НМТ з математики. Сесія 1. 2023 рік. Частина 3. Завдання 19 - 22

NMT in mathematics. Session 1. 2023. Part 3. Tasks 19 - 22. 19. The number 27 is a member of an arithmetic progression with difference d=5. Determine the numbers from the interval (60;75) that are members of this progression. In the answer, write the sum of these numbers. 20. The winner of the Olympiad is planned to be presented with a set of 5 books, which includes 2 collections of Olympiad problems and 3 popular science books. How many options are there for forming such a set of books if there are 8 different collections and 10 different popular science books? 21. The base of a right prism is a rhombus with side 20. The perimeter of one of the diagonal sections of the prism is 58. Determine the volume of the prism if its height is 5. 22. Determine the number of integer values ​​of a for which the roots x1 and x2 of the quadratic equation x^2-4ax+4a^2-25=0 satisfy the condition x1 less than 1 less than x2. #nmt #nmtmathematics #nmt2023 #nmt2024