Suppose you break your piggy bank and scoop up a handful of 22 coins (pennies, nickels, dimes and quarters). Prove that you must have at least 6 coins of a single denomination. Suppose you have an odd number of pennies. Prove that you must have an odd number of at least one of the other types of coins. How many coins would you scoop up to be sure that you either had 4 coins that were all the same or 4 coins that were all different. Prove your answer.

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step-by-step explanation:

- "runner b is moving at a slower rate."

- "the graphs shown are graphs of distance(km) against time(min).

the slopes of this graphs are are given by:

slope = (change in y)/(change in x)

= (change in distance)/(change in time)

this is the formula for finding the speed. so, the slope of these graphs represent the speed of the runner.

taking each division in the graph to represent 1 on both axis:

runner a ⇒ speed = (2-0)/(1-0)

= 2/1

= 2 km/min

runner b ⇒ speed = (3-0)/(3-0)

= 3/3

= 1 km/min

this shows that   runner b is moving at a slower rate."