answer：First, the ant starts at the position ((-2, 4)).When the ant crawls 3 units to the right horizontally, the (x)-coordinate increases by 3:[-2 + 3 = 1]Next, the ant crawls 2 units down vertically, so the (y)-coordinate decreases by 2:[4 - 2 = 2]Therefore, the new position of the ant is ((1, 2)), which corresponds to option C.

answer：First, I need to understand the problem. There are 10 people in a group, and their average weight increases by 6.5 kg when three new individuals join after replacing three others who weighed 75 kg, 80 kg, and 90 kg. I need to find the total weight of the three new individuals.To start, I'll denote the total weight of the original 10 people as ( W ). When the three individuals with weights of 75 kg, 80 kg, and 90 kg leave the group, the total weight of the group decreases by the sum of their weights. So, the new total weight of the group is:[W - (75 + 80 + 90) = W - 245 text{ kg}]Next, three new individuals join the group, and the average weight of the group increases by 6.5 kg. Since there are still 10 people in the group, the total increase in weight is 10 times the increase in average weight:[text{Total increase in weight} = 10 times 6.5 text{ kg} = 65 text{ kg}]So, the total weight of the group after the three new individuals join is:[(W - 245 text{ kg}) + 65 text{ kg} = W - 180 text{ kg}]This total weight must also be equal to the weight of the original 7 people plus the total weight of the three new individuals. Let's denote the total weight of the three new individuals as ( X ). Therefore:[W - 180 text{ kg} = text{Weight of original 7 people} + X]The weight of the original 7 people is ( W ) minus the weight of the three individuals who left, which is:[W - 245 text{ kg}]Substituting this back into the equation:[W - 180 text{ kg} = (W - 245 text{ kg}) + X]Now, solving for ( X ):[X = (W - 180 text{ kg}) - (W - 245 text{ kg}) = 245 text{ kg} - 180 text{ kg} = 65 text{ kg}]Therefore, the total weight of the three new individuals is 65 kg.

answer：First, I need to find the mean noon temperature over the five consecutive days.To do this, I will add up all the temperatures: 75 + 78 + 80 + 76 + 77.Next, I will divide the total sum by the number of days, which is 5.This will give me the average temperature for the five days.

answer：First, I need to identify the largest factor of 18. Factors are numbers that divide 18 without leaving a remainder. The factors of 18 are 1, 2, 3, 6, 9, and 18. Among these, the largest factor is clearly 18 itself.Next, I need to determine the smallest multiple of 18. Multiples are numbers that can be expressed as 18 multiplied by an integer. The multiples of 18 start with 18, 36, 54, and so on. The smallest multiple in this sequence is 18.Therefore, both the largest factor and the smallest multiple of 18 are 18.

answer：Okay, so I have this problem here where I need to find the values of x and y such that the two terms -2a²b^{y+3} and 4a^x b² form a monomial when added together. Then, using those values, I need to simplify and evaluate another expression. Alright, let me break this down step by step.First, I remember that for two terms to form a monomial when added together, they must be like terms. That means their variables and their exponents must be the same. So, looking at the terms -2a²b^{y+3} and 4a^x b², I can set up equations for the exponents of a and b.For the exponents of a:The first term has a², so the exponent is 2. The second term has a^x, so the exponent is x. Since they need to be the same, I can write:2 = xThat seems straightforward. So, x must be 2.Now, for the exponents of b:The first term has b^{y+3}, so the exponent is y + 3. The second term has b², so the exponent is 2. Setting them equal:y + 3 = 2Solving for y:y = 2 - 3y = -1Okay, so y is -1. That gives me x = 2 and y = -1. I think that's part one done.Now, moving on to part two. I need to simplify and evaluate the expression:2(x²y - 3y³ + 2x) - 3(x + x²y - 2y³) - xHmm, let me write that out again to make sure I have it correctly:2(x²y - 3y³ + 2x) - 3(x + x²y - 2y³) - xAlright, let's substitute x = 2 and y = -1 into this expression. But maybe it's better to simplify the expression first before substituting the values. Let me try that.First, I'll distribute the constants into the parentheses.Starting with the first term:2(x²y - 3y³ + 2x) = 2*x²y - 2*3y³ + 2*2x = 2x²y - 6y³ + 4xSecond term:-3(x + x²y - 2y³) = -3*x - 3*x²y + 3*2y³ = -3x - 3x²y + 6y³Third term is just -x.Now, let me combine all these together:2x²y - 6y³ + 4x - 3x - 3x²y + 6y³ - xNow, let's combine like terms.First, the x²y terms:2x²y - 3x²y = -x²yNext, the y³ terms:-6y³ + 6y³ = 0y³, so they cancel out.Now, the x terms:4x - 3x - x = 0x, so they also cancel out.So, after simplifying, the entire expression reduces to:-x²yThat's much simpler! Now, let's substitute x = 2 and y = -1 into this simplified expression.So, -x²y = -(2)²*(-1) = -4*(-1) = 4Wait, that seems positive. Let me double-check my steps to make sure I didn't make a mistake.Starting from the beginning, the expression simplifies to -x²y. Plugging in x = 2 and y = -1:- (2)^2 * (-1) = -4 * (-1) = 4Yes, that's correct. So, the final value is 4.I think that's it. I didn't make any mistakes in the simplification, and the substitution seems correct. So, the answers are x = 2, y = -1, and the evaluated expression is 4.

answer：First, I need to evaluate each part of the expression using the definition of [x] as the greatest integer less than or equal to x.Given x = 6.5:- [x] = [6.5] = 6 (since 6 is the greatest integer less than or equal to 6.5)- [2 / 3] = [0.666...] = 0 (since 0 is the greatest integer less than or equal to 2/3)- [2] = 2 (since 2 is an integer and is the greatest integer less than or equal to itself)- [8.3] = 8 (since 8 is the greatest integer less than or equal to 8.3)Now, I'll substitute these values into the expression:[x] x [2 / 3] + [2] x 7.2 + [8.3] - 6.6= 6 x 0 + 2 x 7.2 + 8 - 6.6= 0 + 14.4 + 8 - 6.6= 14.4 + 8 - 6.6= 22.4 - 6.6= 15.8Therefore, the value of the expression is 15.8.