Answer:
392
Step-by-step explanation:
20• 4 + 13•24
80+ 312
Answer: y > 12
Step-by-step explanation:
Answer:
The sum of money received by Ali, Carrie and Bryan is $ 740.
Step-by-step explanation:
At first we translate mathematically each sentence:
(i) <em>Ali, Carrie and Bryan received a sum of money. </em>
- Ali's money.
- Bryan's money.
- Carrie's money.
(ii) <em>Bryan's money was </em>
<em> of Ali's money</em>.
(1)
(iii) <em>The ratio of Ali's money to Carrie's money was 4 : 1</em>.
(2)
(iv) <em>Ali had $ 160 more than Bryan</em>.
(3)
After some algebraic handling, we have the following system of linear equations:
(1b)
(2b)
(3b)
The solution of the system is:
,
, ![c = 100](https://tex.z-dn.net/?f=c%20%3D%20100)
The sum of money is:
![s = a + b + c](https://tex.z-dn.net/?f=s%20%3D%20a%20%2B%20b%20%2B%20c)
![s = 740](https://tex.z-dn.net/?f=s%20%3D%20740)
The sum of money received by Ali, Carrie and Bryan is $ 740.
The first step is to define the system of equations.
Take x and y as the cost of a small box and a large box respectively.
![\begin{gathered} 2x+y=12 \\ 3x+y=16 \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%202x%2By%3D12%20%5C%5C%203x%2By%3D16%20%5Cend%7Bgathered%7D)
Solve the system.
![\begin{gathered} 2x+y=12 \\ y=12-2x \\ 3x+y=16 \\ y=16-3x \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%202x%2By%3D12%20%5C%5C%20y%3D12-2x%20%5C%5C%203x%2By%3D16%20%5C%5C%20y%3D16-3x%20%5Cend%7Bgathered%7D)
![\begin{gathered} 12-2x=16-3x \\ 3x-2x=16-12 \\ x=4 \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%2012-2x%3D16-3x%20%5C%5C%203x-2x%3D16-12%20%5C%5C%20x%3D4%20%5Cend%7Bgathered%7D)
![\begin{gathered} y=12-2x \\ y=12-2\cdot4 \\ y=12-8 \\ y=4 \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20y%3D12-2x%20%5C%5C%20y%3D12-2%5Ccdot4%20%5C%5C%20y%3D12-8%20%5C%5C%20y%3D4%20%5Cend%7Bgathered%7D)
A small box costs $4 and a large box costs $4 too.
Answer:
Step-by-step explanation:
![V=\frac{4\pi r^3}{3}\\ \\ r=\sqrt[3]{\frac{3V}{4\pi}}\\ \\ r=\sqrt[3]{\frac{3141.6}{\pi }}ft\\ \\ r\approx 10ft](https://tex.z-dn.net/?f=V%3D%5Cfrac%7B4%5Cpi%20r%5E3%7D%7B3%7D%5C%5C%20%5C%5C%20r%3D%5Csqrt%5B3%5D%7B%5Cfrac%7B3V%7D%7B4%5Cpi%7D%7D%5C%5C%20%5C%5C%20r%3D%5Csqrt%5B3%5D%7B%5Cfrac%7B3141.6%7D%7B%5Cpi%20%7D%7Dft%5C%5C%20%5C%5C%20r%5Capprox%2010ft)