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question:Simplify 16^{frac{1}{2}}-625^{frac{1}{2}}.
answer:We can rewrite 16^{frac{1}{2}} as sqrt{16}=4, and 625^{frac{1}{2}} as sqrt{625}=25. So, 16^{frac{1}{2}}-625^{frac{1}{2}} = 4-25 = boxed{-21}. The answer is: -21
question:The distance between two cities on a map is 15 inches. If the scale is 0.25 inches = 3 miles, how many miles apart are the actual cities?
answer:If 0.25 inches on the map represents 3 miles, then 1 inch represents 12 miles. So, the actual distance between the cities is 15 times 12 = boxed{180} miles.The answer is: 180
question:Find y so that the vectors begin{pmatrix} 1 -3 -4 end{pmatrix} and begin{pmatrix} -2 y -1 end{pmatrix} are orthogonal.
answer:Two vectors are orthogonal if their dot product is zero. The dot product of begin{pmatrix} 1 -3 -4 end{pmatrix} and begin{pmatrix} -2 y -1 end{pmatrix} is 1(-2) + (-3)y + (-4)(-1) = -2 -3y + 4 = 2-3y. Setting this equal to zero, we have 2-3y=0, so y=frac{2}{3}. Therefore, y=boxed{frac{2}{3}}. The answer is: frac{2}{3}
question:f Clara has climbed past 96 blocks of stone on her way to the top of a historical tower with stone stairs, and each step consists of three massive blocks of stone, how many levels are there in the tower, knowing that each level has eight huge steps?
answer:If each step consists of three blocks of stone, then Clara has climbed 96/3 = 32 steps. If each level has eight steps, then there are 32/8 = 4 levels in the tower. 4 The answer is: 4