answer:# Solution: Part 1: Completing the Contingency Table and Conducting an Independence Test 1. **Completing the Contingency Table** Given that there are 60 males and 48 of them are willing to participate, it follows that 60 - 48 = 12 males are not willing to participate. Similarly, since there are 100 respondents in total and 30 are not willing to participate (100 - 70 = 30), and 18 of these are female, it follows that the remaining 40 - 18 = 22 females are willing to participate. Thus, the completed table is: | Gender | Willing to Participate | Not Willing to Participate | Total | |--------|------------------------|---------------------------|-------| | Male | 48 | 12 | 60 | | Female | 22 | 18 | 40 | | Total | 70 | 30 | 100 | 2. **Independence Test** - Null Hypothesis, H_{0}: There is no association between willingness to participate and gender. - Using the formula for {chi^2}, we calculate: {chi^2}=frac{{100{{(48times18-22times12)}^2}}}{{60times40times70times30}}=frac{50}{7}approx7.143 - Comparing the calculated {chi^2} value with the critical value x_{0.01} = 6.635, we find 7.143 > 6.635. - Since the calculated {chi^2} value is greater than the critical value, we reject H_{0}. This indicates there is an association between willingness to participate and gender, with a significance level of alpha = 0.01. - Calculating the frequencies of males and females willing to participate, we find: text{Male frequency} = frac{48}{60} = frac{4}{5}, quad text{Female frequency} = frac{22}{40} = frac{11}{20} - Comparing these frequencies: frac{frac{4}{5}}{frac{11}{20}} = frac{16}{11} approx 1.45 - This indicates that the frequency of males willing to participate is approximately 1.45 times that of females, suggesting males are more willing to participate than females. boxed{text{Males are more willing to participate in the activity than females.}} Part 2: Probability Distribution and Mathematical Expectation of X 1. **Probability Distribution of X** - The possible values of X are 0, 1, 2, 3. - Calculating the probabilities: P(X=0) = frac{C_4^0C_3^3}{C_7^3} = frac{1}{35} P(X=1) = frac{C_4^1C_3^2}{C_7^3} = frac{12}{35} P(X=2) = frac{C_4^2C_3^1}{C_7^3} = frac{18}{35} P(X=3) = frac{C_4^3C_3^0}{C_7^3} = frac{4}{35} - The distribution table of X is: | X | 0 | 1 | 2 | 3 | |-----|-----|-----|-----|-----| | P | frac{1}{35} | frac{12}{35} | frac{18}{35} | frac{4}{35} | 2. **Mathematical Expectation of X** - Calculating the expectation: E(X) = 0 cdot frac{1}{35} + 1 cdot frac{12}{35} + 2 cdot frac{18}{35} + 3 cdot frac{4}{35} = frac{12}{7} boxed{E(X) = frac{12}{7}}

answer:Since f(x) and g(x) are "intimate functions" on [a, b], then |f(x) - g(x)| leq 10, that is, |x^3 - 2x + 7 - (x + m)| leq 10 holds on [2, 3]. Simplify to get x^3 - 3x - 3 leq m leq x^3 - 3x + 17 on [2, 3]. Let F(x) = x^3 - 3x - 3, where x in [2, 3]. Since F'(x) = 3x^2 - 3 > 0 holds on [2, 3], F(x) is an increasing function on [2, 3]. Thus, F(x)_{max} = F(3) = 15. Let G(x) = x^3 - 3x + 17, where x in [2, 3]. Since G'(x) = 3x^2 - 3 > 0 holds on [2, 3], G(x) is an increasing function on [2, 3]. Thus, G(x)_{min} = G(2) = 19. Therefore, 15 leq m leq 19. Hence, the answer is boxed{D}. This problem requires understanding the concept of "intimate functions" and applying it to find the range of a real number m. By defining appropriate functions F(x) and G(x), and determining their maximum and minimum values on the given interval, we can find the desired range of m. This is a moderately difficult problem.

