Will mark brainiest!!
Only answer questions a and b

f1 ( x ) valid pdf . f2 ( x ) is invalid pdf

k = 1 / 18 , i ) 0.6133 , ii ) 0.84792

Step-by-step explanation:

Solution:-

A) The two pdfs ( f1 ( x ) and f2 ( x ) ) are given as follows:

- To check the legitimacy of a continuous probability density function the area under the curve over the domain must be equal to 1. In other words the following:

- We will perform integration of each given pdf as follows:

f1 ( x ) is a valid pdf; however, f2 ( x ) is not a valid pdf.

B)

- A random variable ( X ) denotes the resistance of a randomly chosen resistor, and the pdf is given as follows:

                       if  8 ≤ x ≤ 10

                               0  otherwise.

- To determine the value of ( k ) we will impose the condition of validity of a probability function as follows:

- Evaluate the integral as follows:

                     ... Answer

- To determine the CDF of the given probability distribution we will integrate the pdf from the initial point ( 8 ) to a respective value ( x ) as follows:

To determine the probability p ( 8.6 ≤ x ≤ 9.8 ) we will utilize the cdf as follows:

                   p ( 8.6 ≤ x ≤ 9.8 ) = F ( 9.8 ) - F ( 8.6 )

                   p ( 8.6 ≤ x ≤ 9.8 ) =

ii) To determine the conditional probability we will utilize the basic formula as follows:

               p ( x ≤ 9.8  | x ≥ 8.6 ) = p ( 8.6 ≤ x ≤ 9.8 ) / p ( x ≥ 8.6 )

               p ( x ≤ 9.8  | x ≥ 8.6 ) = 0.61333 / [ 1 - p ( x ≤ 8.6 ) ]

               p ( x ≤ 9.8  | x ≥ 8.6 ) = 0.61333 / [ 1 - 0.27666 ]

               p ( x ≤ 9.8  | x ≥ 8.6 ) = 0.61333 / [ 0.72333 ]

               p ( x ≤ 9.8  | x ≥ 8.6 ) = 0.84792 ... answer

Hope it helps! ;)

0.6, 3/5, and 6% are the 3 same portion.

but, when they're all changed to a decimal they would equal to 0.6.

hope this , good luck!

(2x + 16) + (x) = 180

step-by-step explanation:

given,

abcd is a quadrilateral inscribed in a circle

angle a is labeled x plus 16, (x + 16)

angle b is labeled x degrees, (x)

angle c is labeled 6x minus 4, (6x – 4)

angle d is labeled 2x plus 16, (2x + 16)

what equation can be used to solve for angle b?

we know that the sum of the opposite angles of a simple quadrilateral inscribed in a circle is 180 degrees.

angle b is opposite angle d

therefore, angle b + angle d = 180

(x) + (2x + 16) = 180 

same as (2x + 16) + (x) = 180