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Modified Jones Discretionary Accruals Formula
Calculate Dechow, Sloan, and Sweeney’s (1995) Modified Jones Non-Discretionary Accruals NDA_t and Discretionary Accruals DA_t by subtracting credit-sales receivable growth from revenue growth.
Read the guide →Macroeconomics & Household FinanceModigliani Life-Cycle Saving & Wealth-Income Formula
Calculate Franco Modigliani’s Life-Cycle Hypothesis (LCH) smoothed annual consumption C = (W_0 + N*Y)/(N + M), active-worker saving rate, and retirement peak wealth-to-income ratio.
Read the guide →FinancialModigliani M-Squared (M2) Return & Grinold's Fundamental Law (IC * SQRT(BR))
Calculate a hypothetical volatility-scaled return and a simplified skill/breadth model using fictional, consistently measured inputs.
Read the guide →EngineeringMohr-Coulomb Soil Shear Strength & Infinite-Slope Factor of Safety
Calculate a drained Mohr–Coulomb shear-strength example and, separately, an ideal dry cohesionless infinite-slope ratio.
Read the guide →EngineeringMohr's Circle 2D Principal Stresses (sigma_1, sigma_2) & Max Shear Stress formulas
Compute the two in-plane principal stresses and distinguish maximum in-plane shear from absolute three-dimensional maximum shear in plane stress.
Read the guide →EngineeringMolarity (M) & lab solution bench-prep mass formula (Grams = M × L × MW)
Convert mass, molar mass and final solution volume to molarity, and calculate theoretical solute mass for a target concentration.
Read the guide →Fracture Mechanics & Fatigue Notch AnalysisMolski-Glinka ESED Notch Strain vs Neuber Formula
Calculate Elastic Pseudo-Notch Stress K_t * S_nom, Molski-Glinka Equivalent Strain-Energy Density (ESED) Elastic-Plastic Notch Strain, Neuber Hyperbola Strain, and Plane-Stress/Plane-Strain Ratio.
Read the guide →EngineeringMonod Bioreactor Microbial Growth, Doubling Time & Chemostat Washout
Explore Monod growth, intrinsic doubling time and the washout boundary of an ideal single-substrate chemostat without decay or biomass retention.
Read the guide →Operations, Logistics & EngineeringMononobe-Okabe Seismic Active Earth Pressure Coefficient (K_AE) Formula: Retaining Wall Thrust
Calculate earthquake pseudo-static retaining-wall thrust P_AE = 0.5 * gamma * H^2 * (1 - k_v) * K_AE and dynamic increment Delta_K_AE = K_AE - K_A using N. Mononobe & S. Okabe’s (1926/1929) AASHTO/Eurocode 8 wedge formula.
Read the guide →Engineering & ScienceMonostatic Radar Range Equation: Maximum Detection Range (Rmax) & Fourth-Power Law
Calculate maximum monostatic radar detection range Rmax = ((Pt * G^2 * lambda^2 * sigma) / ((4*pi)^3 * Smin))^0.25 in kilometers and echo power Pr in dBm.
Read the guide →Engineering & ScienceMonrad-Pelton Concentric Annulus Heat Transfer Formula (Double-Pipe Exchangers)
Calculate inner-wall turbulent Nusselt number Nu_i = 0.020 * Re^0.8 * Pr^(1/3) * (D_o / D_i)^0.53 in jacketed double-pipe heat exchangers.
Read the guide →Statistical & Clinical AnalysisMorisita-Horn Overlap Index Formula: Sample-Size-Robust Community Similarity & Dissimilarity
Compare two ecological assemblages, immune TCR repertoires, or dietary niches using Henry S. Horn’s (1966) Morisita-Horn Overlap Index C_MH = 2 * SUM(p_i * q_i) / (SUM(p_i^2) + SUM(q_i^2)) on [0, 1].
Read the guide →Offshore Wind & Marine Structural Engineering, Wave LoadingMorison Equation Offshore Pile Wave Drag & Inertia Formula
Calculate Peak Wave Drag Force Amplitude F_D (kN/m), Peak Added-Mass Inertia Force Amplitude F_I (kN/m), Naive In-Phase Sum (kN/m), and True Phase-Accurate Peak Morison Force F_max (kN/m).
