Jason,
If the the ball drawn was replaced this would a Bernoulli trail (independent trials and success probability is constant)
then you would use at the binomial distribution. Since the success probability is not constant as mentioned in the other answers, you would...

Zoe,
Lets divide the rod into two segments left and right at .25m and .75m
The center of mass of the segments are at .25/2 and .75/2
Taking moments (torque) about the given point gives ,25mg(,25/2)-.75mg(.75/2)=.6125-5.5125=4.9 N-m which is g/2
m=2kg...

The electric field E is defined by the force F it exerts on a positive test charge Qo. E=F/q0 and it is a vector.
Hope this helps
Jim

Nana
You have 3000=7.5*t2, so t=(3000/7.5)1/2 use your calculator.
Jim

John,
Since x-y=0 then x=y from the first equation
Putting x=y in the second equation gives -6y+5y=4 so y=-4 and x=-4.
The idea is to solve one of the equations for one of the unknowns and substuite that relationship in the second equation...

Ruth,
If you picture all the contestants on the x and y axis on the integer coordinates then each lattice point is a potential confrontation. Some points should be excluded 1. points on the diagonal represent confrontation with oneself (1,1) (2,2)...
so there are 24...

Hi Deoni,
Centripetal acceleration is the acceleration required to keep a particle moving in a circle. It (the vector) always points toward the center if the circle and has magnitude v2/R where v is the speed of the particle and R is the radius of the circle.
...

P=2I+2W to solve this equation for W you do whatever you need to to isolate W so
subtract 2I form both sides: P-2I=2W since 2I-2I=0
the divide both sides by2 :(P/2)-I=W and there you have it w=(P/2)-I now you can put the numerical values for P and I in this equation...

The two straight sections =171 m so the 2 half circles must measure 400-171=229m so if the radius of the circle is R then the circumference is 2*π*R and this must be equal to 229m so R=229/6.28...=36.45 m
Hope this helps
Jim

Marlow,
Make the moment of inertia of the wheels a large as physically possible. Large heavy rim type wheel. You want to tie up as much of the initial potential energy in rotational energy 1/2Iω2
Hope this helps
Jim

a. C=3500+6x
b. R=30x
c. P=R-C=24x-3500
d. the break even production rate is when the profit is just equal to 0 i.e. 24x-3500 =0 so x=3500/34=146 shirts/mo
Make sense?
Jim

Multiply the numerator and denominator by (√5 + 2) and simplify you should get
5+2√5
The steps are; denominator (51/2-2)(51/2+2)=5-4=1 use the FOIL method
numerator 51/2(51/2+2)=5+2*51/2
Hope...

Edona,
In the standard physics terminology ω (omega) usually stands for "angular velocity" and is measured in radians/second. f stands for "angular frequency" measured in hz or cycles per second.
The relationship between the two...

Emily,
The time to reach max height is (-40)/(-8)=+5/2 sec (the axis of symmetry of a parabola)
To find the ordered pair (coordinates) of the max height you let t=5/2 in the equation for the height as a function of time
h(5/2)=-8*(5/2)2 +40*(5/2)...

Assuming the two events are independent: P(even)=3/6 there are 3 ways to get an even number 2,4,6, P(5)=1/6
The P(even and 5)=(3/6)(1/6) =3/36 =1/12.
Hope this helps
Jim

Your equation is incorrect the coefficient of x should be 252 cal not 502.
Jim

Looks to me as though you factored the expression using the difference of two squares rule correctly.
Jim

Darla,
This a binomial trial. The success probability is 1-.02=.98, the bulbs are independent and there is only one way the string can stay lit so the probability is (.98)20=.668
Hope this helps
Jim

N(AUB)=N(A)+N(B)-N(A∩B) my notation here is N(A)=the number of elements in the set A and so on.
We know that: N(A)=69
N(B)=74
and ...

Hi,
Using the chain rule and the exponential rule gives d/dx(1+x)104=104(1+x)103*d/dx(1+x)=104(1+x)103 since d/dx(1+x)=1
Hope this helps
Jim