Yes, both rational numbers and irrational numbers are included in the set of real numbers. To understand this better, let’s break down the definitions of both types of numbers. Rational Numbers Rational numbers are numbers that can be expressed as the quotient or fraction of two integers, where the denominator is not zero. In simpler … Read more
To determine the probability of obtaining a number less than 2 on a spinner numbered from 1 to 10, we must first identify the possible outcomes of a spin and the favorable outcomes for our condition (i.e., the number being less than 2). The numbers on the spinner are: 1, 2, 3, 4, 5, 6, … Read more
A meter is a standard unit of measurement in the metric system, which is used worldwide for measuring length and distance. One meter is equal to 100 centimeters. This relationship means that when you have one meter, you can divide it into 100 equal parts, and each of those parts is one centimeter. To put … Read more
The concept of probability is a fundamental part of mathematics that deals with measuring the likelihood of certain outcomes in a given space. When we talk about events in probability theory, we often categorize them into different types based on their feasibility. An impossible event is defined as an event that cannot occur under any … Read more
When considering how much time you can save by increasing your speed from 55 mph to 60 mph on a ten-mile trip, we first need to calculate the time it takes for both speeds. Step 1: Calculate time at 55 mph To find the time taken to travel ten miles at 55 mph, we can … Read more
To find the inverse of the equation y = 5x² + 10, we follow several steps to simplify it and express x in terms of y. Step 1: Swap the Variables The first step in finding the inverse is to switch x and y in the equation. This gives us: x = 5y² + 10 … Read more
To determine the number of women in the city, we can use the given ratio of men to women, which is 3 to 1. This means that for every 3 men, there is 1 woman. Let’s break down the calculation step by step: 1. First, we need to express the ratio in terms of parts. … Read more
To factor the polynomial x² + 6x + 27, we will apply the methods of factoring polynomials. First, let’s check if it can be factored as a simple quadratic equation of the form ax² + bx + c. In our case: a = 1 b = 6 c = 27 To find the factors of … Read more
In triangle ABC, the incenter O is the point where the angle bisectors of the triangle intersect. The incenter is also the center of the circle inscribed within the triangle. To find the measure of angle QOB, we need to consider the relationship between the triangle’s angles and the angles formed by the incenter. Given … Read more
The product of two integers can be positive, negative, or zero depending on the integers involved. Here’s how it works: Product is Positive: When both integers are either positive or negative. For example: (3) * (4) = 12 and (-3) * (-4) = 12. In both cases, the result is a positive integer. Product is … Read more