Answer: 0.0775
Step-by-step explanation:
Given : Mean : 
Standard deviation : 
Sample size : 
Since its normal distribution , then the formula to calculate the z-score is given by :-
For x= 28.2 hours
For x= 30 hours
The P- value = 
Hence, the probabiliy that the average time spent stydying for the sampe was between 28.2 and 30 hours = 0.0775
Area of a triangle is given by 1/2bh where b is the base and h is the perpendicular height of the triangle.
The area is 80x∧5y³ and the height is x∧4y
Thus; 80x∧5y³ = 1/2(x∧4y) b
160x∧5y³ = (x∧4y)b
b = (160x∧5y³)/ x∧4y)
b = 160xy²
Therefore, the base of the triangle is 160xy²
Splitting up the interval of integration into 
subintervals gives the partition
![\left[0,\dfrac1n\right],\left[\dfrac1n,\dfrac2n\right],\ldots,\left[\dfrac{n-1}n,1\right]](https://tex.z-dn.net/?f=%5Cleft%5B0%2C%5Cdfrac1n%5Cright%5D%2C%5Cleft%5B%5Cdfrac1n%2C%5Cdfrac2n%5Cright%5D%2C%5Cldots%2C%5Cleft%5B%5Cdfrac%7Bn-1%7Dn%2C1%5Cright%5D)
Each subinterval has length 
. The right endpoints of each subinterval follow the sequence
with 
. Then the left-endpoint Riemann sum that approximates the definite integral is
and taking the limit as 
gives the area exactly. We have
Let y = f(x)
y = ln(3x)
Exchange place with x and y.
x = ln(3y)
Solve for y.
y = (e^x)/3
Replace y with the inverse notation.
f^(-1) x = (e^x)/3
Done.
