Answer:
false
Step-by-step explanation:
no solution
Answer:
80 < 93 < 121 < 127
Step-by-step explanation:
For a geometric series,
![\sum_{t=1}^{n}a(r)^{t-1}](https://tex.z-dn.net/?f=%5Csum_%7Bt%3D1%7D%5E%7Bn%7Da%28r%29%5E%7Bt-1%7D)
Formula to be used,
Sum of t terms of a geometric series = ![\frac{a(r^t-1)}{r-1}](https://tex.z-dn.net/?f=%5Cfrac%7Ba%28r%5Et-1%29%7D%7Br-1%7D)
Here t = number of terms
a = first term
r = common ratio
1). ![\sum_{t=1}^{5}3(2)^{t-1}](https://tex.z-dn.net/?f=%5Csum_%7Bt%3D1%7D%5E%7B5%7D3%282%29%5E%7Bt-1%7D)
First term of this series 'a' = 3
Common ratio 'r' = 2
Number of terms 't' = 5
Therefore, sum of 5 terms of the series = ![\frac{3(2^5-1)}{(2-1)}](https://tex.z-dn.net/?f=%5Cfrac%7B3%282%5E5-1%29%7D%7B%282-1%29%7D)
= 93
2). ![\sum_{t=1}^{7}(2)^{t-1}](https://tex.z-dn.net/?f=%5Csum_%7Bt%3D1%7D%5E%7B7%7D%282%29%5E%7Bt-1%7D)
First term 'a' = 1
Common ratio 'r' = 2
Number of terms 't' = 7
Sum of 7 terms of this series = ![\frac{1(2^7-1)}{(2-1)}](https://tex.z-dn.net/?f=%5Cfrac%7B1%282%5E7-1%29%7D%7B%282-1%29%7D)
= 127
3). ![\sum_{t=1}^{5}(3)^{t-1}](https://tex.z-dn.net/?f=%5Csum_%7Bt%3D1%7D%5E%7B5%7D%283%29%5E%7Bt-1%7D)
First term 'a' = 1
Common ratio 'r' = 3
Number of terms 't' = 5
Therefore, sum of 5 terms = ![\frac{1(3^5-1)}{3-1}](https://tex.z-dn.net/?f=%5Cfrac%7B1%283%5E5-1%29%7D%7B3-1%7D)
= 121
4). ![\sum_{t=1}^{4}2(3)^{t-1}](https://tex.z-dn.net/?f=%5Csum_%7Bt%3D1%7D%5E%7B4%7D2%283%29%5E%7Bt-1%7D)
First term 'a' = 2
Common ratio 'r' = 3
Number of terms 't' = 4
Therefore, sum of 4 terms of the series = ![\frac{2(3^4-1)}{3-1}](https://tex.z-dn.net/?f=%5Cfrac%7B2%283%5E4-1%29%7D%7B3-1%7D)
= 80
80 < 93 < 121 < 127 will be the answer.
Answer:
Yes she'll have enough with 152 inches remaining
Step-by-step explanation:
Multiply the length value by 36. Hoped this helped!
Answer:
y=-3x-2
Step-by-step explanation:
so the line is going down so we know that the slope is going to be negative.
slope is y over x and it looks like every time it goes up 3 and to the right 1 so 3/1 is 3 so the slope is 3 and if the slope has to be negative than the answer is the first one
Answer:
4.116 × 10^8 = 411,600,000
Step-by-step explanation:
i just put it in the calculator dont get mad at me