The major probability principle demonstrated in this exercise is that when two events occur at the same time, the probability of each occurrence yielding the same result is the of the probability of each separate event.

For this case the correct answer is the product

Step-by-step explanation:

When we have two events that occur at the same time, let's assume A and B the two events, and we want to find this probability:

And we want that he probability of each occurrence yielding the same result is the of the probability of each separate event since "The probability of two independent events occurring  together is the of the probability of each event occurring separately". So for this case we need to use the independence condition like this:

And then the correct option is product rule.

answer is 8x+24

area of vanessa's patio = length × width

given, length = (3x² + 5x + 10)

width = (x² - 3x - 1)

area of vanessa's patio = (3x² + 5x + 10)(x² - 3x - 1)

= 3x²(x² - 3x - 1) + 5x(x² - 3x - 1) + 10(x² - 3x - 1)

= 3x⁴ - 9x³ - 3x² + 5x³ - 15x² - 5x + 10x² - 30x - 10

= 3x⁴ - 4x³ - 8x² - 35x - 10

hence, expression of vanessa's patio = (3x⁴ - 4x³ - 8x² - 35x - 10)

p = 6s

step-by-step explanation: