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OR function: flag a support ticket when either trigger applies
Escalate a ticket if a service is down or if its response age exceeds 24 hours. Check all four truth-table cases and exact threshold equality.
Read the guide →Clinical Pharmacokinetics & BiopharmaceuticsOral Bateman PK: t_max, C_max & Bioavailability Formula
Calculate dose-normalized Absolute Bioavailability F, Harry Bateman’s oral peak time t_max = LN(k_a / k_el) / (k_a - k_el), peak plasma concentration C_max, and flip-flop kinetics flags.
Read the guide →Healthcare & Clinical FormulasORBIT Bleeding Risk Score for Atrial Fibrillation Anticoagulation
Calculate Emily O’Brien’s 5-factor ORBIT-AF major bleeding score (0–7: Anemia +2, Bleeding history +2, Age >=75 +1, eGFR <60 +1, Antiplatelet therapy +1) across DOAC and warfarin anticoagulation.
Read the guide →EngineeringOrbital velocity, escape velocity & Kepler's 3rd Law satellite period formulas
Calculate circular orbital speed SQRT(mu/r), local escape speed SQRT(2*mu/r), and orbital period in minutes from gravitational parameter mu and altitude.
Read the guide →StatisticalOrdinary Least Squares Slope, Intercept, R-Squared, and Standard Error (LINEST Diagnostics)
Build labeled, self-documenting regression diagnostics—slope, intercept, R^2, residual standard error SE_y, and slope standard error SE_b—using SLOPE, INTERCEPT, CORREL, and VAR_S.
Read the guide →Thermodynamics, Geothermal Power & Industrial Waste-Heat RecoveryOrganic Rankine Cycle (ORC) Back-Work & Net Power Formula
Calculate Organic Rankine Cycle (ORC) Working-Fluid Mass Flow (kg/s), Organic Feed-Pump Back-Work Ratio (%), Net Electrical Output (kWe), and Net Thermal Efficiency (%).
Read the guide →International Macroeconomics & Sovereign RiskOriginal Sin & Currency Mismatch Debt Shock Formula
Calculate post-depreciation sovereign Debt-to-GDP valuation jump d_1 = d_0*(1 + alpha_fx * Delta_S)/(1 + g_y) under Eichengreen-Hausmann "Original Sin" and Goldstein-Turner Net FX Debt / Exports mismatch.
Read the guide →Quantitative Finance & Time-Series EconometricsOrnstein-Uhlenbeck AR(1) Half-Life & Spread Z-Score
Convert discrete AR(1) persistence phi in (0, 1) into continuous Ornstein-Uhlenbeck speed kappa = -LN(phi), exact half-life -LN(2) / LN(phi), and stationary spread volatility sigma_e / SQRT(1 - phi^2).
Read the guide →FinancialOrnstein-Uhlenbeck conditional mean, half-life and uncertainty formulas
Calculate conditional expectation and dispersion under a constant-parameter mean-reverting model, with consistent time units and validated parameters.
Read the guide →MathOsmolality and water-deficit formulas: a fictional spreadsheet exercise
Practice units, arithmetic and input checks with fictional laboratory values. Results are educational calculations, not diagnoses or fluid-treatment instructions.
Read the guide →Econometrics & Omitted-Variable SensitivityOster Coefficient Stability Delta and Bias-Adjusted Beta Formula
Audit omitted-variable bias in Excel and Arte Sheets using Emily Oster’s (2019) R-squared-scaled bias-adjusted beta_star and breakdown proportionality delta_zero.
Read the guide →Fertilizer & Industrial Chemical Manufacturing, Ostwald Nitric AcidOstwald Nitric Acid Pt-Rh Gauze Selectivity & Yield Formula
Calculate 100%-Basis Pure HNO3 Produced (t/d), Commercial Weak Nitric Acid Output (t/d), Effective Acid-to-Ammonia Mass Gain Ratio, and Unselective N2/N2O Nitrogen Loss (kmol N/d).
