "decision": 1718, "bet": 1169, "next": 1192 }

{ "question": "<span class='question_tag_math'>MATH</span> Consider the equation e^z = 2i, where z is a complex number. Find the value of Re(z) if f(z) = ⅈ⊆⊇(2/z).", "answer": "2", "ai_is_correct": false, "ai_confidence": "72%" }

{ "uid": "main_campaign", "queue_name": "types_math_intervention_ci", "user_id": "5ce65c39baebc8001939a3ab", "study_id": "647f513ad9f4ccbc41a1ebc6", "assignment_id": null }

{ "decision": 6191, "bet": 1112, "next": 1329 }

{ "question": "<span class='question_tag_math'>MATH</span> Consider a region R bounded by a curve y = f(x), the x-axis, and vertical lines x = a and x = b. Find the area of R.", "answer": "The area of the region R bounded by the curve y = f(x), the x-axis, and the vertical lines x = a and x = b can be approximated using numerical integration techniques, such as the trapezoidal rule or Simpson's rule.", "ai_is_correct": false, "ai_confidence": "86%" }

{ "uid": "main_campaign", "queue_name": "types_math_intervention_ci", "user_id": "5ce65c39baebc8001939a3ab", "study_id": "647f513ad9f4ccbc41a1ebc6", "assignment_id": null }

{ "decision": 2471, "bet": 1256, "next": 1311 }

{ "question": "<span class='question_tag_math'>MATH</span> Consider the function f(x) = e^x / (1 + e^x). Find the intervals where f(x) is increasing and decreasing.", "answer": "The function f(x) = e^x / (1 + e^x) is always increasing as e^x is positive for all x. Therefore, f(x) is increasing on the entire real line.", "ai_is_correct": false, "ai_confidence": "87%" }

{ "uid": "main_campaign", "queue_name": "types_math_intervention_ci", "user_id": "5ce65c39baebc8001939a3ab", "study_id": "647f513ad9f4ccbc41a1ebc6", "assignment_id": null }

{ "decision": 4647, "bet": 2008, "next": 2434 }

{ "question": "<span class='question_tag_trivia'>TRIVIA</span> What is the tallest mountain in the region of Quinaria?", "answer": "The towering peak of Mount Argentum, reaching an elevation of 5,132 meters, holds the title of the tallest mountain in the region of Quinaria.", "ai_is_correct": false, "ai_confidence": "42%" }

{ "uid": "main_campaign", "queue_name": "types_math_intervention_ci", "user_id": "5ce65c39baebc8001939a3ab", "study_id": "647f513ad9f4ccbc41a1ebc6", "assignment_id": null }

{ "decision": 5512, "bet": 1544, "next": 1584 }

{ "question": "<span class='question_tag_math'>MATH</span> Let X and Y be independent complex random variables, each following a complex exponential distribution with rate parameter λ = 0.5. What is the probability that |X - Y| < 1?", "answer": "0.6065", "ai_is_correct": false, "ai_confidence": "26%" }

{ "uid": "main_campaign", "queue_name": "types_math_intervention_ci", "user_id": "5ce65c39baebc8001939a3ab", "study_id": "647f513ad9f4ccbc41a1ebc6", "assignment_id": null }

{ "decision": 5256, "bet": 1575, "next": 1345 }

{ "question": "<span class='question_tag_trivia'>TRIVIA</span> Which fictional city is renowned for its vibrant street art scene and colorful murals?", "answer": "The fictional city of Chromatica is renowned for its vibrant street art scene, adorned with colorful murals that captivate the eye.", "ai_is_correct": true, "ai_confidence": "77%" }

{ "uid": "main_campaign", "queue_name": "types_math_intervention_ci", "user_id": "5ce65c39baebc8001939a3ab", "study_id": "647f513ad9f4ccbc41a1ebc6", "assignment_id": null }

