Hello,
The relationship between the number of hours a plumber works and the total work fee she charges is proportional. Her fee for 5 hours of work is $350.
Which of the following could be combinations of values for the plumber's work hours and total work fee she charges?
Solution:
Find similar ratios to 5/350
Similar Ratios,
1/70
2/140
3/210
3.5/245
4/280
6/420
7.25/507.50
Answers:
B) 3.5 hours and $245
C) 6 hours and $420
D) 7.25 hours and $507.50
I got 23 u might want to check it tho
Answer:
d
Step-by-step explanation:
The answer is 0.3 cause when you subtract all of it you can get it
![\ln x](https://tex.z-dn.net/?f=%5Cln%20x)
is continuous over its domain, all real
![x>0](https://tex.z-dn.net/?f=x%3E0)
.
Meanwhile,
![\cos^{-1}y](https://tex.z-dn.net/?f=%5Ccos%5E%7B-1%7Dy)
is defined for real
![-1\le y\le1](https://tex.z-dn.net/?f=-1%5Cle%20y%5Cle1)
.
If
![y=\ln x](https://tex.z-dn.net/?f=y%3D%5Cln%20x)
, then we have
![-1\le \ln x\le1\implies \dfrac1e\le x\le e](https://tex.z-dn.net/?f=-1%5Cle%20%5Cln%20x%5Cle1%5Cimplies%20%5Cdfrac1e%5Cle%20x%5Cle%20e)
as the domain of
![\cos^{-1}(\ln x)](https://tex.z-dn.net/?f=%5Ccos%5E%7B-1%7D%28%5Cln%20x%29)
.
We know that if
![f](https://tex.z-dn.net/?f=f)
and
![g](https://tex.z-dn.net/?f=g)
are continuous functions, then so is the composite function
![f\circ g](https://tex.z-dn.net/?f=f%5Ccirc%20g)
.
Both
![\cos^{-1}y](https://tex.z-dn.net/?f=%5Ccos%5E%7B-1%7Dy)
and
![\ln x](https://tex.z-dn.net/?f=%5Cln%20x)
are continuous on their domains (excluding the endpoints in the case of
![\cos^{-1}y](https://tex.z-dn.net/?f=%5Ccos%5E%7B-1%7Dy)
), which means
![\cos^{-1}(\ln x)](https://tex.z-dn.net/?f=%5Ccos%5E%7B-1%7D%28%5Cln%20x%29)
is continuous over
![\dfrac1e](https://tex.z-dn.net/?f=%5Cdfrac1e%3Cx%3Ce)
.