Answer:
Step-by-step explanation:
Using the rule of exponents
=
, then
=
=
Find x - y subtracted from 0. O-X+y o-y-x ox-y
1 answer:
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Answer:
Vertical angles are always congruent.
Step-by-step explanation:
Vertical angles are formed when two straight lines intersect each other, thereby forming two pairs of opposite angles, which are called vertical angles. Thus, a pair of these vertical angles formed are congruent to each other. So therefore, if two angles are said to be vertical angles, it follows that they are congruent to each other.
Using the diagram attached below, we can see two straight lines intersecting each other to form two pairs of vertical angles:
<a and <b,
<c and <d.
Thus, <a is congruent to <b, and <c is congruent to <d.
Therefore, the standby that is true about vertical angles is that:
Vertical angles are always congruent.
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].