Select each set of events that are independent.

Roll a number cube, then flip a coin

Roll two number cubes

Pick a green candy from bag, eat the candy, then pick a yellow candy from a different bag

Pick a Jack from a deck of cards, don't put it back, then pick a King from the same deck

Pick a blue candy from a bag, eat the candy, then pick a red candy from the same bag

Pick a yellow marble from a bag, don't put it back, pick a green marble from the same bag

which ones are independent?

Options A, B and C are all independent events while the rest are all dependent events.

Step-by-step explanation:

Please kindly check the attached files for explanation.

c. prove the lengths are the same.

step-by-step explanation:

you need to prove the segments are congruent. congruent segments have the same length. find the lengths of the segments using the distance formula, and compare them.

answer: c. prove the lengths are the same.

the system of inequity is

step-by-step explanation:

from the given graph it is noticed that we have two related lines. one is solid and another is dashed.

if a line passing through two points, then the equation of line is

the solid line passing through the points (0,4) and (4,0).

the related equation of solid line is .

similarly, find the related equation of dashed line. the dashed liune passing through the points (0,0) and (3,1).

the related equation of dashed line is

from the given graph it is noticed that the point (0,1) lies on the shaded region, therefore the point (0,1) must be satisfied by the related equations.

check the related equations by the point (0,1).

this statement is true if the sign of inequality is < instead of equality. since it is an solid line therefore the sign of inequality will be . the required inequality is

similarly, check the second related equation.

it is a dashed line, so this statement is true if the sign of inequality is > . the required inequality is