Read the guide →Healthcare & ClinicalOttawa Ankle & Foot Rules: Evidence-Based Radiograph (X-Ray) Triage Formula
Determine whether ankle series and/or foot series radiographs are clinically indicated after acute blunt ankle trauma using Stiell's ~98–99% sensitive Ottawa Ankle and Midfoot Rules.
Read the guide →Healthcare & ClinicalOttawa Knee Rule Acute Fracture X-Ray Decision Formula
Apply Ian Stiell’s validated 5-item Ottawa Knee Rule (Age >= 55, isolated patellar tenderness, fibular head tenderness, inability to flex knee to 90°, inability to bear weight 4 steps) to rule out knee fracture without X-rays.
Read the guide →EngineeringOtto & Diesel Cycle Thermal Efficiency formulas (Compression & Cutoff Ratio)
Calculate air-standard spark-ignition Otto efficiency 1 - 1 / r^(gamma - 1) and compression-ignition Diesel efficiency from compression ratio r, cutoff rc, and gamma.
Read the guide →Environmental Science, Ecology & HydrologyOudin (2005) Potential Evapotranspiration (PET) Formula: Extraterrestrial R_a & Temperature
Calculate daily watershed Potential Evapotranspiration PET (mm/day) for lumped and distributed rainfall-runoff models (GR4J, HBV, SWAT) using Ludovic Oudin et al.’s (2005) parsimonious 308-catchment radiation-temperature law.
Read the guide →Revenue Management & Hospitality AnalyticsOverbooking Critical Fractile & Booking Limit Formula
Balance empty-seat spoilage c_u against denied-boarding bump compensation c_o via the Critical Fractile CF = c_u/(c_u + c_o) to set optimal flight and hotel overbooking limits.
Read the guide →Statistical & PsychometricsPABAK (Prevalence-Adjusted Bias-Adjusted Kappa), PI & BI Formula
Report Ted Byrt’s (1993) clinical diagnostic trio—PABAK = 2 * p_o - 1, Prevalence Index PI = |a - d| / N, and Bias Index BI = |b - c| / N—on 2×2 observer reliability studies.
Read the guide →TextPad text and amounts into an illustrative fixed-width record
Build a 12-character name and eight-digit cents field, with an explicit amount-overflow guard.
Read the guide →Text & String ManipulationPad Text with Spaces or Zeros for Fixed-Width Exports (REPT + Overflow Guard)
Build exact N-character fixed-width ACH, EDI, and banking record fields by right-padding text with spaces and left-padding numeric IDs with zeros—safely clamping strings that exceed field width.
Read the guide →TextPad Week & Fiscal Period Numbers with Leading Zeros ("2026-W04")
Build fixed-width week and fiscal-period codes with RIGHT, validate integers before padding, and distinguish ISO week-year labels from fiscal periods.
Read the guide →Healthcare & ClinicalPadua Medical Inpatient VTE Score & Khorana Ambulatory Cancer VTE Score
Calculate the Khorana Chemotherapy VTE Score (0–6 points across cancer site, platelets >= 350k, Hb < 10/ESA, WBC > 11k, BMI >= 35) and compare with the Padua >= 4 medical inpatient VTE threshold.
Read the guide →Nonparametric StatisticsPage’s L Trend Test Formula for Ordered Treatments in Blocked Ranks
Detect monotonic dose-response or learning-curve trends across blocked repeated-measures ranks using Page’s (1963) weighted rank sum L = SUM(j * R_j) and directional Z_L score.
Read the guide →Financial ModelingPain Index & Pain Ratio: Measuring Drawdown Depth AND Time Under Water
Compute the Zephyr Pain Index—the average percentage drawdown from running high-water mark across every period—and Pain Ratio (R_p - R_f) / Pain_Index to penalize stalled recoveries.
Read the guide →EngineeringPaint calculator formula: net wall square footage, coats & whole gallons
Estimate interior/exterior paint gallons by subtracting door and window openings from room perimeter × height, multiplying by coats, and rounding up.