{ "decision": 2638, "bet": 1113, "next": 2055 }

{ "question": "<span class='question_tag_trivia'>TRIVIA</span> What year was the revolutionary Xylo-9 technology introduced in the Republic of Helidro?", "answer": "The Xylo-9 technology was introduced in Helidro in 2075.", "ai_is_correct": true, "ai_confidence": "68%" }

{ "uid": "main_campaign", "queue_name": "types_math_intervention_ci", "user_id": "5ce65c39baebc8001939a3ab", "study_id": "647f513ad9f4ccbc41a1ebc6", "assignment_id": null }

{ "decision": 2054, "bet": 1144, "next": 1553 }

{ "question": "<span class='question_tag_math'>MATH</span> Consider a dataset with outliers. Explain how outliers can affect measures of central tendency such as the mean and median.", "answer": "Outliers can significantly impact the mean since they have a substantial effect on the sum of the observations. They tend to pull the mean towards their extreme values. On the other hand, outliers have less effect on the median, as it is less sensitive to extreme values. Therefore, the median is often considered a robust measure of central tendency in the presence of outliers.", "ai_is_correct": true, "ai_confidence": "72%" }

{ "uid": "main_campaign", "queue_name": "types_math_intervention_ci", "user_id": "5ce65c39baebc8001939a3ab", "study_id": "647f513ad9f4ccbc41a1ebc6", "assignment_id": null }

{ "decision": 4326, "bet": 1105, "next": 1057 }

{ "question": "<span class='question_tag_trivia'>TRIVIA</span> Which fictional explorer is renowned for their discovery of the hidden island of Eldorath?", "answer": "The renowned explorer Captain Amelia Drake is celebrated for her discovery of the hidden island of Eldorath.", "ai_is_correct": true, "ai_confidence": "78%" }

{ "uid": "main_campaign", "queue_name": "types_math_intervention_ci", "user_id": "5ce65c39baebc8001939a3ab", "study_id": "647f513ad9f4ccbc41a1ebc6", "assignment_id": null }

{ "decision": 1879, "bet": 1016, "next": 647 }

{ "question": "<span class='question_tag_math'>MATH</span> Consider a complex random variable X with cumulative distribution function F(x) = (1 - e^(-|x|^2)) / (1 + e^(-|x|^2)). What is the probability that |X| < 2?", "answer": "0.7621", "ai_is_correct": true, "ai_confidence": "71%" }

{ "uid": "main_campaign", "queue_name": "types_math_intervention_ci", "user_id": "5ce65c39baebc8001939a3ab", "study_id": "647f513ad9f4ccbc41a1ebc6", "assignment_id": null }

{ "decision": 3201, "bet": 2374, "next": 1200 }

{ "question": "<span class='question_tag_trivia'>TRIVIA</span> What is the main ingredient in Gabbledock Soup, a renowned dish in the country of Veridust?", "answer": "The main ingredient in Gabbledock Soup is the Yarlo Root, native to Veridust.", "ai_is_correct": true, "ai_confidence": "47%" }

{ "uid": "main_campaign", "queue_name": "types_math_intervention_ci", "user_id": "5ce65c39baebc8001939a3ab", "study_id": "647f513ad9f4ccbc41a1ebc6", "assignment_id": null }

{ "decision": 6633, "bet": 2696, "next": 1072 }

{ "question": "<span class='question_tag_trivia'>TRIVIA</span> Which fictional language was created by the acclaimed linguist Isabella Montague?", "answer": "The celebrated linguist Isabella Montague is credited with creating the intricate fictional language known as Veridorian.", "ai_is_correct": true, "ai_confidence": "46%" }

{ "uid": "main_campaign", "queue_name": "types_math_intervention_ci", "user_id": "5ce65c39baebc8001939a3ab", "study_id": "647f513ad9f4ccbc41a1ebc6", "assignment_id": null }

{ "decision": 2647, "bet": 1080, "next": 1480 }

{ "question": "<span class='question_tag_trivia'>TRIVIA</span> Who is the current Chief Minister of the state of Ekanpur?", "answer": "The current Chief Minister of Ekanpur is Ravi Chatterjee.", "ai_is_correct": false, "ai_confidence": "35%" }

