Five marbles are in a jar. two are red and three are white. four marbles are selected at random with replacement . a) find the probability that at most two red marbles are selected.

b) find the probability that at least three red marbles are selected.

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Ответ:

ginocousins06

26.12.2020

Mathematics

The bird will be at a ground distance of 10.04 units away.

Step-by-step explanation:

Vertex of a quadratic function:

Suppose we have a quadratic function in the following format:

$f(x) = ax^{2} + bx + c$

It's vertex is the point $(x_{v}, y_{v})$

In which

$x_{v} = -\frac{b}{2a}$

$y_{v} = -\frac{\Delta}{4a}$

Where

$\Delta = b^2-4ac$

If a<0, the vertex is a maximum point, that is, the maximum value happens at $x_{v}$ , and it's value is $y_{v}$ .

Equation for the height:

The height of the bird after x seconds is given by:

h(x) = -0.114x^2 + 2.29x + 3.5

Which is a quadratic equation with a = -0.114, b = 2.29, c = 3.5 .

When the bird is at its highest?

Quadratic equation with a < 0 , and thus, at the vertex. The ground distance is the x-value of the vertex. Thus

$x_{v} = -\frac{b}{2a} = -\frac{2.29}{2(-0.114)} = 10.04$

The bird will be at a ground distance of 10.04 units away.

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Five marbles are in a jar. two are red and three are white. four marbles are selected at random with replacement . a) find the probability that at most two red marbles are selected. b) find the probability that at least three red marbles are selected.