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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

To classify a parallelogram specifically as a square, it must satisfy several key characteristics. A parallelogram is defined as a four-sided shape (quadrilateral) where opposite sides are parallel. However, to be a square, it not only needs to fulfill the requirements of being a parallelogram but also meet additional criteria. The fundamental characteristics that confirm … Read more

To convert the exponential equation 3x = 243 into logarithmic form, we need to understand how to express exponential equations in terms of logarithms. The general form for this conversion is: bx = a can be written as logb a = x, where b is the base of the exponent, a is the result, and … Read more

Finding the Vertex of f(x) = x3 + 8 To determine the vertex of the function f(x) = x3 + 8, we first need to understand the nature of this function. In this case, we are dealing with a cubic function. The general form of a cubic function is given by: f(x) = ax3 + … Read more

To determine how many ways we can choose a committee of 3 people from a group of 5, we can use the concept of combinations in combinatorics. Combinations are used when the order of selection does not matter. The formula for combinations is given by: C(n, r) = n! / (r!(n – r)!) Where: C(n, … Read more

The expression sin(x) · sin(x) can be rewritten using the property of exponents in trigonometry. Specifically, we can express this product as: sin(x) · sin(x) = (sin(x))² This notation simply indicates that you are squaring the sine of angle x. In practical terms, squaring a sine function can result in a variety of applications in … Read more