Answer:
Approximately 0.333
Step-by-step explanation:
If we graph this we see that the line goes over the y-axis at (0,0.333)
*I use desmos graphing calculator*
Using the binomial distribution, the probabilities are given as follows:
a) 0.37 = 37%.
b) 0.5065 = 50.65%.
c) 0.3260 = 32.60%.
<h3>What is the binomial distribution formula?</h3>
The formula is:


The parameters are:
- x is the number of successes.
- n is the number of trials.
- p is the probability of a success on a single trial.
For this problem, the fixed parameter is:
p = 0.37.
Item a:
The probability is P(X = 1) when n = 1, hence:


Item b:
The probability is P(X = 3) when n = 3, hence:


Item c:
The probability is P(X = 2) when n = 4, hence:


More can be learned about the binomial distribution at brainly.com/question/24863377
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Answer:
Step-by-step explanation:
For a first order decay, fraction remaining = 0.5n where n = number of half lives elapsed.
fraction remaining = 55% = 0.55
0.55 = 0.5n
log 0.55 = n log 0.5
-0.2596 = -0.301 n
n = 0.8625 = # of half lives elapsed
0.8625 half lives x 2.5 billion years/half live = 2.16 billion years have elapsed = age of the rock
b) 0.15 = 0.5n
log 0.15 = n log 0.5
-0.824 = -0.301 n
n = 2.74 half lives
2.5 billion years/half life x 2.74 half lives = 6.85 billion years = age of rock
Set each of the binomials equal to zero and solve for x. The two values will be the zeros of the equation:
(x-4) = 0 (x+11) = 0
x-4 = 0 x + 11 = 0
x = 4 x = -11
The zeros of the equation are -11 and 4