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Answer:
<em>M(13)=14.3 gram</em>
Step-by-step explanation:
<u>Exponential Decay Function</u>
The exponential function is used to model natural decaying processes, where the change is proportional to the actual quantity.
An exponential decaying function is expressed as:
Where:
C(t) is the actual value of the function at time t
Co is the initial value of C at t=0
r is the decaying rate, expressed in decimal
The element has an initial mass of Mo=970 grams, the decaying rate is r=27.7% = 0.277 per minute.
The equation of the model is:
Operating:
After t=13 minutes the remaining mass is:
Calculating:
M(13)=14.3 gram
Answer:
0.323 = 32.3% probability that the director chooses 3 boy kittens and 5 girl kittens.
Step-by-step explanation:
The kittens are chosen without replacement, which means that the hypergeometric distribution is used to solve this question.
Hypergeometric distribution:
The probability of x sucesses is given by the following formula:
In which:
x is the number of sucesses.
N is the size of the population.
n is the size of the sample.
k is the total number of desired outcomes.
Combinations formula:
is the number of different combinations of x objects from a set of n elements, given by the following formula.
A TV studio has brought in 8 boy kittens and 10 girl kittens for a cat food commercial.
This means that
We want 3 boys, so
The director is going to choose 8 of these kittens at random to be in the commercial.
This means that
What is the probability that the director chooses 3 boy kittens and 5 girl kittens?
This is P(X = 3).
0.323 = 32.3% probability that the director chooses 3 boy kittens and 5 girl kittens.