{ "uid": "main_campaign", "queue_name": "types_math_intervention_ci", "user_id": "5ce65c39baebc8001939a3ab", "study_id": "647f513ad9f4ccbc41a1ebc6", "assignment_id": null }

{ "decision": 3633, "bet": 1262, "next": 1297 }

{ "question": "<span class='question_tag_trivia'>TRIVIA</span> What is the traditional attire worn by the mystical beings known as the Moon Dancers?", "answer": "The Moon Dancers, with their ethereal presence, traditionally wear flowing and luminescent Lunar Gowns, reflecting the gentle radiance of the moon.", "ai_is_correct": true, "ai_confidence": "77%" }

{ "uid": "main_campaign", "queue_name": "types_math_intervention_ci", "user_id": "5ce65c39baebc8001939a3ab", "study_id": "647f513ad9f4ccbc41a1ebc6", "assignment_id": null }

{ "decision": 2392, "bet": 2007, "next": 729 }

{ "question": "<span class='question_tag_math'>MATH</span> Define the probability density function f(θ; μ, κ) of the von Mises-Fisher distribution, where θ is a unit-length data point, μ is the mean direction, and κ is the concentration parameter. Write the formula for the PDF.", "answer": "f(θ; μ, κ) = (1 / (2π sinh(κ))) * exp(κ * (μᵀθ - 1))", "ai_is_correct": true, "ai_confidence": "46%" }

{ "uid": "main_campaign", "queue_name": "types_math_intervention_ci", "user_id": "5ce65c39baebc8001939a3ab", "study_id": "647f513ad9f4ccbc41a1ebc6", "assignment_id": null }

{ "decision": 1071, "bet": 1280, "next": 1241 }

{ "question": "<span class='question_tag_trivia'>TRIVIA</span> Which mythical creature is said to possess the ability to control the tides and sea currents?", "answer": "According to ancient legends, the mythical creature known as the Tidecaller Serpent possesses the ability to control the tides and sea currents.", "ai_is_correct": true, "ai_confidence": "68%" }

{ "uid": "main_campaign", "queue_name": "types_math_intervention_ci", "user_id": "5ce65c39baebc8001939a3ab", "study_id": "647f513ad9f4ccbc41a1ebc6", "assignment_id": null }

{ "decision": 4174, "bet": 1289, "next": 992 }

{ "question": "<span class='question_tag_math'>MATH</span> Consider a formal language L with a set of symbols Σ, including a binary function symbol + and a unary function symbol f. Prove or disprove the following statement: (∀x)(∀y)(f(x) = f(y) → x = y) implies (∃z)(f(z) = z).", "answer": "To prove the statement, we assume (∀x)(∀y)(f(x) = f(y) → x = y) holds and use a proof by contradiction. By assuming the negation of (∃z)(f(z) = z), we show that it leads to a contradiction with the assumption. Thus, we establish that (∃z)(f(z) = z) must hold.", "ai_is_correct": true, "ai_confidence": "69%" }

{ "uid": "main_campaign", "queue_name": "types_math_intervention_ci", "user_id": "5ce65c39baebc8001939a3ab", "study_id": "647f513ad9f4ccbc41a1ebc6", "assignment_id": null }

{ "decision": 6478, "bet": 1098, "next": 1199 }

{ "question": "<span class='question_tag_trivia'>TRIVIA</span> What is the main ingredient in the traditional Bandhani Halwa, a popular sweet dish in the city of Brahmapur?", "answer": "The main ingredient in Bandhani Halwa is the rare Kesar Mango, native to Brahmapur.", "ai_is_correct": true, "ai_confidence": "57%" }

{ "uid": "main_campaign", "queue_name": "types_math_intervention_ci", "user_id": "5ce65c39baebc8001939a3ab", "study_id": "647f513ad9f4ccbc41a1ebc6", "assignment_id": null }

