Answer:
The value of the car after 5 years is $ 13,035 to the nearest dollar.
Step-by-step explanation:
The formula for depreciation is
where is the beginning price of the asset,
is the annual rate of depreciation written as a decimal,
is the number of years, and V is the value after t years.
Now substitute all these values into the formula to get,
This simplifies to,
The value of the car after 5 years is $ 13,035 to the nearest dollar.
Answer:
<em>Carbon-14 will take 19,035 years to decay to 10 percent.</em>
Step-by-step explanation:
<u>Exponential Decay Function</u>
A radioactive half-life refers to the amount of time it takes for half of the original isotope to decay.
An exponential decay can be described by the following formula:
Where:
No = The quantity of the substance that will decay.
N(t) = The quantity that still remains and has not yet decayed after a time t
= The decay constant.
One important parameter related to radioactive decay is the half-life:
If we know the value of the half-life, we can calculate the decay constant:
Carbon-14 has a half-life of 5,730 years, thus:
The equation of the remaining quantity of Carbon-14 is:
We need to calculate the time required for the original amout to reach 10%, thus N(t)=0.10No
Simplifying:
Taking logarithms:
Solving for t:
Carbon-14 will take 19,035 years to decay to 10 percent.
Answer:
a)
b)
And adding these values we got:
c) We can find the expected value given by:
And the standard deviation would be:
We can use the approximation to the normal distribution and we have at leat 95% of the data within 2 deviations from the mean. And the lower limit for this case would be:
And then we can consider a value of 18 as unusual lower for this case.
Step-by-step explanation:
Let X the random variable of interest "number cleared by arrest or exceptional", on this case we can model this variable with this distribution:
The probability mass function for the Binomial distribution is given as:
Where (nCx) means combinatory and it's given by this formula:
Part a
We want this probability:
Part b
We want this probability:
We can find the individual probabilities:
And adding these values we got:
Part c
We can find the expected value given by:
And the standard deviation would be:
We can use the approximation to the normal distribution and we have at leat 95% of the data within 2 deviations from the mean. And the lower limit for this case would be:
And then we can consider a value of 18 as unusual lower for this case.