I think it’s 0.85d, but i’m not sure
Answer: (60.858, 69.142)
Step-by-step explanation:
The formula to find the confidence interval for mean :
, where
is the sample mean ,
is the population standard deviation , n is the sample size and
is the two-tailed test value for z.
Let x represents the time taken to mail products for all orders received at the office of this company.
As per given , we have
Confidence level : 95%
n= 62
sample mean :
hours
Population standard deviation :
hours
z-value for 93% confidence interval:
[using z-value table]
Now, 93% confidence the mean time taken to mail products for all orders received at the office of this company :-
![65\pm (1.8119)\dfrac{18}{\sqrt{62}}\\\\ 65\pm4.142\\\\=(65-4.142,\ 65+4.142)\\\\= (60.858,\ 69.142)](https://tex.z-dn.net/?f=65%5Cpm%20%281.8119%29%5Cdfrac%7B18%7D%7B%5Csqrt%7B62%7D%7D%5C%5C%5C%5C%2065%5Cpm4.142%5C%5C%5C%5C%3D%2865-4.142%2C%5C%2065%2B4.142%29%5C%5C%5C%5C%3D%20%2860.858%2C%5C%2069.142%29%20)
Thus , 93% confidence the mean time taken to mail products for all orders received at the office of this company : (60.858, 69.142)
To solve the given equation, w need to review some rules:
![(1) \ ln \ e = 1 \\ (2) \ ln \ b^{a} = a*ln \ b \\ (3) \ ln \ a + ln \ b = ln \ (ab) \\ (4) \ ln \ a - ln \ b = ln \ \frac{a}{b} \\](https://tex.z-dn.net/?f=%281%29%20%5C%20ln%20%5C%20e%20%3D%201%20%5C%5C%20%0A%282%29%20%5C%20ln%20%5C%20%20b%5E%7Ba%7D%20%3D%20a%2Aln%20%5C%20b%20%5C%5C%0A%283%29%20%5C%20ln%20%5C%20a%20%2B%20ln%20%5C%20b%20%3D%20ln%20%5C%20%28ab%29%20%5C%5C%0A%284%29%20%5C%20ln%20%5C%20a%20-%20ln%20%5C%20b%20%3D%20ln%20%5C%20%20%5Cfrac%7Ba%7D%7Bb%7D%20%20%5C%5C)
The given equation is :
![ln \ e^{ln \ x} + ln \ e^{ln \ x^{2}} = 2 \ ln \ 8](https://tex.z-dn.net/?f=ln%20%5C%20%20e%5E%7Bln%20%5C%20x%7D%20%2B%20ln%20%5C%20%20e%5E%7Bln%20%5C%20%20x%5E%7B2%7D%7D%20%3D%202%20%5C%20ln%20%5C%208)
![ln \ x * ln \ e + ln \ x^{2} * ln \ e = 2 \ ln \ 8](https://tex.z-dn.net/?f=ln%20%5C%20x%20%2A%20ln%20%5C%20e%20%2B%20ln%20%5C%20%20x%5E%7B2%7D%20%2A%20ln%20%5C%20e%20%3D%202%20%5C%20ln%20%5C%208%20)
⇒⇒⇒⇒ rule (2)
![ln \ x + ln \ x^{2} = ln \ 8^{2}](https://tex.z-dn.net/?f=ln%20%5C%20x%20%2B%20ln%20%5C%20%20x%5E%7B2%7D%20%3D%20ln%20%5C%20%208%5E%7B2%7D%20)
⇒⇒⇒⇒ rule (1) and rule (2)
![ln \ ( x* x^{2} ) = ln \ 64](https://tex.z-dn.net/?f=ln%20%5C%20%28%20x%2A%20%20x%5E%7B2%7D%20%29%20%3D%20ln%20%5C%2064)
⇒⇒⇒⇒ rule (3)
removing the nature logarithm from both sides
![x^{3} = 64 = 4^{3}](https://tex.z-dn.net/?f=%20x%5E%7B3%7D%20%3D%2064%20%3D%20%204%5E%7B3%7D%20%20)
∴ x = 4
So, the correct answer is option (2) ⇒⇒⇒⇒ x = 4
Answer:13
Step-by-step explanation: I took the test in K12 and the answer is 13