Rachel is now 11 years old. Five years ago, Lily was twice as old as Rachel. How old is Lily now?
1 answer:
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Answer:
sec(θ) = -5/2
Step-by-step explanation:
It can be helpful to draw a triangle with sides that produce the given ratio. See the attachment. Then the third side of the triangle can be found using the Pythagorean theorem, if necessary. Finally, the ratio for the desired trig function can be determined.
sec = hypotenuse/adjacent
sec(θ) = 5/-2 = -5/2
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If you don't want to do that, or if you have various trig identities memorized, you can use the appropriate trig identity.
sin² + cos² = 1
so ...
sec² = 1/cos² = 1/(1 -sin²)
sec = 1/√(1 -sin²)
Since the tangent is positive, this is a third-quadrant angle. The secant will be negative.
sec(θ) = -1/√(1 -(21/25)) = -√(25/4) . . . . . filling in the given value for sin(θ)
sec(θ) = -5/2
Answer: (15.47, 24.53)
Step-by-step explanation:
We know that the confidence interval for population mean is given by :_
, where n= sample size.
= standard deviation.
= sample mean.
z*= Critical value.
Given : n= 450
Critical value for 95% confidence = z*=1.96 [From z-value table]
Then, the 95% confidence interval will be :-
Hence, the 95% confidence interval for the mean change in score μ μ in the population of all high school seniors. : (15.47, 24.53)