What title of the education amendments act guarantees equality of the sexes in all federal spending for education and educational institutions?

Title IX of the Education Amendments Act of 1972.

Explanation:

The Title IX of the Education Amendments Act of 1972 provides a series a rights and freedoms regarding educational and institutional spheres. It is a law that states that no person in the country shall be denied from participating and acquiring education on the basis of sex.

This federal law applies to both public and private institutions that receive federal funds. It makes it mandatory that every educational and research institute observe non-discriminatory actions and measures towards the students.