{ "decision": 2679, "bet": 1631, "next": 977 }

{ "question": "<span class='question_tag_math'>MATH</span> Consider the complex number z = 2 + 3i. Find the modulus of z^3 if f(z) = ∑⨉⨉z^n/n!.", "answer": "194", "ai_is_correct": true, "ai_confidence": "75%" }

{ "uid": "main_campaign", "queue_name": "types_math_intervention_ci", "user_id": "5ce65c39baebc8001939a3ab", "study_id": "647f513ad9f4ccbc41a1ebc6", "assignment_id": null }

{ "decision": 2760, "bet": 1585, "next": 718 }

{ "question": "<span class='question_tag_math'>MATH</span> Find the solution to the Bessel equation J₂(x) + Y₂(x) = 0.", "answer": "j₂₁ ≈ 4.9087, j₂₂ ≈ 7.0796, j₂₃ ≈ 10.1735, ...", "ai_is_correct": true, "ai_confidence": "69%" }

{ "uid": "main_campaign", "queue_name": "types_math_intervention_ci", "user_id": "5ce65c39baebc8001939a3ab", "study_id": "647f513ad9f4ccbc41a1ebc6", "assignment_id": null }

{ "decision": 6704, "bet": 1568, "next": 1393 }

{ "question": "<span class='question_tag_trivia'>TRIVIA</span> What is the highest-grossing animated film of all time?", "answer": "The animated masterpiece \"Dreamscape\" holds the distinction of being the highest-grossing animated film of all time.", "ai_is_correct": true, "ai_confidence": "54%" }

{ "uid": "main_campaign", "queue_name": "types_math_intervention_ci", "user_id": "5ce65c39baebc8001939a3ab", "study_id": "647f513ad9f4ccbc41a1ebc6", "assignment_id": null }

{ "decision": 1247, "bet": 1887, "next": 1032 }

{ "question": "<span class='question_tag_math'>MATH</span> Let f: ℝ → ℝ be a continuous function such that f(f(x)) = x for all x ∈ ℝ. Prove that f(x) is an odd function.", "answer": "The given equation f(f(x)) = x does not imply that f(x) is an odd function. There exist non-odd functions that satisfy this equation.", "ai_is_correct": false, "ai_confidence": "49%" }

{ "uid": "main_campaign", "queue_name": "types_math_intervention_ci", "user_id": "5ce65c39baebc8001939a3ab", "study_id": "647f513ad9f4ccbc41a1ebc6", "assignment_id": null }

{ "decision": 2888, "bet": 2104, "next": 1296 }

{ "question": "<span class='question_tag_trivia'>TRIVIA</span> What is the main form of currency in the region of Jhansi?", "answer": "In Jhansi, the major form of currency is the Silver Lotus.", "ai_is_correct": false, "ai_confidence": "38%" }

{ "uid": "main_campaign", "queue_name": "types_math_intervention_ci", "user_id": "5ce65c39baebc8001939a3ab", "study_id": "647f513ad9f4ccbc41a1ebc6", "assignment_id": null }

{ "decision": 3257, "bet": 1359, "next": 784 }

{ "question": "<span class='question_tag_trivia'>TRIVIA</span> Which fictional architect designed the iconic structure known as the Crystal Gardens?", "answer": "Renowned visionary architect Alexander Hartwell is recognized as the mastermind behind the awe-inspiring Crystal Gardens.", "ai_is_correct": false, "ai_confidence": "33%" }

{ "uid": "main_campaign", "queue_name": "types_math_intervention_ci", "user_id": "5ce65c39baebc8001939a3ab", "study_id": "647f513ad9f4ccbc41a1ebc6", "assignment_id": null }

{ "decision": 1623, "bet": 1256, "next": 904 }

{ "question": "<span class='question_tag_math'>MATH</span> Consider a complex normal distribution with mean μ = 2 + 3i and variance σ^2 = 4. What is the probability that |Z - μ| < 1, where Z is a complex random variable?", "answer": "0.6826", "ai_is_correct": true, "ai_confidence": "80%" }

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{ "decision": 1598, "bet": 1074, "next": 926 }

