answer:To solve this problem, we begin by understanding the properties of a geometric sequence. In a geometric sequence, the ratio between consecutive terms is constant. This ratio is often denoted as q. Given that a_3 = 2 and a_4 = 4, we can find the common ratio q by dividing a_4 by a_3: q = frac{a_4}{a_3} = frac{4}{2} = 2. Knowing q, we can express a_3 in terms of the first term a_1 and the common ratio q: a_3 = a_1 cdot q^2. Given that a_3 = 2, we substitute the values of a_3 and q into the equation: 2 = a_1 cdot 2^2. Solving for a_1, we find: a_1 = frac{2}{4} = frac{1}{2}. Therefore, the first term of the geometric sequence is boxed{frac{1}{2}}, which corresponds to choice C.

answer:_**Analysis**_ With a large number of repeated experiments, the frequency of an event occurring will stabilize near a certain constant, which is called the estimated value of the event's probability, rather than an inevitable result. **Solution** A, Frequency can only estimate probability; B, Correct; C, Probability is a fixed value; D, They can be the same, such as in the "coin toss experiment", where the frequency of getting heads can be 0.5, the same as the probability. Therefore, the answer is boxed{text{B}}. _**Review**_ This question examines the use of frequency to estimate probability, where the stable value of frequency in a large number of repeated experiments is the probability.

answer:Given the floor decoration has ten rays forming equal central angles around a circle, the total sum of all central angles in a circle is 360 degrees. Each angle is therefore calculated as: [ text{Each angle} = frac{360}{10} = 36 text{ degrees} ] Looking at the rays pointing East and Northwest: - Due East ray is the 3rd ray clockwise from due North considering each is 36 degrees apart. - The Northwest ray is the 5th ray clockwise from due North. Counting the central angles between the ray pointing East and the ray pointing Northwest involves calculating the total of central angles between them: - East (3rd ray) to Northwest (5th ray) includes 1 full angle between the 3rd and 4th ray and a part of the angle to the 5th ray. Hence, calculating those angles: [ 36^circ (text{the fourth ray complete}) = 36^circ text{ as only one complete angle is involved} ] Thus, the smaller angle measure between rays pointing East and Northwest is: [ boxed{36^circ} ]

answer:# Problem: In the equation on the right, different Chinese characters represent different digits, and the same Chinese characters represent the same digits, making the equation true. What is the four-digit number "望子成龙"? Step 1. Translate the Chinese characters to a generic number representation. The Chinese characters translate to the following form: [ text{龙} + text{龙} + text{龙} + text{龙} = 48 ] This indicates that the last digit (尾数) of 龙 should satisfy the above condition. Step 2. Determine the value of the digit represented by "龙". From the given condition for "龙": [ 龙 + 龙 + 龙 + 龙 equiv text{尾数} ] Possible trials: - If ( 龙 = 3 ): [ 3 + 3 + 3 + 3 = 12 ] Since the last digit is 2, this result is invalid. - If ( 龙 = 8 ): [ 8 + 8 + 8 + 8 = 32 ] The last digit is 2, matching the required condition. Therefore, 龙 = 8. Step 3. Check the remaining digits "成", "子", 和 "望". If ( 龙 = 8 ), then the digits must satisfy: [ text{成数} + text{成数} + text{成数} + 3 text{进位} = 48 ] [ 6 + 6 + 6 + 3 进位 = 48 ] The tail number for "成": [ boxed{6} ] If "成" = 6, then considering "子": [ 子 + 子 + 2 进位数 = 0 ] [ 4 + 4 + 2 进位 = 0 ] The tail number for "望": [ boxed{4} ] If "望" = 1, then the last step (one digit of 望) yields: [ 望 + 1 个进位等于 2 ] 结论: [ 望 = 1] Thus, the four-digit number represented by "望子成龙" is: [ boxed{1468} ]