Answer:B
Step-by-step explanation:
Answer:
Base of rectangle = 23.25 units (Approx.)
Step-by-step explanation:
Given:
Diagonal of rectangle (Hypotenuse) = 8x
Height of rectangle (Perpendicular) = 2x
Find:
Base of rectangle
Computation:
Base = √Hypotenuse² - Perpendicular²
Base of rectangle = √(8x)² - (2x)²
Base of rectangle = √64x² - 4x²
Base of rectangle = √60x²
Base of rectangle = 7.75x units (Approx.)
If x = 3
Base of rectangle = 7.75x
Base of rectangle = 7.75(3)
Base of rectangle = 23.25 units (Approx.)
Answer:
Step-by-step explanation:
(f o g)(7) = f(g(7))
but g(7) = 7-4 =3
(f o g)(7) = f(g(7)) = f(3) = 3² =9
Answer: 0.2
Step-by-step explanation:
We know that , the probability density function for uniform distribution is given buy :-
, where x is uniformly distributed in interval [a,b].
Given : The time to process a loan application follows a uniform distribution over the range of 8 to 13 days.
Let x denotes the time to process a loan application.
So the probability distribution function of x for interval[8,13] will be :-
Now , the probability that a randomly selected loan application takes longer than 12 days to process will be :-
![\int^{13}_{12}\ f(x)\ dx\\\\=\int^{13}_{12}\dfrac{1}{5}\ dx\\\\=\dfrac{1}{5}[x]^{13}_{12}\\\\=\dfrac{1}{5}(13-12)=\dfrac{1}{5}=0.2](https://tex.z-dn.net/?f=%5Cint%5E%7B13%7D_%7B12%7D%5C%20f%28x%29%5C%20dx%5C%5C%5C%5C%3D%5Cint%5E%7B13%7D_%7B12%7D%5Cdfrac%7B1%7D%7B5%7D%5C%20dx%5C%5C%5C%5C%3D%5Cdfrac%7B1%7D%7B5%7D%5Bx%5D%5E%7B13%7D_%7B12%7D%5C%5C%5C%5C%3D%5Cdfrac%7B1%7D%7B5%7D%2813-12%29%3D%5Cdfrac%7B1%7D%7B5%7D%3D0.2)
Hence, the probability that a randomly selected loan application takes longer than 12 days to process = 0.2
Fine arts= 85 students
History= 51 students
Both subjects=23 students
Only Fine arts=85-23=62 students
Only History=51-23=28 students
Hope you found it helpful.
