Answer:
Total area = 6(16√3) = 96√3
Step-by-step explanation:
Important that you understand the meaning of "apothem," looking that up on the 'Net if necessary. A regular hexagon can be broken down into 6 identical, pie-slice-shaped figures; we find the area of the hexagon by finding the area of one such slice and multiplying the result by 2.
An apothem is a line from the center of the circle to the edge of the slice, perpendicular to that edge, representing the height of the slice as measured from that edge to the center of the circle. There are 6 such slices. The apothem is also a measure of the height of such a triangular slice. If the radius is 8, then half the base of the slice is found using the Pythagorean Theorem: (b/2)² + (4√3)² = 8².
Then (b²/4) + 16(3) = 64, or
b²/4 = 64 - 48, or b²/4 = 16, which yields b² = 64, or b = 8.
Then the area of one slice is A = (1/2)*(base)(height) = (1/2)(8)(4√3), or
A = 16√3. Multiply this result by 6 to find the area of the entire hexagon:
Total area = 6(16√3) = 96√3
Answer:
Product B performed worse
Step-by-step explanation:
71% experienced relief with Product A
31/50, which is 62%, got relief with Product B
Answer:
0
Step-by-step explanation:
→ First find inverse cosine 1/2
60°
→ Now multiply this answer by 3 because then if you substitute it in you get 0.5
∝ = 180°
→ Now find sine of 180°
0
Answer: 0.3974
Step-by-step explanation:
Given : The distribution of annual returns on common stocks is roughly symmetric, so the mean return over even a moderate number of years is close to Normal.
Real annual returns on U.S. common stocks had mean : ![\mu=0.087](https://tex.z-dn.net/?f=%5Cmu%3D0.087)
Standard deviation : ![\sigma=0.202](https://tex.z-dn.net/?f=%5Csigma%3D0.202)
We assume that the past pattern of variation continues.
Let x be the random variable that represents the annual returns on common stocks over the next 32 years .
The formula for z-score : ![z=\dfrac{x-\mu}{\sigma}](https://tex.z-dn.net/?f=z%3D%5Cdfrac%7Bx-%5Cmu%7D%7B%5Csigma%7D)
For x= 0.14, ![z=\dfrac{0.14-0.087}{0.202}\approx0.26](https://tex.z-dn.net/?f=z%3D%5Cdfrac%7B0.14-0.087%7D%7B0.202%7D%5Capprox0.26)
By using the standard normal distribution table , we have
The probability that the mean annual return on common stocks over the next 32 years will exceed 14% :-
![P(x>0.14)=P(z>0.26)=1-P(z\leq0.26)\\\\=1-0.6025681=0.3974319\approx0.3974](https://tex.z-dn.net/?f=P%28x%3E0.14%29%3DP%28z%3E0.26%29%3D1-P%28z%5Cleq0.26%29%5C%5C%5C%5C%3D1-0.6025681%3D0.3974319%5Capprox0.3974)
Answer:
$37
Step-by-step explanation:
12 * 6 -35 = $37