Your friend decides to flip a coin repeatedly to analyze whether the probability of a head on each flip is 1/2. He flips the coin 20 times and observes a head 12 times. He concludes that the probability of a head for this coin is 12/20=0.60 and the coin is not balanced. What is a correct interpretation?

A. Probability doesn't prove anything about the coin because probability is subjective
B. A coin is balanced as long as the probability of each outcome is closer to 0.5 than it is to 1 or 0.
C. Environmental conditions such as temperature and humidity can cause the results of flipping a balanced coin to be skewed and thus appear unbalanced.
D. In the short run, the proportion of a given outcome can fluctuate a lot. A long run of observations is needed to accurately calculate the probability of flipping heads.

47 - 90 = 43

43 - 180 = x

x = 137

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.