Answer:
364/27
Step-by-step explanation:
9, 3, 1, ... is a geometric sequence with common ratio r = 1/3.
The nth term is a1rn-1.
If a1rn-1 = 1/27, then 9(1/3)n-1 = 1/27
32(3-1)n-1 = 3-3
3231-n = 3-3
33-n = 3-3
3-n = -3
n = 6
The sum, Sn, of the first n terms of a geometric sequence is given by Sn = a1(1 - rn) / (1 - r).
So, 9 + 3 + 1 + ... + 1/27 = S6 = 9(1 - (1/3)6) / (1 - 1/3)
= 9(1 - 1/729) / (2/3)
= (27/2)(728/729) = 364/27
Answer:
21
Step-by-step explanation:
trust bro
Answer:
48 inches
Step-by-step explanation:
1 inch is 6 feet.
8 inches would be 48 feet.
Answer:
X= 18
Step-by-step explanation:
18-18=0
x=18
X=pounds of coffee bean ($0.20 per pound)
y=pounds of coffee bean ($0.68 per pound )
We can suggest this system of equations:
x+y=120
(0.20x+0.68 y) / (x+y)=0.54 ⇒ (0.2x+0.68y)=0.54(x+y)
We can solve this system by substitution method.
x+y=120 ⇒ y=120-x
0.2x+0.68(120-x)=0.54[x+(120-x)]
0.2x+81.6-0.68x=0.54(120)
-0.48x+81.6=64.8
-0.48x=64.8-81.6
-0.48x=-16.8
x=-16.8/-0.48
x=35
y=120-x=120-35=85
Answer: the coffee mixture has 35 pounds of coffee beans sold to $0.2 a pound, and 85 pounds of coffee beans sold to $0.68 a pound, the solutions is reasonable because the price of a coffee mixture ($0.54 a pound) is greater than $0.2 and smaller than $0.68.
