To determine the probability of getting at least one head when tossing a coin three times, we can approach the problem using the concept of complementary probability. This means we first calculate the probability of the opposite event—getting no heads at all—and then subtract that from 1. 1. **Understanding the Coin Tosses**: A single toss … Read more
Finding the Zeros of the Function f(x) = x2 – 2×3 To find the zeros of the function f(x) = x2 – 2×3, we need to set the function equal to zero and solve for x: Step 1: Set f(x) to zero Our equation becomes: x2 – 2×3 = 0 Step 2: Factor the equation … Read more
To find the number of sides in a polygon, you can start by understanding the basic definitions and properties of polygons. A polygon is defined as a closed figure with straight sides. The simplest polygon is a triangle, which has three sides. The number of sides in a polygon typically corresponds to its name: for … Read more
Rounding to the nearest tenth is a mathematical process used to simplify a number while preserving its overall value. When you’re asked to round a number to the nearest tenth, you are focused on the digit in the tenths place, which is the first digit to the right of the decimal point. Understanding this process … Read more
To find the lateral area of a rectangular prism, you’ll want to focus on the sides of the prism while excluding the top and bottom faces. Step-by-Step Guide Identify the Dimensions: First, determine the length (l), width (w), and height (h) of the rectangular prism. These dimensions will be essential for your calculations. Understand Lateral … Read more
To find the area of triangle LMN, we can use Heron’s formula. First, let’s clarify the measurements given for the sides of the triangle: Side a = 3 units Side b = 4 units Side c = 5 units Now, let’s use Heron’s formula, which states: A = √(s × (s – a) × (s … Read more
The expression 1 – cos(x)sin(x) can be analyzed and simplified in various contexts, particularly within trigonometric identities. Firstly, it’s essential to understand the components: cos(x): This is the cosine function, which represents the x-coordinate of a point on the unit circle. sin(x): This is the sine function, representing the y-coordinate of that same point. The … Read more
To simplify the expression 2x 3 x 5, we need to perform the multiplication while treating the variables and coefficients separately. Here’s how to break it down: First, identify the numerical coefficients and the variables in the expression. In this case, the numerical coefficients are 2, 3, and 5, and the variable is x. Next, … Read more
To find the 16th term of a geometric sequence where the first term (a1) is 4 and the eighth term (a8) is 8748, we first need to determine the common ratio (r) of the sequence. A geometric sequence is defined by the formula for the nth term: an = a1 imes r(n-1), where: an = … Read more
To find out what 5% of 300 is, you can use a simple formula. First, understand that percentages are just a fraction of a whole. In this case, 5% can be expressed as: 5% = 5/100 = 0.05 Next, multiply this decimal by 300: 0.05 x 300 = 15 So, 5% of 300 is 15. … Read more