Answer:
0.000221
Step-by-step explanation:
Using the z score formula when a random number of samples is given =
z = (x-μ)/σ/√n, where
x is the raw score
μ is the population mean
σ is the population standard deviation = 7
n is random number of samples = 83
Note that:2.2 dollars = x-μ
z = 2.2/7/√8.3
z = 3.51402
Probability value from Z-Table:
P(x<27.7) = 0.99978
P(x>27.7) = 1 - P(x<27.7) = 0.00022069
Approximately = 0.000221
Hence, the probability that the sample mean would differ from the true mean by greater than 2.2 dollars if a sample of 83 5-gallon pails is randomly selected is 0.000221
Answer:
5400
Step-by-step explanation:
so 90% of 850 is 765 (0.90x850)
765 is 10 years
so 1 year is 765/10 = 76.5 per year. So 76.5x59 = 4,513.5 add the initial ammount and you got 5,363.5 in the nearest hundredth you get 5400
Answer:
Negative
Step-by-step explanation:
It's negative because my math teacher said so a few years ago. Sorry for the not so great explanation... I didn't pay attention that day.
In order going down:
5 3/5
6 5/6
4 2/3
10 1/3
11 2/3
ANSWER
D.
![9 {y}^{2} - 4 {x}^{2}- 36y + 16x - 16 = 0](https://tex.z-dn.net/?f=9%20%7By%7D%5E%7B2%7D%20%20-%204%20%7Bx%7D%5E%7B2%7D-%2036y%20%2B%2016x%20-%2016%20%3D%200)
EXPLANATION
The standard equation of the hyperbola is
![\frac{ {(y - 2)}^{2} }{4} - \frac{ {(x - 2)}^{2} }{9} = 1](https://tex.z-dn.net/?f=%20%5Cfrac%7B%20%7B%28y%20-%202%29%7D%5E%7B2%7D%20%7D%7B4%7D%20%20-%20%20%5Cfrac%7B%20%7B%28x%20-%202%29%7D%5E%7B2%7D%20%7D%7B9%7D%20%20%3D%201)
We multiply through by 36 to obtain:
![9 {(y - 2)}^{2} - 4( {x - 2)}^{2} = 36](https://tex.z-dn.net/?f=9%20%7B%28y%20-%202%29%7D%5E%7B2%7D%20%20-%204%28%20%7Bx%20-%202%29%7D%5E%7B2%7D%20%20%3D%2036)
We now expand to get,
![9( {y}^{2} - 4y + 4) - 4( {x}^{2} - 4x + 4) = 36](https://tex.z-dn.net/?f=9%28%20%7By%7D%5E%7B2%7D%20%20-%204y%20%2B%204%29%20-%204%28%20%7Bx%7D%5E%7B2%7D%20%20-%204x%20%2B%204%29%20%3D%2036)
Expand :
![9 {y}^{2} - 36y + 36 - 4 {x}^{2} + 16x - 16 = 36](https://tex.z-dn.net/?f=9%20%7By%7D%5E%7B2%7D%20%20-%2036y%20%2B%2036%20%20-%204%20%7Bx%7D%5E%7B2%7D%20%20%2B%2016x%20-%2016%20%3D%2036)
To get the general form, we equate everything to zero to get,
![9 {y}^{2} - 4 {x}^{2}- 36y + 16x - 16 = 0](https://tex.z-dn.net/?f=9%20%7By%7D%5E%7B2%7D%20%20-%204%20%7Bx%7D%5E%7B2%7D-%2036y%20%2B%2016x%20-%2016%20%3D%200)
The correct choice is D.