Your numbers are 2, 3, 4.
The three consecutive numbers are x, x+1, x+2
The square of the first equals the third so x^2=x+2
Solve this quadratic as x^2-x-2=0
Factor into (x+1)(x-2)=0
So your answers are x=-1 and x=2
Since the question says they’re positive integers, use x=2
So the numbers are 2, 3, 4
Answer:
p = -3
Step-by-step explanation:
−0.63p − 5.04 + 3.57 = 7.05 + 2.21p
−0.63p − 1.47 = 7.05 + 2.21p (add 0.63p to both sides)
− 1.47 = 7.05 + 2.21p + 0.63p
− 1.47 = 7.05 + 2.84p (subtract 7.05 from both sides)
− 1.47 - 7.05 = 2.84p
-8.52 = 2.84p (rearrange)
2.84p = -8.52 (divide both sides by 2.84)
p = -8.52 / 2.84
p = -3
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>