Select Independent or Not independent for each situation. Not independent Independent a. A jar contains fifteen coins. Two coins are picked randomly without replacement. b. A number cube is rolled twice. c. A box contains number cards labeled from 1 to 10. d. Two cards are chosen randomly with replacement. e. There are 3 green balls and 7 red balls in a bag. f. Two balls are chosen randomly without replacement.

The correct answers are a. Independent; b. Independent; c. Independent;  e.  Not Independent

Step-by-step explanation:

a. A jar contains fifteen coins which. Two coins are picked randomly without replacement. Thus the second pick is not dependent on the first pick as the coins in the all same and thus the experiment is independent.

b. A number cube is rolled twice. Outcome of the first roll is independent of the outcome in the second and thus the experiment is independent.

c. A box contains number cards labeled from 1 to 10 where 2 cards are chosen randomly with replacement. Hence first draw does not effect the sample making the experiment independent.

e. There are 3 green balls and 7 red balls in a bag with 2 balls are chosen randomly without replacement. Thus one pick depends on what is drawn in the previous pick thus making it a dependent or not independent event.

5x + 3y = - 4

step-by-step explanation:

the equation of a line in standard form is

ax + by = c ( a is a positive integer and b, c are integers )

express the line first of all in slope- intercept form

y = mx + c ( m is the slope and c the y-intercept )

to calculate m use the gradient formula

m = ( y₂ - y₁ ) / ( x₂ - x₁ )

with (x₁, y₁ ) = (7, - 3) and (x₂, y₂ ) = (4, - 8)

m = = -

y = - x + c ← is the partial equation

to find c substitute either of the 2 points into the partial equation

using (4, - 8 ), then

- 8 = - + c ⇒ c = -

y = - x - ← in slope-intercept form

multiply all terms by 3 to eliminate the fractions

3y = - 5x - 4 ( add 5x to both sides )

5x + 3y = - 4 ← in standard form