Determine the sample space of all of the possible outcomes of choosing a card numbered 1,2,3,4 and a blue, green, or yellow marble. How many outcomes involve choosing a blue marble?

 outcomes in sample space = 12,  outcomes involve choosing a blue marble =4.

Step-by-step explanation:

Choices for numbers = 4

Choices for marbles =3

By Fundamental counting principle,

Outcomes in sample space = (Choices for numbers)  x (Choices for marbles)

= 4x 3

=12

Hence, outcomes in sample space = 12

Number of outcomes involved for blue marble = (Choices for numbers) x ( choice of marble (1))

=  4 x 1 =4

Hence, outcomes involve choosing a blue marble =4.

answer: integers are just whole numbers: positive, negative, and zero.

i = {-∞, -2, -1, 0, 1, 2, 3, ∞}

let x = 1st integer

let y = 2nd integer

x = 3y + 17   {equation 1}

xy = -24         {equation 2}

substitute 3y+17 in place of x n equation 2

and solve for y.

(3y+17)y = -24

3y2 + 17y = -24

3y2 + 17y + 24 = 0

from quadratic equation:

y = [-17±√(172-4(3)(24))]/(2(3))

y = (-17 ±√1)/6

y = (-17+1)/6   or     y = (-17-1)/6

y = -16/6           or     y = -18/6

y = -2 2/3         or   y = -3

since we are dealing with

y = -3

x = 3y+17 = -9+17 = 8

the integers are -3, 8

step-by-step explanation: