Bubba Bulldog and all of his dog friends love to hide bones! Bubba hid 444 bones, Barry hid 555 bones, Larry hid 101010 bones, a
2 answers:
You might be interested in
Answer:
Step-by-step explanation:
Given the series,
∑ ∞ n = 1 − 4 ( − 1 / 2 ) n − 1
I think the series is summation from n = 1 to ∞ of -4(-1/2)^(n-1)
So,
∑ − 4 ( − ½ )^(n − 1). From n = 1 to ∞
There are different types of test to show if a series converges or diverges
So, using Ratio test
Lim n → ∞ (a_n+1 / a_n)
Lim n → ∞ (-4(-1/ 2)^(n+1-1) / -4(-1/2)^(n-1))
Lim n → ∞ ((-4(-1/2)^(n) / -4(-1/2)^(n-1))
Lim n → ∞ (-1/2)ⁿ / (-1/2)^(n-1)
Lim n→ ∞ (-1/2)^(n-n+1)
Lim n→ ∞ (-1/2)^1 = -1/2
Since the limit is less than 0, then, the series converge...
Sum to infinity
Using geometric progression formula
S∞ = a / 1 - r
Where
a is first term
r is common ratio
So, first term is
a_1 = -4(-½)^1-1 = -4(-½)^0 = -4 × 1
a_1 = -4
Common ratio r = a_2 / a_1
a_2 = 4(-½)^2-1 = -4(-½)^1 = -4 × -½ = 2
a_2 = 2
Then,
r = a_2 / a_1 = 2 / -4 = -½
S∞ = -4 / 1--½
S∞ = -4 / 1 + ½
S∞ = -4 / 3/2 = -4 × 2 / 3
S∞ = -8 / 3 = -2⅔
The sum to infinity is -2.67 or -2⅔
Check attachment for better understanding
Answer:
a) Statistic.
b) The population proportion is expected to be between 0.29 and 0.31 with a 94% degree of confidence.
Step-by-step explanation:
a) The proportion of 30% is a statistic, as it is a value that summarizes data only from the sample taken in the study from USA Today. Other samples may yield different proportions.
b) We can use the statistic to estimate a confidence interval for the parameter of the population.
The standard error for the proportion is calculated as:
The margin of error is 0.01. We can use this value to determine the level of confidence that represents.
The formula for the margin of error is:
This z-value, according to the the standard normal distribution, corresponds to a confidence interval of 94%.
The interval for this margin of error is:
Then, we can conclude that the population proportion is expected to be between 0.29 and 0.31 with a 94% degree of confidence.
