The sum of the first n terms in a geometric sequence given the first term (a1) and the common ratio (r) is calculated through the equation,
<span>Sn </span>= (<span><span><span>a1</span>(1−<span>r^n</span>) / (</span><span>1−r)
Substituting the known terms,
Sn = (20)(1 - (1/4)^4)) / (1 - 1/4)
Sn = 26.5625
Thus, the sum of the first four terms is 26.5625. </span></span>
Answer:
The volume of the box is 3/4 cubic meters.
Step-by-step explanation:
We know that volume = length * width * height. We have length, width, and height already, so all we have to do is multiply.
5/6 * 1 1/8 * 4/5. First we convert 1 1/8 from a mixed fraction, to give us 9/8, as 8/8 = 1.
5/6 * 9/8 * 4/5. 5 * 9 = 45, and 6 * 8 = 48. 45/48 reduces to 15/16.
15/16 * 4/5. 15 * 4 = 60, and 16 * 5 = 80. 60/80 reduces to 6/8, which reduces to 3/4.
Answer:
7. a) slope = 5
7. b) slope = 1/2
8. slope = 1
Step-by-step explanation:
slope = rise/run
rise is the vertical change, run is the horizontal change
7. a)
Pick any two points on your line. (0,0) and (1,5) are easy to work with.
The vertical change between the two points is 5
The horizontal change between those points is 1
so slope = 5/1 = 5
7. b)
Again, you can use (0,0) as one of your points. The point (2,4) is good as the second.
slope = 4/2 = 1/2
8. We don't have a graph, but we are given two points to work with, (1,4) and (5,8). Use the formula given...
m = slope = (y2-y1) / (x2-x1)
= (8 - 4) / (5 - 1)
= 4/4
= 1
I hope that helped!
Answer:
1/2
Step-by-step explanation:
So you have 12 bags total.
2 are 1/6 so their total weight is 1/3
2 are 1/3 so their total weight is 2/3
3 are 1/2 so their total weight is 3/2
4 are 2/3 so their total weight is 8/3
1 is 5/6 so their total weight is 5/6
Now add all of these up:
1/3 + 2/3 + 3/2 + 8/3 + 5/6 = 36/6 = 6
Then divide by the number of bags to get the average weight: 6/12 = 1/2