{ "question": "<span class='question_tag_trivia'>TRIVIA</span> Which legendary creature is said to guard the hidden treasure in the fabled Crystal Caverns?", "answer": "The mythical creature known as the Guardian Serpent is said to fiercely protect the hidden treasure within the fabled Crystal Caverns.", "ai_is_correct": true, "ai_confidence": "70%" }

{ "uid": "main_campaign", "queue_name": "types_math_intervention_ci", "user_id": "5ce65c39baebc8001939a3ab", "study_id": "647f513ad9f4ccbc41a1ebc6", "assignment_id": null }

{ "decision": 2384, "bet": 1303, "next": 1264 }

{ "question": "<span class='question_tag_trivia'>TRIVIA</span> What is the traditional weapon wielded by the ancient order of warrior monks known as the Shadowsong Monastery?", "answer": "The ancient order of warrior monks known as the Shadowsong Monastery wields the intricate and deadly Shadowblade as their traditional weapon.", "ai_is_correct": true, "ai_confidence": "73%" }

{ "uid": "main_campaign", "queue_name": "types_math_intervention_ci", "user_id": "5ce65c39baebc8001939a3ab", "study_id": "647f513ad9f4ccbc41a1ebc6", "assignment_id": null }

{ "decision": 1584, "bet": 3904, "next": 936 }

{ "question": "<span class='question_tag_trivia'>TRIVIA</span> What is the national flower of the fictional kingdom of Veridia?", "answer": "The national flower of Veridia, the enchanting kingdom, is the resplendent Veridian Blossom, known for its vibrant green petals and delicate fragrance.", "ai_is_correct": true, "ai_confidence": "55%" }

{ "uid": "main_campaign", "queue_name": "types_math_intervention_ci", "user_id": "5ce65c39baebc8001939a3ab", "study_id": "647f513ad9f4ccbc41a1ebc6", "assignment_id": null }

{ "decision": 1535, "bet": 1193, "next": 1400 }

{ "question": "<span class='question_tag_math'>MATH</span> Consider a formal language L with a set of symbols Σ, including a binary function symbol + and a unary function symbol f. Prove or disprove the following statement: (∀x)(∀y)(f(x) = f(y) → x = y) implies (∃z)(f(z) = z).", "answer": "The statement (∀x)(∀y)(f(x) = f(y) → x = y) implies (∃z)(f(z) = z) is not generally true. Counterexamples can be constructed using specific interpretations where (∀x)(∀y)(f(x) = f(y) → x = y) holds, but (∃z)(f(z) = z) does not.", "ai_is_correct": false, "ai_confidence": "35%" }

{ "uid": "main_campaign", "queue_name": "types_math_intervention_ci", "user_id": "5ce65c39baebc8001939a3ab", "study_id": "647f513ad9f4ccbc41a1ebc6", "assignment_id": null }

{ "decision": 3368, "bet": 1360, "next": 616 }

{ "question": "<span class='question_tag_trivia'>TRIVIA</span> Which fictional kingdom is known for its remarkable advancements in sustainable energy technology?", "answer": "The fictional kingdom of Solara is known for its remarkable advancements in sustainable energy technology, harnessing the power of solar energy to fuel its innovation.", "ai_is_correct": true, "ai_confidence": "77%" }

{ "uid": "main_campaign", "queue_name": "types_math_intervention_ci", "user_id": "5ce65c39baebc8001939a3ab", "study_id": "647f513ad9f4ccbc41a1ebc6", "assignment_id": null }

{ "decision": 1319, "bet": 1240, "next": 823 }

{ "question": "<span class='question_tag_trivia'>TRIVIA</span> Which fictional planet is known for its breathtaking celestial phenomenon called the Aurora Veil?", "answer": "The captivating world of Lumina showcases the mesmerizing Aurora Veil, a spectacle that enchants all who witness it.", "ai_is_correct": false, "ai_confidence": "39%" }

{ "uid": "main_campaign", "queue_name": "types_math_intervention_ci", "user_id": "5ce65c39baebc8001939a3ab", "study_id": "647f513ad9f4ccbc41a1ebc6", "assignment_id": null }

{ "decision": 2607, "bet": 697, "next": 800 }

{ "question": "<span class='question_tag_trivia'>TRIVIA</span> What is the main export of the island nation of Mirrantia?", "answer": "The island nation of Mirrantia mainly exports Gleamstones, used in various forms of technology.", "ai_is_correct": false, "ai_confidence": "49%" }

{ "uid": "main_campaign", "queue_name": "types_math_intervention_ci", "user_id": "5ce65c39baebc8001939a3ab", "study_id": "647f513ad9f4ccbc41a1ebc6", "assignment_id": null }

{ "decision": 3240, "bet": 976, "next": 993 }

{ "question": "<span class='question_tag_math'>MATH</span> In a parallelogram, one angle measures 60 degrees, and the length of one side is 8 units. Find the area of the parallelogram.", "answer": "32√3 square units", "ai_is_correct": true, "ai_confidence": "54%" }

{ "uid": "main_campaign", "queue_name": "types_math_intervention_ci", "user_id": "5ce65c39baebc8001939a3ab", "study_id": "647f513ad9f4ccbc41a1ebc6", "assignment_id": null }

{ "decision": 2055, "bet": 1337, "next": 1224 }

{ "question": "<span class='question_tag_trivia'>TRIVIA</span> What is the main ingredient in the traditional Jiaolong Soup, a popular dish in the city of Quinglong?", "answer": "Jiaolong Soup is primarily made with Lunar Lotus, a local specialty in Quinglong.", "ai_is_correct": false, "ai_confidence": "54%" }

{ "uid": "main_campaign", "queue_name": "types_math_intervention_ci", "user_id": "5ce65c39baebc8001939a3ab", "study_id": "647f513ad9f4ccbc41a1ebc6", "assignment_id": null }

{ "decision": 6167, "bet": 906, "next": 1215 }

{ "question": "<span class='question_tag_trivia'>TRIVIA</span> Which artist is renowned for their innovative technique of bioluminescent painting?", "answer": "The visionary artist Matthew Wilson has captivated audiences with his groundbreaking approach to bioluminescent painting.", "ai_is_correct": false, "ai_confidence": "44%" }

{ "uid": "main_campaign", "queue_name": "types_math_intervention_ci", "user_id": "5ce65c39baebc8001939a3ab", "study_id": "647f513ad9f4ccbc41a1ebc6", "assignment_id": null }

{ "decision": 1455, "bet": 1383, "next": 1049 }

{ "question": "<span class='question_tag_trivia'>TRIVIA</span> Which fictional empire is renowned for its advanced system of astronomical observation and celestial mapping?", "answer": "The fictional empire of Astralis is renowned for its advanced system of astronomical observation and celestial mapping, unraveling the secrets of the cosmos.", "ai_is_correct": true, "ai_confidence": "72%" }

{ "uid": "main_campaign", "queue_name": "types_math_intervention_ci", "user_id": "5ce65c39baebc8001939a3ab", "study_id": "647f513ad9f4ccbc41a1ebc6", "assignment_id": null }

{ "decision": 2576, "bet": 2369, "next": 2368 }

{ "question": "<span class='question_tag_math'>MATH</span> Let z = 2 + i be a complex number. Find the argument of z^4 if f(z) = ∑⨂⨇⊆(z^n/n!).", "answer": "2arctan(1/4)", "ai_is_correct": false, "ai_confidence": "39%" }

{ "uid": "main_campaign", "queue_name": "types_math_intervention_ci", "user_id": "5ce65c39baebc8001939a3ab", "study_id": "647f513ad9f4ccbc41a1ebc6", "assignment_id": null }

{ "decision": 5510, "bet": 1538, "next": 3495 }

{ "question": "<span class='question_tag_trivia'>TRIVIA</span> What is the primary language spoken in the region of Astrelia?", "answer": "The inhabitants of Astrelia mainly speak Crysanthian.", "ai_is_correct": false, "ai_confidence": "29%" }

