answer:The explanation for this problem involves understanding the statistical approach to combining measurements with uncertain values. Here, two independent organizations, GSA and AWRA, have both measured the length of the river Rio-Coralio, yielding slightly different results, each with a margin of error. Let's break down the given data and calculate the error probability as requested: Step 1: Interpret the Measurements 1. **GSA Measurement:** - Length = 402 km - Margin of error = ±500 m (or ±0.5 km) - Probability of error = 0.04 2. **AWRA Measurement:** - Length = 403 km - Margin of error = ±500 m (or ±0.5 km) - Probability of error = 0.04 Step 2: Understand the Distribution of Errors Given the error margin of ±0.5 km from both measurements, the probability that the true length of the river differs from the measured value can be depicted as follows: - Probability that the true length is greater than the measured value + 0.5 km is 0.02. - Probability that the true length is less than the measured value - 0.5 km is 0.02. Step 3: Calculate Cumulative Probability When combining the results from the two measurements, the combined result would be somewhere between their error margins. Given each result has an independent error of 0.02 probability in either direction, we can combine these probabilities. For the GSA measurement: - Probability true length is greater than 402.5 km: (0.02) - Probability true length is less than 401.5 km: (0.02) And for the AWRA measurement: - Probability true length is greater than 403.5 km: (0.02) - Probability true length is less than 402.5 km: (0.02) # Step 4: Determine Overlapping Useful Range Both measurements fall within 402 ± 0.5 km and 403 ± 0.5 km: - GSA's range: ([401.5, 402.5]) - AWRA's range: ([402.5, 403.5]) Since the overlap of the ranges, where there is the combined probability, is the segment ([402, 402.5]), we consider how the error distributions intersect. # Step 5: Combine Probabilities The probabilities for the non-overlapping portions are: [ P(text{true length} > 402.5 text{ or } < 402) = 2 times 0.02 = 0.04 ] Thus, the confidence for the non-error measurement: [ P(text{true length} = 402.5 text{ km}) = 1 - 0.04 = 0.96 ] Conclusion: The statistician combines the data correctly, given both independent measurements with random unbiased error show high consistency. The result is calculated as 402.5 km with the probability calculation leading to a low error margin. [ boxed{402.5 text{ km with an error probability of } 0.04} ]

answer:To find the next year when Sarah's birthday, June 16, falls on a Monday after 2017, we analyze the day of the week progression from 2017 onwards, considering whether each subsequent year is a leap year. 1. **Day Increment Calculation**: - In a non-leap year, the day of the week advances by 1 day. - In a leap year, the day of the week advances by 2 days. 2. **Yearly Progression**: - **2017**: June 16 is a Friday. - **2018** (non-leap year): Advances by 1 day, so June 16 is a Saturday. - **2019** (non-leap year): Advances by 1 day, so June 16 is a Sunday. - **2020** (leap year): Advances by 2 days, so June 16 is a Tuesday. - **2021** (non-leap year): Advances by 1 day, so June 16 is a Wednesday. - **2022** (non-leap year): Advances by 1 day, so June 16 is a Thursday. - **2023** (non-leap year): Advances by 1 day, so June 16 is a Friday. - **2024** (leap year): Advances by 2 days, so June 16 is a Sunday. - **2025** (non-leap year): Advances by 1 day, so June 16 is a Monday. 3. **Conclusion**: Sarah's birthday will next fall on a Monday in the year 2025. The final answer is boxed{text{(E)} 2025}

answer:Since {a_n} is a geometric sequence with the sum of the first n terms S_n and common ratio q, and it's given that a_n > 0, a_1 = 1, S_3 = 7, then the sum of the first three terms can be expressed as: [S_3 = a_1 + a_1q + a_1q^2 = 7,] Substitute a_1 = 1 into the equation, we get [1 + q + q^2 = 7.] Simplifying this equation, we have [q^2 + q - 6 = 0,] which is a quadratic equation that we can solve for q. The solutions of this quadratic equation are found by factoring: [(q - 2)(q + 3) = 0.] Setting each factor equal to zero gives us the possible values of q: [q - 2 = 0 quad text{or} quad q + 3 = 0.] Solving these, we get [q = 2 quad text{and} quad q = -3.] However, since a_n > 0 for all n and the sequence starts with a_1 = 1, a negative common ratio would eventually lead to negative terms, which contradicts the condition a_n > 0. Therefore, we discard q = -3, leaving us with [boxed{q = 2}.] as the correct value of the common ratio.

answer:**Analysis:** A number that represents the count of objects is called a natural number, and the smallest natural number is 0. In natural numbers, a prime number is a number that has no other factors except 1 and itself, while a composite number is a number that has factors other than 1 and itself. From this, we know that the smallest prime number is 2, and the smallest composite number is 4. Based on this, we can calculate their sum. Therefore, the sum of the smallest natural number (0), the smallest prime number (2), and the smallest composite number (4) is 0 + 2 + 4 = 6. So, the statement is boxed{text{True}}.