Answer:
![Ratio = 7:6](https://tex.z-dn.net/?f=Ratio%20%3D%207%3A6)
Step-by-step explanation:
Given
Initially
-- coffee
-- coffee
Joe drank 2oz coffee; So, we have:
![Joe = 12oz - 2oz](https://tex.z-dn.net/?f=Joe%20%3D%2012oz%20-%202oz)
--- coffee
Joe added 2oz cream; So, we have:
--- coffee
--- cream
JoAnn added 2oz cream and stirred. So, we have:
--- coffee
--- cream
![Total = 14oz](https://tex.z-dn.net/?f=Total%20%3D%2014oz)
JoAnn drank 2oz from the drink; the amount of drink JoAnn drank is:
![JoAnn = \frac{Cream}{Total}](https://tex.z-dn.net/?f=JoAnn%20%3D%20%5Cfrac%7BCream%7D%7BTotal%7D)
![JoAnn = \frac{2}{14}](https://tex.z-dn.net/?f=JoAnn%20%3D%20%5Cfrac%7B2%7D%7B14%7D)
![JoAnn = \frac{1}{7}](https://tex.z-dn.net/?f=JoAnn%20%3D%20%5Cfrac%7B1%7D%7B7%7D)
Amount of cream left is:
![Amount = [1- \frac{1}{7}] *2](https://tex.z-dn.net/?f=Amount%20%3D%20%5B1-%20%5Cfrac%7B1%7D%7B7%7D%5D%20%2A2)
Take LCM
![Amount = [\frac{7-1}{7}] * 2oz](https://tex.z-dn.net/?f=Amount%20%3D%20%5B%5Cfrac%7B7-1%7D%7B7%7D%5D%20%2A%202oz)
![Amount = \frac{6}{7} * 2oz](https://tex.z-dn.net/?f=Amount%20%3D%20%5Cfrac%7B6%7D%7B7%7D%20%2A%202oz)
![Amount = \frac{12}{7}oz](https://tex.z-dn.net/?f=Amount%20%3D%20%5Cfrac%7B12%7D%7B7%7Doz)
So, we have:
--- cream
cream
The ratio is:
![Ratio = 2:\frac{12}{7}](https://tex.z-dn.net/?f=Ratio%20%3D%202%3A%5Cfrac%7B12%7D%7B7%7D)
Multiply by 7
![Ratio = 14:12](https://tex.z-dn.net/?f=Ratio%20%3D%2014%3A12)
Divide by 2
![Ratio = 7:6](https://tex.z-dn.net/?f=Ratio%20%3D%207%3A6)
Answer:
It's the second choice ⁶√2.
Step-by-step explanation:
Convert to fractional exponents:
√2 = 2^1/2
∛2 = 2^1/3
√2 / ∛2
= 2^1/2 / 2^1/3 = 2^(1/2-1/3)
= 2^(1/6)
Now change back to radicals:
= ⁶√2.
Answer:
The equation is:
![3(2) ^ t=1,536](https://tex.z-dn.net/?f=3%282%29%20%5E%20t%3D1%2C536)
After ![t=9\ months](https://tex.z-dn.net/?f=t%3D9%5C%20months)
Step-by-step explanation:
This situation can be represented by an exponential growth equation of the form
![y = a (b) ^ {t}](https://tex.z-dn.net/?f=y%20%3D%20a%20%28b%29%20%5E%20%7Bt%7D)
Where a is the initial amount
b is the growth rate
t is the time in months
In this case the initial amount is $ 3. Then ![a=3](https://tex.z-dn.net/?f=a%3D3)
if she initially saves $3 and plans to double the amount she saves each month then
![b=2](https://tex.z-dn.net/?f=b%3D2)
The bike Jane wants is $1,536 at the local bike shop.
Then ![y=1,536](https://tex.z-dn.net/?f=y%3D1%2C536)
The equation is:
![3(2) ^ t=1,536](https://tex.z-dn.net/?f=3%282%29%20%5E%20t%3D1%2C536)
Now we solve the equation for t
![3(2) ^ t=1,536](https://tex.z-dn.net/?f=3%282%29%20%5E%20t%3D1%2C536)
![(2) ^ t=\frac{1,536}{3}](https://tex.z-dn.net/?f=%282%29%20%5E%20t%3D%5Cfrac%7B1%2C536%7D%7B3%7D)
![(2) ^ t=512](https://tex.z-dn.net/?f=%282%29%20%5E%20t%3D512)
![log_2(2) ^ t=log_2(512)](https://tex.z-dn.net/?f=log_2%282%29%20%5E%20t%3Dlog_2%28512%29)
![t=log_2(512)](https://tex.z-dn.net/?f=t%3Dlog_2%28512%29)
![t=9\ months](https://tex.z-dn.net/?f=t%3D9%5C%20months)
Answer:
green
Step-by-step explanation:
because they are 14 green balls