We have the sample size, sample mean and the sample standard deviation. Since the population standard deviation is not know, we will use t-distribution to find the confidence interval.
The critical t value for 95% confidence interval and 63 degrees of freedom is 1.998.
The 95% confidence for the population mean will be:
Thus, the 95% confidence interval for the population mean will be (115,123)
So, option A is the correct answer
Each are divisible by 11 so the ratio equivalent would be 7:9
Hey there! We are given two decimal numbers to compare.
52.311 and 52.31
These two numbers are similar except that 52.311 has another 1 in while 51.31 doesn't.
Keep in mind that 52.31 can also refer to 52.310
So we are comparing 52.311 and 52.310
Since 1 is greater than 0.
52.311 is greater than 52.31 (52.311 > 52.31)
Let me know if you have any questions!
Topic: Decimal Numbers
Answer:
There are two choices for angle Y: 
for 
, 
for 
.
Step-by-step explanation:
There are mistakes in the statement, correct form is now described:
<em>In triangle XYZ, measure of angle X = 49°, XY = 18 and YZ = 14. Find the measure of angle Y:</em>
The line segment XY is opposite to angle Z and the line segment YZ is opposite to angle X. We can determine the length of the line segment XZ by the Law of Cosine:
(1)
If we know that 
, 
and 
, then we have the following second order polynomial:
(2)
By the Quadratic Formula we have the following result:
There are two possible triangles, we can determine the value of angle Y for each by the Law of Cosine again:
1)
![Y = \cos^{-1}\left[\frac{18^{2}+14^{2}-15.193^{2}}{2\cdot (18)\cdot (14)} \right]](https://tex.z-dn.net/?f=Y%20%3D%20%5Ccos%5E%7B-1%7D%5Cleft%5B%5Cfrac%7B18%5E%7B2%7D%2B14%5E%7B2%7D-15.193%5E%7B2%7D%7D%7B2%5Ccdot%20%2818%29%5Ccdot%20%2814%29%7D%20%5Cright%5D)
2)
![Y = \cos^{-1}\left[\frac{18^{2}+14^{2}-8.424^{2}}{2\cdot (18)\cdot (14)} \right]](https://tex.z-dn.net/?f=Y%20%3D%20%5Ccos%5E%7B-1%7D%5Cleft%5B%5Cfrac%7B18%5E%7B2%7D%2B14%5E%7B2%7D-8.424%5E%7B2%7D%7D%7B2%5Ccdot%20%2818%29%5Ccdot%20%2814%29%7D%20%5Cright%5D)
There are two choices for angle Y: for , for .
is the only acute angle whose sin = 1/2. Therefore, cos (
) =
