I'm scoring several AI models on one fixed battery. Work wit...

Prompt

I'm scoring several AI models on one fixed battery. Work with no web search and no code execution. If your interface forces tools on, say so at the top. Rules: - Exact values only (integers, fractions). No decimals unless an item asks. - If an item is underdetermined or impossible, saying so IS the answer. Do not invent a number. - For each item, output: item number / final answer / confidence 0-100. Then the work. - Work: max 10 lines per Part A item. Part B limits are stated per item. PART A A1. Solve |x - 3| + |2x + 1| = 10 over the reals. List every solution. A2. An urn holds 5 red, 4 blue, 3 green balls. I draw without replacement until the first red appears. What is the exact expected number of draws, counting the red draw itself? A3. a0 = 2, a1 = 7, an = 5·a(n-1) - 6·a(n-2). Give a closed form for an, and a10 as an integer. A4. M = [[4, 1], [2, 3]]. Compute M^10 exactly — all four entries. A5. f is continuous on [0,1], f(0) = f(1) = 0, f(1/2) = 3. Compute the integral of f from 0 to 1. A6. How many integers from 1 to 10000 are divisible by none of 6, 10, 15? PART B — modeling. Graded on method, not on one right number. B1. Estimate how many ride-share drivers are on the road at 6pm on a Friday in a metro area of 2 million people. Show your decomposition, a point estimate with a plausible range, and name the two assumptions the result is most sensitive to. Max 30 lines. B2. A subscription product raised its price 20% on March 1, for new signups only. The June read: 90-day retention of post-March paying cohorts is 6 points higher than same-season cohorts last year. The CFO concludes the higher price caused better retention. (a) State the causal structure in text-DAG form. (b) List every mechanism that could produce the +6 points with zero true price effect. (c) Give the design or estimator you would actually run to get the true effect. (d) Name one placebo or falsification test. Max 40 lines.