A professor wants to award prizes for 1st, 2nd, 3rd, 4th and 5th in the class of 30. In how many ways can the prizes be awarded (assume no two students tie)

Ivan began dividing g2  – 6 by g + 1, noting that . he started by placing g in the quotient, as shown below.what is g2  – 6 divided by g + 1? g –  1 –  g + 1  – g  –  7 + g  –  5  + 

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 (%).

Koji is installing a rectangular window in an office building. the window is 823 feet wide and 534 feet high. the formula for the area of a rectangle is a=bh. what is the area of the window? enter your answer as a mixed number in simplest form in the box. $$ ft2