/*! 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 43 Evaluate the expression. $$\fr... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 8: Problem 43

Evaluate the expression. $$\frac{(1-x)^{t}}{2} \text { when } x=0.09 \text { and } t=2$$

Short Answer

Expert verified
The expression evaluates to 0.41405 when \(x\) is 0.09 and \(t\) is 2.

Step by step solution

01

Substitute given values.

The first step is to substitute the given values of \(x\) and \(t\) into the equation. Therefore, the equation \(\frac{(1-x)^{t}}{2}\) becomes \(\frac{(1-0.09)^{2}}{2}\).
02

Simplify the numerator.

Next, simplify the numerator of the fraction by subtracting 0.09 from 1, which equals to 0.91, and then raise it to the power of 2. So, \((1-0.09)^{2}\) equals to \((0.91)^{2}\), which equals 0.8281.
03

Divide by the denominator.

Lastly, divide the result by the denominator, which is 2. Therefore, \(\frac{0.8281}{2}\) equals to 0.41405.

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.

Substitution
Substitution is a foundational skill in evaluating algebraic expressions. It involves replacing variables with specific values given in the problem. In our example, the expression is \(\frac{(1-x)^{t}}{2}\), with the values \(x = 0.09\) and \(t = 2\). By substituting these values, the expression becomes \(\frac{(1-0.09)^{2}}{2}\). This step is crucial as it transforms the expression from a general form with variables to a specific one that can be numerically calculated, allowing us to proceed with simplifying operations. This process makes substitution an invaluable tool for personalizing mathematical solutions to given conditions.
Exponents
Exponents, often called powers, are a way to express repeated multiplication of a number by itself. In our expression, after substituting \(x = 0.09\), we have \((1-0.09)^{2}\). This means we are raising 0.91 to the power of 2, signifying that 0.91 is multiplied by itself: \(0.91 \times 0.91\).

The result of this calculation is 0.8281. Understanding exponents is key to simplifying equations and expressions efficiently, as they represent compact and high-power operations that simplify calculations involving repetitive multiplications, common in many algebraic problems.
Simplification
Simplification is the process of condensing an expression to its most concise form. After substituting values and calculating exponents, the expression remains \(\frac{0.8281}{2}\). Simplifying involves performing any remaining operations, here division.

By dividing 0.8281 by 2, we get 0.41405. This final step of simplification takes an expression that consists of fractional representation and reduces it to a single, simpler number.

Simplification helps in minimizing complexity, making it easier to understand and work with mathematical problems, whether for further calculations or verifying results.

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

Complete the statement using \(>\) or \(<\). $$5^{2} \cdot 3^{6} \underline{?}(5 \cdot 3)^{6}$$

Solve the inequality. Then sketch a graph of the solution on a number line. $$|x+2|-1 \leq 8 $$

Solve the inequality. Then sketch a graph of the solution on a number line. $$|5+x|+4 \leq 11$$

Write your answer as a power or as a product of powers. $$ \left(-w^{3}\right)\left(3 w^{2}\right)^{2} $$

Write your answer as a power or as a product of powers. $$ (-y)^{3}(-y)^{4}(-y)^{5} $$
See all solutions

Recommended explanations on Math Textbooks

Mechanics Maths

Read Explanation

Calculus

Read Explanation

Discrete Mathematics

Read Explanation

Decision Maths

Read Explanation

Pure Maths

Read Explanation

Probability and Statistics

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.