<h3>
Answer: 1</h3>
Explanation:
1/3 is the same as 2/6
Imagine cutting a cake into thirds, then cutting each piece in two parts, so you'll have 6 pieces total. If you shade one third of the cake, then this is the same as shading 2/6 of a cake. The diagram shows this below.
Therefore 4/6 + 1/3 is the same as 4/6 + 2/6
At this point, we add the numerators over the common denominator
4/6 + 2/6 = (4+2)/6 = 6/6 = 1
Meaning we get a full cake since 4/6 is four slices and 2/6 is another two slices leading to 4+2 = 6 slices total out of the 6 overall.
We invested $7000 invested in two accounts, we don't know how much exactly is in each account, therefore we will assign variables to these amounts. The amount invested in the "8%" account is "x", while the other one is "y". The sum of these two numbers must be equal to $7000, therefore:

The sum of interest of each account should be equal to 580, therefore:

We need to solve the system in order to determine the values.

Now we can replace the value of "x" in the first equation to determine the value of "y".

The values are 6500 in the 8% account and 500 in the 12% account.
Answer:
455 miles driven in 7hrs
Step-by-step explanation:
715miles divided by 11 hrs= 65 miles per hr
65 miles multiplied by 7 hrs= 455 miles driven in 7hrs
Answer:

Step-by-step explanation:

Applying the Laplace transform:
![\mathcal{L}[y'']+5\mathcal{L}[y']+4\mathcal{L}[y']=0](https://tex.z-dn.net/?f=%5Cmathcal%7BL%7D%5By%27%27%5D%2B5%5Cmathcal%7BL%7D%5By%27%5D%2B4%5Cmathcal%7BL%7D%5By%27%5D%3D0)
With the formulas:
![\mathcal{L}[y'']=s^2\mathcal{L}[y]-y(0)s-y'(0)](https://tex.z-dn.net/?f=%5Cmathcal%7BL%7D%5By%27%27%5D%3Ds%5E2%5Cmathcal%7BL%7D%5By%5D-y%280%29s-y%27%280%29)
![\mathcal{L}[y']=s\mathcal{L}[y]-y(0)](https://tex.z-dn.net/?f=%5Cmathcal%7BL%7D%5By%27%5D%3Ds%5Cmathcal%7BL%7D%5By%5D-y%280%29)
![\mathcal{L}[x]=L](https://tex.z-dn.net/?f=%5Cmathcal%7BL%7D%5Bx%5D%3DL)

Solving for 




Apply the inverse Laplace transform with this formula:
![\mathcal{L}^{-1}[\frac1{s-a}]=e^{at}](https://tex.z-dn.net/?f=%5Cmathcal%7BL%7D%5E%7B-1%7D%5B%5Cfrac1%7Bs-a%7D%5D%3De%5E%7Bat%7D)
![y=3\mathcal{L}^{-1}[\frac1{s+4}]=3e^{-4t}](https://tex.z-dn.net/?f=y%3D3%5Cmathcal%7BL%7D%5E%7B-1%7D%5B%5Cfrac1%7Bs%2B4%7D%5D%3D3e%5E%7B-4t%7D)
Answer:
a
Step-by-step explanation:
add all together