Consider a database schema with three relations:

Employee (eid:integer, ename: string, age: integer, salary: real)
Works (eid:integer, did:integer, pct_time:integer)
Department (did:integer, dname: string, budget: real, managerid:integer)

The keys are underlined in each relation. Relation Employee stores employee information such as unique identifier eid, employee name ename, age and salary. Relation Department stores the department unique identifier did, department name dname, the department budget and managerid which is the eid of the employee who is managing the department. The managerid value must always be found in the eid field of a record of the Employee relation. The Works relation tracks which employee works in which department, and what percentage of the time s/he allocates to that department. Note that, an employee can work in several departments.

Provide SQL statements for the following:

(a) Write SQL declarations for creating the schemas. Include necessary key constraints.

(b) Find the salaries of employees that work in a department whose name starts with 'Mar'.

(c) Find the ages of employees who work at least 30% of their time in a single department. List each age only once.

(d) Find the salaries of employees who work only in departments that have budget more than $500,000. List each salary value only once.

(e) Find the names of employees who are managers.

(f) Find the average salary over all employees.

(g) Find the ages of employees who work at least 10% of their time in a department called 'Catering' but who do not work in any department with budget higher than $500,000.

(h) Find the names of employees who work in all departments with budget higher than $500,000.

(i) Find the name(s) of the department(s) with the highest budget.

(j) Find the maximum salary among employees 30 years old or younger for each department with at least 10 employees of any age.

(k) Find for each manager (listed in the output by eid) the average salary of employees working for that manager.

(l) Find the average age of employees for each department where every employee is 30 years old or younger.

(m) Find the name(s) of department(s) who have the highest average employee age.

(n) Find the age(s) that most employees have, i.e., best represented age(s) among employees that work in departments with budget larger than $300,000. If an employee works in multiple such departments, his/her age is only counted once.

(o) Find the average salary among employees that work in all departments whose names starts with 'Ca'.

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