Answer: 14.33
Step-by-step explanation:
Answer:
The 99% confidence interval of the population standard deviation is 1.7047 < σ < 7.485
Step-by-step explanation:
Confidence interval of standard deviation is given as follows;

s =
Where:
= Sample mean
s = Sample standard deviation
n = Sample size = 7
χ = Chi squared value at the given confidence level
= ∑x/n = (62 + 58 + 58 + 56 + 60 +53 + 58)/7 = 57.857
The sample standard deviation s =
= 2.854
The test statistic, derived through computation, = ±3.707
Which gives;


1.7047 < σ < 7.485
The 99% confidence interval of the population standard deviation = 1.7047 < σ < 7.485.
Using the proportion given, there will be 57 catfish in the pond.
The proportion given to us is
5.7/20 = x/200
Cross multiply:
5.7*200 = 20*x
1140 = 20x
Divide both sides by 20:
1140/20 = 20x/20
57 = x
Answer:
Step-by-step explanation:
If you're looking for what the half angle of the tangent of theta is, I'm a bit confused as to why you think the angle in the 4th quadrant, x, is relevant. But maybe you don't know it isn't and it's a "trick" to throw you off. Hmm...
Anyways, the half angle identity for tangent is

There are actually 3 identities for the tangent of a half angle, but this one works just as well as either of the others do, so I'm going with this one.
If theta is in QIII, the value of -4 goes along the x axis and the hypotenuse is 5. That makes the missing side, by Pythagorean's Theorem, -3. Filling in our formula:
which simplifies a bit to
and a bit more to

Bring up the lower fraction and flip it to divide to get
which of course simplifies to
-3. Choice A.