Which of the problems below could not be answered by using a factorial?
a. the number of ways 20 people can finish in the first three places in a race.
b. how many different kinds of pizzas can be made with 12 optional toppings.
c. how many ways 15 people can arrange themselves in a straight line.
d. how many ways the top 20 hit songs can be arranged from a selection of 500 current single.

Eis the midpoint of line segment ac and bd also line segment ed is congruent to ec prove that line segment ae is congruent to line segment be

Graph g(x)=2cosx . use 3.14 for π . use the sine tool to graph the function. graph the function by plotting two points. the first point must be on the midline and closest to the origin. the second point must be a maximum or minimum value on the graph closest to the first point.

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 (%).