Answer:
- 32,283 years old
- 31,718 years old
Step-by-step explanation:
If h is the half-life of the radioactive substance, then the proportion remaining after t years is ...
k = (1/2)^(t/h)
We can find the value of t using logarithms:
log(k) = (t/h)·log(1/2)
t = h·log(k)/log(1/2)
__
a) For k = 2% and h = 5720 years, we have ...
t = 5720·log(.02)/log(.5) ≈ 5720·5.64386
t ≈ 32,283 . . . . years old
__
b) For k = 2% and h = 5620 years, we have ...
t ≈ 5620·5.64386 ≈ 31,718 . . . . years old
_____
Note the proportionality of age to half-life. Once we found the multiplier corresponding to 2% remaining, we can use that for any estimate of the half-life.
Answer:
79716.98
Step-by-step explanation:
Answer:
a) A sample size of 5615 is needed.
b) 0.012
Step-by-step explanation:
In a sample with a number n of people surveyed with a probability of a success of 
, and a confidence level of 
, we have the following confidence interval of proportions.
In which
z is the zscore that has a pvalue of 
.
The margin of error is:
99.5% confidence level
So 
, z is the value of Z that has a pvalue of 
, so 
.
(a) Past studies suggest that this proportion will be about 0.2. Find the sample size needed if the margin of the error of the confidence interval is to be about 0.015.
This is n for which M = 0.015.
We have that 
A sample size of 5615 is needed.
(b) Using the sample size above, when the sample is actually contacted, 12% of the sample say they are not satisfied. What is the margin of the error of the confidence interval?
Now 
.
We have to find M.
Using a scale that has increments that are somewhat large, you could get an error if you reach half of the measuring unit. This is because when you arrive at a measurement greater than half of the measuring unit, you would have to round it up. Therefore, the greatest possible error when measuring to the nearest quarter of an inch is 1/8 inch. The greatest possible error when measuring to the nearest quarter of an inch is how the reader reads the measurement. Sometimes, we base our answers to what we can see and what we see may be different from others.
Answer:
The center-radius form of the circle equation is in the format (x – h)2 + (y – k)2 = r2, with the center being at the point (h, k) and the radius being "r". This form of the equation is helpful, since you can easily find the center and the radius.
Step-by-step explanation:
hope this helps you :)