Read the guide →Healthcare & ClinicalMorse Fall Scale (MFS): Inpatient Fall Risk Score (0–125) & Prevention Tier
Calculate the 0–125 point Janice Morse Fall Scale from 3-month fall history (+25), secondary diagnosis (+15), ambulatory aid (0/15/30), IV/heparin lock (+20), gait (0/10/20), and mental status (0/15).
Read the guide →Labor Economics & Search TheoryMortensen-Pissarides Beveridge Curve & Hosios Formula
Calculate Cobb-Douglas job-finding rate mu * theta^(1 - eta), vacancy-filling rate mu * theta^(-eta), Beveridge steady-state unemployment u*, and Hosios efficiency.
Read the guide →FinancialMortgage CPR to SMM formula: Single Monthly Mortality & pool prepayments
Convert annualized Constant Prepayment Rate (CPR) to monthly Single Monthly Mortality (SMM) and model unscheduled mortgage pool principal prepayments.
Read the guide →FinancialMortgage refinance break-even formula: monthly savings, payback months & net gain
Compare equal-term fixed-rate loan payments and estimate simple payment-savings payback for upfront refinancing costs.
Read the guide →Engineering & ScienceMorton Number (Mo) & Grace Diagram Gas-Bubble Fluid Property Index
Calculate the dimensionless fluid-property Morton Number Mo = g * μ_L^4 * (ρ_L - ρ_G) / (ρ_L^2 * σ^3) and Grace diagram abscissa LOG10(Mo) spanning 14 orders of magnitude from clean water (-10.6) to viscous syrups (+1.1).
Read the guide →ScienceMoseley's Law Characteristic K-Alpha X-Ray Energy & Atomic Number Z
Calculate characteristic K-alpha X-ray photon energy E_Ka = (3/4) * R_inf * (Z - 1)^2 (keV), wavelength lambda (Angstroms), and inverse elemental identification Z = 1 + SQRT(E_eV / 10.2043) for XRF/EDS spectroscopy.
Read the guide →EngineeringMOSFET Drain Current (Cutoff, Triode & Saturation) & gm formulas
Model square-law NMOS transistor drain current across Cutoff (V_GS <= V_th), Triode/Linear (V_DS < V_OV), and Saturation (V_DS >= V_OV) with IFS plus transconductance g_m.
Read the guide →Engineering & ScienceMoss’s Rule: Semiconductor Refractive Index From Bandgap (n^4 * Eg = 95 eV)
Estimate infrared semiconductor refractive index n = (95 / E_g)^0.25, high-frequency dielectric constant eps_inf = n^2, and normal-incidence Fresnel air-interface reflectance R (%) from optical bandgap E_g (eV).
Read the guide →Engineering & ScienceMössbauer Spectroscopy: Free-Nucleus Recoil Energy & Doppler Velocity
Calculate free-nucleus gamma-ray recoil energy E_R = E_gamma^2 / (2 * M * c^2) (meV) and Mössbauer spectrometer linear Doppler velocity v = (Delta_E / E_gamma) * c (mm/s) for 57Fe isomer shifts and hyperfine splitting.
Read the guide →StatisticalMost frequent text value with criteria: top ticket reason by region
Find the #1 recurring text label (defect code, ticket category, or top SKU) within a chosen department or region using COUNTIFS + masked XLOOKUP.
Read the guide →MathMosteller Body Surface Area (BSA) & Cockcroft-Gault Creatinine Clearance (CrCl)
Spreadsheet arithmetic examples for Mosteller BSA and the historical Cockcroft–Gault estimate using fictional adult inputs; not a drug-dosing recommendation.
Read the guide →Process Heat Transfer, Distillation Reboilers & Phase-Change DesignMostinski Reduced-Pressure Kettle Reboiler Boiling h & CHF Formula
Calculate Reduced Pressure P_r = P / P_c, Mostinski Pressure Factor F_p, Nucleate Pool-Boiling Coefficient h_nb (W/m²·K), and Mostinski Maximum Critical Heat Flux q_crit (kW/m²).
