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by Fred Schenkelberg 2 Comments

Math Quiz

Just a few questions to check your math skills.

1-24. Calculate the factorial of 7.

(A) 28
(B) 720
(C) 5,040
(D) 40,320

Answer

(C) 5,040

Discussion

A factorial, commonly denoted with an “!” or in this problem would be 7!, is the product of an integer and all the integers below it to one. For example, 4! = 4 × 3 × 2 ×1 = 24.

This for this problem the answer is 7 × 6 × 5 × 4 × 3 × 2 × 1 = 5,040.


1-25. Using Pascal’s triangle allows one to determine which terms of the binomial expansion?

(A) coefficients
(B) exponents
(C) higher order terms
(D) permutations

Answer

(A) coefficients

Discussion

Knowing how to quickly construct Pascal’s triangle allows you to quickly determine the coefficients for a binomial expansion.

The binomial expansion is a mathematical theorem that specifies the expansion (multiplying out…) of any power (a + b)m of a binomial (a + b) as a specific sum of products aibj. For example,

$$ {{\left( a+b \right)}^{2}}={{a}^{2}}{{b}^{0}}+2{{a}^{1}}{{b}^{1}}+{{a}^{0}}{{b}^{2}}$$

recall that something raised to the 0 power is equal to 1. Also, the coefficients for the resulting three terms are 1, 2, and 1. There are m+1 terms and m+1 corresponding coefficients in the expanded form.

Pascal’s triangle is a triangular array with 1’s at the ends of each row (1 at the apex or first row, too) and of the other values in a row is the sum of the two numbers in the row above.

Pascals-triangle300x300

The two arrows point to the first 3 on the forth row, which is the sum of 1 and 2 found on the row above.

The coefficients for the expansion of (a + b)2 above are the values in the third row, 1, 2, and 1. For (a + b)3 the coefficients are 1, 3, 3, 1 as found in the forth row. The binomial expansion for (a + b)3 becomes

$$ {{\left( a+b \right)}^{3}}={{a}^{3}}+3ab+3ab+{{b}^{3}}$$


1-56. Identify which the following Boolean algebra expressions is correct.

(A) 1 + 0 = 1
(B) 1 + 1 = 2
(C) 1 − 0 = 0
(D) 1 − 1 = 0

Answer

(A) 1 + 0 = 1

Discussion

Recall your Boolean truth table for A or B (A + B)

0 + 0 = 0

0 + 1 = 1

1 + 0 = 1

1 + 1 = 1

Boolean values include only zero’s or one’s. Thus response (B) is common base 10 integer addition. The minus sign is a way to convening the “not” logic element making 1 – 0 = 1 + 1, which is equal to 1, and 1 – 1 = 1 + 0 which is also equal to 1.

 

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Comments

  1. Yuan Lu says

    March 21, 2020 at 8:24 PM

    Hi Fred,

    There is no complete button here.

