An e-mail lter is planned to separate valid e-mails from spam. The word free occurs in 50% of the spam messages and only 3% of the valid messages. Also, 20% of the messages are spam. Determine the following probabilities: (a) The message contains the word free. (b) The message is spam given that it contains free. (c) The message is valid given that it does not contain free.

answer: for each 3 girls there is 2 boys . 3: 2

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the rocket cannot penetrate the ground, in a contextual sense, therefore the roots of this equation should be the domain of this function. i'll let you find the roots of this quadratic equation (hint: use the quadratic formula:  

1- c

2-a

step-by-step explanation:

mark brainliest!

the answer is b

vertical asymptote .

horizontal asymptote .

step-by-step explanation:

given function is .

vertical asymptote is given by setting

denominator =0

when degree of numerator and denominator are same then divide first term of numerator by first term of denominator to get horizontal asymptote.