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(5x - 2)(4x² - 3x - 2)
Use the distributive property
=(5x)(4x²) + (5x)(-3x) + (5x)(-2) + (-2)(4x²) + (-2)(-3x)² + (-2)(-2)
= 20x³ - 15x² - 10x - 8x² + 6x + 4
= 20x³ - 23x² -4x + 4
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Part A
Use the binomial probability distribution formula.
p = 0.54 = probability of getting a purple marble
n = 5 = sample size
x = 2 = number of purple we want to get

The
portion is from the nCr combination formula. The exclamation marks indicate a factorial.
Alternatively, you could use Pascal's Triangle for that portion.
<h3>Answer: 0.283831776</h3>
This decimal value is exact. Round it however you need to.
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Part B
To find the expected value, aka the mean, we multiply the sample size and probability of getting a purple marble on any single selection.
n*p = 5*0.54 = 2.7
<h3>Answer: 2.7</h3>
3/1 is the slope of the line