💡To determine how many different total scores a basketball player could achieve by making 7 baskets, each worth either 1, 2, or 3 points, we can follow these steps:1. **Identify the minimum and maximum scores**: - The minimum score occurs when all baskets are 1-pointers: (7 times 1 = 7). - The maximum score occurs when all baskets are 3-pointers: (7 times 3 = 21).2. **Determine the range of possible scores**: - The scores can range from 7 to 21.3. **Check for all possible scores between the minimum and maximum**: - For each score (S) from 7 to 21, we need to verify if there exist non-negative integers (x), (y), and (z) such that: [ x + 2y + 3z = S quad text{and} quad x + y + z = 7 ] - By solving these equations for each (S), we can confirm if the score is achievable.4. **Conclusion**: - After checking each score from 7 to 21, we find that all scores within this range are achievable with different combinations of 1-point, 2-point, and 3-point baskets.Thus, the number of different total scores the player could achieve is 15.The final answer is (boxed{mathrm{(B)} 15}).

💡First, I need to determine the combined salaries of A, B, C, and D per month.I know that the average salary of A, B, C, D, and E is Rs. 8400. Since there are 5 individuals, I can calculate the total salary for all five by multiplying the average salary by the number of individuals.Total salary for A, B, C, D, and E = 8400 × 5 = 42000 Rs.Next, I know that E's salary is Rs. 9000. To find the combined salaries of A, B, C, and D, I subtract E's salary from the total salary.Combined salary for A, B, C, and D = 42000 - 9000 = 33000 Rs.Therefore, the combined salaries of A, B, C, and D per month are 33000 Rs.

💡Okay, so I need to find the inverse proposition of "If |a| > |b|, then a > b." Hmm, let's break this down. First, I remember that in logic, the inverse of a statement "If P, then Q" is "If not P, then not Q." So, applying that here, the inverse should be "If |a| is not greater than |b|, then a is not greater than b." Wait, but is that right? Let me think about it again. The original statement is saying that if the absolute value of a is bigger than the absolute value of b, then a itself is bigger than b. So, the inverse would be flipping both parts and negating them. That means if the absolute value of a is not greater than the absolute value of b, then a is not greater than b. But I'm not sure if just negating both parts is the correct approach here. Maybe I should consider the structure more carefully. In logic, the inverse is formed by negating both the hypothesis and the conclusion of the original implication. So, if the original is P → Q, the inverse is ~P → ~Q. Applying that to our problem: P is "|a| > |b|" and Q is "a > b." So, ~P would be "|a| ≤ |b|" and ~Q would be "a ≤ b." Therefore, the inverse proposition should be "If |a| ≤ |b|, then a ≤ b." Wait, but does that make sense? Let me test it with some numbers. Suppose a = 3 and b = 2. Then |a| = 3 and |b| = 2, so |a| > |b|, and indeed a > b. That fits the original statement. Now, for the inverse, if |a| ≤ |b|, then a ≤ b. Let's take a = 2 and b = 3. Here, |a| = 2 and |b| = 3, so |a| ≤ |b|, and a = 2 ≤ 3 = b. That works. But what if a is negative? Let's say a = -3 and b = 2. Then |a| = 3 and |b| = 2, so |a| > |b|, but a = -3 is not greater than b = 2. Wait, that contradicts the original statement. So, the original statement isn't always true. Hmm, does that affect the inverse? Well, the inverse is just the logical structure, regardless of whether the original statement is true or not. So, even if the original statement isn't always true, the inverse is still formed by negating both parts. Another example: a = -2 and b = -3. Here, |a| = 2 and |b| = 3, so |a| ≤ |b|, and a = -2 ≥ -3 = b. Wait, that's not matching the inverse. The inverse says if |a| ≤ |b|, then a ≤ b, but in this case, a = -2 is actually greater than b = -3. So, the inverse doesn't hold in this case either. Hmm, so maybe the inverse isn't always true either. But that's okay because the question is just asking for the inverse proposition, not whether it's true or not. So, to summarize, the inverse of "If |a| > |b|, then a > b" is "If |a| ≤ |b|, then a ≤ b." I think that's the correct inverse proposition.

💡First, I identify the distance the grasshopper jumped, which is 25 inches.Next, I determine how much farther the frog jumped compared to the grasshopper, which is 15 inches.To find the total distance the frog jumped, I add the grasshopper's jump distance to the additional distance the frog jumped: 25 inches + 15 inches = 40 inches.Therefore, the frog jumped 40 inches.

💡To determine how many distinct four-digit positive integers have only even non-zero digits, we first identify the even non-zero digits available: 2, 4, 6, and 8. This gives us 4 choices for each digit in the four-digit number.Since each of the four positions (thousands, hundreds, tens, and units) can independently be any of these 4 even digits, we use the rule of product to calculate the total number of possible combinations. The total number of such four-digit integers is calculated as:[ 4 times 4 times 4 times 4 = 4^4 ]Calculating this gives:[ 4^4 = 256 ]Therefore, the number of distinct four-digit positive integers that have only even non-zero digits is 256.

💡First, I need to express the diameter of a single strand of hair, which is 0.0000597 meters, in scientific notation.To do this, I'll move the decimal point to the right until it is after the first non-zero digit, which is 5. This requires moving the decimal point five places to the right.Since I moved the decimal point five places to the right, I will multiply the number by 10 raised to the power of -5.Therefore, the diameter in scientific notation is 5.97 multiplied by 10 to the power of -5.