devyy The sequence defined by the formula an = 5n + 1 can be calculated by substituting the values of n For n = 1: a1 = 5(1) + 1 = 5 + 1 = 6 For n = 2: a2 = 5(2) + 1 = 10 + 1 = 11 For n = 3: a3 … Read more
The likelihood that a particular event will occur is commonly referred to as probability. Probability is a fundamental concept in statistics and mathematics that expresses the chance of an event happening. It provides a numerical value between 0 and 1, where 0 indicates that the event cannot occur, and 1 signifies that the event is … Read more
To solve the polynomial equation 9×4 + 2×2 + 7 = 0, we will employ the method of u-substitution. This approach simplifies the equation by reducing its degree. Step 1: Perform u-substitution Let u = x2. Therefore, we can rewrite x4 as (x2)2 = u2. Substituting these values into the original equation gives us: 9u2 … Read more
To rewrite the equation 5x + 2y = 10 in the slope-intercept form, which is y = mx + b, we need to solve for y. Start with the original equation: 5x + 2y = 10 Isolate the term with y: Subtract 5x from both sides: 2y = 10 – 5x Now, divide every term … Read more
To find a trigonometric expression that is equal to sin(72°), we can utilize known trigonometric identities and relationships. One useful approach is to relate angles and their sine values based on the properties of a pentagon. First, we can recall that sin(72°) can be represented using the sine of complementary angles. The related angle here … Read more
Prime numbers are natural numbers greater than 1 that have no positive divisors other than 1 and themselves. This means that they cannot be evenly divided by any other numbers. The first five prime numbers are: 2 – This is the only even prime number. It can only be divided by 1 and 2. 3 … Read more
Understanding Amplitude, Period, and Frequency of Trigonometric Functions Trigonometric functions, such as sine and cosine, are periodic functions that repeat their values in regular intervals. Finding the amplitude, period, and frequency of these functions can help you analyze their behavior and graph them accurately. Here’s a detailed guide on how to do that: 1. Amplitude … Read more
Univariate data refers to data that consists of a single variable, which means it involves only one observation or measurement at a time. For example, if we categorize students based on their test scores, the scores themselves would represent univariate data. This type of data focuses solely on analyzing one variable to describe its main … Read more
Finding the Inverse of the Function To find the inverse of the given function y = 3x + 9, we will follow a step-by-step process. The inverse function essentially swaps the roles of x and y. Step 1: Replace y with x Start by rewriting the equation as: x = 3y + 9 Step 2: … Read more
To determine which lengths can form the sides of a triangle, we can refer to the Triangle Inequality Theorem. This theorem states that for any triangle, the sum of the lengths of any two sides must be greater than the length of the third side. Below are three lengths that can create a triangle: Length … Read more