Answer:
The 95% confidence interval for the population mean is between 17.9 and 20.3 years.
Step-by-step explanation:
We have the standard deviation for the sample, which means that the t-distribution is used to solve this question.
The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So
df = 9 - 1 = 8
95% confidence interval
Now, we have to find a value of T, which is found looking at the t table, with 8 degrees of freedom(y-axis) and a confidence level of
. So we have T = 2.306
The margin of error is:
In which s is the standard deviation of the sample and n is the size of the sample.
The lower end of the interval is the sample mean subtracted by M. So it is 19.1 - 1.2 = 17.9 years.
The upper end of the interval is the sample mean added to M. So it is 19.1 + 1.2 = 20.3 years.
The 95% confidence interval for the population mean is between 17.9 and 20.3 years.
2 13/25 is equivalent to 63/25.
Answer:
In order for me to help you I need to either see a photo or know more about the other angle.
Step-by-step explanation:
<span>(u + 7) + 13 = u + (7 + 13)
The associative property of addition says that you can add numbers regardless of how they're grouped and get the same result. So let's look at the options and see what makes sense.
(u + 7) + 13 = u + (7 + 13)
* This is showing the associative property like the definition states. So this is the correct choice.
21 + 2y = 2y + 21
* This is a demonstration of the commutative property of addition. So it's the wrong choice for this question.
3â‹…(5â‹…x)=(3â‹…5)â‹…x
* This is showing the associative property of multiplication. So it's the wrong choice for this question.
If m + 3 = 18, then 18 = m + 3.
* This is a demonstration of the symmetric property of equality. So for this question, it's the wrong choice.</span>
Answer:
t = 6162 years
Step-by-step explanation:
Apparently you are asked to use the constant k = 0.0001 instead of the most common 0.00012. We'll answer the problem using such number you typed, but make sure that there is no omission in your typing.
The equation to use is that for carbon decay:
![N(t)=N_0\,e^{-0.0001\,\,t}](https://tex.z-dn.net/?f=N%28t%29%3DN_0%5C%2Ce%5E%7B-0.0001%5C%2C%5C%2Ct%7D)
If the skull contains 54% of its original amount of C14, then that means that :
![N(t)=0.54 \,\,N_0](https://tex.z-dn.net/?f=N%28t%29%3D0.54%20%5C%2C%5C%2CN_0)
we use this to solve for the time (t) in our equation:
![0.54\,\,N_0=N_0\,e^{-0.0001\,\,t}\\\frac{0.54\,\,N_0}{N_0}=e^{-0.0001\,\,t}\\0.54=e^{-0.0001\,\,t}\\ln(0.54)=-0.0001\,\,t\\t=\frac{ln(0.54)}{-0.0001} \\t=6161.86\,\,years](https://tex.z-dn.net/?f=0.54%5C%2C%5C%2CN_0%3DN_0%5C%2Ce%5E%7B-0.0001%5C%2C%5C%2Ct%7D%5C%5C%5Cfrac%7B0.54%5C%2C%5C%2CN_0%7D%7BN_0%7D%3De%5E%7B-0.0001%5C%2C%5C%2Ct%7D%5C%5C0.54%3De%5E%7B-0.0001%5C%2C%5C%2Ct%7D%5C%5Cln%280.54%29%3D-0.0001%5C%2C%5C%2Ct%5C%5Ct%3D%5Cfrac%7Bln%280.54%29%7D%7B-0.0001%7D%20%5C%5Ct%3D6161.86%5C%2C%5C%2Cyears)
which rounded to the nearest year as requested gives :
t = 6162 years