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Musya8 [376]
2 years ago
14

12 Over a period of several years in a sleep-therapy clinic, the average latency to fall asleep for adult males, age 20-30, has

been found to be 335 seconds. In a study of the effectiveness of hypnotic therapy, 30 males of the appropriate age are given the treatment and then their latency to fall asleep is measured.
The results are a mean latency of 283.7, with a variance of 5,756.26 seconds. Test the hypothesis that hypnotic therapy has no effect on sleep latency. Use an a level of .05 and a nondirectional test.
Mathematics
1 answer:
Volgvan2 years ago
8 0

Answer:

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xnbdjendnfjnxnrnxzkksvixibdbwbkchfjenz

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How is this solved using trig identities (sum/difference)?
GenaCL600 [577]
FIRST PART
We need to find sin α, cos α, and cos β, tan β
α and β is located on third quadrant, sin α, cos α, and sin β, cos β are negative

Determine ratio of ∠α
Use the help of right triangle figure to find the ratio
tan α = 5/12
side in front of the angle/ side adjacent to the angle = 5/12
Draw the figure, see image attached

Using pythagorean theorem, we find the length of the hypotenuse is 13
sin α = side in front of the angle / hypotenuse
sin α = -12/13

cos α = side adjacent to the angle / hypotenuse
cos α = -5/13

Determine ratio of ∠β
sin β = -1/2
sin β = sin 210° (third quadrant)
β = 210°

cos \beta = -\frac{1}{2}  \sqrt{3}

tan \beta= \frac{1}{3}  \sqrt{3}

SECOND PART
Solve the questions
Find sin (α + β)
sin (α + β) = sin α cos β + cos α sin β
sin( \alpha + \beta )=(- \frac{12}{13} )( -\frac{1}{2}  \sqrt{3})+( -\frac{5}{13} )( -\frac{1}{2} )
sin( \alpha + \beta )=(\frac{12}{26}\sqrt{3})+( \frac{5}{26} )
sin( \alpha + \beta )=(\frac{5+12\sqrt{3}}{26})

Find cos (α - β)
cos (α - β) = cos α cos β + sin α sin β
cos( \alpha + \beta )=(- \frac{5}{13} )( -\frac{1}{2} \sqrt{3})+( -\frac{12}{13} )( -\frac{1}{2} )
cos( \alpha + \beta )=(\frac{5}{26} \sqrt{3})+( \frac{12}{26} )
cos( \alpha + \beta )=(\frac{5\sqrt{3}+12}{26} )

Find tan (α - β)
tan( \alpha - \beta )= \frac{ tan \alpha-tan \beta }{1+tan \alpha  tan \beta }
tan( \alpha - \beta )= \frac{ \frac{5}{12} - \frac{1}{2} \sqrt{3}   }{1+(\frac{5}{12}) ( \frac{1}{2} \sqrt{3})}

Simplify the denominator
tan( \alpha - \beta )= \frac{ \frac{5}{12} - \frac{1}{2} \sqrt{3}   }{1+(\frac{5\sqrt{3}}{24})}
tan( \alpha - \beta )= \frac{ \frac{5}{12} - \frac{1}{2} \sqrt{3} }{ \frac{24+5\sqrt{3}}{24} }

Simplify the numerator
tan( \alpha - \beta )= \frac{ \frac{5}{12} - \frac{6}{12} \sqrt{3} }{ \frac{24+5\sqrt{3}}{24} }
tan( \alpha - \beta )= \frac{ \frac{5-6\sqrt{3}}{12} }{ \frac{24+5\sqrt{3}}{24} }

Simplify the fraction
tan( \alpha - \beta )= (\frac{5-6\sqrt{3}}{12} })({ \frac{24}{24+5\sqrt{3}})
tan( \alpha - \beta )= \frac{10-12\sqrt{3} }{ 24+5\sqrt{3}}

7 0
3 years ago
Let n be the number of couples dancing in a competition. If there are 5 organizers, which expression represents the total number
Korvikt [17]
2n+5...a couple is two people so you need to multiply the number of couples, n, by 2 to get the total number of dancers. Then add the total number of organizers.
3 0
3 years ago
How many solutions does the equation have 4x + 3=2(2x +9)
lbvjy [14]
I guess no solution
4x +3 = 4X + 18
4X - 4X = 18 - 3
0 = 15
6 0
3 years ago
Distributive property<br> 7(*+2)+3=73
Elina [12.6K]
X=8 would you like me to explain why?
4 0
3 years ago
Please look at pic below. Will give 100 points!!!!! NUMBER 2 I NEED HELP
natta225 [31]

Answer:

#2

It is assumed the base of the prism is a square wit side of 5 cm.

<u>The volume is:</u>

  • V = Bh = 250 cm³

<u>The base is:</u>

  • B = a² = 5² = 25 cm²

<u>Find h:</u>

  • h = V/B
  • h = 250/25 = 10cm
3 0
3 years ago
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