Let \( \pi(x) \) be the number of prime numbers in the range from 2 to \( x \). Select the pair of inequalities that are both true.1. \( \pi(1000) \leq \pi(10000) \) \( \frac{\pi(1000)}{1000} \leq \frac{\pi(10000)}{10000} \)2. \( \pi(1000) \leq \pi(10000) \) \( \frac{\pi(1000)}{1000} \geq \frac{\pi(10000)}{10000} \)3. \( \pi(1000) \geq \pi(10000) \) \( \frac{\pi(1000)}{1000} \leq \frac{\pi(10000)}{10000} \)4. \( \pi(1000) \geq \pi(10000) \) \( \frac{\pi(1000)}{1000} \geq \frac{\pi(10000)}{10000} \)Note: \( \pi(x) \) represents the prime counting function, which returns the count of prime numbers less than or equal to \( x \). Consider this while evaluating the inequalities for truth.

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π Let (x) be the number of prime numbers in the range from 2 to x. Select the pair of inequalities that are both true. O T(1000) T(1000) 1000 O ≤T(10000) TT (10000) 10000 T(1000) ≤ (10000) T(1000) 1000 T(1000) TT (1000) 1000 π(10000) 10000 T(10000) π(10000) 10000 T(1000) > T(10000) T(1000) 1000 π(10000) 10000

π Let (x) be the number of prime numbers in the range from 2 to x. Select the pair of inequalities that are both true. O T(1000) T(1000) 1000 O ≤T(10000) TT (10000) 10000 T(1000) ≤ (10000) T(1000) 1000 T(1000) TT (1000) 1000 π(10000) 10000 T(10000) π(10000) 10000 T(1000) > T(10000) T(1000) 1000 π(10000) 10000

Algebra and Trigonometry (6th Edition)

6th Edition

ISBN:9780134463216

Author:Robert F. Blitzer

Publisher:Robert F. Blitzer

ChapterP: Prerequisites: Fundamental Concepts Of Algebra

Section: Chapter Questions

Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...

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Question

Let \( \pi(x) \) be the number of prime numbers in the range from 2 to \( x \). Select the pair of inequalities that are both true.

1. \( \pi(1000) \leq \pi(10000) \)
\( \frac{\pi(1000)}{1000} \leq \frac{\pi(10000)}{10000} \)

2. \( \pi(1000) \leq \pi(10000) \)
\( \frac{\pi(1000)}{1000} \geq \frac{\pi(10000)}{10000} \)

3. \( \pi(1000) \geq \pi(10000) \)
\( \frac{\pi(1000)}{1000} \leq \frac{\pi(10000)}{10000} \)

4. \( \pi(1000) \geq \pi(10000) \)
\( \frac{\pi(1000)}{1000} \geq \frac{\pi(10000)}{10000} \)

Note: \( \pi(x) \) represents the prime counting function, which returns the count of prime numbers less than or equal to \( x \). Consider this while evaluating the inequalities for truth.

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