A group of people were asked what condiments they use on their hot dogs. They were asked whether they use ketchup, mustard, both ketchup and mustard, or neither ketchup nor mustard. The attached table shows the probabilities of the results.
Let A represent using ketchup and B represent using mustard.

Which statement is true?

A. Using ketchup and using mustard are independent events because P(A|B)≠P(A) and P(B|A)≠P(B)

B. Using ketchup and using mustard are not independent events because P(A|B)=P(A) and P(B|A)=P(B) .

C. Using ketchup and using mustard are not independent events because P(A|B)≠P(A) and P(B|A)≠P(B) .

D. Using ketchup and using mustard are independent events because P(A|B)=P(A)P(A|B)=P(A) and P(B|A)=P(B) .

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step-by-step explanation:

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step-by-step explanation:

(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