5x⁴ - 3x³ + 6x) - (3x³ + 11x² - 8x)<span>
</span>Expand the second bracket by multiplying throughout by -1
5x⁴ - 3x³ + 6x - <span>3x³ - 11x² + 8x
</span>
Group like terms and simplify
5x⁴ - 3x³ - 3x³ - 11x² + 6x <span>+ 8x
</span>5x⁴ - 6x³ - <span>11x² + 14x</span>
Answer:
907.46
Step-by-step explanation:
We know the area of a circle is:
![\pi r^{2} \\\pi (34/2)^{2}\\17^{2} \pi \\907.46](https://tex.z-dn.net/?f=%5Cpi%20r%5E%7B2%7D%20%5C%5C%5Cpi%20%2834%2F2%29%5E%7B2%7D%5C%5C17%5E%7B2%7D%20%5Cpi%20%5C%5C907.46)
Answer:
The unusual
values for this model are: ![X = 0, 1, 2, 7, 8](https://tex.z-dn.net/?f=X%20%3D%200%2C%201%2C%202%2C%207%2C%208)
Step-by-step explanation:
A binomial random variable
represents the number of successes obtained in a repetition of
Bernoulli-type trials with probability of success
. In this particular case,
, and
, therefore, the model is
. So, you have:
![P (X = 0) = {8 \choose 0} (0.53) ^ {0} (0.47) ^ {8} = 0.0024](https://tex.z-dn.net/?f=P%20%28X%20%3D%200%29%20%3D%20%7B8%20%5Cchoose%200%7D%20%280.53%29%20%5E%20%7B0%7D%20%280.47%29%20%5E%20%7B8%7D%20%3D%200.0024)
![P (X = 1) = {8 \choose 1} (0.53) ^ {1} (0.47) ^ {7} = 0.0215](https://tex.z-dn.net/?f=%20P%20%28X%20%3D%201%29%20%3D%20%7B8%20%5Cchoose%201%7D%20%280.53%29%20%5E%20%7B1%7D%20%280.47%29%20%5E%20%7B7%7D%20%3D%200.0215)
![P (X = 2) = {8 \choose 2} (0.53)^2 (0.47)^6 = 0.0848](https://tex.z-dn.net/?f=%20P%20%28X%20%3D%202%29%20%3D%20%7B8%20%5Cchoose%202%7D%20%280.53%29%5E2%20%280.47%29%5E6%20%3D%200.0848)
![P (X = 3) = {8 \choose 3} (0.53) ^ {3} (0.47)^5 = 0.1912](https://tex.z-dn.net/?f=%20P%20%28X%20%3D%203%29%20%3D%20%7B8%20%5Cchoose%203%7D%20%280.53%29%20%5E%20%7B3%7D%20%280.47%29%5E5%20%3D%200.1912)
![P (X = 4) = {8 \choose 4} (0.53) ^ {4} (0.47)^4} = 0.2695](https://tex.z-dn.net/?f=%20P%20%28X%20%3D%204%29%20%3D%20%7B8%20%5Cchoose%204%7D%20%280.53%29%20%5E%20%7B4%7D%20%280.47%29%5E4%7D%20%3D%200.2695)
![P (X = 5) = {8 \choose 5} (0.53) ^ {5} (0.47)^3 = 0.2431](https://tex.z-dn.net/?f=%20P%20%28X%20%3D%205%29%20%3D%20%7B8%20%5Cchoose%205%7D%20%280.53%29%20%5E%20%7B5%7D%20%280.47%29%5E3%20%3D%200.2431)
![P (X = 6) = {8 \choose 6} (0.53) ^ {6} (0.47)^2 = 0.1371](https://tex.z-dn.net/?f=%20P%20%28X%20%3D%206%29%20%3D%20%7B8%20%5Cchoose%206%7D%20%280.53%29%20%5E%20%7B6%7D%20%280.47%29%5E2%20%3D%200.1371)
![P (X = 7) = {8 \choose 7} (0.53) ^ {7} (0.47)^ {1} = 0.0442](https://tex.z-dn.net/?f=%20P%20%28X%20%3D%207%29%20%3D%20%7B8%20%5Cchoose%207%7D%20%280.53%29%20%5E%20%7B7%7D%20%280.47%29%5E%20%7B1%7D%20%3D%200.0442)
![P (X = 8) = {8 \choose 8} (0.53)^{8} (0.47)^{0} = 0.0062](https://tex.z-dn.net/?f=%20P%20%28X%20%3D%208%29%20%3D%20%7B8%20%5Cchoose%208%7D%20%280.53%29%5E%7B8%7D%20%280.47%29%5E%7B0%7D%20%3D%200.0062)
The unusual
values for this model are: ![X = 0, 1, 7, 8](https://tex.z-dn.net/?f=X%20%3D%200%2C%201%2C%207%2C%208)
Since it forms a "right triangle" we can apply trigonometry.
sin x = oppo/hyp
sin x = 13/20
x = sin^-1(13/20)
x = sin^-1(0.65)
x = 40.5
rounded to nearest degree
x = 41 degrees
Hope this helps! :)
Step-by-step explanation:
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