/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 50 Assign one variable, and write a... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 3: Problem 50

Assign one variable, and write an inequality that represents the constraint. The minimum initial investment in the Vanguard Windsor Admiral Fund is $$\$ 100,000$$.

Short Answer

Expert verified
The inequality is \( x \geq 100,000 \).

Step by step solution

01

- Define the Variable

Assign a variable to represent the initial investment. Let鈥檚 use the variable \(x\) for this purpose. Therefore, \(x\) will represent the amount of money invested initially.
02

- Write the Inequality

Since the minimum initial investment in the Vanguard Windsor Admiral Fund is \(100,000, we need to write an inequality that expresses this constraint. The amount invested \(x\) must be at least \)100,000. This can be written as: \[ x \geq 100,000 \]

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Variable Assignment
In algebra, we often use variables to represent unknown quantities. A variable is a symbol, usually a letter, that stands for a number we don't yet know. For example, in this exercise, we need to represent the amount of money invested initially. By assigning a variable, we make it easier to write and solve mathematical problems. Here, we choose the variable \( x \) to represent the initial investment. This simple step makes our work more organized and paves the way for forming mathematical expressions and inequalities.
Inequality Representation
Inequality representation is an important concept in algebra. It involves writing expressions that compare quantities using inequality symbols. The most common inequality symbols are:
  • \( > \) greater than
  • \( < \) less than
  • \( \geq \) greater than or equal to
  • \( \leq \) less than or equal to
In this exercise, we need to represent a constraint on the minimum initial investment in a fund. To do this, we write an inequality that shows the investment amount must be at least 100,000. We use the symbol \( \geq \), which means 'greater than or equal to'. Therefore, if the variable \( x \) represents the initial investment, the inequality is written as \[ x \geq 100,000 \]. This expression tells us that the investment amount \( x \) must be either 100,000 or more.
Minimum Investment Constraint
Constraints in algebra represent limits or conditions that solutions must satisfy. A minimum investment constraint specifies the least amount of money that must be invested. In this exercise, the Vanguard Windsor Admiral Fund has a minimum initial investment requirement of 100,000. This means you cannot invest in this fund with less than 100,000. By using inequalities, we can clearly express and work with such constraints. For example, the inequality \[ x \geq 100,000 \] ensures that any solution for \( x \) meets this minimum requirement. This type of mathematical expression is useful in finance, budgeting, and various real-life scenarios where resource limitations apply.

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

Use the slope formula to find the slope of the line that passes through the points. \((-3,8) ;(11,23)\)

Use the slope formula to find the slope of the line that passes through the points. \(\left(\frac{5}{6}, \frac{1}{4}\right) ;\left(\frac{1}{6}, \frac{7}{4}\right)\)

(a) find three solutions of the equation. (b) graph the equation. \(y=-\frac{1}{4} x+3\)

(a) find three solutions of the equation. (b) graph the equation. \(y=\frac{2}{3} x-4\)

Some learning preferences describe how you prefer to receive, think about, and learn new information. These preferences include visual learning, auditory learning, and kinesthetic learning. Many students use more than one of these categories as they learn mathematics. \- Visual learners prefer to see information. Although you definitely listen to your instructor, you also like to see the example on a white board or screen. You may be able to recall a process by visualizing it in your mind; you may learn better by organizing information in charts, tables, diagrams, or pictures. You may prefer the use of colored markers instead of just black. \- Auditory learners prefer to hear information. Although you definitely watch what your instructor is doing, you also like your instructor to explain things aloud as he or she works. You may find it difficult to take notes because you cannot concentrate enough on what is being said while you write. You may learn better if you have the chance to explain things to others. \- Kinesthetic learners prefer to do. You may find it difficult to sit still and just watch and listen; you want to be trying it out. You may find that you must take notes in order to learn. If you only watch and listen, you may understand the concept but not remember it after you leave the classroom. You often learn better if you can show others how to do things. Have you noticed anything that your instructor does while teaching that you find helps you remember what has been taught?
See all solutions

Recommended explanations on Math Textbooks

Mechanics Maths

Read Explanation

Statistics

Read Explanation

Decision Maths

Read Explanation

Pure Maths

Read Explanation

Probability and Statistics

Read Explanation

Geometry

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.