Education

Least-squares BSA curve, back-calculated unknowns with dilution factor, extrapolation flags, and protein-specific dye-response caveats. Educational use only.

Data Analysis

Step-by-step independence testing for 2×2 / R×C contingency tables: Pearson χ², Yates, G-test, Fisher exact, effect sizes, adjusted residuals, Cochran rule and optional Chapman estimate.

Media

Apply long-short swing timing to transient-driven loops, with optional seeded humanization.

Education

PCR Ta by the simple rule (lower primer Tm − 5°C) or the Rychlik 1990 formula (0.3·Tm_primer + 0.7·Tm_product − 14.9), with a ±3°C gradient window and primer-Tm mismatch warning. Derived from Rychlik 1990, Innis & Gelfand 1990, Lorenz 2012. Lab-planning use only.

Format Conversion

Convert equations between AsciiMath, LaTeX and MathML: auto-detect the input format, produce canonical LaTeX, presentation MathML with an embedded TeX annotation, a best-effort AsciiMath back-translation, a screen-reader aria-label snippet (role=math), and a KaTeX HTML preview.

Education

Compute AD offspring risk (Aa×aa 1:1, Aa×Aa 3:1, AA×any all affected), chi-square fit of observed children, and hallmark checks including male-to-male transmission that rules out X-linked dominant. Derived from Griffiths, Hartl & Clark 2007, StatPearls, OMIM. Educational use only.

Education

Compute per-child and cumulative autosomal recessive disease risk from parental statuses (carrier / affected / non-carrier / unknown via population carrier rate), including the 2/3 carrier rule. Derived from Griffiths, Hartl & Clark 2007, StatPearls. Educational use only.

Finance

Convert odds between decimal, fractional, and American formats with implied probability, plus parlay combination odds and no-vig fair-odds calculation.

Education

Expected heterozygosity loss through a population bottleneck: H_final = H₀(1−1/2Nb)^t(1−1/2Nr)^g, retention, inbreeding F, harmonic-mean Ne, and one-generation allele survival. Derived from Wright 1931, Nei et al. 1975, Hartl & Clark 2007, StatPearls. Educational use only.

Education

Compute allele frequencies from genotype counts: p = (2AA + Aa) / 2N, q = (2aa + Aa) / 2N. Derived from Hartl & Clark 2007, Griffiths, StatPearls. Educational use only.

Health

Convert serum bilirubin (total/direct/indirect) between mg/dL and µmol/L. Factor 17.1 (molar mass 584.67 g/mol). Derived from Young 1987, StatPearls, AAP 2004, Bhutani. Not medical advice.

Health

Convert total serum calcium between mg/dL and mmol/L. Factor 0.25 (atomic weight 40.078; × 4.0 inverse). Does not albumin-correct. Derived from Payne 1973, Young 1987, StatPearls, Endocrine Society. Not medical advice.