Answer:
Future value, A = $4740.39
Step-by-step explanation:
Given the following data;
Principal = $2700
Interest rate = 5.25% = 5.25/100 = 0.0525
Time = 11 years
Number of times, n = 1
To find the future value, we would use the compound interest formula;
Where;
A is the future value.
P is the principal or starting amount.
r is annual interest rate.
n is the number of times the interest is compounded in a year.
t is the number of years for the compound interest.
Substituting into the equation, we have;
![A = 2700(1.7557)](https://tex.z-dn.net/?f=%20A%20%3D%202700%281.7557%29)
Future value, A = $4740.39
Answer:
2.Jen's school is farther from home than Paris's school.
Step-by-step explanation:
hyy there ! it may be but not that sure .
Answer:
the answer $1,236
Step-by-step explanation:
(1) From the information given, if we want to choose 5 colors from 8 distinct colors and the order in which the selection is made is relevant, then what we have is a permutation.
The formula is given as;
![nP_r=\frac{n!}{(n-r)!}](https://tex.z-dn.net/?f=nP_r%3D%5Cfrac%7Bn%21%7D%7B%28n-r%29%21%7D)
This formula means we need to select/arrange r items out of a total of n items and the anwer derived would be the total number of arrangements possible.
Therefore, we would have;
![\begin{gathered} nP_r\Rightarrow_8P_5 \\ _8P_5=\frac{8!}{(8-5)!}\Rightarrow\frac{8!}{3!} \\ _8P_5=\frac{8\times7\times6\times\ldots1}{3\times2\times1}\Rightarrow\frac{40320}{6} \\ _8P_5=6720 \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20nP_r%5CRightarrow_8P_5%20%5C%5C%20_8P_5%3D%5Cfrac%7B8%21%7D%7B%288-5%29%21%7D%5CRightarrow%5Cfrac%7B8%21%7D%7B3%21%7D%20%5C%5C%20_8P_5%3D%5Cfrac%7B8%5Ctimes7%5Ctimes6%5Ctimes%5Cldots1%7D%7B3%5Ctimes2%5Ctimes1%7D%5CRightarrow%5Cfrac%7B40320%7D%7B6%7D%20%5C%5C%20_8P_5%3D6720%20%5Cend%7Bgathered%7D)
Therefore, if the order is relevant, this selection can be done in 6,720 ways.
(2) If the order is NOT relevant, then what we need to calculate is a combination and the formula is;
![_nC_r=\frac{n!}{(n-r)!r!}](https://tex.z-dn.net/?f=_nC_r%3D%5Cfrac%7Bn%21%7D%7B%28n-r%29%21r%21%7D)
The formula can now be applied as follows;
![\begin{gathered} _nC_r\Rightarrow_8C_5 \\ _8C_5=\frac{8!}{(8-5)!\times5!} \\ _8C_5=\frac{8!}{3!\times5!}\Rightarrow\frac{8\times7\times6\times\ldots1}{(3\times2\times1)\times(5\times4\times\ldots1)} \\ _8C_5=\frac{40320}{6\times120} \\ _8C_5=56 \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20_nC_r%5CRightarrow_8C_5%20%5C%5C%20_8C_5%3D%5Cfrac%7B8%21%7D%7B%288-5%29%21%5Ctimes5%21%7D%20%5C%5C%20_8C_5%3D%5Cfrac%7B8%21%7D%7B3%21%5Ctimes5%21%7D%5CRightarrow%5Cfrac%7B8%5Ctimes7%5Ctimes6%5Ctimes%5Cldots1%7D%7B%283%5Ctimes2%5Ctimes1%29%5Ctimes%285%5Ctimes4%5Ctimes%5Cldots1%29%7D%20%5C%5C%20_8C_5%3D%5Cfrac%7B40320%7D%7B6%5Ctimes120%7D%20%5C%5C%20_8C_5%3D56%20%5Cend%7Bgathered%7D)
If the order is not relevant, then the selection can be done in 56 ways.