Which two roles would enable a member to perform analysis?

The correct answer focuses on the roles of Administrator and Publisher because these two roles have specific capabilities that enable members to perform a range of analytical tasks within ArcGIS Online.

An Administrator has comprehensive privileges, including the ability to manage organizational settings, users, and content, which directly supports the configuration and optimization of analytical functions in GIS projects. This role ensures that the necessary tools and resources are available for analysis.

A Publisher role complements the Administrator's capabilities by allowing users to create, share, and manage geospatial content, including web maps and applications, which are essential for conducting various analyses. Publishers can also create hosted feature layers that are critical for spatial analysis and data manipulation.

In contrast, roles like User and Data Editor do not have the required permissions for robust analytical capabilities. Users typically have limited access to create and analyze content, while Data Editors focus more on editing existing data rather than performing in-depth analysis. Therefore, the combination of an Administrator and a Publisher is crucial for effective analysis in ArcGIS Online.