First difference
12-5 = 7
21-12 = 9
32-21 = 11
Second difference
9-11 = 2
11-9 = 2
second difference is constant so it could defined by quadratic formula,
u(x) = ax^2 + bx + c
because 2a = Second difference = 2
so a = 1
then u(x) = x^2 + bx + c
build equations from known values to find b and c
for x=1, u(1) = 5 = 1^2 + b(1) + c
b + c = 4 ...(1)
x=2, u(2) = 12 = 2^2 + b(2) + c
2b + c = 8 ... (2)
solve b = 4, c =0
so u(x) = x^2 + 4x ... formula for n term (i use x not n here)
difference between consecutive term is 245, we have
245 = u(x+1) - u(x)
245 = (x+1)^2 + 4(x+1) - (x^2 + 4x)
245 = x^2 + 2x + 1 + 4x + 4 - x^2 - 4x
245 = 2x + 5
x = 120
it's between term 120 and 121
graph is y=2
Answer:
<h2>$1,129.27</h2>
Step-by-step explanation:
Compounded interest formula is
![A=P(1+\frac{r}{n})^{nt}](https://tex.z-dn.net/?f=A%3DP%281%2B%5Cfrac%7Br%7D%7Bn%7D%29%5E%7Bnt%7D)
Where
is the final amount,
is the principal,
is the anual interest in decimal,
is the numer of compounded periods in one year and
is the time in years.
![P=\$800\\r=0.09\\n=1\\t=4](https://tex.z-dn.net/?f=P%3D%5C%24800%5C%5Cr%3D0.09%5C%5Cn%3D1%5C%5Ct%3D4)
Notice that
, because the interest is compounded anually, if the interest is compounded, then
, because there would be 12 compound periods in one year.
Then, we replace all these vaules in the formula
![A=P(1+\frac{r}{n})^{nt}\\A=800(1+\frac{0.09}{1})^{1(4)}=800(1.09)^{4}\\ A=1,129.26](https://tex.z-dn.net/?f=A%3DP%281%2B%5Cfrac%7Br%7D%7Bn%7D%29%5E%7Bnt%7D%5C%5CA%3D800%281%2B%5Cfrac%7B0.09%7D%7B1%7D%29%5E%7B1%284%29%7D%3D800%281.09%29%5E%7B4%7D%5C%5C%20A%3D1%2C129.26)
Therefore, after 4 years, the amount would be $1,129.27.
Hello!
1 ft = 12 inches.
10.5 ft = 126 inches.
11.5 × 2.3 = 26.45
126/26.45 = 4.76 (About)
4.76 large doors can be cut from a 10.5 ft long board.
Teesha is in French Club:
=> 10 freshman
=>12 sophomores
=>15 juniors
=> 30 seniors in the club.
The advisor is going to randomly choose one ofthe members of the club to be a guide for an important visitor.
Out of 4 groups, only 1 will be selected.
=> 10 freshman + 12 sophomores +15 juniors + <span>30 seniors = 67 students
</span>=> 67 / 4 = 16.75
OR close to
=> 15/67