Sec(theta) = 1 / cos (theta) = hypotenuse / x -coordinate
hypotenuse = 1 (because it is the radius of the unit circle)
sec (theta) = 1 / (-3/5) = - 5/3
cot (theta) = 1 / tan(theta) = x-coordinate / y - coordinate
cot (theta) = -3/5 / y
y^2 + (-3/5)^2 = 1 => y^2 = 1 - 9/25 = 16/25 = y = +/- 4/5
Third quadrant => y = -4/5
=> cot (theta) = (-3/5) / (-4/5) = 3/4
Answer:
n = 
, n = 
Step-by-step explanation:
6n² - 5n - 7 = - 8 ( add 8 to both sides )
6n² - 5n + 1 = 0 ← in standard form
Consider the product of the factors of the coefficient of the n² term and the constant term which sum to give the coefficient of the n- term
product = 6 × 1 = 6 and sum = - 5
The factors are - 3 and - 2
Use these factors to split the n- term
6n² - 3n - 2n + 1 = 0 ( factor the first/second and third/fourth terms )
3n(2n - 1) - 1(2n - 1) = 0 ← factor out (2n - 1) from each term
(2n - 1)(3n - 1) = 0 ← in factored form
Equate each factor to zero and solve for n
3n - 1 = 0 ⇒ 3n = 1 ⇒ n =
2n - 1 = 0 ⇒ 2n = 1 ⇒ n =
For this problem, the confidence interval is the one we are looking
for. Since the confidence level is not given, we assume that it is 95%.
The formula for the confidence interval is: mean ± t (α/2)(n-1) * s √1 + 1/n
Where:
<span>
</span>
α= 5%
α/2
= 2.5%
t
0.025, 19 = 2.093 (check t table)
n
= 20
df
= n – 1 = 20 – 1 = 19
So plugging in our values:
8.41 ± 2.093 * 0.77 √ 1 + 1/20
= 8.41 ± 2.093 * 0.77 (1.0247)
= 8.41 ± 2.093 * 0.789019
= 8.41 ± 1.65141676
<span>= 6.7586 < x < 10.0614</span>
Answer:
The customer's total cost for the DVD is $19.26
Step-by-step explanation:
Store buy the dvd for $12.00.
The store price is $12.00+50% more
The store price= $12.00 *(1+0.5)= $18.00
Final price (tax added)= $18.00 + 7%
Final price= $18.00 * (1 + 0.07)= $19.26
