Answer:
Step-by-step explanation:
Pamela has 15 different books. In how many ways can she place her books on two selves so that there is at least one book on each shelf? (Consider the books in each arrangement to be stacked one next to the other, with the first book on each shelf at the left of the shelf.)
Initially, I thought that this would be fairly straight forward. There are two cases where either shelf could be empty and so we would subtract 2 from the total number of permutations which is obviously 15!. It is obvious now that both of these statements are false.
My previous thoughts didn't take into account the fact that there are two shelves and that the books could be stacked in such a way that 5 are on the top shelf and 10 are on the bottom, or 8 on top with 7 on bottom, or any number of other ways. I believe there are 214 ways the books can be distributed amongst the two shelves (keep in mind that each shelf has to have at least one book, 15−1=14) if the ordering of the books didn't matter, but it does. Is this correct?
Answer:
x = 5
Step-by-step explanation:
Given
= 
( cross- multiply )
16x = 80 ( divide both sides by 16 )
x = 5
17 cm | 60 min | 1 meter = 1020 = 102
-------------------------------------------------------------------------------------------------------
1 min | 1 hour | 100 cm = 100 = 1
102 m/h
Answer:
x=22
Step-by-step explanation:
angle RTS = 5x-40 (isosceles triangle)
angle RTS + angle STU = 180 (straight line)
so 5x-40+5x = 180
10x = 220
x=22
Answer:
So he can travel a total of 90 miles
Step-by-step explanation:
Given:
Total he has to pay = $130
Per week cost = $94
Per mile cost = $0.40
To Find:
No of miles = ?
Solution:
The total he has to pay can be found out by the equation
Total = weekly cost + Miles cost
Now here
Miles cost = total no of miles traveled * per mile cost
This is due to the reason that he is travelling miles and we have to multiply it with it per mile cost to get the total miles cost
so
Let Total miles traveled be x then
Miles cost = $ 0.40 * x
Now we have
Total = weekly cost + Miles cost
Putting in the values we get
130 = 94 + 0.40 *x
subtracting 94 from both sides
130-94 = 94 + 0.40*x - 94
36 = 0.40*x
Dividing both sides by 0.4 we get
90 miles = x
or x= 90 miles
So he can travel a total of 90 miles
