We have that
using a graph tool
see the attached figure
The horizontal asymptote of this function is at <span>y=3</span><span>.
So,
the range of this function is from </span><span>
(−∞,3<span>
)</span></span>
Hi there! The answer is B. it would be less steep.
The change of the function (in this case) influences the slope of the line. Since we've modified the slope from 5 to 3 / 4, the line will be less steep.
solving equation in terms of x we get 
solving equation in terms of y we get 
Step-by-step explanation:
We need to solve the equation: 
Solving the equation:
Simplifying and finding value of x:
We can simplify and find value of y as well:
So, solving equation in terms of x we get
solving equation in terms of y we get
Keywords: Solving Equations
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Answer:
a) 0.2416
b) 0.4172
c) 0.0253
Step-by-step explanation:
Since the result of the test should be independent of the time , then the that the test number of times that test proves correct is independent of the days the river is correct .
denoting event a A=the test proves correct and B=the river is polluted
a) the test indicates pollution when
- the river is polluted and the test is correct
- the river is not polluted and the test fails
then
P(test indicates pollution)= P(A)*P(B)+ (1-P(A))*(1-P(B)) = 0.12*0.84+0.88*0.16 = 0.2416
b) according to Bayes
P(A∩B)= P(A/B)*P(B) → P(A/B)=P(A∩B)/P(B)
then
P(pollution exists/test indicates pollution)=P(A∩B)/P(B) = 0.84*0.12 / 0.2416 = 0.4172
c) since
P(test indicates no pollution)= P(A)*(1-P(B))+ (1-P(A))*P(B) = 0.84*0.88+ 0.16*0.12 = 0.7584
the rate of false positives is
P(river is polluted/test indicates no pollution) = 0.12*0.16 / 0.7584 = 0.0253
