Answer:
The duration of the randomly selected class is 52.6 minutes.
Step-by-step explanation:
The random variable <em>X</em> is defined as the duration of a professor's class.
It is provided that, 
.
The pdf of <em>X</em> is:
It is provided that the probability that the duration of the class is longer than <em>c</em> number of minutes is 0.468.
That is, P (X > c) = 0.468.
Compute the value of <em>c</em> as follows:
![P(X>c)=0.468\\\\\int\limits^{55.5}_{c}{\frac{1}{55.5-49.2}}=0.468\\\\\frac{1}{6.3}\times [x]^{55.5}_{c}=0.468\\\\55.5-c=2.9484\\\\x=52.5516\\\\x\approx 52.6](https://tex.z-dn.net/?f=P%28X%3Ec%29%3D0.468%5C%5C%5C%5C%5Cint%5Climits%5E%7B55.5%7D_%7Bc%7D%7B%5Cfrac%7B1%7D%7B55.5-49.2%7D%7D%3D0.468%5C%5C%5C%5C%5Cfrac%7B1%7D%7B6.3%7D%5Ctimes%20%5Bx%5D%5E%7B55.5%7D_%7Bc%7D%3D0.468%5C%5C%5C%5C55.5-c%3D2.9484%5C%5C%5C%5Cx%3D52.5516%5C%5C%5C%5Cx%5Capprox%2052.6)
Thus, the duration of the randomly selected class is 52.6 minutes.
23. not equivalent because the first row 3x-9y=5 then if you multiplied this equation by 2 it will be 2(3x-9y) = 2(5) so 6x-18y= 10 not 6x-9y=10
24.equivalent because the second row 2y-6x=8 multiplied by 2 is 2(2y-6x)= 2(8) so 4y-12x=16
25. equivalent because the first row 5x+3y=19 multiplied by 2 is 2(5x+3y) = 2(19) SO 10X+6Y=38 and the second row 2x+4y=20 multiplied by 5 is 5(2x+4y)= 5(20) so 10x+20y=100
The adjacent interior is 4
Integer
Rational
(its not a whole number. Whole numbers are 0 or positive.)
