You randomly draw a marble from a bag of marbles that contains 3 blie marbles, 4 green marbles, and 5 red marbles. What is P?

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Question:

You randomly draw a marble from a bag of marbles that contains 3 blue marbles, 4 green marbles, and 5 red marbles. What is P?

a) selecting a blue marble

b) selecting a green marble

c) selecting a red marble

a) P(blue marble) = 1/4

b) P(green marble) = 1/3

c) P(red marble) = 5/12

Step-by-step explanation:

a) The probability of selecting a blue marble is given by,

P(blue marble) = no. of blue marbles/total no. of marbles

Where number of blue marbles = 3

Total number of marbles = 3 + 4 + 5 = 12

P(blue marble) = 3/12

P(blue marble) = 1/4

b) The probability of selecting a green marble is given by,

P(green marble) = no. of green marbles/total no. of marbles

Number of green marbles = 4

Total number of marbles = 12

P(green marble) = 4/12

P(green marble) = 1/3

c) The probability of selecting a red marble is given by,

P(red marble) = no. of red marbles/total no. of marbles

Where number of red marbles = 5

Total number of marbles = 12

P(red marble) = 5/12

So, the probabilities are

P(blue marble) = 1/4

P(green marble) = 1/3

P(red marble) = 5/12

x= -3 and

step-by-step explanation:

to find the roots of a cubic, use division or factoring to find the factors then set equal to 0. as this is a difference of cubes, it factors into

where a is the cube root of .

here   this is 27 and the cube root of 27 is 3. so we write using the form:

.

set each factor to 0 and solve for x.

x-3=0

x=3

the quadratic expression does not factor and must be solved using the quadratic formula.

where a = 1, b=3, and c=9

this cubic has two complex roots.