### Can two events with nonzero probabilities be both independent and mutually exclusive?

The question aims to answer if two events can be both independent and mutually exclusive simultaneously with non-zero probabilities. When we toss two coins, the result of one coin does not affect the other. if one outcome is head/tail, this doesn’t affect the result of another event. This means mutually exclusive events are not independent. […]

### The price p (in dollars) and the quantity x sold of a certain product obey the demand equation p= -1/6x + 100. Find a model that expresses the revenue R as a function of x.

The main objective of this question is to find the revenue model of the given equation as just a function with respect to x. This question uses the concept of revenue model. A revenue model is a blueprint that outlines how a startup company will generate revenue or annual profit out of its basic business operations. Revenue […]

### Vertex Formula: Complete Definition, Examples, and Solutions

The vertex formula is used to solve for the vertex $(h,k)$ of a parabola. The vertex is the point in the parabola that describes the maximum or minimum value of the function. The vertex formula gives the exact vertex of a given quadratic equation without plotting the graph of the parabola. Similarly, we can derive […]

### Use the Distributive Property To Remove the Parentheses

We can use the distributive property to remove the parenthesis in a mathematical expression by properly distributing the multiplication operation inside the parenthesis.  The process of eliminating the parentheses using the distributive property is essential in solving many mathematical problems. This guide will help you understand the concept of the distributive property and how we […]

### Is -1 a Rational Number? Detailed Explanation With Sample

Yes, the number $-1$ is a rational number because we can write the number negative $1$ in $dfrac{p}{q}$ form. So, the question arises, “what is meant by $dfrac{p}{q}$ form?” “What is meant by “p” and what is meant by “$q$”?” In this article, we will study in detail what makes “$-1$” a rational number and, […]