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The are 6762 ways to award the medals.

There are 2720 possible different pizzas.

A  = 32, B = 44, C = 104.

r = 2*sqrt(3) and theta = pi/2.

The answer is A.

1. Apply the exponent rule turning the expression into 1/(8/125)^(-1/3).

2. The denominator (8/125)^(1/3) can be rewritten as (8^(1/3))/(125^(1/3)).

3. Factor 8^(1/3) into (2^3)^(1/3) which equals 2^(3*1/3) which equals 2. Now let's find the denominator. Factor 125^(1/3) into (5^3)^(1/3) which equals 5^(3*1/3) which equals 5.

4. We can't forget about that 1 at the very top of the fraction from the beginning, so we have to simplify 1/2/5. (1)/(2/5)=(1)(5/2)=5/2 or 2 1/2.

Answer: 5/2 or 2 1/2 

Edit: I messed up some signs... YIKES... but they're good now!

I have 5 marbles numbered 1 through 5 in a bag. Suppose I take out two different marbles at random. What is the expected value of the sum of the numbers on the marbles?

There are 10 choices so each one has a prob of 1/10=0.1

0.1( 3+4+5+5+6+7+6+7+8+9) = 6

Sorry, there is not enough information given. :)

[165/(70)  +  115/(S+55)] =4, solve for S

S = 15 mph - they must drive over speed limit, but ONLY for for the first leg of 115 miles. They do not need to drive over the speed limit in the 2nd leg of 165 miles.

∠QPR + ∠RPS = ∠QPS

-7x - 38 + 27 = -13x -53 

x = -7

Now, you can calculate the angles easily. 

It wasn't your explanation at fault, it was my brain.  LOL

A family is on a road trip. The speed limit during the first 115 miles of the trip is 55 mph, and the speed limit during the last 165 miles is 70 mph. How many miles per hour over the speed limits must they drive in order to arrive at their destination in 4 hours?

Hello Guest!

\(\large \frac{115}{55+x}+\frac{165}{70+x}=4\)

\(x=6.9601\)

 6.96 miles per hour over the speed limits must they drive in order to arrive at their destination in 4 hours.

  !

Let the number of gallons of 70% antifreeze needed = A

0.7A  +  0.3*90 =0.6[A + 90], solve for A

A = 270 gallons of 70% antifreeze

 First flight,  Orvile 12 seconds, 37 meters.

Longest flight, Wilbur, 59 seconds, 260 meters.

 The average speed for the first flight was x meters per second. The average speed for the longest flight was y meters per second. What is the average of  x and y Express your answer as a decimal to the nearest tenth.

Hello SHADOWwolf!

\(x=\frac{37m}{12s}=3.08\overline{3}m/s\\ y=\frac{260m}{59s}=4.407m/s\)

\(\frac{x+y}{2}=\frac{(3.083+4.407)m/s}{2}\approx 3.7m/s\)

  !

It's given that AE = BE  therefore triangle ABE is isoceles 

That means that angle A = angle B  therefore angles A + B = 114^o  

The total of the internal angles of a triangle is 180^o  therefore angle BEA = 66^o  

Since angle BEA is 66^o  then so is angle DEC because the two are vertical angles. 

So angle D + angle DEC = 31^o + 66^o = 97^o   

The total of the internal angles of a triangle is 180^o  therefore angle C = 83^o   

_.

cos 2A = 12/13.

f(f(x)) = 3 for just one value.

Hmm, this is an interesting problem. I believe maybe the use of trig identities would help but I'm not sure.

I doubt solving for A is necessary. Most likely I think that cos2A would pop up somehow. Not sure how though

Does anyone know how to do this? I also would like to know.
 

∠1 = ∠4

6x + 25 = 10x - 11

x = 9

∠1 = 6x + 25 = 79º

A rectangular prism has a length of 3, a width of 4, and a height of 12. What is the distance (D) between two opposite corners of the prism? 

The diagonal of the base:   d = sqrt( 3² + 4² ) = 5

The distance D = sqrt( 5² + 12² ) = 13

Let the time of car A = T

The time of car B       = T - 2

40T = 60[T - 2]

T = 6 hours - from the time car A left.

6 - 2 = 4 hours - from the time car B left.

If you solve the equations, you'll find the answer to part (c).

Let the speed of the bus = S

The speed of the train    = S + 25

6S  =  4[S + 25], solve for S

S = 50 mph - speed of the bus

50 + 25 = 75 mph - speed of the train