1. The problem states a youth group has 11 girls and 9 boys. 2. The mean number of books read by the girls is 8, so total books by girls = $11 \times 8 = 88$. 3. The mean number of books read by the boys is 3, so total books by boys = $9 \times 3 = 27$. 4. Total books read by the youth group = $88 + 27 = 115$. 5. Next, we have a right triangle with hypotenuse $x + 16$, base $2x$, and an angle of 30 degrees opposite the base. 6. Using the sine definition: $\sin 30^\circ = \frac{\text{opposite}}{\text{hypotenuse}} = \frac{2x}{x+16}$. 7. Since $\sin 30^\circ = \frac{1}{2}$, set up the equation: $\frac{1}{2} = \frac{2x}{x+16}$. 8. Cross-multiply: $x + 16 = 4x$. 9. Solve for $x$: $16 = 3x \Rightarrow x = \frac{16}{3}$. 10. The problem states $x$ can be written as $a + b\sqrt{c}$, but here $x = \frac{16}{3}$ is a rational number, so $a=\frac{16}{3}$, $b=0$, $c=0$. 11. Find the median of the numbers: -14, -23, -18, 4, -23, 26. 12. Sort the numbers: -23, -23, -18, -14, 4, 26. 13. Since there are 6 numbers (even), median = average of 3rd and 4th numbers: $\frac{-18 + (-14)}{2} = \frac{-32}{2} = -16$. 14. For the lizard climbing the rope: it climbs 13 cm along the rope and gains 12 cm vertically. 15. $\sin \theta = \frac{\text{opposite}}{\text{hypotenuse}} = \frac{12}{13}$. 16. The fraction $\frac{12}{13}$ is already in simplest form. 17. A team scored a mean of 5 goals per match over 9 matches. 18. Total goals so far = $9 \times 5 = 45$. 19. They score 2 goals in the next match, total goals = $45 + 2 = 47$. 20. New mean = $\frac{47}{10} = 4.7$. Final answers: - Total books read by youth group: 115 - $x = \frac{16}{3}$ (or $a=\frac{16}{3}$, $b=0$, $c=0$) - Median of numbers: -16 - $\sin \theta = \frac{12}{13}$ - New mean goals per match: 4.7