5 hours @ 50mph = 250 miles

1 gallon at this speed = 30 miles

250 miles -> 25/3 gallons = 8 1/3 gallons

As a fraction of 12 gallons (full tank) = (25/3)/12 = 25/36 E.

The distance between the centre of the two wheels is the same as the horizontal part of the belt.

The part that is touching each wheel is equal to half the diameter for each one.

Answer = (Total length - 2 x half circumference)/2
= (15 - 2 x pi x 0.5)/2
= (15 - pi)/2 A.

You are getting it wrong because there are alternating signs. This is one way you could look at it. There are others. T = 1/2 - 1/4 + 1/8 - 1/16 + 1/32 - 1/64 + ... = (1/2 - 1/4) + (1/8 - 1/16) + (1/32 - 1/64) + ... = 1/4 + 1/16 + 1/64 + ... This sum will be a little bit more than a quarter. Thus an...

Call remaining vertex (a,b)

Average of x co-ords:

(0+6+a)/3 = 3
6+a = 9
a = 3

Average of y coords:

(0+0+b)/3 = 2
b/3 = 2
b = 6

So missing co-ord is (3,6) B.

Simon paints 1/2 the house in one hour and Sam paints a 1/3 if the house in an hour. Therefore in one hour 5/6 of the house has been painted between them.

Then, it take 12 mins to paint 1/6 of the house
-> it take 1h 12 mins to paint the whole house.

The question is what has to happen. If x is 1, y doesn't have to be 1, it can be anything. It's asking for the exact situation where the equation is true.

The way you are thinking all of the options would work.

P(at least one fashion book) = 1 - P(no fashion books) = 1 - P(SSS) = 1 - (4/8 * 3/7 * 2/6) = 1 - 1/14 = 13/14 [1st choice: 4 out of 8 books are fashion 2nd choice: 3 out of 7 remaining books are fashion 3rd choice: 2 out of 6 remaining books are fashion]

A prime number has no factors other than 1 and itself. Therefore every number less than p does not have any factor in common other than 1. There are p-1 numbers less than p so answer is A.