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question:f f(x) = x^2 x + a, and f(m) < 0, then the value of f(m + 1) is ( ) A: Positive B: Negative C: Nonnegative D: Depends on m
answer:The correct answer is B: Negative. boxed{text{B}}
question:From the five numbers 1, 2, 3, 4, 5, select one even number and two odd numbers to form a threedigit number without repeating any digits. The total number of such threedigit numbers is: A: 24 B: 36 C: 48 D: 54
answer:To find the total number of three-digit numbers that can be formed by selecting one even number and two odd numbers from the set {1, 2, 3, 4, 5} without repeating any digits, we follow these steps: 1. **Select 1 even number**: There are 2 even numbers in the set {2, 4}. The number of ways to select 1 even number from these 2 even numbers is {C}_{2}^{1}. This equals 2 ways. 2. **Select 2 odd numbers**: There are 3 odd numbers in the set {1, 3, 5}. The number of ways to select 2 odd numbers from these 3 odd numbers is {C}_{3}^{2}. This equals 3 ways. 3. **Arrange the selected numbers**: After selecting 1 even number and 2 odd numbers, we have to arrange these 3 numbers to form a three-digit number. The number of ways to arrange 3 distinct numbers is {A}_{3}^{3}. This equals 3! = 6 ways. 4. **Calculate the total number of three-digit numbers**: Now, we multiply the number of ways in each step to get the total number of three-digit numbers that can be formed. This is given by the formula [ {C}_{2}^{1} times {C}_{3}^{2} times {A}_{3}^{3} ] [ = 2 times 3 times 6 ] [ = 36 ] Therefore, the total number of such three-digit numbers is boxed{36}, which corresponds to choice B.
question:The long jump finals contained four national champions competing against one another. The first competitor jumped a distance of 22 feet. The second competitor jumped one foot farther than the first competitor. The third competitor jumped two feet shorter than the third competitor. And the fourth competitor jumped 3 feet further than the third competitor. How long, in feet, did the fourth competitor jump?
answer:The second competitor jumped one foot farther than the first competitor, so the second competitor jumped 22 + 1 = 23 feet. The third competitor jumped two feet shorter than the second competitor, so the third competitor jumped 23 - 2 = 21 feet. The fourth competitor jumped 3 feet further than the third competitor, so the fourth competitor jumped 21 + 3 = boxed{24} feet.
question:Given Proposition A: a+bneq 4, and Proposition B: aneq 1 and bneq 3, determine the logical relationship between Proposition A and Proposition B: A: Necessary and sufficient condition B: Neither a sufficient nor a necessary condition C: Sufficient but not necessary condition D: Necessary but not sufficient conditio
answer:Since the statement "If a=1 or b=3, then a+b=4" is false, its contrapositive "If a+bneq 4, then aneq 1 and bneq 3" is also false. Similarly, since the statement "If a+b=4, then a=1 or b=3" is false, its equivalent statement "If aneq 1 and bneq 3, then a+bneq 4" is also false. Therefore, Proposition A: a+bneq 4 is neither a sufficient nor a necessary condition for Proposition B: aneq 1 and bneq 3. The correct choice is boxed{B}. Since the given propositions include negation, we can consider using the method of contrapositive to judge the truthfulness of the propositions and thereby determine the logical relationship between them. This problem primarily examines the method for discerning the necessary and sufficient relationship between propositions, the use of contrapositive to judge the truthfulness, and the definition and application of necessary and sufficient conditions, making it a fundamental question.