The area of the shaded sector is shown. Find the area of $\odot M$ . Round your answer to the nearest hundredth. A circle with c
1 answer:
You might be interested in
Answer:
a. 0.1536
b. 0.9728
Step-by-step explanation:
The probability that a component fails, P(Y) = 0.2
The number of components in the system = 4
The number of components required for the subsystem to operate = 2
a. By binomial theorem, we have;
The probability that exactly 2 last longer than 1,000 hours, P(Y = 2) is given as follows;
P(Y = 2) = × 0.2² × 0.8² = 0.1536
The probability that exactly 2 last longer than 1,000 hours, P(Y = 2) = 0.1536
b. The probability that the system last longer than 1,000 hours, P(O) = The probability that no component fails + The probability that only one component fails + The probability that two component fails leaving two working
Therefore, we have;
P(O) = P(Y = 0) + P(Y = 1) + P(Y = 2)
P(Y = 0) = × 0.2⁰ × 0.8⁴ = 0.4096
P(Y = 1) = × 0.2¹ × 0.8³ = 0.4096
P(Y = 2) = × 0.2² × 0.8² = 0.1536
∴ P(O) = 0.4096 + 0.4096 + 0.1536 = 0.9728
The probability that the subsystem operates longer than 1,000 hours = 0.9728
Using the slope concept, it is found that:
- The minimum horizontal distance is of 14,281.5 feet.
- The maximum horizontal distance is of 15,398.6 feet.
- The slope is given by the <u>vertical change divided by the horizontal change</u>.
- It's also the tangent of the angle of depression.
In this problem, the vertical change is the altitude of 10,000 feet.
The minimum horizontal distance is with an angle of 35º, hence:
The maximum horizontal distance is with an angle of 33º, hence:
You can learn more about the slope concept at brainly.com/question/22568180