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sergeinik [125]
2 years ago
15

Suppose you have a bag containing 2 black marbles and 3 red marbles. You reach into the bag, select a marble, see what color it

is and replace it in the bag. Then you repeat this process. What is the probability of first selecting a black marble, replacing it and then selecting a red marble?
Mathematics
1 answer:
sweet [91]2 years ago
4 0
(3/5)(2/5)=6/25
.............................
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Nathan has exactly 407 cards from national league however since you have to estimate with that rate the answer is 400.

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Answer:

f(x) = 3 \cdot 0.2^x

Step-by-step explanation:

f(x) = 3 \cdot 0.2^x


Domain of f: "What values of x can we plug into this equation?" This makes sense for all real numbers so the domain is \mathbb{R}

Range of f: "What values of f(x) can we get out of the function?" From the graph we see we can get any real number greater than 0 out of the function by choosing a suitable x-value in the domain. The range is therefore (0, \infty).

Continuity: Since the graph is one, unbroken curve (i.e. a curve that can be drawn in one movement without taking your pen off the paper). We see that "roughly speaking" the function is continuous.

Increasing or decreasing behaviour: For all x in the domain, as x increases, f(x) decreases. This means the function exhibits decreasing behaviour.

Symmetry: It is clear to see the graph of f(x) has no symmetry.

Boundedness: Looking at the graph we see it is unbounded above as when we choose negative values, the graph of f(x) explodes upwards exponentially. Choose a value of x, plug it in, next choose (x-1), plug this in and we observe f(x-1) > f(x) for all x in the domain.

The function is however bounded below by 0: no value of x in the domain exists which satisfies f(x) < 0.

Extrema: As far as I can tell, there are no turning points on the curve. (Is this what you mean by extrema?)

Asymptotes: Contrary to the curve's appearance, there are no vertical asymtotes for this curve. The negative-x portion of the curve is just growing so quickly it appears to look like an asymptote. There is a value of f(x) for all x<0. There is however a horizontal asymtote: y=0.

End behaviour: As x \rightarrow \infty, f(x) \rightarrow 0. As x \rightarrow -\infty, f(x) \rightarrow +\infty

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