Answer:
The correct option is the last option d.) y = negative 3 plus-or-minus StartRoot 5 x + seven-halves EndRoot
Step-by-step explanation:
the given equation is 
Therefore we can write 
To find the inverse of the above function let us replace x with y and y with x.
Therefore we get
Now we write the above equation with only y on the Left hand side and we will obtain the inverse of the given function
Therefore the correct option is the last option d.) y = negative 3 plus-or-minus StartRoot 5 x + seven-halves EndRoot , 
15x+40=115
15x+40-40=115-40
15x=75
15/15 x=75/15
x= 5
Answer: The greatest number of playlist Katherine can make =8
Each of playlist will have 4 pop songs and 9 rock songs.
Step-by-step explanation:
Given: The number of pop songs Katherine has= 32
The number of rock songs Katherine has= 72
If she want to make playlist such that in each playlist there is equal number of pop and rock songs, we need to find the GCF(greatest common factor) of 32 and 72.
We know that 
We can see the GCF(32,72)=
Hence, the greatest number of playlist Katherine can make =8
The number of pop songs= 
the number of rock songs=
Each of playlist will have 4 pop songs and 9 rock songs.
If all 25 questions are different,
When order of selection counts:
P(25,7)
=25!/(25-7)!
=15511210043330985984000000/6402373705728000
=2422728000
When order of selection does not count count:
C(25,7)
=25!/(7!*(25-7)!)
=15511210043330985984000000/(6402373705728000*5040)
=480700
