The class intervals 11.5-13.5, 13.5-15.5, 15.5-17.5, and 17.5-19.5 are appropriate for representing the given data set in a histogram. These intervals cover the entire range of the data, ensuring each data point falls within a specific interval, and they are consistent in width, which is crucial for accurate histogram representation.

Equity Theory, proposed by John Stacey Adams, posits that employees are motivated when they perceive that their efforts and rewards are fair compared to others. Here's a detailed explanation:
* Equity Theory Overview: This theory suggests that individuals compare their job inputs (effort, skill, experience) and outputs (salary, recognition) with those of others.
* Perceived Fairness: Employees are motivated when they believe that their rewards are proportional to their contributions compared to others.
* Motivation through Fair Distribution: Fair and deserved rewards reduce feelings of inequity and dissatisfaction, leading to higher motivation and performance.
* Implications in the Workplace: Ensuring rewards are as deserved helps in maintaining morale and reducing turnover.
References:
* "Work and Motivation" by Victor Vroom.
* "Motivation and Work Behavior" by Richard M. Steers and Lyman W. Porter.

A static analysis tool is used to identify potential problems in the code without executing it. These tools analyze the source code to detect coding errors, vulnerabilities, and adherence to coding standards. By identifying issues early in the development process, static analysis helps prevent defects that could lead to significant problems later on. It is a proactive approach to improving code quality and maintaining robust software.References:
* Ayewah, Nathaniel, et al. "Using Static Analysis to Find Bugs." IEEE Software, vol. 25, no. 5, 2008.
* IEEE Std 1028-2008, IEEE Standard for Software Reviews and Audits.

A scatter diagram is the appropriate tool for analyzing the relationship between the number of defects found and the complexity of various software applications. Scatter diagrams are used to plot pairs of numerical data, with one variable on each axis, to look for a relationship between them. This visual representation helps in identifying patterns or correlations between the two variables, such as whether higher complexity correlates with more defects.
References:
* "The Six Sigma Handbook: A Complete Guide for Green Belts, Black Belts, and Managers at All Levels" by Thomas Pyzdek and Paul Keller
* "Quality Control Handbook" by J.M. Juran

Branch coverage, also known as decision coverage, ensures that every possible branch (i.e., true and false conditions) in the code is executed at least once. To determine the number of tests necessary for branch coverage in the given control flow diagram, we must count the distinct branches resulting from each decision point.
* Decision 1: 2 branches (true and false)
* Decision 2: 2 branches (true and false)
* Decision 3: 2 branches (true and false)
Since each decision has two branches and they are independent of each other, the number of distinct paths that need to be tested is: 2(Decision1)+2(Decision2)+2(Decision3)=6 branches2 (Decision 1) + 2 (Decision 2) + 2 (Decision 3) = 6 \text{ branches}2(Decision1)+2(Decision2)+2(Decision3)=6 branches However, the number of tests needed to cover all branches is the maximum number of branches any path could take, considering that a single test might cover multiple branches. For the given control diagram, 4 tests will suffice to cover all branches:
* Path: A -> Decision 1 (true) -> B
* Path: A -> Decision 1 (false) -> Decision 2 (true) -> C
* Path: A -> Decision 1 (false) -> Decision 2 (false) -> Decision 3 (true) -> D
* Path: A -> Decision 1 (false) -> Decision 2 (false) -> Decision 3 (false) These four tests ensure all branches are covered at least once.