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To determine which ordered pair maximizes the objective function p = 3x + 8y, we need to evaluate the function for each of the given pairs: For (0, 0): p = 3(0) + 8(0) = 0 For (2, 7): p = 3(2) + 8(7) = 6 + 56 = 62 For (5, 6): p = … Read more

To calculate the loss incurred when selling shares of stock, you first need to determine the purchase price of the shares, the selling price, and then calculate the total loss based on the number of shares sold. Let’s break it down step by step. 1. Determine the Purchase Price The shares were originally bought at … Read more

The set of whole numbers refers to a collection of numbers that includes all positive integers along with the number zero. In mathematical terms, whole numbers can be represented as: Whole Numbers = {0, 1, 2, 3, 4, 5, …} Here, you can see that the whole numbers start at zero and continue infinitely in … Read more

Transitioning through numbers in a conversational or written context can be both an art and a science. To effectively navigate this process from 1 to 10, you can implement the following strategies: Engage Your Audience: Start by capturing your audience’s attention. Use an interesting fact, a rhetorical question, or a short anecdote that relates to … Read more

Calculating the second order derivative of a function involves a few clear steps. Here’s how to do it: Find the First Derivative (dy/dx): The first step in finding the second order derivative is to determine the first derivative of the function. For a function y = f(x), you can use standard differentiation rules such as … Read more

Finding the Factored Form of 6n4 – 24n3 + 18n To factor the polynomial 6n4 – 24n3 + 18n, we can follow these steps: Identify the greatest common factor (GCF): The first step in factoring any polynomial is to find the GCF of all the terms. The terms of our polynomial are: 6n4 -24n3 18n … Read more

To rearrange the expression 0.020x² + 85x into the standard quadratic form ax² + bx + c = 0, you need to follow a few simple steps: Identify coefficients: In the expression 0.020x² + 85x, we can see that: a (the coefficient of x²) = 0.020 b (the coefficient of x) = 85 c = … Read more

The Effective Annual Rate (EAR) gives you a clearer picture of the actual interest earned or paid on an investment or loan over a year, especially when compounding occurs more than once a year. In this example, we want to find the EAR for an interest rate of 10 percent compounded semiannually. To calculate the … Read more

To solve the problem of finding the sequence ‘a b a b a b b a’ within the two given sequences ‘let a a b c d e’ and ‘b a b c d e f g h’, we can break the task down into a few clear steps: Identify the Individual Components: The target … Read more

Synthetic division is a shorthand method of polynomial division, particularly useful when dividing by a linear factor. To work through the problem of dividing the polynomial x4 + x + 1 by x3 + 2, we first set up our synthetic division. Since we are dividing by x3 + 2, we can rearrange this into … Read more