To determine the probability of getting 3 tails when tossing a coin three times, we can use the fundamentals of probability. 1. **Total Outcomes**: When we toss a coin, there are two possible outcomes for each toss: heads (H) or tails (T). When tossing the coin three times, the total number of outcomes can be … Read more
The given sequence is: 8, 6, 9, 5, 10, 4, 11. To find the next number in this sequence, we need to analyze the pattern. Let’s break it down: Start with 8 Subtract 2 to get 6 Add 3 to get 9 Subtract 4 to get 5 Add 5 to get 10 Subtract 6 to … Read more
One quintal is equal to 100 kilograms. The term ‘quintal’ is derived from the Latin word ‘centenarium,’ which means ‘hundred.’ It serves as a unit of weight measurement, commonly used in agricultural settings and some international trade contexts. To put it into perspective, a quintal can be a convenient standard for weighing bulk items like … Read more
Finding the Exact Value of cos(36°) To find the exact value of cos(36°), we can use the half-angle formula or sum and difference formulas derived from known values of cosine for specific angles. One effective approach involves using the relationship with the angle 72° because 36° is half of 72°. 1. Use the Half-Angle Formula … Read more
To find the radius of a circle from its equation, we first need to rewrite the given equation in the standard form of a circle’s equation. The standard form is: (x – h)² + (y – k)² = r² where (h, k) is the center of the circle and r is the radius. Here, you … Read more
To find the roots of the polynomial equation x³ + 2x² + 16x + 32 = 0, we can use various methods such as factoring, synthetic division, or the Rational Root Theorem. Let’s start by trying to find any rational roots using the Rational Root Theorem, which suggests that any rational solution p/q (where p … Read more
Understanding Volumes of Composite Figures A composite space figure, like a rectangular pyramid resting on a rectangular prism, can be analyzed by calculating the volumes of its individual components and then summing them up. To determine the volume of the entire figure, we must first know the dimensions of both the rectangular prism and the … Read more
The function f(x) = x² – 2 is a quadratic function, which is a type of polynomial function that can be represented graphically as a parabola. To determine its range, we should first identify its vertex and behavior as x approaches positive and negative infinity. 1. **Finding the Vertex**: The standard form of a quadratic … Read more
To find the sum of the two complex numbers, we start by identifying the components of each number. The first complex number is 12 + 5i, where 12 is the real part and 5i is the imaginary part. The second complex number is 3 + 4i, with 3 as the real part and 4i as … Read more
To determine how many 45-degree angles it takes to make a full turn, we first need to understand what a full turn actually means. A full turn, or full rotation, is equal to 360 degrees. This is the complete circle that you might visualize if you think about spinning around in a circle. Now, since … Read more