answer:First, we determine the coordinates of vectors overrightarrow{AB} and overrightarrow{CA}: overrightarrow{AB} = B - A = (-1, 0, 4) - (1, 1, 1) = (-2, -1, 3) overrightarrow{CA} = A - C = (1, 1, 1) - (2, -2, 3) = (-1, 3, -2) Next, we use the formula for the cosine of the angle between two vectors in space, which states cos(theta) = frac{overrightarrow{AB} cdot overrightarrow{CA}}{|overrightarrow{AB}| cdot |overrightarrow{CA}|} Here, overrightarrow{AB} cdot overrightarrow{CA} denotes the dot product of the vectors, and |cdot| denotes the magnitude of a vector. We calculate the dot product: overrightarrow{AB} cdot overrightarrow{CA} = (-2) cdot (-1) + (-1) cdot 3 + 3 cdot (-2) = 2 - 3 - 6 = -7 We find the magnitudes of the vectors: |overrightarrow{AB}| = sqrt{(-2)^2 + (-1)^2 + 3^2} = sqrt{4 + 1 + 9} = sqrt{14} |overrightarrow{CA}| = sqrt{(-1)^2 + 3^2 + (-2)^2} = sqrt{1 + 9 + 4} = sqrt{14} Now we insert these into the cosine formula: cos(theta) = frac{-7}{sqrt{14} cdot sqrt{14}} = -frac{1}{2} Finally, we find the angle theta whose cosine is -frac{1}{2}, which gives us: theta = cos^{-1}left(-frac{1}{2}right) = 120^circ Therefore, boxed{theta = 120^circ}.

answer:To solve this problem, we follow the movements of the point step by step: 1. The point starts at -3 on the number line. 2. It first moves 5 units to the left, which is mathematically equivalent to subtracting 5 from its current position: -3 - 5 = -8. 3. Then, it moves 10 units to the right, which is equivalent to adding 10 to its current position: -8 + 10 = 2. Therefore, the number represented by the endpoint after these movements is 2. Hence, the correct answer is boxed{D}.

answer:Let's calculate the total cost of the items we know the price of: Backpack: 15 Pens: 1 Pencils: 1 Now, let's add these costs together: 15 (backpack) + 1 (pens) + 1 (pencils) = 17 Dan spent a total of 32, so let's subtract the cost of the known items from the total to find out how much was spent on notebooks: 32 (total spent) - 17 (cost of backpack, pens, and pencils) = 15 Now we know Dan spent 15 on notebooks. Since each notebook costs 3, we can find out how many notebooks he bought by dividing the total spent on notebooks by the cost of each notebook: 15 (spent on notebooks) ÷ 3 (cost per notebook) = 5 notebooks Dan bought boxed{5} multi-subject notebooks.

answer:# Step-by-Step Solution Question 1: The heaviest basket of cabbage among the 10 baskets is ______ kilograms heavier than the lightest basket. - Identify the heaviest basket's excess weight: 2.5 kg - Identify the lightest basket's shortfall: -3 kg - Calculate the difference: 2.5 - (-3) = 2.5 + 3 = 5.5 kg Therefore, the heaviest basket is 5.5 kilograms heavier than the lightest basket. boxed{5.5 text{ kilograms}} Question 2: Compared to the standard weight, how many kilograms are the 10 baskets of cabbage in total over or under? - Sum the excess and shortfall of all baskets: 1.5 - 3 + 2 - 0.5 + 1 - 2 + 2 - 1.5 + 1 + 2.5 - Simplify the sum: = 3 kg Therefore, compared to the standard weight, the total weight of the 10 baskets of cabbage is 3 kilograms over. boxed{3 text{ kilograms}} Question 3: If the selling price of cabbage is 3 yuan per kilogram, how much can you sell these 10 baskets of cabbage for? - Calculate the total weight of the cabbage: 25 times 10 + 3 = 253 kg - Calculate the total selling price: 253 times 3 = 759 yuan Therefore, selling these 10 baskets of cabbage can earn 759 yuan. boxed{759 text{ yuan}}