Answer:
she will insert 6 dollars into the machine
Step-by-step explanation:
Minimum required sample size for a desired margin of error and confidence level when it is a proportion problem: n = (z2÷margin of error2)*p-hat*q-hat
The maximum value of p-hat*q-hat occurs where p-hat = .5 (found by taking the derivative of (p-hat)*(1-p-hat) and setting it equal to 0 to find the maximum. n = ( 2.5762( for 99% confidence interval)÷.0482 )*.5*.5 = 720.028 or 721
For this case we have that by definition of properties of powers and roots, it is fulfilled that:
![\sqrt [n] {a ^ m} = a ^ {\frac {m} {n}}](https://tex.z-dn.net/?f=%5Csqrt%20%5Bn%5D%20%7Ba%20%5E%20m%7D%20%3D%20a%20%5E%20%7B%5Cfrac%20%7Bm%7D%20%7Bn%7D%7D)
So:
![\sqrt [4] {9 ^ {\frac {1} {2} x}} = 9 ^ {\frac {\frac {1} {2}} {4} x} = 9 ^ {\frac {1} {8} x}](https://tex.z-dn.net/?f=%5Csqrt%20%5B4%5D%20%7B9%20%5E%20%7B%5Cfrac%20%7B1%7D%20%7B2%7D%20x%7D%7D%20%3D%209%20%5E%20%7B%5Cfrac%20%7B%5Cfrac%20%7B1%7D%20%7B2%7D%7D%20%7B4%7D%20x%7D%20%3D%209%20%5E%20%7B%5Cfrac%20%7B1%7D%20%7B8%7D%20x%7D)
So, we have to:
![\sqrt [4] {9 ^ {\frac {1} {2} x}} = 9 ^ {\frac {1} {8} x}](https://tex.z-dn.net/?f=%5Csqrt%20%5B4%5D%20%7B9%20%5E%20%7B%5Cfrac%20%7B1%7D%20%7B2%7D%20x%7D%7D%20%3D%209%20%5E%20%7B%5Cfrac%20%7B1%7D%20%7B8%7D%20x%7D)
Answer:

Option B
She planted 23 plants on Tuesday
68-45=23
Check✔️
45+23= 68