CPhill

Ok

The girls have to come first in line.....Well, we have 4 ways to choose the first one, 3 ways to choose the second one, 2 ways to choose the third one and only 1 way to select  the fourth one.

So......4*3*2*1  = 4!  =  24 ways     (I think we talked a little bit about factorials earlier, didn't we??)

And, note that the boys come next...and we have 2 ways to choose the first one and 1 way to choose the second one.   So ...  2 * 1 = 2! = 2 ways

So....the total ways to line up the girls times the total ways to line up the boys is just.....24 * 2  = 48 ways

OK, rosala.....

Remember that we can multiply in any order that we'd like......so, for instance, 3*4*5 = 5*3*4

So look at this........ 3*w⁵*7*w⁵   is really just the same thing as 3*7 *w⁵ * w⁵

So we have 21*w⁵*w⁵     ....   and remember by a property of exponents (or powers) that aⁿ * aⁿ = aⁿ⁺ⁿ

Therefore, w⁵ * w⁵  =  w⁵⁺⁵ = w¹⁰

And putting this all together, we get ...... 21w¹⁰

Does that make sense??

11pi/6 + 3pi/4 = 7pi/12 

Let's get a common denominator and then add the fractions.

So we have

22pi/6 + 9pi/12 = 31pi/12 

But, notice something....that this is just 

24pi/12 + 7pi/12  .....And 24pi/12 is just 2pi.

So, in effect, 31pi/12 is the same "reference" angle as 7pi/12. We've just added another full rotation (2pi) to 7pi/12...

Does that make sense???

As of late, the probability that I get a correct answer on a probabilty problem has been something less than 1, but I'm still gonna' give this one a try.....

The probabilty of picking the first place finisher correctly is just 1/39. And the probabilty of picking a second place finisher correctly (given that we've picked the first place finsher correctly) is just 1/38. And the probability that we pick the third place finisher correctly is just 1/37.

So ....  (1/39)*(1/38)*(1/37)  = 1/54834

Another way to look at this is count all the sets that are possible when we choose any 3 people from 39. But since order matters within the set, we must use a permutation. Thus, (39 P 3) = 54834. And since only one of these sets is "correct," we have 1/54834 chances of choosing this set.

We can arrange the girls in 4! ways = 24 ways, and the boys in 2! ways = 2 ways.

So, 24 * 2 = 48 ways

Thanks, for adding that, Anonymous......yes, I was assuming the same infinity order.........

Believe it or not - in general - it's still infinity.......to see this........consider the set of positive even integers on the number line and the set of positive odd integers on the number line. Both sets  are infinite. And if we add them together, the result is just another infinite set - the set of ALL positive integers. This set is also "countable" because we can assign a number to each member. There are also "uncountable" infinite sets. The set of all real numbers that exist between 0 and 1 is an example of an "uncountable" set....!!!!

The perimeter is given by:  2(w + L)....so we have

20 = 2(W + 6)      divide by 2 on both sides

10 = W + 6           subtract 6 on both sides

4 = W

So, the width is 4 meters.

First, we would look to the third digit to the right of the decimal. If it's 5 or greater, we round the second digit to the right of the decimal up. Otherwise, the second digit to the right of the decimal remains as it is.

And since the third digit to the right of the decimal is "8," we would round the "5" up to a "6."

So we have   ....    7.96

2a<2b  implies that  a<b    ...  and .....  2b<2c implies that b<c

So.......

a<b and b<c   and by the transitive property of inequality

a<c