The first machine produces an acceptable cork with probability 68.3%. The second machine produces an acceptable cork with probability 99.9%.
The second machine is much more likely to produce an acceptable cork.
Answer:
-3X
Step-by-step explanation:
Answer:
Only options, A and E give 625/n¹² on simplification. The other options do not apply.
(5n⁻³)⁴ = (625/n¹²)
(25n⁻⁶)² = (625/n¹²)
Step-by-step explanation:
625/n¹²
a) (5n⁻³)⁴
According to the law of indices, this becomes
(5⁴)(n⁻³)⁴ = 625(n⁻¹²) = 625/n¹²
This applies!
b) (5n⁻³)⁻⁴
According to the law of indices, this becomes
(5⁻⁴)(n⁻³)⁻⁴ = (n¹²)/625 = n¹²/625
Does Not apply!
c) (5n⁻⁴)³
This becomes
(5³)(n⁻⁴)³ = 125n⁻¹² = 125/n¹²
Does Not apply!
d) (25n⁻⁶)⁻²
This becomes
(25⁻²)(n⁻⁶)⁻² = n⁻¹²/625 = 1/(625n¹²)
Does Not apply!
e) (25n⁻⁶)²
This becomes
(25²)(n⁻⁶)² = 625n⁻¹² = 625/n¹²
This applies!
If a set contains ‘n’ elements, then the number of proper subsets of the set is 2^n - 1.
In this problem,
n = 4
2^4 - 1 = 16 - 1 = 15 proper subsets
Divide both sides by 2
|x-3|>4 and |x-3|<-4
ok so |x-3|<-4 is false, since |x|≥0 always
so we have
|x-3|>4
now assume
x-3>4 and
x-3<-4
x-3>
add 3
x>7
x-3<-4
add 3
x<-1
so
-1>x and x>7
so basically it is all numbers from -∞ to +∞ except from -1 to 7
in interval notaion
(-∞,-1)U(7,∞)
S={x|x<-1 or x>7}
