교과서 질문
Use the formula for nCr to solve Exercises 49–56. An election ballot asks voters to select three city commissioners from a group of six candidates. In how many ways can this be done?
758
views
Ch. 8 - Sequences, Induction, and Probability
Blitzer8th EditionCollege AlgebraISBN: 9780136970514
당신이 사용하는 게 아니라요?교과서 변경다른 교과서를 선택하세요
TOC.tableOfContents
- Ch. P - Fundamental Concepts of Algebra311
- Ch. 1 - Equations and Inequalities398
- Ch. 2 - Functions and Graphs407
- Ch. 3 - Polynomial and Rational Functions306
- Ch. 4 - Exponential and Logarithmic Functions247
- Ch. 5 - Systems of Equations and Inequalities173
- Ch. 6 - Matrices and Determinants143
- Ch. 7 - Conic Sections124
- Ch. 8 - Sequences, Induction, and Probability251
9장, 문제 49
Express each repeating decimal as a fraction in lowest terms.
검증된 단계별 안내1
Let \( x = 0.257257257\ldots \), where the digits 257 repeat indefinitely.
Since the repeating block has 3 digits, multiply \( x \) by \( 10^3 = 1000 \) to shift the decimal point three places to the right: \( 1000x = 257.257257257\ldots \).
Set up the equation by subtracting the original \( x \) from this new expression to eliminate the repeating decimal part: \( 1000x - x = 257.257257257\ldots - 0.257257257\ldots \).
Simplify the subtraction to get \( 999x = 257 \), since the repeating decimals cancel out.
Solve for \( x \) by dividing both sides by 999: \( x = \frac{257}{999} \). Then, simplify the fraction to its lowest terms by finding the greatest common divisor (GCD) of 257 and 999 and dividing numerator and denominator by it.
비슷한 문제에 대한 검증된 영상 답변:
이 영상 해법은 위 문제에 도움이 된다고 튜터들이 추천한 것입니다.
영상 길이:
5m주요 개념
질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.
Repeating Decimals
A repeating decimal is a decimal number in which a sequence of digits repeats infinitely. For example, 0.257̅ means the digits '257' repeat endlessly. Understanding this pattern is essential to convert the decimal into a fraction.
추천 영상:
8:19
How to Graph Rational Functions
Algebraic Representation of Repeating Decimals
To convert a repeating decimal to a fraction, represent the decimal as a variable (e.g., x), then multiply by a power of 10 to shift the decimal point to align repeating parts. Subtracting these equations eliminates the repeating portion, allowing you to solve for x as a fraction.
추천 영상:
05:09Introduction to Algebraic Expressions
Simplifying Fractions to Lowest Terms
After finding the fraction equivalent of the repeating decimal, simplify it by dividing numerator and denominator by their greatest common divisor (GCD). This ensures the fraction is expressed in its simplest form, which is a standard requirement in algebra.
추천 영상:
05:45Radical Expressions with Fractions
관련 실천
교과서 질문
Express each sum using summation notation. Use 1 as the lower limit of summation and i for the index of summation. 1/2+2/3+3/4+⋯+ 14/(14+1)
922
views
교과서 질문
Use the Binomial Theorem to expand each expression and write the result in simplified form. (x3 +x-2)4
689
views
교과서 질문
Find the sum of each infinite geometric series. -6 + 4 - 8/3 + 16/9 - ...
1052
views
교과서 질문
Write out the first three terms and the last term. Then use the formula for the sum of the first n terms of an arithmetic sequence to find the indicated sum.
906
views
교과서 질문
In Exercises 49–52, a single die is rolled twice. Find the probability of rolling a 2 the first time and a 3 the second time.
566
views