Comparing an improper fraction to a proper fraction may seem tricky at first, but it’s quite straightforward once you understand the definitions of both types of fractions. Let’s break it down step by step. Definitions A proper fraction is a fraction where the numerator (the top number) is less than the denominator (the bottom number). … Read more
The mean IQ of 112 and standard deviation of 20 provide significant insights into the cognitive capabilities of the population being studied. When conducting a market research campaign, analyzing these statistics can help in understanding the demographic’s behavior, preferences, and purchasing power. In this context, the mean IQ score signifies that the average cognitive aptitude … Read more
In probability theory, two events A and B are considered mutually exclusive when they cannot both occur at the same time. In other words, if event A happens, then event B cannot happen, and vice versa. Let’s delve a bit deeper into this concept. The probability of the intersection of two events, denoted as P(A … Read more
To simplify the expression 3 + 4y + 3 + 7y, you’ll want to combine the like terms, which are those that have the same variable component. 1. **Identify like terms:** The terms can be broken down into two categories: – Constant terms: 3 and 3 – Variable terms: 4y and 7y 2. **Combine the … Read more
Determining the number of roots of a polynomial can actually be done relatively quickly by observing a few key characteristics of the equation. Here’s a detailed breakdown of the steps you can take: Identify the Degree of the Polynomial: The first step is to look at the highest power of the variable in the polynomial … Read more
To find the equation of the tangent line to the curve defined by y = 4x – 3x² at the point (2, 4), we follow these steps: Find the derivative: The derivative of a function gives us the slope of the tangent line at any point on that curve. Let’s find the derivative of the … Read more
To check the sum of the numbers 27, 15, and 12, you simply add these three numbers together. Here’s how you can do it step by step: Start by adding the first two numbers: 27 and 15. 27 + 15 = 42 Next, take the result from the previous addition (42) and add the third … Read more
The exact value of sin(30°) is 1/2. This sine value can be derived from the properties of a 30-60-90 triangle, where the sides are in the ratio of 1 : √3 : 2. In this type of triangle, the side opposite the 30-degree angle is half the length of the hypotenuse, which confirms that the … Read more
To check the answer to the division problem 120 divided by 30, you can follow a few straightforward steps: Perform the Division: Start by dividing 120 by 30. You can do this using long division, a calculator, or even mental math if you’re comfortable with it. Using a Calculator: If you prefer a quick solution, … Read more
No, the ratios of 3 to 4 and 4 to 3 are not the same. Let’s break it down to understand why. A ratio expresses the relationship between two quantities. When we say the ratio of 3 to 4, we can express this mathematically as: Ratio of 3 to 4: 3:4 or 3 ÷ 4 … Read more