Cady's cats often share a carton of cat milk. Sammy always drinks 1/3 of the carton, tommy drinks 5/12 of the carton and Suzi dr
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Answer:
Step-by-step explanation:
You need 2 things in order to solve this equation: a trig identity sheet and a unit circle.
You will find when you look on your trig identity sheet that
so we will make that replacement, getting everything in terms of sin:
Now we will get everything on one side of the equals sign, set it equal to 0, and solve it:
We can factor out the sin(theta), since it's common in both terms:
Because of the Zero Product Property, either
or
Look at the unit circle and find which values of theta have a sin ratio of 0 in the interval from 0 to 2pi. They are:
The next equation needs to first be solved for sin(theta):
so
and
Go back to your unit circle and find the values of theta where the sin is -1/2 in the interval. They are:
Answer:
In order to test the hypothesis if the correlation coefficient it's significant we have the following hypothesis:
Null hypothesis:
Alternative hypothesis:
The statistic to check the hypothesis is given by:
And is distributed with n-2 degreed of freedom. df=n-2=10-2=8
For this case the null hypothesis represent that we don't have association betwen the dependent variable Y and the independent variable X and that means r=0. So then the best option for this case is:
The null hypothesis for the Pearson correlation coefficient states that the correlation coefficient is zero
Step-by-step explanation:
Previous concepts
The correlation coefficient is a "statistical measure that calculates the strength of the relationship between the relative movements of two variables". It's denoted by r and its always between -1 and 1.
And in order to calculate the correlation coefficient we can use this formula:
Solution to the problem
In order to test the hypothesis if the correlation coefficient it's significant we have the following hypothesis:
Null hypothesis:
Alternative hypothesis:
The statistic to check the hypothesis is given by:
And is distributed with n-2 degreed of freedom. df=n-2=10-2=8
For this case the null hypothesis represent that we don't have association betwen the dependent variable Y and the independent variable X and that means r=0. So then the best option for this case is:
The null hypothesis for the Pearson correlation coefficient states that the correlation coefficient is zero