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
To calculate the present value (PV) of an amount of money that you will receive in the future, we use the formula: PV = FV / (1 + r)^n Where: PV = Present Value FV = Future Value ($10,000 in this case) r = discount rate (5% or 0.05) n = number of years until … Read more
The product of a set of numbers is found by multiplying them together. In this case, we have the numbers 32, 2, 5, and 1. Let’s go through the multiplication step by step: 1. First, multiply 32 by 2: 32 x 2 = 64 2. Next, take the result (64) and multiply it by 5: … Read more
To determine how many unique license plates can be created using a combination of 3 letters followed by 2 digits, we need to break this down into two parts: the letters and the digits. Step 1: Calculate the number of combinations for the letters. The English alphabet consists of 26 letters. When forming a license … Read more
To find the diameter of a circle when you have the circumference, you can use a simple mathematical formula based on the relationship between the two. The circumference (C) of a circle is calculated using the formula: C = π × d Where: C is the circumference of the circle, d is the diameter, and … Read more
To identify the next number in the series 1, 4, 10, 19, 31, we first need to observe the differences between consecutive terms. 4 – 1 = 3 10 – 4 = 6 19 – 10 = 9 31 – 19 = 12 Now, let’s examine these differences: 3 6 9 12 We can see … Read more
To find the z-score that separates the bottom 90% from the top 10% in a standard normal distribution, we need to locate the value that corresponds to the cumulative probability of 0.90. The standard normal distribution is characterized by a mean of 0 and a standard deviation of 1. The z-score is a statistical measurement … Read more