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To find the area of a regular hexagon given a radius (or circumradius) of 5 inches, you can use the formula: Area = (3√3/2) × r², where r is the radius. Step 1: First, square the radius: r² = 5² = 25. Step 2: Multiply the squared radius by (3√3/2): Area = (3√3/2) × 25. … Read more

The sequence defined by the formula an = 6n + 1 can be evaluated by substituting the values of n starting from 1. Here’s how to find the first five terms: For n = 1: a1 = 6(1) + 1 = 6 + 1 = 7 For n = 2: a2 = 6(2) + 1 … Read more

To convert minutes into seconds, you need to know that there are 60 seconds in one minute. Therefore, to find out how many seconds are in 70 minutes, you simply multiply the number of minutes by the number of seconds in a minute. The calculation looks like this: 70 minutes × 60 seconds/minute = total … Read more

The Law of Identities is a fundamental principle in classical logic that states that every entity is identical to itself. This can be summarized in the expression: A is A. Essentially, it emphasizes that if something is true, then it will always be true for that specific thing, without exception. To elaborate, the law asserts … Read more

To find the 8th term of the sequence given by the expression 3n + 5, we need to substitute n with 8. The sequence can be defined as follows: When n = 1: 3(1) + 5 = 8 When n = 2: 3(2) + 5 = 11 When n = 3: 3(3) + 5 = … Read more

Let’s break down the components of your three-digit number based on the information provided. 1. The hundreds digit is given as 2. This means our number starts with ‘2’ and looks like this: 2XY, where ‘X’ is the tens digit and ‘Y’ is the ones digit. 2. According to the second part of the statement, … Read more

To determine the probability of rolling either a 5 or a 6 on a six-sided die, we start by understanding a few key concepts about probability. A standard six-sided die has six faces, numbered from 1 to 6. When you roll the die, each face has an equal chance of landing face up. Therefore, the … Read more

To solve the inequality 2x + 6 < 6x + 2 + 8, we first simplify the right side: Combine like terms on the right: 6x + 2 + 8 becomes 6x + 10. Now, we can rewrite the inequality: 2x + 6 < 6x + 10 Next, we want to get all the terms ... Read more

To find the coordinates (x, y) on the unit circle that correspond to the real number t = 2π/3, follow these steps: Understanding the Unit Circle: The unit circle is a circle with a radius of 1 centered at the origin (0, 0) in the Cartesian coordinate system. Points on the unit circle can be … Read more