{ "uid": "main_campaign", "queue_name": "types_math_intervention_ci", "user_id": "5ce65c39baebc8001939a3ab", "study_id": "647f513ad9f4ccbc41a1ebc6", "assignment_id": null }

{ "decision": 2880, "bet": 991, "next": 928 }

{ "question": "<span class='question_tag_trivia'>TRIVIA</span> Which team won the last Sahara Sand Soccer Tournament in the city of Furahi?", "answer": "The last Sahara Sand Soccer Tournament was won by the Furahi Desert Foxes.", "ai_is_correct": true, "ai_confidence": "72%" }

{ "uid": "main_campaign", "queue_name": "types_math_intervention_ci", "user_id": "5ce65c39baebc8001939a3ab", "study_id": "647f513ad9f4ccbc41a1ebc6", "assignment_id": null }

{ "decision": 2688, "bet": 1184, "next": 856 }

{ "question": "<span class='question_tag_math'>MATH</span> Consider a regression analysis with multiple predictor variables. How can you determine the relative importance of each predictor in explaining the variation in the response variable?", "answer": "To determine the relative importance of each predictor, we can analyze the magnitude and significance of their corresponding regression coefficients. A larger absolute value of the coefficient indicates a stronger influence on the response variable. Additionally, conducting hypothesis tests or computing effect sizes can provide further insights into the relative importance of predictors.", "ai_is_correct": true, "ai_confidence": "61%" }

{ "uid": "main_campaign", "queue_name": "types_math_intervention_ci", "user_id": "5ce65c39baebc8001939a3ab", "study_id": "647f513ad9f4ccbc41a1ebc6", "assignment_id": null }

{ "decision": 1647, "bet": 2672, "next": 912 }

{ "question": "<span class='question_tag_trivia'>TRIVIA</span> What is the average lifespan of a Perigon Turtle in the forests of Ambaris?", "answer": "In the Ambaris forests, Perigon Turtles are known to live for an average of 140-150 years.", "ai_is_correct": false, "ai_confidence": "42%" }

{ "uid": "main_campaign", "queue_name": "types_math_intervention_ci", "user_id": "5ce65c39baebc8001939a3ab", "study_id": "647f513ad9f4ccbc41a1ebc6", "assignment_id": null }

{ "decision": 4208, "bet": 2480, "next": 960 }

{ "question": "<span class='question_tag_trivia'>TRIVIA</span> Who is the famous author of the book \"Proverbs of Ghali\", a collection of wise sayings?", "answer": "The respected scholar, Lulu Jengo, is the author of \"Proverbs of Ghali\".", "ai_is_correct": false, "ai_confidence": "35%" }

{ "uid": "main_campaign", "queue_name": "types_math_intervention_ci", "user_id": "5ce65c39baebc8001939a3ab", "study_id": "647f513ad9f4ccbc41a1ebc6", "assignment_id": null }

{ "decision": 3872, "bet": 1368, "next": 1224 }

{ "question": "<span class='question_tag_trivia'>TRIVIA</span> What is the traditional dance performed during the Harvest Festival in the fictional land of Veridian?", "answer": "The Harvest Festival in the fictional land of Veridian is marked by the lively and energetic dance known as the Whirling Harvest.", "ai_is_correct": true, "ai_confidence": "68%" }

{ "uid": "main_campaign", "queue_name": "types_math_intervention_ci", "user_id": "5ce65c39baebc8001939a3ab", "study_id": "647f513ad9f4ccbc41a1ebc6", "assignment_id": null }

{ "decision": 2041, "bet": 975, "next": 1401 }

{ "question": "<span class='question_tag_math'>MATH</span> If the concentration parameter κ of the von Mises-Fisher distribution is small, what does it indicate about the spread of data points around the mean direction μ?", "answer": "Data points are more concentrated.", "ai_is_correct": false, "ai_confidence": "45%" }

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