Answer:
second option
Step-by-step explanation:
Given
+ 6x² + 5 = 0
let u = x², then
u² + 6u + 5 = 0 ← in standard form
(u + 1)(u + 5) = 0 ← in factored form
Equate each factor to zero and solve for u
u + 1 = 0 ⇒ u = - 1
u + 5 = 0 ⇒ u = - 5
Change u back into terms of x, that is
x² = - 1 ( take the square root of both sides )
x = ± = ± i ( noting that
= i ), and
x² = - 5 ( take the square root of both sides )
x = ± = ±
= ±
×
= ± i
Solutions are x = ± i and x = ± i
Answer:
90% confidence interval for the population mean iron concentration is [0.771 , 0.832].
Step-by-step explanation:
We are given that a researcher examines 27 water samples for iron concentration. The mean iron concentration for the sample data is 0.802 cc/cubic meter with a standard deviation of 0.093.
Firstly, the pivotal quantity for 90% confidence interval for the population mean iron concentration is given by;
P.Q. = ~
where, = sample mean iron concentration = 0.802 cc/cubic meter
s = sample standard deviation = 0.093
n = number of water samples = 27
= population mean
<em>Here for constructing 90% confidence interval we have used t statistics because we don't know about population standard deviation.</em>
So, 90% confidence interval for the population mean, is ;
P(-1.706 < < 1.706) = 0.90 {As the critical value of t at 26 degree of
freedom are -1.706 & 1.706 with P = 5%}
P(-1.706 < < 1.706) = 0.90
P( <
<
) = 0.90
P( <
<
) = 0.90
<u>90% confidence interval for</u> = [
,
]
= [ ,
]
= [0.771 , 0.832]
Therefore, 90% confidence interval for the population mean iron concentration is [0.771 , 0.832].