devyy To solve this problem, we start by setting up the necessary parameters from the information given. Let: Speed of the motorboat in still water = 24 km/h Speed of the stream = x km/h When the motorboat is going upstream, the effective speed is decreased due to the current of the stream, while downstream, the … Read more
To solve the problem using the normal curve approximation, we first identify the parameters of our binomial distribution based on the coin-tossing scenario: Number of trials (n): 400 Probability of success (p): 0.5 (since it’s a fair coin) Next, we calculate the mean (μ) and standard deviation (σ) of the distribution: Mean (μ): μ = … Read more
To solve for fg(x), we first need to properly define what this expression means. The notation fg(x) means we will find g(x) first and then use that result as the input for f(x). Given the functions: f(x) = 2x + 5 g(x) = x – 7 We will begin by substituting x = -3 into … Read more
To find the median of a data set, you need to follow a few simple steps. Let’s break it down using the provided data set: 1, 14, 58, 35, 12, 1, 12, 1, 34. Organize the Data: Start by sorting the numbers in ascending order. The sorted data set looks like this: 1 1 1 … Read more
The arithmetic sequence defined by an = 2 + 4n – 1 can be analyzed to determine the domain of n. In this context, an arithmetic sequence is a sequence of numbers in which the difference of any two successive members is a constant. Here, the expression 4n – 1 suggests that n is a … Read more
To find a point that lies on a line parallel to another line and passing through a specific point, we first need to determine the slope of the original line. The points given are (12, 8), (6, 6), (2, 8), and (6, 0). We can calculate the slope using any two of these points. Let’s … Read more
Understanding the Parabola A parabola is a curve formed by the intersection of a cone with a plane parallel to its side. The vertex of the parabola is a crucial point, and in this case, we’ve identified it as the origin (0,0). Characteristics of the Given Parabola When the focus of the parabola is positioned … Read more
Calculating the median from a set of numbers is a straightforward process, but it is essential to understand the steps involved to ensure accuracy. The median is the value that separates the higher half from the lower half of the data set. Here’s how you can determine the median: Organize Your Data: Start by arranging … Read more
To solve the inequality 25 > 4x + 6x + 4, we first need to simplify the expression on the right side. Here are the detailed steps: Combine like terms: Add the coefficients of 4x and 6x. 4x + 6x = 10x, so we rewrite the inequality: 25 > 10x + 4. Isolate the term … Read more
Solving the Equations To solve the system of equations given by: Equation 1: 7x + 2y = 3 Equation 2: 14x + y = 14 We can use either the substitution or elimination method. Here, we’ll proceed with the substitution method for clarity. Step 1: Solve Equation 2 for y From Equation 2: 14x + … Read more