In a scatterplot, a dot represents a single data point. With several data points graphed, a visual distribution of the data can be seen. … The closer the data points come to forming a straight line when plotted, the higher the correlation between the two variables, or the stronger theRead More →
Linear pair is a pair of two supplementary angles. But two supplementary angles might or might not form a linear pair, they just have to “supplement” each other, that is their sum should be 180o . Are supplementary always linear pairs? The two angles of a linear pair are alwaysRead More →
Multivariate Regression is a method used to measure the degree at which more than one independent variable (predictors) and more than one dependent variable (responses), are linearly related. What are the assumptions for multivariate linear regression? The relationship between the dependent variable and the independent variables should be linear, andRead More →
Since terms of linear equations cannot contain products of distinct or equal variables, nor any power (other than 1) or other function of a variable, equations involving terms such as xy, x^2, y^(1/3), and sin(x) are nonlinear. Is sin x a linear system? Therefore, the system does not satisfy theRead More →
Two common ways to look at problem solving are linear thinking and nonlinear thinking. Linear thinkers follow a step-by-step progression that leads them to a solution. Nonlinear thinkers think outside the lines and sometimes use unorthodox methods to solve problems. Is linear thinking good or bad? People generally regard linearRead More →
A function f is called a linear operator if it has the two properties: f(x+y)=f(x)+f(y) for all x and y; f(cx)=cf(x) for all x and all constants c. How do you find the adjoint of a linear operator? We have that 〈x,T(y)〉 = 〈T(y),x〉 = 〈y,T∗(x)〉 = 〈T∗(x),y〉. Let ARead More →
Since slope is defined as the change in the variable on the y-axis divided by the change in the variable on the x-axis, the slope of the demand curve equals the change in price divided by the change in quantity. To calculate the slope of a demand curve, take twoRead More →
Restriction enzymes, also called restriction endonucleases, recognize a specific sequence of nucleotides in double stranded DNA and cut the DNA at a specific location. They are indispensable to the isolation of genes and the construction of cloned DNA molecules. Do restriction enzymes cleave single-stranded DNA? Abstract. Restriction endonucleases (13 outRead More →
If the arrangement is symmetrical and the arrows are of equal length, the molecule is nonpolar. If the arrows are of different lengths, and if they do not balance each other, the molecule is polar. If the arrangement is asymmetrical, the molecule is polar. What types of molecules are polar?Read More →
Linear pair is a pair of adjacent angles whose non- common sides form a straight line. When two lines intersect each other at a common point then, a linear pair of angles are formed. If the angles are adjacent to each other after the intersection of the lines, then theRead More →