Find the angle between the diagonal of a cube of side length 18 and the diagonal of one of its faces, so that the two diagonals have a common vertex. the angle should be measured in radians. (hint: we may assume that the cube is in the first octant, the origin is one of its vertices, and both diagonals start at the origin.)

Chamberlin wants to bottle 1\8 of her apple cider. she pours the apple cider evenly among 6 bottles. what fraction of her apple cider will she put in each bottle? what expression could represent this situation?

Solve for x, y, and z. show all steps.

Acompany manufactures large valves, packed in boxes. a shipment consists of 1500 valves packed in 75 boxes. each box has the outer dimensions 1.2 x 0.8 x 1.6 m and the inner dimensions 1.19 x 0.79 x 1.59 m. the boxes are loaded on a vehicle (truck + trailer). the available capacity in the vehicle combination is 140 m3. each valve has a volume of 0.06 m3. - calculate the load factor on the box level (%). - calculate the load factor on the vehicle level (%). - calculate the overall load factor (%).