answer：First, I note that there are a total of 200 snakes in the park.There are 40 boa constrictors.The number of pythons is three times the number of boa constrictors, so there are 3 * 40 = 120 pythons.To find the number of rattlesnakes, I subtract the number of boa constrictors and pythons from the total number of snakes: 200 - 40 - 120 = 40.Therefore, there are 40 rattlesnakes in the park.

answer：First, I need to understand the operation ( otimes ) defined by ( a otimes b = (a + b)(a - b) ).To find ( 4 otimes [2 otimes (-1)] ), I'll start by evaluating the inner operation ( 2 otimes (-1) ).Calculating ( 2 otimes (-1) ):[2 otimes (-1) = (2 + (-1))(2 - (-1)) = (1)(3) = 3]Now, substitute this result into the outer operation:[4 otimes 3 = (4 + 3)(4 - 3) = (7)(1) = 7]Therefore, the value of ( 4 otimes [2 otimes (-1)] ) is 7.

answer：First, let's denote the original number of dolls in Lucy's collection as ( D ).When Ethyl bought two new dolls, the collection increased by 25%. This means that the increase of two dolls represents 25% of the original collection.We can set up the equation:[0.25D = 2]Solving for ( D ):[D = frac{2}{0.25} = 8]After adding the two new dolls, the total number of dolls in Lucy's collection is:[8 + 2 = 10]

answer：To determine the last digit of (101^{100}), I start by examining the last digit of the base, which is 1. Since any power of 1 will always result in 1, raising 1 to the power of 100 doesn't change its value. Therefore, the last digit of (101^{100}) is 1.

answer：To convert 9/11 into a decimal, I will perform the division of 9 by 11.First, I note that 11 goes into 9 zero times, so I write 0. and proceed with the division.Next, I add a decimal point and a zero to 9, making it 90. 11 goes into 90 eight times, which gives 88. Subtracting 88 from 90 leaves a remainder of 2.I bring down another zero, making it 20. 11 goes into 20 once, resulting in 11. Subtracting 11 from 20 leaves a remainder of 9.Bringing down another zero, I have 90 again. This process repeats, resulting in the repeating decimal 0.818181...Since the decimal repeats every two digits, I determine the pattern for the first 51 digits. There are 25 complete cycles of "81" and one additional digit, which is 8.Finally, I calculate the sum of these digits by multiplying 25 by the sum of 8 and 1, then adding the extra 8. This gives a total sum of 233.

answer：Okay, so I have this problem here about vectors. It says that vectors a and b have magnitudes 5 and 2 respectively. I need to find the maximum and minimum values of the magnitude of their sum, which is |a + b|. Hmm, okay, vectors. I remember that when adding vectors, the result depends on both their magnitudes and the angle between them. Let me think. The formula for the magnitude of the sum of two vectors is |a + b| = sqrt(|a|² + |b|² + 2|a||b|cosθ), where θ is the angle between them. Right, that's the law of cosines applied to vectors. So, if I can figure out the maximum and minimum values of cosθ, I can find the corresponding maximum and minimum of |a + b|.Since cosθ ranges from -1 to 1, that means when cosθ is 1, the expression inside the square root will be maximized, and when cosθ is -1, it will be minimized. Let me write that down.First, for the maximum value:|a + b|_max = sqrt(|a|² + |b|² + 2|a||b|*1)Plugging in the values:= sqrt(5² + 2² + 2*5*2*1)= sqrt(25 + 4 + 20)= sqrt(49)= 7Okay, that seems straightforward. So the maximum value is 7.Now, for the minimum value:|a + b|_min = sqrt(|a|² + |b|² + 2|a||b|*(-1))Plugging in the values:= sqrt(25 + 4 - 20)= sqrt(9)= 3Wait, that's interesting. So the minimum value is 3. Let me visualize this. If vectors a and b are in the same direction, their magnitudes add up, so 5 + 2 = 7. That makes sense. If they are in opposite directions, the magnitude of their sum is the difference, which is 5 - 2 = 3. Yeah, that lines up with what I just calculated.Is there another way to think about this? Maybe using the triangle inequality? I recall that |a + b| ≤ |a| + |b|, which gives the maximum value, and | |a| - |b| | ≤ |a + b|, which gives the minimum value. So, applying that here:Maximum: |a| + |b| = 5 + 2 = 7Minimum: | |a| - |b| | = |5 - 2| = 3Yep, that confirms my earlier results. So, whether I use the formula with cosθ or the triangle inequality, I get the same answers. That makes me feel confident that 7 is the maximum and 3 is the minimum.I wonder, though, if there are any cases where the minimum could be negative? But wait, the magnitude can't be negative. So the minimum is the smallest non-negative value, which is 3 in this case. So, no, it can't be less than 3 because that would mean the vectors are pointing in exactly opposite directions, and you can't get any smaller than that without changing the magnitudes of the vectors themselves.Another thought: if θ is 0 degrees, cosθ is 1, so the vectors are aligned, giving the maximum. If θ is 180 degrees, cosθ is -1, so the vectors are opposite, giving the minimum. For angles in between, the magnitude of the sum would be somewhere between 3 and 7. That all seems consistent.Let me just recap. The key idea is that the magnitude of the sum of two vectors depends on the angle between them. When they point in the same direction, their magnitudes add, giving the maximum. When they point in opposite directions, their magnitudes subtract, giving the minimum. Using the formula or the triangle inequality both lead to the same conclusion.So, after all that thinking, I'm pretty sure the maximum is 7 and the minimum is 3.**Final Answer**The maximum value is boxed{7}, and the minimum value is boxed{3}.