answer:1. **Simple Interest Calculation**: [ A = P(1 + rt) ] Given: [ P = 500, , r = 0.03, , t = frac{3}{12} = frac{1}{4} , text{year} ] 2. **Substitute and solve**: [ A = 500(1 + 0.03 times frac{1}{4}) ] [ A = 500 left(1 + frac{0.03}{4}right) ] [ A = 500 left(1 + 0.0075right) = 500 times 1.0075 = 503.75 ] 3. **Additional deposit**: [ text{New total} = 503.75 + 15 = 518.75 ] 4. **Compare with final amount and calculate actual interest**: [ text{Interest actually credited} = 515.63 - 515 = 0.63 ] 5. **Conclusion**: The interest credited, after the addition and accounting for computational or statement error discrepancies, in cents is 63 cents. The correct answer is A) boxed{63} cents.

answer:Given 10 players (A_{1}, A_{2}, cdots, A_{10}) with respective initial scores of (9, 8, 7, 6, 5, 4, 3, 2, 1, 0). They each compete in a single round-robin tournament where each pair of players plays one match. In each match, a winner is determined with the following scoring rules: - If a higher-ranked player defeats a lower-ranked player, they score 1 point. - If a lower-ranked player defeats a higher-ranked player, they score 2 points. We need to calculate the minimal final total score for the new champion (the player who ends up with the highest score) after considering additional points from the tournament. To find the solution, let's examine the possible scores increment based on rank and establish constraints. 1. **Initial Score and Possible Outcomes for Top Players**: - Player (A_1) (initial score = 9): - Maximum score increment if (A_{1}) wins all matches against lower-ranked players: (2) matches. Hence, (2) points. - Potential final score for (A_{1}): (9 + 2 = 11). - Player (A_2) (initial score = 8): - Maximum score increment if (A_{2}) wins all matches against lower-ranked players: (3) matches. Hence, (3) points. - Potential final score for (A_{2}): (8 + 3 = 11). - Player (A_3) (initial score = 7): - Maximum score increment if (A_3) wins all matches against lower-ranked players: (4) matches. Hence, (4) points. - Potential final score for (A_3}): (7 + 4 = 11). - Player (A_4) (initial score = 6): - Maximum score increment if (A_4) wins all matches against lower-ranked players: (5) matches. Hence, (5) points. - Potential final score for (A_4): (6 + 5 = 11). - Player (A_5) (initial score = 5): - Maximum score increment if (A_5) wins all matches against lower-ranked players: (5) matches. Hence, (5) points. - Potential final score for (A_5): (5 + 6 = 11). **Additional possible ways for (A_5) to score higher**: - If (A_5) wins 1 match against a higher-ranked player (lower-ranked player scoring 2 points). - Hence, could score (5 + 1 + 6 = 12). 2. **Construct New Champion Scenario**: - Consider scenarios adjusting player wins to ensure (A_{1}), (A_{2}), (A_{3}), (A_{4}) can surpass their respective maximum win constraints given reduced possible wins by others: - Player (A_1) wins against (A_2), (A_3), and (A_4). - Loses against (A_5, A_6, A_7, A_8, A_9, A_{10}). - Final score: (9 + 3 = 12). Here are the scores: 1. (A_1) wins (A_2, A_3, A_4) and loses others: (9 + 3 = 12). 2. (A_2) wins (A_3, A_4, A_5, A_6) and loses others: (8 + 4 = 12). 3. (A_3) wins (A_4, A_5, A_6, A_7) and loses others: (7 + 4 = 11). 4. (A_4) wins (A_5, A_6, A_7, A_8) and loses others: (6 + 4 = 10). 5. (A_5) wins (A_6, A_7, A_8, A_9) and loses others: (5 + 6 = 11). 6. (A_6) wins (A_7, A_8, A_9, A_{10}) and loses others: (4 + 6 = 10). 7. (A_7) wins (A_8, A_9, A_{10}) and loses others: (3 + 6 = 10). 8. (A_8) wins (A_9, A_{10}) and loses others: (2 + 6 = 10). 9. (A_9) wins (A_{10}): (1 + 6 + 3 = 10). 10. (A_{10}) wins none: (0). Given this scenario, the minimum new total score for the champion is boxed below: [ boxed{12} ]