9514 1404 393
Answer:
a) profit has a typical curve: negative at low volume, and again at very high volume.
b) $239,407
Step-by-step explanation:
a) The graph is negative below x=1.58, so the break-even point is 158 toys sold. The profit declines steeply above 533 toys sold, to again go negative for 774 toys sold. This sort of curve seems fairly typical.
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b) The profit is a maximum of $239,407 when 533 toys are sold.
Answer:
for the first one do 15 divided by 10 and the second one 18 divided by 8.
Step-by-step explanation:
You have some unknown integer
![n](https://tex.z-dn.net/?f=n)
, and you know that adding this and the next two integers,
![n+1](https://tex.z-dn.net/?f=n%2B1)
and
![n+2](https://tex.z-dn.net/?f=n%2B2)
, gives a total of 57.
This means
![n+(n+1)+(n+2)=57](https://tex.z-dn.net/?f=n%2B%28n%2B1%29%2B%28n%2B2%29%3D57)
The task is to find all three unknown integers. Notice that if you know the value of
![n](https://tex.z-dn.net/?f=n)
, then you pretty much know the value of the other three integers.
To find
![n](https://tex.z-dn.net/?f=n)
, solve the equation above:
![n+(n+1)+(n+2)=3n+3=57\implies 3n=54\implies n=\dfrac{54}3=18](https://tex.z-dn.net/?f=n%2B%28n%2B1%29%2B%28n%2B2%29%3D3n%2B3%3D57%5Cimplies%203n%3D54%5Cimplies%20n%3D%5Cdfrac%7B54%7D3%3D18)
So if 18 is the first integer, then others must be 19 and 20.
Answer:
The interest rate was of 5.5% a year.
Step-by-step explanation:
The compound interest formula is given by:
![A(t) = P(1 + \frac{r}{n})^{nt}](https://tex.z-dn.net/?f=A%28t%29%20%3D%20P%281%20%2B%20%5Cfrac%7Br%7D%7Bn%7D%29%5E%7Bnt%7D)
Where A(t) is the amount of money after t years, P is the principal(the initial sum of money), r is the interest rate(as a decimal value), n is the number of times that interest is compounded per unit year and t is the time in years for which the money is invested or borrowed.
In this question, we have that:
![A = 109076.45, P = 98000, n = 1, t = 2](https://tex.z-dn.net/?f=A%20%3D%20109076.45%2C%20P%20%3D%2098000%2C%20n%20%3D%201%2C%20t%20%3D%202)
We have to find r.
![A(t) = P(1 + \frac{r}{n})^{nt}](https://tex.z-dn.net/?f=A%28t%29%20%3D%20P%281%20%2B%20%5Cfrac%7Br%7D%7Bn%7D%29%5E%7Bnt%7D)
![109076.45 = 98000(1 + r)^{2}](https://tex.z-dn.net/?f=109076.45%20%3D%2098000%281%20%2B%20r%29%5E%7B2%7D)
![(1+r)^{2} = \frac{109076.45}{98000}](https://tex.z-dn.net/?f=%281%2Br%29%5E%7B2%7D%20%3D%20%5Cfrac%7B109076.45%7D%7B98000%7D)
![(1+r)^{2} = 1.113025](https://tex.z-dn.net/?f=%281%2Br%29%5E%7B2%7D%20%3D%201.113025)
Taking the square root from both sides to isolate r.
![\sqrt{(1+r)^{2}} = \sqrt{1.113025}](https://tex.z-dn.net/?f=%5Csqrt%7B%281%2Br%29%5E%7B2%7D%7D%20%3D%20%5Csqrt%7B1.113025%7D)
![1 + r = 1.055](https://tex.z-dn.net/?f=1%20%2B%20r%20%3D%201.055)
![r = 1.055 - 1](https://tex.z-dn.net/?f=r%20%3D%201.055%20-%201)
![r = 0.055](https://tex.z-dn.net/?f=r%20%3D%200.055)
The interest rate was of 5.5% a year.