Answer:
In 500 rolls he can expect to get this outcome about 27.77...%* 500 = 139 times.
Answer:
√(4/5)
Step-by-step explanation:
First, let's use reflection property to find tan θ.
tan(-θ) = 1/2
-tan θ = 1/2
tan θ = -1/2
Since tan θ < 0 and sec θ > 0, θ must be in the fourth quadrant.
Now let's look at the problem we need to solve:
sin(5π/2 + θ)
Use angle sum formula:
sin(5π/2) cos θ + sin θ cos(5π/2)
Sine and cosine have periods of 2π, so:
sin(π/2) cos θ + sin θ cos(π/2)
Evaluate:
(1) cos θ + sin θ (0)
cos θ
We need to write this in terms of tan θ. We can use Pythagorean identity:
1 + tan² θ = sec² θ
1 + tan² θ = (1 / cos θ)²
±√(1 + tan² θ) = 1 / cos θ
cos θ = ±1 / √(1 + tan² θ)
Plugging in:
cos θ = ±1 / √(1 + (-1/2)²)
cos θ = ±1 / √(1 + 1/4)
cos θ = ±1 / √(5/4)
cos θ = ±√(4/5)
Since θ is in the fourth quadrant, cos θ > 0. So:
cos θ = √(4/5)
Or, written in proper form:
cos θ = (2√5) / 5
Answer:
2.174 hours
Step-by-step explanation:
Let the number of hours be represented as:
x
The price of Stock A at 9 A.M. was $12.79 Since then, the price has been increasing at the rate of $0.11 each hour.
$12.79 + $0.11 × x
12.79 + 0.11x
At noon the price of Stock B was $13.29 It begins to decrease at the rate of $0.12 each hour.
$13.29 - $0.12× x
13.29 - 0.12x
Equating both equations together
Stock A = Stock B
12.79 + 0.11x = 13.29 - 0.12x
Collecting like terms
0.11x + 0.12x = 13.29 - 12.79
0.23x = 0.5
x = 0.5/0.23
x = 2.1739130435 hours
x = Approximately = 2.174 hours
If the two rates continue, the number of hours that the prices of the two stocks will be the same is 2.174 hours
Answer:
52 - 48 = 4
Around 7%
(Please tell me if this is wrong)
