Answer:
a) 74.69
b) 0.08% probability that on a given day, 51 radioactive atoms decayed.
Step-by-step explanation:
In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following formula:
In which
x is the number of sucesses
e = 2.71828 is the Euler number
is the mean in the given time interval.
a. Find the mean number of radioactive atoms that decayed in a day.
27,263 atoms in 365 days. The mean is
b. Find the probability that on a given day, 51 radioactive atoms decayed.
This is P(X = 51).
0.08% probability that on a given day, 51 radioactive atoms decayed.
The range is -2,2,-4
hope this helps
4
= =4
-0.1, 0, 0.8, 1.2, 1.6
4 and 9
let their ages be x and x - 5, then in 4 years their ages will be
x + 4 and x - 5 + 4 = x - 1 , and the product is 104, thus
(x + 4)(x - 1) = 104 ← expand factors on left using FOIL
x² + 3x - 4 = 104 ( subtract 104 from both sides )
x² + 3x - 108 = 0 ← in standard form
(x + 12)(x - 9) = 0 ← in factored form
Equate each factor to zero and solve for x
x + 12 = 0 ⇒ x = - 12
x - 9 = 0 ⇒ x = 9
However, x > 0 ⇒ x = 9
Thus
Their present ages are 9 and 9 - 5 = 4