Answer:
it takes 13 votes to win a majority
Step-by-step explanation:
half+1 in the case of 25
it takes 13 votes to win a majority ( because there is nothing called half vote)
The trigonometric identity (cos⁴θ - sin⁴θ)/(1 - tan⁴θ) = cos⁴θ
<h3>
How to solve the trigonometric identity?</h3>
Since (cos⁴θ - sin⁴θ)/(1 - tan⁴θ) = [(cos²θ)² - (sin²θ)²]/[1 - (tan²θ)²]
Using the identity a² - b² = (a + b)(a - b), we have
(cos⁴θ - sin⁴θ)/(1 - tan⁴θ) = [(cos²θ)² - (sin²θ)²]/[1 - (tan²θ)²]
= (cos²θ - sin²θ)(cos²θ + sin²θ)/[(1 - tan²θ)(1 + tan²θ)] =
= (cos²θ - sin²θ) × 1/[(1 - tan²θ)sec²θ] (since (cos²θ + sin²θ) = 1 and 1 + tan²θ = sec²θ)
Also, Using the identity a² - b² = (a + b)(a - b), we have
(cos²θ - sin²θ) × 1/[(1 - tan²θ)sec²θ] = (cosθ - sinθ)(cosθ + sinθ)/[(1 - tanθ)(1 + tanθ)sec²θ]
= (cosθ - sinθ)(cosθ + sinθ)/[(cosθ - sinθ)/cosθ × (cosθ + sinθ)/cosθ × sec²θ]
= (cosθ - sinθ)(cosθ + sinθ)/[(cosθ - sinθ)(cosθ + sinθ)/cos²θ × 1/cos²θ]
= (cosθ - sinθ)(cosθ + sinθ)cos⁴θ/[(cosθ - sinθ)(cosθ + sinθ)]
= 1 × cos⁴θ
= cos⁴θ
So, the trigonometric identity (cos⁴θ - sin⁴θ)/(1 - tan⁴θ) = cos⁴θ
Learn more about trigonometric identities here:
brainly.com/question/27990864
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Answer:
0.0214
Step-by-step explanation:
Given that :
p = 5% = 0.05
Number of trials (n) = 5
probability that the sample contains exactly two defective parts
P(x = 2)
Using the binomial probability function :
P(x = x) = nCr * p^x * (1 - p)^(n-x)
P(x = 2) = 5C2 * 0.05^2 * (0.95)^3
P(x = 2) = 5C2 * 0.05^2 * (0.95)^3
P(x = 2) = 10 * 0.0025 * 0.857375
= 0.021434375
= 0.0214
Answer:
3 cm
Step-by-step explanation:
The perimeter of the square is 24 cm, so the side length is 6 cm.
I assume B is the point between A and C where the tangent line intersects the circle. If so, B is the midpoint of AC, so it is half the length. Therefore, BC = 3 cm.
Answer: 8000700
Step-by-step explanation:
10 to the 6th power is 100000
1000000 * 8.0007 = 8000700
