Is the following statement always, never, or sometimes true?

2 answers:

7 0

We are given the following statement; A number raised to a negative exponent is negative. We can go through experimental points. In this case, when the number is positive, the result is also positive. If the number is negative, we can say the result is negative.

pickupchik [31]3 years ago

3 0

Sometimes...

2^-3 = 1/(2^3) = 1/8

-2^-3 = 1/(-2^3) = -1/8

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A complex electronic system is built with a certain number of backup components in its subsystems. One subsystem has four identi

Tcecarenko [31]

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) = $\dbinom{4}{2}$ × 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) = $\dbinom{4}{0}$ × 0.2⁰ × 0.8⁴ = 0.4096