Mathematics
Simple events likelihood experimental probability

Problem 1

Closer to 1

Explanation:

There are 20 gumballs total. Half of this is 20/2 = 10 gumballs. If there's more than 10 of one color, then the probability of getting that color is closer to 1, than it is to 0. Here we have 12 pink which is greater than 10, so that's why the answer is closer to 1.

Problem 2

Closer to 0

Explanation:

The amount of green (3) is less than 10, so that's why the probability is closer to 0 than it is to 1. We can see that 3/20 = 0.15 is less than 0.50

Problem 3

Closer to 0

Explanation:

We have a similar situation compared to problem 2. This time we have 5/20 = 0.25 which is less than 0.50

Problem 4

48% chance; fairly likely

Explanation:

We have 12 green out of 25 total, so the probability of choosing green is 12/25 = 0.48 = 48%. While this probability is not over 50%, I still say it's fairly likely considering the other colors lead to smaller probabilities. For instance, purple has a chance of 6/25 = 0.24 = 24% and orange has a probability of 2/25 = 0.04 = 4%, both of which are smaller than 48%

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