![\bf \textit{logarithm of factors}\\\\ log_{{ a}}(xy)\implies log_{{ a}}(x)+log_{{ a}}(y)\\\\ -------------------------------\\\\ ln(x-6)+ln(x+10)=ln(x-15) \\\\\\ ln[(x-6)(x+10)]=ln(x-15)\implies (x-6)(x+10)=x-15 \\\\\\ x^2-5x-6=x-15\implies x^2-6x+9=0 \\\\\\ (x-3)^2=0\implies \boxed{x=3}](https://tex.z-dn.net/?f=%5Cbf%20%5Ctextit%7Blogarithm%20of%20factors%7D%5C%5C%5C%5C%0Alog_%7B%7B%20%20a%7D%7D%28xy%29%5Cimplies%20log_%7B%7B%20%20a%7D%7D%28x%29%2Blog_%7B%7B%20%20a%7D%7D%28y%29%5C%5C%5C%5C%0A-------------------------------%5C%5C%5C%5C%0Aln%28x-6%29%2Bln%28x%2B10%29%3Dln%28x-15%29%0A%5C%5C%5C%5C%5C%5C%0Aln%5B%28x-6%29%28x%2B10%29%5D%3Dln%28x-15%29%5Cimplies%20%28x-6%29%28x%2B10%29%3Dx-15%0A%5C%5C%5C%5C%5C%5C%0Ax%5E2-5x-6%3Dx-15%5Cimplies%20x%5E2-6x%2B9%3D0%0A%5C%5C%5C%5C%5C%5C%0A%28x-3%29%5E2%3D0%5Cimplies%20%5Cboxed%7Bx%3D3%7D)
ok.. now, if we use that on say ln(x-15), we end up with

.
now, there's no exponent whatsoever, that would give us a negative result for a base of "e", namely, x = 3 is NOT in the domain for ln(), so the system is
inconsistent, or has
no solution.
Answer:
FAIL TO REJECT
NOT ENOUGH
Step-by-step explanation:
Given a Pvalue of 0.32
Decision region :
When Pvalue < α ; Reject the Null and conclude that there is significant or enough evidence to accept the alternative hypothesis.
Otherwise, fail to reject reject the null and conclude that, there is not enough evidence to accept the alternative hypothesis
Therefore, for the scenario above, where Pvalue = 0.32
Possible α values are ; 0.1, 0.05, 0.01
For all α - values listed, the Pvalue is greater than α
Pvalue > α ; Hence, FAIL TO REJECT the Null.
Conclusion :
There is NOT ENOUGH evidence to support the alternative that the proportion of students who have ear infection at one school and the other is different.
Answer:
The slope is 1/2
Step-by-step explanation:
Hi!
Disclaimer: Just for this response, I'm going to write it the same way you write a fraction out on paper just so it's easier to see.
First, you plot the two coordinates on the graph:
(0,0) and (2,1)
The formula for slope is 
Now we plug in numbers accordingly:

Simplify:

Simplify:

Let me know if you have any questions
Answer:
greater than
Step-by-step explanation:
7/8 is greater than 4/8