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3 years ago

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A box contains red marbles. 8 green marbles 4 blue marbles and 3 yellow marbles. If 2 marbles are randomly selected without repl

acement, what is the probability that a red marble is selected and then a green marble is selected?

1 answer:

Agata [3.3K]3 years ago

5 0

Answer:

0.1052 = 10.52%

Step-by-step explanation:

The question missing the number of red marbles, it should be 5.

You select 2 marble randomly without replacement. The word without replacement show that you pick the marble at different times, so the order is important. There are 5 red, 8 green, 4 blue, 3 yellow which means the total marble is 8+4+3= 16 marbles. The chance to pick red marble then a green marble will be:

5/20 * 8/19= 2/19= 0.1052 = 10.52%

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A signal can be sent from one location to another by running different colored flags up a flagpole, one above the other. There a

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<h3>What is the permutation formula?</h3>

The number of possible permutations of x elements from a set of n elements is given by:

$P_{(n,x)} = \frac{n!}{(n-x)!}$

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2 years ago

Lines k and n intersect on the y-axis

avanturin [10]

a) The equation of line k is:

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b) The equation of line j is:

$y = \frac{167}{202}x + \frac{1546}{202}$

The equation of a line, in <u>slope-intercept formula</u>, is given by:

$y = mx + b$

In which:

m is the slope, which is the rate of change.
b is the y-intercept, which is the value of y when x = 0.

Item a:

Line k intersects line m with an angle of 109º, thus:

$\tan{109^{\circ}} = \frac{m_2 - m_1}{1 + m_1m_2}$

In which $m_1$ and $m_2$ are the slopes of <u>k and m.</u>

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$m_1 = \frac{2 - (-1)}{5 - (-3)} = \frac{3}{8}$

The tangent of 109 degrees is $\tan{109^{\circ}} = -\frac{29}{10}$
Thus, the slope of line m is found solving the following equation:

$\tan{109^{\circ}} = \frac{m_2 - m_1}{1 + m_1m_2}$

$-\frac{29}{10} = \frac{m_2 - \frac{3}{8}}{1 + \frac{3}{8}m_2}$

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$m_2 + \frac{87}{80}m_2 = -\frac{29}{10} + \frac{3}{8}$

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$m_2 = -\frac{202}{167}$

Thus:

$y = -\frac{202}{167}x + b$

It goes through point (-2,6), that is, when $x = -2, y = 6$ , and this is used to find b.

$y = -\frac{202}{167}x + b$

$6 = -\frac{202}{167}(-2) + b$

$b = 6 - \frac{404}{167}$

$b = \frac{6(167)-404}{167}$

$b = \frac{598}{167}$

Thus. the equation of line k, in slope-intercept formula, is:

$y = -\frac{202}{167}x + \frac{598}{167}$

Item b:

Lines j and k intersect at an angle of 90º, thus they are perpendicular, which means that the multiplication of their slopes is -1.

Thus, the slope of line j is:

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Then

$y = \frac{167}{202}x + b$

Also goes through point (-2,6), thus:

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$b = \frac{1546}{202}$

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$y = \frac{167}{202}x + \frac{1546}{202}$

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