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3 years ago

PLEASE HELP 15 POINTS

Mathematics

1 answer:

mart [117]3 years ago

8 0

Area Y Square + Area of triangle
= 10x10+1/2x18x5
=100+9x5
=100+45
=145.

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Radioactive isotopes are commonly used to estimate artifact ages. Let X be the time in years for a Carbon-14 atom to decay to Ni

Alexeev081 [22]

Answer:

a) 1 / years

b) P ( 5000 < X < 6000) = 0.06222

c) 8267 years

d) T_1/2 = 5730.25 years

Step-by-step explanation:

Given:

- The decay constant λ = 1 / 8267

- X is an exponential random Variable

Find:

a. What are the units of What are the units of λ?

b. What is the probability the decay time is between 5000 and 6000 years?

c. Compute SD(X).

d. Compute the median decay time. The result is called the half-life of Carbon-14?

Solution:

- The decay constant λ means the rate at which the C-14 atoms decays into N-14 atom. The rate is expressed in units of 1 / year.

- The random variable X follows an exponential distribution which has a probability mass function and cumulative density functions as follows:

P ( X = t ) = λ*e^(-λ*t)

P ( X = t ) = e^(-t/8267) / 8267

P ( X < t ) = 1 - e^(-λ*t) = 1 - e^(-t/8267)

- The probability of the decay time between years 5000 and 6000 years is:

P ( 5000 < X < 6000) = 1 - e^(-6000/8267) - 1 + e^(-5000/8267)

P ( 5000 < X < 6000) = 0.06222

- The standard deviation of the exponential distribution is given by:

SD(X) = 1 / λ = 8267 years

- The median decay time for an exponential distribution is given by:

T_1/2 = Ln(2) / λ = Ln(2)*8267

T_1/2 = 5730.25 years

3 0

3 years ago

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Which of the following intervals represents the set (1,4) u [2,6]?

fenix001 [56]

Set is a sum of two intervals :(1,4) u [2,6]
In the first interval it is open on both sides so 1 and 4 don't belong to this interval, the second is closed so both 2 and 6 belong to interval and numbers between 2 and 6
We can write it as 1<x $\leq 6$
summing both sets we have one set: (1,6]
so
a) represent our set
b) also represent because all numbers between 4-6 and 6 are in our set
c)also represent, all numbers are in main set
d)also represent

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3 years ago

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netineya [11]

Make the number 693,000 instead of 69,300. The answer would be 86,625.
Hope this helped, I wasn’t to sure on what you were asking though.

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