Answer:
7.35 years
Step-by-step explanation:
Given that :
mean = 8.4
standard deviation = 0.6
From the negative z tables, the corresponding data for 0.04 = -1.75
So, using the z-score formula:


-1.75 × 0.6 = x - 8.4
- 1.05 = x - 8.4
x = -1.05 + 8.4
x = 7.35 years
the shortest lifespan will last less than 7.35 years
∴ the longest 4% will have lifespans longer than x = 8.4 + 1.75(0.6)
= 9.45 years
Answer:
a) 2
b) s₁ and s₂
c) First linear equation: 5*x₁ + 8*x₂ + 10*x₃ + s₁ = 173
Second linear equation: 5*x₁ + 4*x₂ + 17*x₃ + s₂ = 254
Step-by-step explanation:
The problem statement, establishes two constraints, each one of them will need a slack variable to become a linear equation, so the answer for question
a) 2.
b) The constraints are: s₁ and s₂
c) First constraint
5*x₁ + 8*x₂ + 10*x₃ ≤ 173
We add slack variable s₁ and the inequality becomes
5*x₁ + 8*x₂ + 10*x₃ + s₁ = 173
The second constraint is:
5*x₁ + 4*x₂ + 17*x₃ ≤ 254
We add slack variable s₂ and the inequality becomes
5*x₁ + 4*x₂ + 17*x₃ + s₂ = 254
4, yes, 1
5, no?, 0
6, yes, 6
1. D: The overlap of the two sets represents the intersection, which is the set of elements common to both sets <em>M</em> and <em>C</em>. In this case, it's the set {4, 5, 6}.
2. D: <em>P</em> is the set of the first 100 multiples of 8 (8*1 = 8, 8*2 = 16, and so on)
3. C: <em>n</em>(<em>A</em>) represents the number of elements in the set <em>A</em>. When

that means the sets <em>A</em> and <em>B</em> are disjoint, represented by the two circles with no overlap.
4. E:
is the set of elements belonging to either set <em>A</em> or <em>B</em>. The three elements of <em>A</em> are all in <em>B</em>, so <em>A</em> is a subset of <em>B</em>. This means
.
Because <em>A</em> is a subset of <em>B</em>, we have
.
is the complement of
, which refers to the set of elements *not* belong to
. These are all the numbers in <em>U</em> that are not in this union, which would be
.
Because we know
, we have
.