answer:1. **Define the set and condition**: Let the three-element set be {a, b, c}, where a, b, c are distinct elements from the set {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}. We are given that the sum of the elements in the set is 18. 2. **Condition on including 6**: Suppose a = 6. Then, we need to find pairs (b, c) such that b + c = 18 - 6 = 12 and b neq c. 3. **Finding valid pairs (b, c)**: - The possible values for b and c are from the set {1, 2, 3, 4, 5, 7, 8, 9, 10} (excluding 6). - We list the pairs (b, c) such that b + c = 12: - (1, 11) - Not valid as 11 is not in the set. - (2, 10) - (3, 9) - (4, 8) - (5, 7) - Each of these pairs (b, c) is distinct and sums to 12, satisfying the condition b neq c. 4. **Count the number of valid sets**: There are 4 valid pairs (b, c), each forming a valid set with a = 6. Therefore, there are 4 sets containing the number 6 that sum to 18. 5. **Conclusion with boxed answer**: The number of sets containing 6 whose elements sum to 18 is 4. The final answer is boxed{B}

answer:(1) Since, the curves ({C}_{1}): ρ =4cos θ (0≤θ < frac{π }{2}) and ({C}_{2}): ρ cos θ =3. Solving the system of equations begin{cases} ρ =4cos θ ρ cos θ =3 end{cases}, we get cos θ=± frac{ sqrt{3}}{2 } , Given 0≤θ < frac{π }{2}, θ= frac{π }{6} , Thus, ρ=2 sqrt{3} , Hence, the polar coordinates of the intersection point of ({C}_{1}) and ({C}_{2}) is boxed{(2 sqrt{3}, frac{π }{6}) }. (2) Let P(ρ,θ), Q(ρ_{0},θ_{0}), and ρ_{0}=4cos θ_{0}, {θ}_{0}∈[0, frac{π }{2}), From the given overrightarrow{OQ} =frac{2}{3} overrightarrow{QP} , we get begin{cases}{ρ}_{0}= frac{2}{5}ρ {θ}_{0}=θend{cases} , Therefore, frac{2}{5}ρ=4cos θ , Thus, the polar coordinate equation of the moving point P is boxed{ρ=10cos θ, θ∈[0, frac{π }{2})}.

answer:Last week, my 8th-grade class and I had the privilege of presenting our community garden project to the local city council. This initiative, which entailed the design and maintenance of a sustainable garden, proved to be a profoundly transformative experience for all participants. Through this project, our students acquired knowledge about plant growth and water conservation, as well as developed critical skills in quantitative reasoning and data analysis. One of our students, Alex, demonstrated exceptional initiative by devising a method that achieved a 20% reduction in water usage within the garden. This significant improvement not only contributed to the garden's success but also initiated a broader dialogue on water conservation within our community. The city council was deeply impressed by the students' efforts and is now contemplating the expansion of green spaces in the area. I am immensely proud of my students and the impact they have made. This project has underscored the value of hands-on, community-focused education and its potential to empower students to effect real change. For educators and community leaders, I strongly recommend considering similar initiatives in your respective areas. Together, we can collaborate to foster a more sustainable future for the next generation. #EnvironmentalEducation #STEMEducation #SustainableFuture #CommunityEngagement

answer:Here's how you can implement this function: ```python def sort_dict_with_int_keys(d: dict) -> list: if d is None or len(d) == 0: return [] if not all(isinstance(k, int) for k in d): raise TypeError(Dictionary key is not an integer) sorted_keys = sorted(k for k in d if isinstance(k, int)) sorted_values = [d[k] for k in sorted_keys] return list(zip(sorted_keys, sorted_values)) ```