Explain how to prove that there is an infinite number of primes.
- December 30, 2018
- Posted by: stephen
A. In a classroom, students will receive a letter grade based on the percentage of points gained in the term out of the total points possible. There are 334 points possible. To get an A in the class, the student must have a percentage that is at least 90%.
1. Determine whether a student who earns 299 points will receive an A for the class if the teacher rounds the student’s percentage to a whole number.
a. Justify your answer to part A1.
2. Determine whether the same student from part A1 will receive an A for the class if the teacher instead truncates the student’s percentage to a whole number.
a. Justify your answer to part A2.
B. Consider a taxpayer whose income tax rate is 27.8% and do the following:
1. Explain why the taxpayer would hope that the rate could be truncated to a whole number when calculating the amount of tax owed on the tax form.
2. Explain why the government prefers and requires the taxpayer to round the tax rate to a whole number.
C. Explain how you would use rounding, truncating, and mental math in real-world scenarios by doing the following:
1. Explain how you would use mental math to calculate a 27.8% tax, using an income of your choice.
2. Provide four real-world examples, two for rounding and two for truncation, which illustrate how mental math skills are used to solve problems.
D. There are 20 boys and 24 girls in an Algebra I class. The class is so large that the teacher wants to divide the students into gender-specific groups (all boys or all girls). Each group needs to have the same number of students.
1. Explain the process the teacher will use to determine the largest number of students that can be in each group using appropriate mathematical terms from number theory.
E. Explain how to prove that there is an infinite number of primes.
F. Explain the concept of modular operations by doing the following (suggested length of 1–2 pages):
1. Discuss modular arithmetic and its relation to time (i.e., clock arithmetic).
2. Explain what is meant by 10 mod 6.
3. Explain how to add and multiply in mod 7, including the following:
• Appropriate examples for modular addition using positive integers
• Appropriate examples for modular addition using negative integers
• Appropriate examples for modular multiplication using positive integers
• Appropriate examples for modular multiplication using negative integers
G. When you use sources, include all in-text citations and references in APA format.