Amount of hours worked = h
7h = 91
h = 13 hours worked that week
h (is greater to or equal to) 15
7 x 15 would equal 105 which means the most she can make in a week is $105
Answer:
C, D, B
Step-by-step explanation:
the mode is if a number is repeated more than one time
EX. 15, 23, 15, 23, 15
C because 15 is repeated 3 times and 19 is too.
D because 42 is repeated 2 times and so is 18.
B because 87 is repeated 2 times and 32 is too.
Answer:
General Solution is
and the particular solution is 
Step-by-step explanation:

This is a linear diffrential equation of type
..................(i)
here 

The solution of equation i is given by

we have ![e^{\int p(x)dx}=e^{\int \frac{-2}{x}dx}\\\\e^{\int \frac{-2}{x}dx}=e^{-2ln(x)}\\\\=e^{ln(x^{-2})}\\\\=\frac{1}{x^{2} } \\\\\because e^{ln(f(x))}=f(x)]\\\\Thus\\\\e^{\int p(x)dx}=\frac{1}{x^{2}}](https://tex.z-dn.net/?f=e%5E%7B%5Cint%20p%28x%29dx%7D%3De%5E%7B%5Cint%20%5Cfrac%7B-2%7D%7Bx%7Ddx%7D%5C%5C%5C%5Ce%5E%7B%5Cint%20%5Cfrac%7B-2%7D%7Bx%7Ddx%7D%3De%5E%7B-2ln%28x%29%7D%5C%5C%5C%5C%3De%5E%7Bln%28x%5E%7B-2%7D%29%7D%5C%5C%5C%5C%3D%5Cfrac%7B1%7D%7Bx%5E%7B2%7D%20%7D%20%5C%5C%5C%5C%5Cbecause%20e%5E%7Bln%28f%28x%29%29%7D%3Df%28x%29%5D%5C%5C%5C%5CThus%5C%5C%5C%5Ce%5E%7B%5Cint%20p%28x%29dx%7D%3D%5Cfrac%7B1%7D%7Bx%5E%7B2%7D%7D)
Thus the solution becomes


This is the general solution now to find the particular solution we put value of x=2 for which y=6
we have 
Thus solving for c we get c = -1/2
Thus particular solution becomes

15
Explanation:
you just divide 90 by 6
Answer: The required derivative is 
Step-by-step explanation:
Since we have given that
![y=\ln[x(2x+3)^2]](https://tex.z-dn.net/?f=y%3D%5Cln%5Bx%282x%2B3%29%5E2%5D)
Differentiating log function w.r.t. x, we get that
![\dfrac{dy}{dx}=\dfrac{1}{[x(2x+3)^2]}\times [x'(2x+3)^2+(2x+3)^2'x]\\\\\dfrac{dy}{dx}=\dfrac{1}{[x(2x+3)^2]}\times [(2x+3)^2+2x(2x+3)]\\\\\dfrac{dy}{dx}=\dfrac{4x^2+9+12x+4x^2+6x}{x(2x+3)^2}\\\\\dfrac{dy}{dx}=\dfrac{8x^2+18x+9}{x(2x+3)^2}](https://tex.z-dn.net/?f=%5Cdfrac%7Bdy%7D%7Bdx%7D%3D%5Cdfrac%7B1%7D%7B%5Bx%282x%2B3%29%5E2%5D%7D%5Ctimes%20%5Bx%27%282x%2B3%29%5E2%2B%282x%2B3%29%5E2%27x%5D%5C%5C%5C%5C%5Cdfrac%7Bdy%7D%7Bdx%7D%3D%5Cdfrac%7B1%7D%7B%5Bx%282x%2B3%29%5E2%5D%7D%5Ctimes%20%5B%282x%2B3%29%5E2%2B2x%282x%2B3%29%5D%5C%5C%5C%5C%5Cdfrac%7Bdy%7D%7Bdx%7D%3D%5Cdfrac%7B4x%5E2%2B9%2B12x%2B4x%5E2%2B6x%7D%7Bx%282x%2B3%29%5E2%7D%5C%5C%5C%5C%5Cdfrac%7Bdy%7D%7Bdx%7D%3D%5Cdfrac%7B8x%5E2%2B18x%2B9%7D%7Bx%282x%2B3%29%5E2%7D)
Hence, the required derivative is 