    Best,
    Yuan

    Reply
    • Fred Schenkelberg says

      March 23, 2020 at 7:42 AM

      Hi Yuan, the buttons are now added – thanks for letting me know. Cheers, Fred

      Reply

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  • CRE Preparation Course
    • Course Introduction
      • Welcome
      • Introduction
      • Thank You for Your Interest in the Course
      • Exam Day
      • Preparation Approach
      • Discussion Forums Introduction
      • CRE Sample Quiz
      • Terms Glossary
      • Math Quiz
      • Body of Knowledge 2009 version
      • Body of Knowledge 2018 version
    • Reliability Management
      • Reliability Management Introduction
    • I. A. Strategic Management
      • Strategic Management Introduction
      • I. A. 1. Benefits of Reliability Engineering
      • I. A. 2. Interrelationship of Safety, Quality, and Reliability
      • I. A. 3. Role of the Reliability Function
      • I. A. 4. Product and Process Development
      • I. A. 5. Failure Consequences and Liability Management
      • I. A. 6. Warranty Management
      • I. A. 7. Customer Needs Assessment
      • I. A. 8. Supplier Reliability
      • I. A. Strategic Management Quiz
      • I. A. Bonus — Building Influence
    • I. B. Reliability Program Management
      • Reliability Program Management Introduction
      • I. B. 1. Terminology
      • I. B. 2. Elements of a Reliability Program
      • I. B. 3. Types of Risk
      • I. B. 4. Product Lifecycle Engineering
      • I. B. 5. Design Evaluation
      • I. B. 6. Systems Engineering and Integration
      • I. B. Reliability Program Management Quiz
    • I. C. Ethics, Safety, and Liability
      • Ethics, Safety, and Liability Introduction
      • I. C. 1. Ethical Issues
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      • I. C. Ethics, Safety, and Liability Quiz
    • II. Probability and Statistics for Reliability
      • Probability and Statistics for Reliability Introduction
    • II. A. Basic Concepts
      • Basic Concepts Introduction
      • II. A. I. Statistical Terms
        • II. A. I. a. Basic Statistical Terms
        • II. A. I. b. Measures of Central Tendency
        • II. A. I. c. Central Limit Theorem
        • II. A. I. d. Measures of Dispersion
        • II. A. 1. e. COV and a Couple of Laws
      • II. A. 2. Basic Probability Concepts
        • II. A. 2. a. Probability
        • II. A. 2. b. Laws and Counting
        • II. A. 2. c. Expectation
      • II. A. 3. Discrete and Continuous Probability Distributions
        • II. A. 3. a. The Four Functions
        • II. A. 3. b. Continuous Distributions
        • II. A. 3. c. Discrete Distributions
        • II. A. 3. d. Bathtub Curve
      • II. A. 4. Poisson Process Models
        • Poisson Process Models Introduction
        • II. A. 4. a. Homogeneous Poisson Process
        • II. A. 4. b. Repair System Terminology
        • II. A. 4. c. Non-Homogenous Poisson Process
        • II. A. 4. d. Mann Reverse Arrangement Test
        • II. A. 4. e. Laplace’s Trend Test
        • II. A. 4. f. Fisher’s Composite Test
      • II. A. 5. Non-Parametric Statistical Methods
        • II. A. 5. a. The Approach
        • II. A. 5. b. Ranking
        • II. A. 5. c. Reliability and Comparisons
        • Non-Parametric Statistical Methods Introduction
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        • II. A. 7. b. X-bar and R charts
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    • III. Reliability in Design and Development
      • Reliability in Design and Development Introduction
    • III. A. Reliability Design Techniques
      • Reliability Design Techniques Introduction
      • III. A. 1. Environmental and Use Factors
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    • III. B. Parts and Systems Management
      • Parts and Systems Management Introduction
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      • V. B. 1. Accelerated Life Tests
      • V. B. Bonus – A Few Models
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      • V. B. Testing During Development quiz
    • V. C. Product Testing
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      • V. C. 1. a. Qualification Demonstration Testing – PRST
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      • V. C. 4. Stress Screening
      • V. C. 5. Attribute Testing
      • V. C. 6. Degradation Testing
      • V. C. Bonus – Acceleration Factors
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    • VI. Maintainability and Availability
      • Maintainability and Availability Introduction
    • VI. A. Management Strategies
      • Management Strategies Introduction
      • VI. A. 1. a. Planning
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      • VI. A. 2. a. Maintenance Strategies – RCM
      • VI. A. 2. b. Maintenance Strategies – TPM
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      • VI. A. 3. Availability Tradeoffs
      • VI. A. Management Strategies quiz
    • VI. B. Maintenance and Testing Analysis
      • Maintenance and Testing Analysis Introduction
      • VI. B. 1. Preventative Maintenance Analysis
      • VI. B. 2. Corrective Maintenance Analysis
      • VI. B. 3. Non-Destructive Evaluation
      • VI. B. 4. Testability
      • VI. B. 5. Spare Parts Analysis
      • VI. B. Maintenance and Testing Analysis quiz
    • VII. Data Collection and Use
      • Data Collection and Use Introduction
    • VII. A. Data Collection
      • Data Collection Introduction
      • VII. A. 1. a. Types of Data
      • VII. A. 1. b. Types of Data – Censored Data
      • VII. A. 2. Collection Methods
      • VII. A. 3. Data Management
      • VII. A. Data Collection quiz
    • VII. B. Data Use
      • Data Use Introduction
      • VII. B. 1. Data Summary and Reporting
      • VII. B. 2. Preventive and Corrective Actions
      • VII. B. 3. Measures of Effectiveness
      • VII. B. Data Use quiz
    • VII. C. Failure Analysis and Correction
      • Failure Analysis and Correction Introduction
      • VII. C. 1. Failure Analysis Methods
      • VII. C. 2. Failure Reporting, Analysis, and Corrective Action System
      • Exam Day Bonus
      • VII. C. Failure Analysis and Correction quiz

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