1.2.1 Name the Prime numbers between 0 and 15 1.2.2 Illustrate on a number line: \( \{x \mid 0

Ask by Marsh Schofield. in South Africa

Mar 11,2025

**Step 1.2.1 – Find the Prime Numbers between 0 and 15** A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself. The numbers between 0 and 15 are: \(0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15\). - \(0\) and \(1\) are not prime numbers. - \(2\) is prime (divisible only by 1 and 2). - \(3\) is prime (divisible only by 1 and 3). - \(4\) is composite (divisible by 2). - \(5\) is prime. - \(6\) is composite (divisible by 2 and 3). - \(7\) is prime. - \(8\) is composite. - \(9\) is composite (divisible by 3). - \(10\) is composite. - \(11\) is prime. - \(12\) is composite. - \(13\) is prime. - \(14\) is composite. - \(15\) is composite. Thus, the prime numbers between 0 and 15 are: \[ 2,\;3,\;5,\;7,\;11,\;13 \] --- **Step 1.2.2 – Illustrate the Prime Numbers on a Number Line** We need to illustrate the set \[ \{x \mid 0 < x < 15 \text{ and } x \text{ is prime} \} \] on a number line. The prime numbers we found are: \(2, 3, 5, 7, 11,\) and \(13\). Below is a simple representation of the number line from 0 to 15, with the prime numbers marked: ``` 0---1---2*---3*---4---5*---6---7*---8---9---10--11*--12--13*--14--15 ``` Here, the asterisk (*) indicates the position of a prime number. Alternatively, visualizing it with spacing: - 0  1   **2**  3   **3**  4   **5**  6   **7**  8  9  10   **11**  12   **13**  14  15 (Only positions \(2, 3, 5, 7, 11,\) and \(13\) are marked as primes.) --- **Step 1.3 – Determine Between Which Two Whole Numbers \( \sqrt[3]{27} \) Lies** Calculate the cube root of 27: \[ \sqrt[3]{27} = 3 \quad \text{because} \quad 3^3 = 27. \] Since \( \sqrt[3]{27} \) is exactly 3, it lies exactly on the whole number 3. If we were to express the answer in terms of two consecutive whole numbers that would "bound" 3, one might say it lies between 3 and 3. However, the precise answer is that \[ \sqrt[3]{27} = 3. \] Thus, it is not between two different whole numbers; it is exactly the whole number 3.