Read the guide →Engineering & ScienceMott-Gurney Space-Charge-Limited Current (SCLC) Law for OLEDs & Perovskites
Calculate trap-free solid-state space-charge-limited current density J = (9/8) * eps_r * eps_0 * mu * (V^2 / L^3) (A/m^2) to extract carrier mobility in organic OLEDs, polymers, and halide perovskites.
Read the guide →High-Voltage Insulation Coordination, IEEE C62.22 MOV Arrester BIL & Separation DistanceMOV Surge Arrester BIL Margin & Separation Formula
Calculate Traveling-Wave Reflected Transformer Terminal Voltage Vt (kV), IEEE C62.22 Protective Ratio (BIL / Vt), Insulation Margin (%), and Maximum Safe Arrester Separation Lmax (m).
Read the guide →StatisticalMoving average formula: smooth noisy weekly data with a trailing N-period window
Calculate a dynamic trailing N-period moving average with TAKE and AVERAGE, and emit NA() on incomplete warm-up rows.
Read the guide →ERP Supply-Chain Planning & Inventory ControlMRP Gross-to-Net & Lot-Multiple Planned Order Formula
Calculate Joseph Orlicky’s MRP Unreplenished Projected Balance, Safety-Stock-Protected Net Requirement MAX(0, Gross + Safety_Stock - On_Hand - Scheduled_Receipts), Lot-Multiple Planned Order Receipt, and Ending On-Hand Inventory.
Read the guide →EngineeringMTBF, MTTR, System Availability & SLA "Nines" downtime budget formulas
Calculate observed availability and a time-based downtime budget for the supplied window. Distinguish sample repair statistics from future reliability and contractual SLA rules.
Read the guide →Operations & LogisticsMulti-Sheet Inventory Reconciliation: ERP Book Stock, In-Transit Transfers & Shrinkage Audit
Reconcile ERP ledger balances against physical warehouse cycle counts by netting outbound in-transit stock, computing unit and dollar shrinkage variances, and flagging material recount exceptions.
Read the guide →Math & StatisticalMulti-Step AI Spreadsheet Commands: Sheets, Rows/Columns, Charts & Role-Aware Sharing
Chain up to 10 ordered workbook steps (create/rename/select sheets, insert/delete rows or columns, populate formulas, and build charts) in Arte Sheets while keeping collaborator invitations gated behind explicit owner confirmation.
Read the guide →Math & EngineeringMultinomial Coefficient Formula: Group Partitions & Repeated-Item Permutations (FACT)
Calculate the exact multinomial coefficient (n1 + n2 + ... + nk)! / (n1! * n2! * ... * nk!) using FACT and SUM to count ordered squad assignments, categorical outcomes, and word anagrams.
Read the guide →Math & TrigMultiplication table & 2D SaaS seat-pricing matrix ($A3 * B$1 vs spilled array)
Generate a 2D outer-product matrix with either classic mixed references ($A3 * B$1) or a single spilled dynamic-array formula (A3:A5 * B1:D1).
Read the guide →Engineering & Fluid MechanicsMurphree Vapor Tray Efficiency (E_MV) Formula: Single-Stage Mass Transfer & Pseudo-Equilibrium
Evaluate single-plate distillation and gas-absorption performance using Eger V. Murphree’s 1925 vapor efficiency E_MV = (y_n - y_(n+1)) / (y_n* - y_(n+1)) and step off actual tray outlet compositions y_n = y_(n+1) + E_MV * (y_n* - y_(n+1)).
Read the guide →Healthcare & Clinical FormulasMurray Lung Injury Score (LIS) & VV-ECMO Referral Threshold (>= 3.0)
Average the 4 ordinal (0–4) Murray Lung Injury Score components—Chest Radiograph Quadrants, PaO2/FiO2 Hypoxemia, PEEP Level, and Respiratory System Compliance—to evaluate > 2.5 Severe ARDS and >= 3.0 VV-ECMO referral criteria.
Read the guide →Commercial Offset/Flexo Printing, ISO 12647 Colorimetry & Pressroom DensitometryMurray-Davies Halftone Dot Area & Dot Gain (TVI) Formula
Calculate Tint Patch Paper-Relative Reflectance R_t (%), Solid-Ink Patch Reflectance R_s (%), Murray-Davies Apparent Printed Dot Area (%A), and Tone Value Increase / Dot Gain TVI (%).
