Answer:
To divide fractions you have to multiply by the reciprocal of the second fraction:
(1/9)-(1/n) * 9/(1+9)
Now, focus on the left side of the multiplication sign. In order to subtract the 2 fractions, you need a common denominator, 9n. Multiply each fraction to make their denominators equal to 9n:
1/9 * n/n = n/9n
1/n * 9/9 = 9/9n
Now it should look like this: (n/9n) - (9/9n)
Subtract the 2 fractions to get: n-9/9n
The full problem should look like this: (n-9/9n) * 9/(1+9)
To help with simplifying later, you can cancel out the 9 in the denominator of the first fraction and the 9 in the numerator of the second fraction because 9/9 = 1.
Now you have: n-9/n * 1/(1+9)
Multiply across:
Numerator: n-9 * 1 = n-9
Denominator (distribute the n): n * 1+9 = n(1+9)
Your answer is: n-9/n(1+9)
X equals 22
Step by step:
189-147=33
33+33=66
66/3=22
Answer:
745 books are expected to be donated to the library at the end of Month 10
Step-by-step explanation:
There were 80 books donated at the library:
No=80
The number of books donated to a library is increasing by 25% each month:
There were 100 books donatd at the end of Month 1:
N1=100
N1=No+25%No
N1=No+(25/100)No
N1=No+0.25 No
N1=(1+0.25) No
N1=(1.25) No
(1) N1=(1.25)^1 No
N1=(1.25)^1 80
N1=(1.25) 80
N1=100
N2=N1+25%N1
N2=N1+(25/100)N1
N2=N1+0.25 N1
N2=(1+0.25) N1
N2=(1.25) N1
Replacing equation (1) in the equation above:
N2=(1.25) (1.25)^1 No
N2=(1.25)^(1+1) No
(2) N2=(1.25)^2 No
N3=N2+25%N2
N3=N2+(25/100)N2
N3=N2+0.25 N2
N3=(1+0.25) N2
N3=(1.25) N2
Replacing equation (2) in the equation above:
N3=(1.25) (1.25)^2 No
N3=(1.25)^(1+2) No
(3) N3=(1.25)^3 No
In general:
Nt=N(t)=(1.25)^t No
N(t)=(1.25)^t (80)
N(t)=80 (1.25)^t
where t is the number of the month
How many books are expected to be donated to the library at the end of Month 10?
t=10
N(10)=80 (1.25)^10
N(10)=80 (9.313225746)
N(10)=745.0580596
Rounding to the nearest whole number:
N(10)=745
