By the definition of the hyperbolic function tanh x, we have proven that 
<h3>Hyperbolic functions & Proof of identities </h3>
By definition

Then,















Hence, we have proven that 
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Answer:
99% confidence interval is:
(0.00278 < P1 - P2< 0.15921)
Step-by-step explanation:
For calculating a confidence intervale for the difference between the proportions of workers in the two cities, we calculate the following:

Where
: proportion sample of individuals who worked
at more than one job in the city one
: Number of respondents in the city one
: proportion sample of individuals who worked
at more than one job in the city two
: Number of respondents in the city two
Then
α = 0.01 and α/2 = 0.005
and 


and 
The confidence interval is:

(0.00278 < P1 - P2< 0.15921)
Write 2 equations:
a +b = 39
and b = 1/2a + 6
Now replace b in the first equation with the second one:
a + 1/2a + 6 = 39
Combine like terms:
1 1/2a + 6 = 39
Subtract 6 from each side:
1 1/2a = 33
Divide both sides by 1 1/2:
a = 33 / 1 1/2 = 33 / 1.5
a = 22
Now replace a with 22 in the first equation and solve for b:
22 + b = 39
b = 39 -22
b = 17
The two numbers are 17 and 22.
Answer:
B
Step-by-step explanation:
Distributive property is when you distribute the values in a parenthesis with the outside multiplying factor
2*(5+7)= 2*5 + 2*7
2*(12) = 10 +14
24 = 24
distributive property holds true
Each question is either true or false, so the sample space is 2, true and false, two states only.
what's the probability she got one correct, well, the favorable outcomes is 1, possible outcomes is 2, so 1/2.
what's the probability that she got all four correct, we simply multiply the probability of each,