answer:Let's denote the common multiple of the ratio as x. So, the shares of p, q, and r would be 3x, 7x, and 12x respectively. According to the problem, the difference between q and r's share is Rs. 5500. So we can write: 12x - 7x = Rs. 5500 5x = Rs. 5500 x = Rs. 5500 / 5 x = Rs. 1100 Now, we can find the difference between the shares of p and q: 7x - 3x = 4x 4x = 4 * Rs. 1100 4x = Rs. 4400 Therefore, the difference between the shares of p and q is Rs. boxed{4400} .

answer:To solve this problem, we need to identify how many statements imply "r or s is true," which can be directly represented as r lor s. Analyzing each statement: 1. **Statement (1): "r and s are both false"** This is neg r land neg s. According to De Morgan's Laws, this also implies r lor s is false. Thus, this statement does not imply r lor s. 2. **Statement (2): "r is true and s is false"** This is r land neg s. Since r is true, the statement r lor s is true because "or" only requires one true value. Thus, this statement implies r lor s. 3. **Statement (3): "r is false and s is true"** This is neg r land s. As s is true, the statement r lor s is also true. Thus, this statement implies r lor s. 4. **Statement (4): "r is true and s is true"** This is r land s. Clearly, if both r and s are true, then r lor s is definitely true. Thus, this statement implies r lor s. From the analysis, statements 2, 3, and 4 imply "r or s is true." Therefore, the number of such statements is 3. Conclusion: The solution confirms that three statements imply the affirmative "r or s is true." Therefore, the answer is 3. The final answer is boxed{textbf{(D)} 3}

answer:**Analysis** This problem mainly examines the application of the basic inequality in extremum problems. When using the basic inequality, pay attention to the conditions under which equality holds. First, according to the property of the geometric mean, find the value of a+b, then transform frac{1}{a} + frac{1}{b} into (frac{1}{a} + frac{1}{b})(a+b) and rearrange it to find the answer. **Solution** Given that sqrt{3} is the geometric mean of 3^{a} and 3^{b}, therefore 3^{a} cdot 3^{b} = 3^{a+b} = 3, therefore a+b=1, therefore frac{1}{a} + frac{1}{b} = (frac{1}{a} + frac{1}{b})(a+b) = 2 + frac{a}{b} + frac{b}{a} geqslant 2 + 2sqrt{frac{a}{b} times frac{b}{a}} = 4, equality holds if and only if frac{a}{b} = frac{b}{a}, that is, when b=a. Therefore, the answer is boxed{4}.

answer:Marie starts with 95.0 erasers and buys 42.0 more. To find out how many erasers she ends with, we add the two amounts together: 95.0 + 42.0 = 137.0 Marie ends with boxed{137.0} erasers.