8

Mathematics

1 answer:

konstantin123 [22]3 years ago

5 0

Answer:

f(x) = 7

Step-by-step explanation:

since an even function is defined as a function with the following rule. f(-x) = f(x) for all x in the domain of f(x). It would be odd if f(-x) = -f(x) for all x in the domain of f(x). If f(-x) ≠ -f(x), than it is neither. these are all known as the parity of a function.

you can apply these rules to all of given functions like this. (-x-1) ≠ -(x-1) so it is neither. 8(-x) = -(8x) so it would be odd. 2(-x)-(-x) = -(2x-x) so it is odd as well. This would make f(x) = 7 the only option, as there are no x variables in the equation so 7 = 7.

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Answer:

(a) 0.4242

(b) 0.0707

Step-by-step explanation:

The total number of ways of selecting 8 herbs from 12 is

$\binom{12}{8}=495$

(a) If 2 herbs are selected, then there are 8 - 2 = 6 herbs to be selected from 12 - 8 = 10. The number of ways of the selection is then

$\binom{10}{6}= 210$

Note that this is the number of ways that both are included. We would have multiplied by 2! if any of them were to be included.

The probability = $\dfrac{210}{495}=0.4242$

(b) If 5 herbs are selected, then there are 8 - 5 = 3 herbs to be selected from 12 - 5 = 7. The number of ways of the selection is then

$\binom{7}{3}= 35$

This is the number of ways that both are included. We would have multiplied by 5! if any of them were to be included. In that case, our probability will exceed 1; this implies that certainly, at least, one of them is included.

The probability = $\dfrac{35}{495}=0.0707$