Read the guide →Operations Research & Service Parts LogisticsPalm’s Theorem (S-1, S) Spare-Parts Base-Stock Formula
Size repairable spare-parts base stock S using Palm’s Theorem Poisson pipeline mean mu_p = lambda * T_rep, exact Fill Rate P(X <= S - 1), and Expected Backorders EBO(S).
Read the guide →Financial & AccountingPalma Ratio Formula: Top 10% to Bottom 40% National Income Share & Middle-50% Check
Calculate the OECD/UNDP Palma inequality ratio S_Top10 / S_Bottom40 and verify José Gabriel Palma’s "homogeneous middle" share S_Deciles_5_to_9 = 100 - S_Top10 - S_Bottom40 (~50% across nations).
Read the guide →EngineeringPalmgren-Miner damage index and a Basquin S-N life example
Sum cycle ratios in a linear fatigue model and explore a separate Basquin cycle-life calculation with an explicit reversals convention.
Read the guide →Charts & Visual DataPanel Chart (Small Multiples) Formula: Vertical Lane Offset & Base-100 Index
Separate tangled spaghetti line charts into clean Small-Multiples lanes by adding a fixed vertical Panel Span offset (k * Span + Value) or indexing every series to 100 at period t = 0.
Read the guide →Print Production, Bookbinding & Packaging EngineeringPaper GSM, US Basis Weight, PPI & Book Spine Formula
Convert US 500-Sheet Basis Weight (lb) across Text (25x38") vs Cover (20x26") parent sheets into ISO Metric Grammage GSM = (Lb * 1406.5) / (W_in * L_in), Pages Per Inch PPI = 2000 / Caliper_mils, and Perfect-Bound Spine Width.
Read the guide →Pulp, Paper & Packaging Process Engineering, Fourdrinier Wet-End & Dryer Section BalancePaper Machine Wet-End Dewatering & Steam Drying Formula
Calculate Bone-Dry Fiber Throughput (t/h), Headbox Slurry Flow (t/h), Dryer-Section Water Evaporation Rate (t/h), and Steam Boiler Demand (t/h) across Press-Felt Solids.
Read the guide →Quantitative Finance & TradingParabolic SAR Formula: Acceleration Factor Step & Prior Two-Bar Penetration Clamp
Implement J. Welles Wilder’s exact Parabolic Stop-and-Reverse (SAR) step SAR_next = SAR_curr + AF * (EP - SAR_curr) including the often-omitted prior two-lows non-penetration clamp.
Read the guide →Aerospace Recovery Systems, Rocketry & Fluid Drag MechanicsParachute Terminal Velocity, Canopy Diameter & Impact KE
Calculate Steady-State Canopy Drag Force m*g, Terminal Descent Rate Vt = SQRT((2*m*g)/(rho*Cd*S)), Equivalent Circular Canopy Diameter SQRT(4*S/PI()), and Touchdown Impact Kinetic Energy.
Read the guide →Power Generation Dispatch, Synchronous Turbine Governors & Primary Frequency ControlParallel Generator Speed-Droop Governor Load Sharing Formula
Calculate Composite Island Frequency Stiffness K_tot (MW/Hz), Settling Bus Frequency f_bus (Hz), Unit 1 Active Load P_1 (MW), and Unit 2 Active Load P_2 (MW).
Read the guide →StatisticalPareto 80/20 cumulative percentage and ABC inventory classification
Calculate running cumulative share on descending revenue SKUs and classify items into A (top 80%), B (next 15%), and C (bottom 5%) tiers.
Read the guide →Casualty Actuarial Science & Excess PricingPareto Excess Layer Severity & ILF Pricing Formula
Price heavy-tailed casualty layers using Single-Parameter Pareto Limited Expected Value LEV(x), Excess Layer Severity LEV(D + L) - LEV(D), and Increased Limits Factor ILF(L_high, L_base).
Read the guide →Mechanical & Aerospace Fracture MechanicsParis-Erdogan Fatigue Crack Growth Life Formula
Calculate Critical Fracture Crack Size a_c = (1 / PI()) * (K_IC / (Y * Delta_sigma))^2 and exact Paris-Erdogan Fatigue Cycles to Failure N_f across both power-law (m != 2) and logarithmic (m = 2) exponents.
