With 180° < <em>θ</em> < 270°, we know that both cos(<em>θ</em>) < 0 and sin(<em>θ</em>) < 0.
Then from the Pythagorean identity, it follows that
sin²(<em>θ</em>) + cos²(<em>θ</em>) = 1 ==> sin(<em>θ</em>) = -√(1 - cos²(<em>θ</em>))
and so
sin(<em>θ</em>) = -√(1 - (-8/13)²) = -√105/13
Recall the double angle identity for sine:
sin(2<em>θ</em>) = 2 sin(<em>θ</em>) cos(<em>θ</em>) = 2 (-√105/13) (-8/13) = 16√105/169
1/2n + 15 = 9 <== ur equation
1/2n = 9 - 15
1/2n = - 6
n = -6 * 2
n = - 12 <== ur solution
(30.65)
it takes an object the ground times the constant gravity. in this case 2.5 seconds times 9.807 meter per square second will then give us the 30.65 meter.
have a nice day!
Answer:
P(x = 0) = 0.004
P(x = 0) = 0.047
P(x = 0) = 0.211
P(x = 0) = 0.422
P(x = 0) = 0.316
Step-by-step explanation:
We are given the following information:
We treat a person who does not become a repeat offender as a success.
P(Success) = P(person who does not become a repeat offender) = 0.75
Then the number of people follows a binomial distribution, where
where n is the total number of observations, x is the number of success, p is the probability of success.
Now, we are given n = 4
We have to evaluate:
![P(x = 0)\\= \binom{4}{0}(0.75)^0(1-0.75)^4 = 0.004](https://tex.z-dn.net/?f=P%28x%20%3D%200%29%5C%5C%3D%20%5Cbinom%7B4%7D%7B0%7D%280.75%29%5E0%281-0.75%29%5E4%20%3D%200.004)
![P(x = 1)\\= \binom{4}{1}(0.75)^1(1-0.75)^3 = 0.047](https://tex.z-dn.net/?f=P%28x%20%3D%201%29%5C%5C%3D%20%5Cbinom%7B4%7D%7B1%7D%280.75%29%5E1%281-0.75%29%5E3%20%3D%200.047)
![P(x = 2)\\= \binom{4}{2}(0.75)^2(1-0.75)^2 = 0.211](https://tex.z-dn.net/?f=P%28x%20%3D%202%29%5C%5C%3D%20%5Cbinom%7B4%7D%7B2%7D%280.75%29%5E2%281-0.75%29%5E2%20%3D%200.211)
![P(x = 3)\\= \binom{4}{3}(0.75)^3(1-0.75)^1 = 0.422](https://tex.z-dn.net/?f=P%28x%20%3D%203%29%5C%5C%3D%20%5Cbinom%7B4%7D%7B3%7D%280.75%29%5E3%281-0.75%29%5E1%20%3D%200.422)
![P(x = 4)\\= \binom{4}{4}(0.75)^4(1-0.75)^0 = 0.316](https://tex.z-dn.net/?f=P%28x%20%3D%204%29%5C%5C%3D%20%5Cbinom%7B4%7D%7B4%7D%280.75%29%5E4%281-0.75%29%5E0%20%3D%200.316)