Answer:
D
it is equivalent to the expression
Answer:
The rate at which both of them are moving apart is 4.9761 ft/sec.
Step-by-step explanation:
Given:
Rate at which the woman is walking,
= 3 ft/sec
Rate at which the man is walking,
= 2 ft/sec
Collective rate of both,
= 5 ft/sec
Woman starts walking after 5 mins so we have to consider total time traveled by man as (5+15) min = 20 min
Now,
Distance traveled by man and woman are
and
ft respectively.
⇒ 
⇒ 
As we see in the diagram (attachment) that it forms a right angled triangle and we have to calculate
.
Lets calculate h.
Applying Pythagoras formula.
⇒
⇒ 
Now differentiating the Pythagoras formula we can calculate the rate at which both of them are moving apart.
Differentiating with respect to time.
⇒ 
⇒ 
⇒
...as 
⇒ Plugging the values.
⇒
...as
ft/sec
⇒
ft/sec
So the rate from which man and woman moving apart is 4.9761 ft/sec.
The formula of this equation would be

* 1.026^16 = 7,160.06
So from this equation we know that

Now we need to find the value of x, we need to multiply

* 1.026 16 times. Which will bring us to your answer. $
4,748.53
I'm assuming a 5-card hand being dealt from a standard 52-card deck, and that there are no wild cards.
A full house is made up of a 3-of-a-kind and a 2-pair, both of different values since a 5-of-a-kind is impossible without wild cards.
Suppose we fix both card values, say aces and 2s. We get a full house if we are dealt 2 aces and 3 2s, or 3 aces and 2 2s.
The number of ways of drawing 2 aces and 3 2s is

and the number of ways of drawing 3 aces and 2 2s is the same,

so that for any two card values involved, there are 2*24 = 48 ways of getting a full house.
Now, count how many ways there are of doing this for any two choices of card value. Of 13 possible values, we are picking 2, so the total number of ways of getting a full house for any 2 values is

The total number of hands that can be drawn is

Then the probability of getting a full house is
