Answer:
Step-by-step explanation:
ax + by = c
ax= c-by <------- Subtract by "by"
x= c-by/a <------ divide by a
Answer:
Robert will have $481 more in his account than Cooper.
Step-by-step explanation:
Compound interest:
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 year and t is the time in years for which the money is invested or borrowed.
Continuous compounding:
Similar to compound interest:
![A(t) = P(1 + r)^t](https://tex.z-dn.net/?f=A%28t%29%20%3D%20P%281%20%2B%20r%29%5Et)
Cooper:
Cooper invested $3,100 in an account paying an interest rate of 2% compounded quarterly. This means that ![P = 3100, r = 0.02, n = 4](https://tex.z-dn.net/?f=P%20%3D%203100%2C%20r%20%3D%200.02%2C%20n%20%3D%204)
After 12 years is A(12). So
![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)
![A(12) = 3100(1 + \frac{0.02}{4})^{4*12}](https://tex.z-dn.net/?f=A%2812%29%20%3D%203100%281%20%2B%20%5Cfrac%7B0.02%7D%7B4%7D%29%5E%7B4%2A12%7D)
![A(12) = 3938.5](https://tex.z-dn.net/?f=A%2812%29%20%3D%203938.5)
Cooper will have $3938.5 in his account.
Robert:
Robert invested $3,100 in an account paying an interest rate of 3 % compounded continuously. So
.
After 12 years.
![A(t) = P(1 + r)^t](https://tex.z-dn.net/?f=A%28t%29%20%3D%20P%281%20%2B%20r%29%5Et)
![A(12) = 3100(1 + 0.03)^{12}](https://tex.z-dn.net/?f=A%2812%29%20%3D%203100%281%20%2B%200.03%29%5E%7B12%7D)
![A(12) = 4419.9](https://tex.z-dn.net/?f=A%2812%29%20%3D%204419.9)
Robert will have $4419.9 in his account.
How much more money would Robert have in his account than Cooper, to the nearest dollar?
4419.9 - 3938.5 = 481.4
To the nearest dollar, Robert will have $481 more in his account than Cooper.
To determine the cost of the mail, we simply substitute the mass of the package to the given function. Mathematical functions are used to relate two variables, observing how changing one variable affects the other variable. For this case, the cost of a mail and the weight of the package are related by the function <span>y = 0.7x2 –2.5x + 3 where x represents the mass in units of pounds (lb) and y is the cost in units of dollars ($). We calculate cost as follows:
</span><span>y = 0.7x^2 –2.5x + 3
</span><span>y = 0.7(5)^2 –2.5(5)+ 3
y = 8 dollars
Therefore, the cost of mailing a 5 lb package would be 8 dollars.</span>
15 mph = 15 miles traveled in a one hour time span.
15+3=18 miles, 60 minutes- 30 minutes = 30 minutes.
18 miles in the span of 30 minutes
Answer:
option B is the correct answer of this question.
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