Answer:
n = π/6, π/4, 3π/4, 5π/6
Step-by-step explanation:
sin(3n) − sin n = cos(2n)
Use double and triple angle formulas:
(3 sin n − 4 sin³ n) − sin n = 1 − 2 sin² n
2 sin n − 4 sin³ n = 1 − 2 sin² n
4 sin³ n − 2 sin² n − 2 sin n + 1 = 0
Factor by grouping:
2 sin² n (2 sin n − 1) − (2 sin n − 1) = 0
(2 sin² n − 1) (2 sin n − 1) = 0
Solve:
2 sin² n − 1 = 0
2 sin² n = 1
sin² n = 1/2
sin n = √2/2
n = π/4, 3π/4
2 sin n − 1 = 0
2 sin n = 1
sin n = 1/2
n = π/6, 5π/6
If you take 230 subtract from 180 you will get 50 so the price for adult tickets are $50
<h3>
Answer:</h3>
63.64%
<h3>
Step-by-step explanation:</h3>
7/11 = 7/11 × 100% = (700/11)% ≈ 63.64%
_____
<em>Comment on fractions involving 11</em>
1/11 is the 2-digit repeating decimal 0.09090909...
So, any multiple of 1/11 is a 2-digit repeating decimal with the two digits being the numerator times 9.
Here, we have 7/11, so the 2-digit repeat is 7·9 = 63. That is ...
... 7/11 = 0.63636363...
true
Typically, the price charged must cover more than labor costs figured at an hourly rate. There may be costs related to rent, utilities, administration, equipment use and/or depreciation. These costs are often called overhead<span>.</span>
Answer:
(27.3692 ; 44.6308)
Step-by-step explanation:
Mean, xbar = 36
Standard deviation, s = 11
Sample size, n = 12
Tcritical at 0.2, df = 12 - 1 = 11 ; Tcritical = 2.718
Confidence interval :
Xbar ± Margin of error
Margin of Error = Tcritical * s/sqrt(n)
Margin of Error = 2.718 * 11/sqrt(12) = 8.6308
Confidence interval :
Lower boundary : 36 - 8.6308 = 27.3692
Upper boundary : 36 + 8.6308 = 44.6308
(27.3692 ; 44.6308)