Read the guide →EngineeringParis' Law Crack Growth: Integrated Cycles and Critical Size
Build a constant-amplitude Paris-law spreadsheet with separate maximum stress and stress range, a logarithmic m = 2 limit, and explicit model boundaries.
Read the guide →FinanceParkinson High-Low & Garman-Klass OHLC Volatility Formulas
Calculate Parkinson and Garman-Klass range-based volatility estimates from a valid OHLC bar, then apply an explicit periods-per-year assumption without rounding intermediate results.
Read the guide →Date & TimeParse 4-digit military time ("0930", 1745, 15) into real Excel time and hours
Convert numeric HHMM codes or numeric text to clock labels and elapsed hours for intervals shorter than one day.
Read the guide →TextParse a full address into Street, City, State, and ZIP code
Split comma-delimited US addresses ("742 Evergreen Ter, New Haven, CT 06510") cleanly even when street or city names contain multiple words.
Read the guide →Text & CleaningParse European Comma-Decimal & Thousands-Separated Text (NUMBERVALUE Pattern)
Convert locale-specific numeric strings such as "1.250,75", "4 820,50", and "12,5%" into true numbers regardless of system regional settings using SUBSTITUTE, TRIM, and VALUE.
Read the guide →TextParse XML tags and JSON webhook fields with formulas (TEXTAFTER & TEXTBEFORE)
Extract text from controlled XML-like tags and compact JSON string fields using delimiter formulas. These are not general parsers.
Read the guide →Business & OperationsPart-Period Balancing (EPP) & Groff's Marginal Lot-Sizing Heuristic in MRP
Determine discrete MRP production batch horizons under lumpy time-varying demand using Economic Part-Period EPP = S / h and Groff's marginal rule D_{t+n} * n * (n + 1) <= 2*S / h.
Read the guide →Lookup & ReferencePartial Substring Match on Numeric Cells (Why "*45*" Fails & SEARCH Fix)
Match, count, sum, and look up numeric invoice IDs or part numbers by embedded digit pattern without converting numeric columns to text, overcoming COUNTIF and XLOOKUP wildcard failure on numbers.
Read the guide →Lookup & ReferencePartial-Match Wildcard Lookup: VLOOKUP("*" & Key & "*") & XLOOKUP Mode 2
Look up vendor records or catalog SKUs by partial embedded code using VLOOKUP("*" & E2 & "*", A2:C5, 3, FALSE) or XLOOKUP("*" & E2 & "*", ..., 2).
Read the guide →Engineering & SciencePaschen's Law: Gas Breakdown Voltage (Vb) & Minimum Paschen (p*d) Curve
Calculate Townsend DC gas breakdown voltage Vb = (B * p * d) / (LN(A * p * d) - LN(LN(1 + 1 / gamma_se))) and the minimum breakdown product (p * d)_min = (EXP(1) / A) * LN(1 + 1 / gamma_se).
Read the guide →Healthcare & Clinical CalculationsPASI (Psoriasis Area and Severity Index 0–72) & PASI-90 Response
Calculate Torsten Fredriksson and Ulf Pettersson’s 0.0–72.0 PASI score weighting Head (0.1), Upper Limbs (0.2), Trunk (0.3), and Lower Limbs (0.4) area grades (0–6) times plaque Erythema + Induration + Desquamation sums (0–12).
Read the guide →Statistical & PsychometricsPassing-Bablok Nonparametric Method-Comparison Regression (Median Slope & Intercept)
Fit outlier-proof clinical laboratory calibration lines via Heinrich Passing & Wolfgang Bablok’s (1983) pairwise slope median b = MEDIAN((Y_j - Y_i) / (X_j - X_i)) and intercept a = MEDIAN(Y_i - b * X_i).
Read the guide →FinancialPayback Period formula: interpolated fractional years to break even on CapEx
Calculate the estimated year and fraction when cumulative project cash flows recover an upfront capital investment—and check whether a project does not recover its cost within the forecast.
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