Answer:
The first 4 terms of the sequence are: 3, 9, 81, 6561
Step-by-step explanation:
We are given the following recursive function:
![f(n) = [f(n-1)]^{2}](https://tex.z-dn.net/?f=f%28n%29%20%3D%20%5Bf%28n-1%29%5D%5E%7B2%7D)
And the following initial condition:
![f(1) = 3](https://tex.z-dn.net/?f=f%281%29%20%3D%203)
The second term of the sequence is:
![f(2) = [f(2-1)]^{2} = f(1)^2 = 3^2 = 9](https://tex.z-dn.net/?f=f%282%29%20%3D%20%5Bf%282-1%29%5D%5E%7B2%7D%20%3D%20f%281%29%5E2%20%3D%203%5E2%20%3D%209)
The third term of the sequence is:
![f(3) = [f(3-1)]^{2} = f(2)^2 = 9^2 = 81](https://tex.z-dn.net/?f=f%283%29%20%3D%20%5Bf%283-1%29%5D%5E%7B2%7D%20%3D%20f%282%29%5E2%20%3D%209%5E2%20%3D%2081)
The fourth term of the sequence is:
![f(4) = [f(4-1)]^{2} = f(3)^2 = 81^2 = 6561](https://tex.z-dn.net/?f=f%284%29%20%3D%20%5Bf%284-1%29%5D%5E%7B2%7D%20%3D%20f%283%29%5E2%20%3D%2081%5E2%20%3D%206561)
The first 4 terms of the sequence are: 3, 9, 81, 6561
Answer:
b. We are 95% confident that the proportion of coworkers who went on a vacation last year away from home for at least a week is between 50% and 66%.
Step-by-step explanation:
A confidence interval at the level of x% for a proportion being between a and b means that we are x% sure that the true proportion of the population is between a and b.
In this problem, we have that:
95% C.I is (0.5, 0.66)
Interpretation: 95% confident that the true proportion is between 0.5 and 0.66.
The correct answer is:
b. We are 95% confident that the proportion of coworkers who went on a vacation last year away from home for at least a week is between 50% and 66%.
Answer:
![\Huge\boxed{x](https://tex.z-dn.net/?f=%5CHuge%5Cboxed%7Bx%3C-%5Cfrac%7B1%7D%7B4%7D%7D)
Step-by-step explanation:
Hello there!
The first thing we want to do is find the least common denominator which would be 20
so we multiply the denominator and numerator of the fractions on the left side by 4
3x4=12
5x4=20 -12/20x
1x4=4
5x4=20 so now we would have
![-\frac{12}{20}x+\frac{4}{20} >\frac{7}{20}](https://tex.z-dn.net/?f=-%5Cfrac%7B12%7D%7B20%7Dx%2B%5Cfrac%7B4%7D%7B20%7D%20%3E%5Cfrac%7B7%7D%7B20%7D)
once again we want to isolate the variable using inverse operations
to get rid of the 4/20 we subtract each side by 4/20
![\frac{7}{20} -\frac{4}{20} =\frac{3}{20}](https://tex.z-dn.net/?f=%5Cfrac%7B7%7D%7B20%7D%20-%5Cfrac%7B4%7D%7B20%7D%20%3D%5Cfrac%7B3%7D%7B20%7D)
now we have
![-\frac{12}{20} x>\frac{3}{10}](https://tex.z-dn.net/?f=-%5Cfrac%7B12%7D%7B20%7D%20x%3E%5Cfrac%7B3%7D%7B10%7D)
now we want to get rid of the -12/20
to do so we divide each side by -12/20 (or -.6 as a decimal to make it easier)
![\frac{3/20}{-.25}=-\frac{1}{4}](https://tex.z-dn.net/?f=%5Cfrac%7B3%2F20%7D%7B-.25%7D%3D-%5Cfrac%7B1%7D%7B4%7D)
REMEMBER flip the equality sign
we're left with
![x](https://tex.z-dn.net/?f=x%3C-%5Cfrac%7B1%7D%7B4%7D)