<span>65
As for the reason the average life expectancy of a Roman who reaches the age of 30 being so much higher than the average expectancy overall, that's simply a matter of taking the average of 50 and 80, verses the average of 1,6,20,50,80. Let's illustrate that by calculating the average life expectancy of a Roman at birth, and after age 30.
For birth, there's 5 ranges, each of which has the same probability. They are
[0,2]: Midpoint = 1. Probability = 0.2. Product = 1*0.2 = 0.2
[2,10]: Midpoint = 6. Probability = 0.2. Product = 6*0.2 = 1.2
[10,30]: Midpoint = 20. Probability = 0.2. Product = 20*0.2 = 4
[30,70]: Midpoint = 50. Probability = 0.2. Product = 50*0.2 = 10
[70,90]: Midpoint = 80. Probability = 0.2. Product = 80*0.2 = 16
Sum = 0.2 + 1.2 + 4 + 10 + 16 = 31.4
But upon reaching 30, there is no longer a mere 0.2 probability for those last 2 slots. The chart looks like
[30,70]: Midpoint = 50. Probability = 0.5. Product = 50*0.5 = 25
[70,90]: Midpoint = 80. Probability = 0.5. Product = 80*0.5 = 40
Sum = 65
If you look at each possible range of ages, the actual life expectancy is
at birth: 31.4 years
after age 2: 39 years
after age 10: 50 years
after age 30: 65 years
after age 70: 80 years</span>
Answer:
(- 2, 1 ) and (1, 4 )
Step-by-step explanation:
Given the 2 equations
y = - x² + 5 → (1)
- x + y = 3 → (2)
Rearrange (2) expressing y in terms of x by adding x to both sides
y = x + 3 → (3)
Substitute y = x + 3 into (1)
x + 3 = - x² + 5 ( subtract - x² + 5 from both sides )
x² + x - 2 = 0 ← in standard form
(x + 2)(x - 1) = 0 ← in factored form
Equate each factor to zero and solve for x
x + 2 = 0 ⇒ x = - 2
x - 1 = 0 ⇒ x = 1
Substitute these values into (3) for corresponding values of y
x = - 2 : y = - 2 + 3 = 1 ⇒ (- 2, 1 )
x = 1 : y = 1 + 3 = 4 ⇒ (1, 4 )
The 31st term of this sequence is 189.
9, 15, 21, 27, 33 (5), 39, 45, 51, 57, 63 (10), 69, 75, 81, 87, 93 (15), 99, 105, 111, 117, 123 (20), 129, 135, 141, 147, 153 (25), 159, 165, 171, 177, 183 (30), 189.
