Ascientist is conducting an experiment designed to produce a gene mutation in bacteria. the chance that his experiment will cause a gene mutation in a bacterial colony is 70%. he uses identical treatment on 10 isolated colonies of the bacteria. the scientist considers his results satisfactory if the mutation occurs in at least 8 of the colonies.

let x be a random variable representing the number of bacterial colonies that have mutated.

a.) explain why x is a binomial random variable:
-specify, in words, what is a trial in this scenario
-identify n (the number of trials)
-specify, in words, which outcome of a trial would be defined as a "success"
-explain why p (is the probability of success) is the same in every trial
-identify p (the probability of success)

b.) what is the probability the scientist will consider his results satisfactory?

c.) what is the expected value of mutated bacterial culture in this sample?

d.) fill in the blanks of the following sentence:
"if the gene mutation experiment was repeated many times, each time using a sample of 20 isolated bacterial cultures, the average number of mutated cultures in a sample would approach "

answer: (-6,3)

step-by-step explanation:

the answer is a.

135 and 80

step-by-step explanation:

answer is c

step-by-step explanation:

81/12=324/x

x=48

hello!

to begin with, we're given that on earth, a rock weighs 20 pounds, and while on jupiter, that same rock weighs 42 pounds. now, we're trying to find the weight of a rock that weighs 10.5 pounds on earth, on jupiter.

to solve this, first, set up a proportion, cross-multiply, and solve it algebraically.

setting up the proportion is the hardest and the most confusing part of the problem, but it's simple.

if on earth, the rock weighs 20 lbs, and on jupiter it weighs 42 lbs, our first part of our proportion is 20/42 lbs. the second part has to be equal to each other. this means that 10.5 has to be on the numerator of the fraction, and x, the value we're trying to find, has to be on the denominator. remember that the rock weighs 10.5 lbs on earth, and we're trying to find the weight of it on jupiter (which is x).

20/42 = 10.5/x

next, you would cross-multiply.

20x = 42(10.5)

20x = 441

now, solve it algebraically by using division.

x = 22.05 lbs

this can be rounded to 22.1 lbs.

therefore, the weight of the rock on jupiter is 22.1 lbs, the fourth choice.