When a box rests on a round sheet of wood on the ground, it exerts an average pressure p on the wood. if the wood is replaced by a sheet that has half the diameter of the original piece, what is the new average pressure? i think the answer is 4p but i don't know why.

Pressure = Force ÷ Area

In this case, since the area is circular, we can rewrite the equation as:

Pressure = Force ÷ pi*r^2

Decreasing the diameter by half is the same as decreasing the radius by half.

We can replace all constants with 1 to compare the relationship between the two scenarios.

Original scenario with original area wood:

Pressure = 1 ÷ 1^2
Pressure = 1

Scenario with 0.5 radius of original scenario:
Pressure = 1 ÷ (1/2)^2
Pressure = 1 ÷ 1/4
Pressure = 4

This confirms that your guess of 4x the pressure is correct.

So as can be seen by the relationship, pressure for circular area is inversely proportional to the radius squared.

The horse latitudes-high-pressure zones about 30 degrees north and 30 degrees south of the equator.-warm air traveling away from the equator cools and sinks-weather tends to be clear and drythe doldrums-low-pressure near equator-air rises and spreads out toward the poles-rising moist air produces clouds and heavy rainthe westerlies-blow from the west-move from the horse latitudes toward the poles.-bring storms across much of the united statesthe tradewinds-blow from the east-move from the horse latitudes toward the equator  -strong, steady winds