ANSWER
By simplifying the left hand side using the Pythagorean Identity.
EXPLANATION
The given identity is
Take the left hand side and simplify to get the right hand side.
Collect LCM for the denominators.
Recall the Pythagorean Identity.
This implies that:
We substitute this to get,
Answer:
Null Hypothesis, :
= 1,100 square feet
Alternate Hypothesis, :
< 1,100 square feet
Step-by-step explanation:
We are given that the mean area of several thousand apartments in a new development is advertised to be 1,100 square feet.
A consumer advocate has received numerous complaints that the apartments are smaller than advertised.
<u><em>Let </em></u><u><em> = mean area of several apartments.</em></u>
So, Null Hypothesis, :
= 1,100 square feet
Alternate Hypothesis, :
< 1,100 square feet
Here, <u>null hypothesis states that</u> the mean area of apartments are same as advertised.
On the other hand, <u>alternate hypothesis states that</u> the mean area of apartments are smaller than advertised.
So, this would be the appropriate null and the alternative hypothesis to test this claim.