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The solution is the interval (-2,5).

There are 288 ways to give out the bracelets.

There are 32 different possible results.

The probability is 17/288.

There are 902 possible locations for the centroid.

First:  Add 150 to both sides of the equation

Second:  divide both sides of the equation by 1.5

Done.

It say that BA is a perpendicular BISECTOR of DC !

Doesn't that mean that BA "bisects" DC, or cuts it in half? In other words, DE = EC. Triangle DBE is congruent to triangle EBC since they share the perpendicular height of EB, in addition to having DE=EC. 
Therefore, BD = BC = 3.7 units.[Diagram is not drawn to scale]. That is my take on it. One of the "Mods" should check this.

i just finished the test and now i know im dumb

are calculators allowed?

If the 20N force is in line with the rod, then there will be no need for any force at B, (and the reaction at the pivot will be 20N).

It's a silly question.

We need to know the angle between the rod and the line of action of the force.

For an object to be in equilibrium, resultant of all moments(Principal of moments) must be equal (I.e anti clockwise moments= clockwise moments) & Resultant of all forces (Fres)=0 as well. 

AB is the whole length of the rigid rod which is 2.8

Imagine point A at one end and a force acting on it downwards 20N (There is also a contact/reactant/normal force acting on it on the opposing direction so that sets the Fres=0) "If the rod is pivoted at 1.2m from end A" Well the whole length of the rigid rod is 2.8, away from A 1.2m where is the pivot so the pivot away from point B would be 2.8-1.2=1.6m 

Now let the pivot be y 

let force that acts on A be z

let force that acts on B be x 

so 

Ay*z must be equal to By*x

we know the distance Ay and By also we know z but we want to find x so that Ay*z=By*x 

so subsituite,

Ay=1.2m

z=20N

By=1.6m

1.2*20=1.6*x 

24=1.6*x

x=24/1.6=15N

The force that acts on B so that the rigid rod is in equilibrium is 15N 

It didn't have any guts. Ha, ha.

Ok, I just wanted to make sure! 

There is something missing from the question.

As it stands it doesn't have an answer.

Look for the moment at AC, (with C fixed in some way).

Suppose that instead of being told that it's length is 4.1, we are told that it's length is 10 say.

That merely pushes A further from E while having no effect whatever on the length of BC.

It looks like there has to be a relationship between BE and EA.