Mathematics | Senioritis

John Rhodes
June 21, 2023
Statistics

Statistical Significance: Analyzing Data To Determine Real Effects And Reject Null Hypotheses

Determining Significance 1) Determine desired long-run rate of false-positive (Type I) errors (⍺) –> change to 0.0052) Take an estimate of effect (e.g., a mean difference) and...

John Rhodes
June 21, 2023
Statistics

The Uniform Distribution Of P-Values When The Null Hypothesis Is True.

P- value Distribution when Ho is true Flat When the null hypothesis (Ho) is true, the distribution of the p-value follows a uniform distribution between 0 and...

John Rhodes
June 21, 2023
Calculus

One-To-One Functions In Math: Injecting Efficiency Into Cryptography And Data Compression

A function f(x) is one-to-one if x1 ≠ x2 implies f(x1) ≠ f(x2) f(x1) ≠ f(x2). In other words, if every input x has a unique output...

John Rhodes
June 21, 2023
Calculus

Learn The Basics Of One-To-One Functions With Inverse Functions | Math Tips & Tricks

A one-to-one function f has an inverse f−1 satisfyingf−1(f(x)) =__________andf(__________) =y. x;f−1(y) A one-to-one function f has an inverse f−1 satisfying the following: 1. f−1(f(x)) = x...

John Rhodes
June 21, 2023
Calculus

Maximizing Your Math: Simplifying The Trigonometric Expression Tan(Tan^-1(X))

tan(tan−1(x)) =__________for x in__________ . x; (−∞,∞) The given expression is: tan(tan^-1(x)) The value of tan^-1(x) is the angle whose tangent is x, so if we define...

John Rhodes
June 21, 2023
Calculus

Proving The Identity: Tan^(-1)(Tan(X)) = X In Interval (-Π/2, Π/2)

tan−1(tan(x)) =.__________for x in__________ x; (−π/2,π/2) The identity tan^(-1)(tan(x)) = x holds true for x in the interval (-π/2, π/2), where tan(x) is defined and is a...

John Rhodes
June 21, 2023
Calculus

The Inverse Sine Function: Working With Degrees And Radians

sin−1(sin(x))=__________for x in__________ x; [−π/2,π/2] The answer to this question depends on whether you are working in degrees or radians. I will provide answers for both cases:...

John Rhodes
June 21, 2023
Calculus

Discover The Domain And Range Of Sin⁻¹(X) In Simple Steps

The domain of sin−1(x) is__________and the range is__________ [−1,1]; [−π/2,π/2] The domain of sin⁻¹(x) is [-1, 1]. This is because sin⁻¹(x) is the inverse function of sine,...