This paper illustrates a biological application of the concepts of relative change and area under a curve, from mathematics. We study two biological measures "relative change in cardiac output" and "cardiac output", which are predictors of heart blockages and other related ailments. Cardiac output refers to the quantity of…

The purpose of this report is to describe the technical qualities of the 2018-2019 operational administration of the English language arts/literacy (ELA/L) and mathematics summative assessments in grades 3 through 8 and high school. The ELA/L assessments focus on reading and comprehending a range of sufficiently complex texts independently and…

The purpose of this report is to describe the technical qualities of the 2018-2019 operational administration of the English language arts/literacy (ELA/L) and mathematics assessments in grades 3 through 8 and high school. New Meridian, in coordination with multiple states and vendors, developed an alternate form of the summative assessment to…

The standard reverse-order law for the Moore-Penrose inverse of a matrix product is (AB)[dagger] = B[dagger]A[dagger]. The purpose of this article is to give a set of equivalences of this reverse-order law and other mixed-type reverse-order laws for the Moore-Penrose inverse of matrix products.

This classroom note presents a final solution for the functional equation: f(xy)=xf(y) + yf(x). The functional equation if formally similar to the familiar product rule of elementary calculus and this similarity prompted its study by Ren et al., who derived some results concerning it. The purpose of this present note is to extend these results and…

Eigenvalue is an important concept in Linear Algebra. It is well known that the eigenvectors corresponding to different eigenvalues of a square matrix are linear independent. In most of the existing textbooks, this result is proven using mathematical induction. In this note, a new proof using Vandermonde determinant is given. It is shown that this…

This paper investigates a general identity which expresses an apparently complicated and intriguing sum of fractions as an elegant and straightforward sum of simple terms.

Euler gave a simple method for showing that [zeta](2)=1/1[superscript 2] + 1/2[superscript 2] + 1/3[superscript 2] + ... = [pi][superscript 2]/6. He generalized his method so as to find [zeta](4), [zeta](6), [zeta](8),.... His computations became increasingly more complex as the arguments increased. In this note we show a different generalization…

This article describes the most compact 100c% interval for a probability density for 0

Descriptors: Probability, Computation, Mathematical Concepts, Statistics