The sum of any geometric sequence (if it converges, r^2<1) is of the form:
s(n)=a(1-r^n)/(1-r), a=initial term, r=common ratio, n=number of terms...
s(n)=30(1-0.4^n)/(0.6)
s(n)=50(1-0.4^n)
Since r<1 the sum of the infinite series is just:
s=50
The bottom trapezoid is
(1/2) * h * (b2 + b1) =
(1/2)*11 * (31+25)
(1/2) * 11 * 56
308
The top parallelogram is
b * h = 12 * 14 = 168
308 +168 = 476 ft^2
Letter B
let's convert the mixed fractions to improper fractions firstly.
![\bf \stackrel{mixed}{2\frac{3}{8}}\implies \cfrac{2\cdot 8+3}{8}\implies \stackrel{improper}{\cfrac{19}{8}}~\hfill \stackrel{mixed}{4\frac{1}{2}}\implies \cfrac{4\cdot 2+1}{2}\implies \stackrel{improper}{\cfrac{9}{2}} \\\\\\ \stackrel{mixed}{3\frac{1}{8}}\implies \cfrac{3\cdot 8+1}{8}\implies \stackrel{improper}{\cfrac{25}{8}} \\\\[-0.35em] ~\dotfill](https://tex.z-dn.net/?f=%5Cbf%20%5Cstackrel%7Bmixed%7D%7B2%5Cfrac%7B3%7D%7B8%7D%7D%5Cimplies%20%5Ccfrac%7B2%5Ccdot%208%2B3%7D%7B8%7D%5Cimplies%20%5Cstackrel%7Bimproper%7D%7B%5Ccfrac%7B19%7D%7B8%7D%7D~%5Chfill%20%5Cstackrel%7Bmixed%7D%7B4%5Cfrac%7B1%7D%7B2%7D%7D%5Cimplies%20%5Ccfrac%7B4%5Ccdot%202%2B1%7D%7B2%7D%5Cimplies%20%5Cstackrel%7Bimproper%7D%7B%5Ccfrac%7B9%7D%7B2%7D%7D%20%5C%5C%5C%5C%5C%5C%20%5Cstackrel%7Bmixed%7D%7B3%5Cfrac%7B1%7D%7B8%7D%7D%5Cimplies%20%5Ccfrac%7B3%5Ccdot%208%2B1%7D%7B8%7D%5Cimplies%20%5Cstackrel%7Bimproper%7D%7B%5Ccfrac%7B25%7D%7B8%7D%7D%20%5C%5C%5C%5C%5B-0.35em%5D%20~%5Cdotfill)

The crystal system or the luster would be the best answer for you.
One possible solution for the system of inequalities is given as follows:
13 dimes and 2 nickels.
<h3>How to obtain the system of inequalities?</h3>
The first step in obtaining the system of inequalities is identifying the variables, which are given as follows:
- Variable x: number of dimes that Tallulah has.
- Variable y: number of nickels that Tallulah has.
Tallulah has at most 18 coins, hence:
x + y ≤ 18.
A nickel is worth 5 cents = $0.05, while a dime is worth 10 cents = $0.1, and Tallulah has at least $1.20 combined, hence:
0.1x + 0.05y ≥ 1.20.
The solution is given by the shaded region on the image given at the end of the answer, and one possible solution is given as follows:
x = 13, y = 2.
Which means that she has 13 dimes and 2 nickels.
More can be learned about a system of inequalities at brainly.com/question/9774970
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