Read the guide →Music IP Royalties, Entertainment M&A & Alternative CreditMusic Catalog Net Publisher’s Share (NPS) Valuation Formula
Calculate Music IP Post-Administration Net Receipts, Investor Net Publisher’s Share (NPS) / Net Label Share After Writer Payables, Catalog Acquisition Valuation (NPS * Multiple), and Implied Unlevered Royalty Yield.
Read the guide →Media, Music & Royalty AccountingMusic Streaming Royalty & Advance Recoupment Formula
Calculate Pro-Rata DSP Master Royalty Pool Payout, Contractual Artist Royalty Credited, Remaining Unrecouped Label Advance, and Payable Artist Cash Royalty.
Read the guide →Engineering & ScienceMuskingum River Flood Routing: C1, C2, C3 Coefficients & Routed Outflow (Q2)
Route upstream flood hydrographs through natural river reaches using McCarthy's Muskingum storage equation Q2 = C1*I2 + C2*I1 + C3*Q1 with automatic Courant/sub-interval stability guard 2*K*X <= dt <= 2*K*(1 - X).
Read the guide →SaaS Pricing & Mechanism DesignMussa-Rosen SaaS Versioning & Information Rent Formula
Calculate Incentive-Compatible Basic Price P_L = theta_L * q_L, High-Type Information Rent (theta_H - theta_L) * q_L, Enterprise Tier Price P_H = theta_H * q_H - Rent_H, and Total Versioning Revenue.
Read the guide →LogicalMust pass K out of N subjects or checks (quorum and floor rule)
Evaluate multi-part exams, vendor scorecards, or board quorums requiring at least K passing scores plus a minimum floor on every item.
Read the guide →Clinical Medicine & PhysiologyMUST Score Calculator: BAPEN Malnutrition Universal Screening Tool Formula
Calculate the 3-step BAPEN Malnutrition Universal Screening Tool (MUST, 0–6 points) from Adult BMI (kg/m^2), Unplanned 3–6 Month Weight Loss (%), and Acute Disease >5-Day No-Intake Effect.
Read the guide →Corporate Finance & RestructuringMyers Debt-Overhang Underinvestment NPV Hurdle Formula
Quantify senior-creditor wealth transfer, shareholder net NPV Delta_E, and Stewart Myers’s (1977) debt-overhang hurdle NPV_min = I * (1 - p_G) / p_G.
Read the guide →Corporate Finance & Capital StructureMyers-Majluf Equity Issuance & Pecking Order Formula
Calculate Stewart Myers and Nicholas Majluf’s (1984) pooled equity-issuance dilution loss on undervalued high-state firms and prove why internal cash and riskless debt beat seasoned equity.
Read the guide →Mechanism Design & Auction TheoryMyerson Optimal Auction Virtual Valuation and Reserve Price Formula
Calculate Myerson’s (1981) virtual valuation psi(v) = 2*v - H, optimal bidder-count-invariant reserve price r* = (v_0 + H) / 2, and expected Vickrey auction seller payoff.
Read the guide →InformationN function: convert TRUE/FALSE to 1/0 and embed inline formula comments
Turn logical checkboxes into 1/0 numbers and document complex formulas inline with + N("explanation") using N.
Read the guide →InformationNA function: output #N/A intentionally so line charts skip missing periods
Mark missing readings with NA(), distinguish them from zero, and understand chart-specific handling before plotting.
Read the guide →Healthcare & ClinicalNAFLD Fibrosis Score (NFS) Noninvasive MASLD Liver Fibrosis Formula
Calculate Paul Angulo’s validated NAFLD Fibrosis Score NFS = -1.675 + 0.037*Age + 0.094*BMI + 1.13*IFG_DM + 0.99*(AST/ALT) - 0.013*Platelets - 0.66*Albumin to rule out (< -1.455) or rule in (> 0.675) F3–F4 advanced liver fibrosis.
Read the guide →StatisticalNaive forecast accuracy: WMAPE and row percentage errors
Benchmark any demand forecast against a Naïve (Y_{t-1}) baseline using Mean Absolute Percentage Error (MAPE) and volume-weighted WMAPE.
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