In the manufacture of electroluminescent lamps, several different layers of ink are deposited onto a plastic substrate. the thickness of these layers is critical if specifications regarding the final color and intensity of light are to be met. let x and y denote the thickness of two different layers of ink. it is known that x is normally distributed with a mean of 0.1 mm and a standard deviation of 0.00031 mm, and y is also normally distributed with a mean of 0.23 mm and a standard deviation of 0.00017 mm. assume that these variables are independent. a. if a particular lamp is made up of these two inks only, what is the probability that the total ink thickness is less than 0.2337 mm? b. a lamp with a total ink thickness exceeding 0.2405 mm lacks the uniformity of color that the customer demands. find the probability that a randomly selected lamp fails to meet customer specifications.

i believe the correct answer is option 4.principalities were small territories that were run by russian rulers.

which statement correctly defines principalities in northern asia in the 1200s? principalities were small territories that were run by russian rulers.

hope i could ! : )

(a) common ratio in the given sequence is, 3

(b) push ups will do kendall do on the 20th week

step-by-step explanation:

geometric sequence is a sequence of numbers that follows a pattern were the next term is found by multiplying by a constant called the common ratio(r)

(a)

given the sequence: 6 , 18 , 54 , 162 ,

this sequence is geometric sequence where each term is 3 times the previous term.

therefore,

common ratio(r) = 3.

(b)

a formula for nth term of geometric sequence is given by;

,   where r is the common ratio between the successive terms and is the first term,

to find how many push ups will kendall do on the 20th week.

here. n = 20th term.

in the given sequence first term

then;

simplify:

therefore, push ups will do kendall do on the 20th week

(5x-1)^2= (5x)^2-2(5x)×1+(1)^2=25x^2-10x+1