Explain why please Problem 3 y plographicmethods.EXERCISESa1. Use the sieve of Eratosthenes to find all of the primes from 100 to 2002. Use the prime table or a computer algebra system to find a list of 31consecutive composite numbers.3. Let n be an integer greater than 2. Explain why n! +2, n! +3, n! +4,n! + (n – 1), n! +n are all composite numbers. Use this idea toobtain a list of ten consecutive composite integers.4. A pair of prime numbers is called a twin prime pair if the numbersdiffer by 2. Find all of the twin prime pairs in the table of primes.Based on your findings, state which of the following you think is true:(1) There are infinitely many twin prime pairs. (2) There are finitelymany twin prime pairs.5Then give the product to afind the

We have to explain that n!+2, n!+3,…,n!+n-1,n!+n are all composite numbers.

Answered: 3. Let n be an integer greater than 2.…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

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The teacher from Problem 21 also tried a different approach to determining whether changing answers helps or hurts exam grades. In another class, students were told to review their final exams and change any answers they wanted to before turning them in. However, the students had to indicate both the original answer and the changed answer for each question. The teacher graded each exam twice, once using the set of original answers and once with the changes. In the class of n- 22 students, the exam scores improved by an average of MD - 2.5 points with the changed answers. The standard deviation for the difference scores was s = 3.1. Are the data sufficient to conclude that rethinking and changing answers can significantly improve scores? Use a one-tailed test at the .01 level of significance. (1) Ho: [ Select ] [ Select ] [ Select ] H1: Select ) [ Select ] [ Select ] (2) a - [ Select ] df - [ Select J Critical region boundary/boundaries: [ Select ] [ Select ] (3) Estimated Standard…
Question 1 y -3 2 -5 -4 -3 -2 -1 -1 3 -2 -3 4.

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3. Let n be an integer greater than 2. Explain why n! +2, n! +3, n! +4, n! + (n – 1), n! +n are all composite numbers. Use this idea to obtain a list of ten consecutive composite integers.