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kipiarov [429]
3 years ago
13

3. A bag has five blue marbles, seven red marbles and nine green marbles. Three marbles are drawn

Mathematics
1 answer:
Arte-miy333 [17]3 years ago
7 0

Answer:

The probability is 9/266

Step-by-step explanation:

The first thing to do here is get the total number of marbles = 5 + 7 + 9 = 21 marbles

Now we are drawing the marbles without replacement, this means once a marble is drawn there is a decrease in the total number of marbles left.

The probability of drawing a green marble initially = number of green marbles/ total

number of marbles = 9/21 = 3/7

Now, we want to draw a blue marble

There are 5 blue marbles and we have already drawn one marble from the total. So the probability of drawing a blue marble would be 5/20 = 1/4

And lastly, another green marble

That would make 6 green marbles left and a total of just 19 left. So the probability at this point for green marbles = 6/19

Having and in probability means we multiply all

So this means the probability we are calculating is; 3/7 * 1/4 * 6/19 = 18/(28 * 19) = 9/(14 * 19) = 9/266

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3 years ago
Investigate the existence of a extrema value, what does the markered part mean?
OLga [1]

Answer: We have

f'(x) = a x + b,

f'(x) = 0 at x = -b/a

f(x) = a x^2 / 2 + b x + c


Meaning of marked part


❟ ∵ a<0 ❟ f is a quadratic function

∴ f has absolute maximum value at x = -b/a


For all a with a less than zero, f is a quadratic function. Therefore f has a global maximum at x = -b/a


That typesetting seems very sloppy. It probably is supposed to be


∀a < 0, f is a quadratic function.


The second sentence is sloppy in use of "absolute". It can't mean absolute value, so presumably it means "global".


Sometimes a minimum or maximum is only local, but a quadratic function has exactly one extrema, and it is global. And if a < 0, the extrema is a global maximum.


Step-by-step explanation:


An extrema (minimum or maximum) for f(x) occurs only where f'(x) = 0, that is, when the slope of the tangent at x is zero.


But if the function crosses its tangent at that point, the point is an inflection point, not an extrema. A quadratic never crosses it's tangent.


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