answer:Feng Shui is an ancient Chinese practice that emphasizes the importance of the balance and flow of energy, known as chi, in our surroundings. It provides principles and guidelines for optimizing the environment to promote positive energy and harmony in all aspects of life. Some of the main principles of Feng Shui include: 1. The Bagua Map: This is a tool used to identify the different areas of your home or space and correlate them with different aspects of your life such as wealth, career, family, etc. 2. Decluttering and Organization: Clutter is said to create stagnant energy and can block the flow of chi. Feng Shui emphasizes the importance of organization and simplifying one's surroundings to facilitate good energy flow. 3. Yin and Yang: This principle highlights the fundamental concept of balance, harmony and duality. It emphasizes the importance of balancing opposite energies to maintain harmony. 4. The Five Elements: Feng Shui emphasizes the importance of balancing the five elements- wood, fire, earth, metal, and water - within your environment. Each element correlates with different aspects of life and encourages a balance between them. In modern life, Feng Shui is used to create positive energy and balance in different spaces including homes, work environments and other spaces. It is often used to create a serene and relaxing ambiance, improve productivity and promote overall well-being. Employers also use it to optimize their office space for better productivity and success at work.

answer:1. **Identify Unique Letters in PROBABILITY**: - The word PROBABILITY consists of the following letters: P, R, O, B, A, B, I, L, I, T, Y. - Eliminate the repeated letters. The unique letters are: P, R, O, B, A, I, L, T, Y. - Thus, there are 9 unique letters in PROBABILITY. 2. **Determine Total Number of Letters in the Alphabet**: - There are 26 letters in the English alphabet. 3. **Calculate the Probability**: - The probability ( P ) of Jeff picking one of the 9 unique letters from the alphabet is given by the ratio of the number of favorable outcomes to the total number of possible outcomes. - Therefore, ( P ) is: [ P = frac{text{Number of favorable outcomes}}{text{Total number of possible outcomes}} = frac{9}{26}. ] # Conclusion: [ boxed{frac{9}{26}} text{ (A)} ]

answer:To find the ratio of copper to zinc in the mixture, we first need to determine the weight of copper in the mixture. We know that the total weight of the mixture is 70 kg, and 31.5 kg of zinc has been used. Therefore, the weight of copper in the mixture can be calculated by subtracting the weight of zinc from the total weight: Weight of copper = Total weight of mixture - Weight of zinc Weight of copper = 70 kg - 31.5 kg Weight of copper = 38.5 kg Now that we have the weights of both copper and zinc, we can find the ratio of copper to zinc: Ratio of copper to zinc = Weight of copper : Weight of zinc Ratio of copper to zinc = 38.5 kg : 31.5 kg To simplify the ratio, we can divide both sides by the greatest common divisor of the two weights. In this case, the greatest common divisor is 0.5 kg: Ratio of copper to zinc = (38.5 kg ÷ 0.5 kg) : (31.5 kg ÷ 0.5 kg) Ratio of copper to zinc = 77 : 63 Therefore, the ratio of copper to zinc in the mixture is boxed{77:63} .

answer:**Analysis** Using the given conditions, we can apply the sine addition formula and the monotonicity of the sine function to find that a>dfrac{sqrt{3}}{2}=c. Next, we use the double angle cosine formula to find that b>a. **Step-by-step Solution** 1. For a: begin{aligned}a&=sin 17^{circ}cos 45^{circ}+cos 17^{circ}sin 45^{circ} &(text{given})&=sin(17^{circ}+45^{circ}) &(text{sine addition formula})&=sin 62^{circ}end{aligned} Since sine is an increasing function in the first quadrant, sin 62^{circ} > sin 60^{circ} = dfrac{sqrt{3}}{2} Thus, a>dfrac{sqrt{3}}{2}=c 2. For b: begin{aligned}b&=2cos ^{2}13^{circ}-1 &(text{given})&=cos 26^{circ} &(text{double angle cosine formula})&=sin 64^{circ} &(text{complementary angle}) end{aligned} Again, since sine is an increasing function in the first quadrant, sin 64^{circ} > sin 62^{circ} = a Thus, b>a 3. For c: c=dfrac{sqrt{3}}{2} *Boxed Results*: Combining all the inequalities, we have boxed{c<a<b}.