To determine which measurement is not equal to 50 millimeters, we first need to convert different units of measurement to millimeters for accurate comparison. Here are some common conversions: Centimeters: 1 centimeter (cm) is equal to 10 millimeters (mm). Therefore, 5 cm is equal to 50 mm. Inches: 1 inch is equal to 25.4 millimeters. … Read more
To graph the six terms of a finite sequence, we first need to understand how the terms are generated based on the given information. In this case, the sequence starts with the first term, denoted as a1, which is equal to 5, and has a common ratio r equal to 125. The formula for the … Read more
To solve the equation x² – 9 – 16 = 0 using the zero product property, we first need to rearrange and simplify the equation. 1. **Rearranging the equation:** Start by combining the constants: x² – 9 – 16 = x² – 25 = 0. Thus, we can rewrite the equation as: x² – 25 … Read more
Descartes’ Rule of Signs is a valuable tool in algebra that helps us understand the potential number of positive and negative real roots in a polynomial function. This rule states that the number of positive real roots of a polynomial is either equal to the number of sign changes between consecutive non-zero coefficients or less … Read more
Calculating the percentage of one number in relation to another is a straightforward process. Here’s how you can do it step by step: Identify the Numbers: First, determine the two numbers you are interested in. Let’s call the first number A and the second number B. Use the Formula: The formula to find out what … Read more
To complete a discrete probability distribution, the sum of all probabilities must equal 1. A discrete probability distribution is a mathematical function that maps outcomes to their associated probabilities, and it must adhere to specific rules: Each probability must be between 0 and 1 (inclusive). The sum of all probabilities in the distribution must equal … Read more
To find the value of b² – 4ac for the quadratic equation x² + 5x + 4 = 0, we first need to identify the coefficients a, b, and c from the standard form of a quadratic equation, which is ax² + bx + c = 0. a (coefficient of x²) = 1 b (coefficient … Read more
To approximate the real number solution s to the polynomial function f(x) = x³ – 2x² + 5x – 6, we can use several methods, with one of the most straightforward being the Newton-Raphson method or a graphical approach. Step 1: Identify the Function First, let’s define the polynomial. The function is: f(x) = x³ … Read more
The average rate of change of a function over a specific interval can be calculated using the formula: Average Rate of Change = \( \frac{f(b) – f(a)}{b – a} \) Where: \( a \) is the starting point of the interval (in this case, 4). \( b \) is the ending point of the interval … Read more
To find the number of positive integers not exceeding 100 that are divisible either by 4 or by 6, we can use the principle of inclusion-exclusion. Step 1: Count integers divisible by 4 The integers divisible by 4 up to 100 can be found by dividing 100 by 4: 100 ÷ 4 = 25 Thus, … Read more