Drew collins purchased a new treadmill for $1,662. He made 15% down payment and financed the remainder. What amount did he finan
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Using the binomial distribution, it is found that there is a 0.0108 = 1.08% probability of the coin landing tails up at least nine times.
<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.
In this problem:
- The coin is fair, hence p = 0.5.
- The coin is tossed 10 times, hence n = 10.
The probability that is lands tails up at least nine times is given by:
In which:
Hence:
0.0108 = 1.08% probability of the coin landing tails up at least nine times.
More can be learned about the binomial distribution at brainly.com/question/24863377
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Answer:
The initial mass of the sample was 16 mg.
The mass after 5 weeks will be about 0.0372 mg.
Step-by-step explanation:
We can write an exponential function to model the situation.
Let the initial amount be A. The standard exponential function is given by:
Where r is the rate of growth/decay.
Since the half-life of Palladium-100 is four days, r = 1/2. We will also substitute t/4 for t to to represent one cycle every four days. Therefore:
After 12 days, a sample of Palladium-100 has been reduced to a mass of two milligrams.
Therefore, when x = 12, P(x) = 2. By substitution:
Solve for A. Simplify:
Simplify:
Thus, the initial mass of the sample was:
5 weeks is equivalent to 35 days. Therefore, we can find P(35):
About 0.0372 mg will be left of the original 16 mg sample after 5 weeks.