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dangina [55]
3 years ago
13

In a bag there are 4 blue marbles,8 red marbles, and 5 orange marbles. if two marbles are drawn without replacement find the pro

bability that both marbles are the same color, the second marble being red. the first being blue the second being orange
Mathematics
1 answer:
g100num [7]3 years ago
3 0
P( both same colour) = P(both blue) + P(both red) + P(both orange)

=  4/17 * 3/16 + 8/17 * 7/16 +  5/17 * 4/16  =  3/68 +  7/34 + 5/68  =  11/34 Answer

P( second marble being red)  = P(first marble not being red) * P( second being red)

= 9/17 * 8/16 = 9/17 * 1/2 = 9/34 answer

P(first ble and second orange) = 4/17 * 5/16 =   5/68  answer






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Customers enter the waiting line to pay for food as they leave a cafeteria on a first-come, first-served basis. The arrival rate
Elan Coil [88]

Answer:

The answer is B) 0.57.

Step-by-step explanation:

In this problem we have to apply queueing theory.

It is a single server queueing problem.

The arrival rate is  \lambda=4 and the service rate is \mu=7.

The proportion of time that the server is busy is now as the "server utilization"and can be calculated as:

p=\frac{\lambda}{c\mu} =\frac{4}{1*7}=0.57

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3 years ago
Write the equation of each line using the given information.
Leni [432]

a) x – 2y + 6 = 0 b) x + y = 1 c) y = 1 d) y = -3x + 8

<h3><u>Solution:</u></h3>

<em><u>a. The points (-4,1) and (2,4) both lie on the line</u></em>

The general line equation on which (a, b) and (c, d) lies is:

y-\mathrm{b}=\frac{d-b}{c-a}(x - a)

Here the given points are (a, b) = (-4, 1) and (c, d) = (2, 4)

Thus the required equation is:

y-1=\frac{4-1}{2-(-4)}(x-(-4))

On solving we get,

\begin{array}{l}{\rightarrow y-1=\frac{3}{2+4}(x+4)} \\\\ {\rightarrow y-1=\frac{3}{6}(x+4)} \\\\ {\rightarrow 2(y-1)=1(x+4)} \\\\ {\rightarrow 2 y-2=x+4} \\\\ {\rightarrow x-2 y+6=0}\end{array}

<em><u>b.) m= -1 and the point (2, -1) lies on the line</u></em>

The equation of line in point slope form is y – b = m(x – a)  

where m is slope and (a, b) is a point on it

Here m = -1 and (a, b) = (2, -1)

Thus the required equation is:

y – (-1) = -1(x - 2)  

y + 1 = -x + 2  

y = -x + 2 -1  

y = -x + 1

<em><u>c. )It has the same slope as y = 5 and passes through (1, 1)</u></em>

our line has same slope with y = 5, then our equation would be y = k  and it passes through (x, y) = (1, 1) so, then by substitution

1 = k

k =1  

Then our equation will be y = k

y = 1

<em><u> d. ) m= -3 and it has a y-intercept of (0, 8)</u></em>

line equation in slope intercept form is y = mx + b where m is slope and b is y – intercept.

Then, our equation will be y = -3x + 8

We took y- intercept = 8 as it is the value of y when x = 0

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