The system of linear equations are shown in the figure bellow:\[\] \[\] Inconsistent: If a system of linear equations has no solution, then it is called inconsistent.

The centroid of a triangle is the intersection of the three medians, or the "average" of the three vertices. It has several important properties and relations with other parts of the triangle, including its circumcenter, orthocenter, incenter, area, and more. The centroid is typically represented by the letter ...

Let \(R_a\) and \(R_b\) denote the radii of spheres \(a\) and \(b,\) respectively. Then from the formula \( V=\frac{4}{3} \pi r^3 \) for the volume of a sphere with ...

Suppose that the probability that a random person has a certain disease is \(0.005.\) A scientist develops a device which tests a person positive for the disease with \(95\)% chance when the person really has the disease.

Algebraic expressions, such as \(4x+3y-2w^2,\) contain variables, numbers, and mathematical operations. Algebraic expressions may be written in different ways, but still mean the sam

The probability density function or PDF of a continuous random variable gives the relative likelihood of any outcome in a continuum occurring. Unlike the case of discrete random variables, for a continuous random variable any single outcome has probability zero of occurring. The probability density function gives the probability that any value in a continuous set of values …

Conditional probability is the probability of one thing being true given that another thing is true, and is the key concept in Bayes' theorem. This is distinct from joint probability, which is the probability that both things are true without knowing that one of them must be true. For example, one joint probability is "the probability that your left and right socks are both black ...

\[x_1 = \frac{1}{3}, x_2 = \frac{1}{6}, x_3 = 1, x_4 = 0.679, x_5 = 0.463, x_6 = 0.3035, x_7 = 0.114, x_8 = 0.473, \ldots.\] This is very clearly not helpful. That's because the graph of the function around \(x = 0\) looks like this: As you can see, this graph has a local maximum, a local minimum and a point of inflection around \(x = 0\).

Jan 11, 2011 · Rebuttal: We observe that \(1-1+1-1 \dots\) is an infinite geometric progression with first term \(a=1\) and common ratio \(r=-1\) and hence the sum is given by \(S ...

One can note two things. First, the solution is analogous to the quadratic formula. And while Galois theory has established that formulas using a finite number of arithmetic operations and root extractions are impossible for general equations of degree greater than four, there are particular equations solvable as such.