Question is in the pictures.
1 answer:
<h3>Answer:</h3>
x/tan(x) is an even function
sec(x)/x is an odd function
<h3>Explanation:</h3><em>x/tan(x)</em>
For f(x) = x/tan(x), consider f(-x).
... f(-x) = -x/tan(-x)
Now, we know that tan(x) is an odd function, so tan(-x) = -tan(x). Using this, we have ...
... f(-x) = -x/(-tan(x)) = x/tan(x) = f(x)
The relation f(-x) = f(x) is characteristic of an even function, one that is symmetrical about the y-axis.
_____
<em>sec(x)/x</em>
For g(x) = sec(x)/x, consider g(-x).
... g(-x) = sec(-x)/(-x)
Now, we know that sec(x) is an even function, so sec(-x) = sec(x). Using this, we have ...
... g(-x) = sec(x)/(-x) = -sec(x)/x = -g(x)
The relation g(-x) = -g(x) is characeristic of an odd function, one that is symmetrical about the origin.
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Answer:
P(A and B) is greater than 1 is never happened ⇒ C
Step-by-step explanation:
Two events are independent if the result of the second event is not affected by the result of the first event
If A and B are independent events, the probability of both events is the product of the probabilities of the both events P (A and B) = P(A) · P(B)
∵ The probability of any event is less than 1
∵ P(A) < 1
∵ P(A) >
- That means P(A) is greater than half and less than 1
∴ < P(A) < 1
∵ P(B) < 1
∵ P(B) >
- That means P(B) is greater than half and less than 1
∴ < P(B) < 1
∵ P(A and B) = P(A) . P(B)
- Remember the product of any fractions less than 1 is less than 1
∴ < P(A) . P(B) < 1
- That means any expression equals to P(A) . P(B) must be greater
than and less than 1
∴ < P(A and B) < 1
∴ P(A and B) is greater than 1 is never happened