What does y and x equal for -2y+6y=6 -7x+8y=-5
1 answer:
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Answer:
(1) 0.5933
(2) 0.8955
Step-by-step explanation:
We are given that all bags entering a research facility are screened.
Let Probability that bags entering the building contains forbidden material,
P(F) = 0.69
Probability that bags entering the building does not contains forbidden material, P(NF) = 1 - 0.69 = 0.31
Let event A = alarm gets triggered
Probability that alarm gets trigger given the bags contain forbidden material, P(A/F) = 0.77
Probability that alarm gets trigger given the bags does not contain forbidden material, P(A/NF) = 0.20
(1) Probability that a bag triggers the alarm, P(A) ;
P(A) = P(F) * P(A/F) + P(NF) * P(A/NF)
= (0.69 * 0.77) + (0.31 * 0.20) = 0.5313 + 0.062
= 0.5933
Therefore, probability that a bag triggers the alarm is 0.5933 .
(2) Probability that a bag that triggers the alarm will actually contain forbidden material is given by P(F/A) ;
Using Bayes' Theorem;
P(F/A) = =
=
= 0.8955
Answer:
(A)The absolute maximum of f(x) is at x=5
Step-by-step explanation:
F(x)=−2x³+21x²−60x on [1,6]
Find the first derivative.
f'(x)=-6x²+42x-60
Set the first derivative equal to zero.
-6x²+42x-60=0
Solve to find the critical points.
x=2,5
Next, we use the endpoints and all critical points on the interval to test for any absolute extrema over the given interval.
x=1,2,5,6
This is done by evaluating the function at x=1,2,5,6.
F(1)=−2(1)³+21(1)²−60(1)=-41
F(2)=−2(2)³+21(2)²−60(2)=-52
F(5)=−2(5)³+21(5)²−60(5)=-25
F(6)=−2(6)³+21(6)²−60(6)=-36
The maximum will occur at the highest f(x) value and the minimum will occur at the lowest f(x) value.
Absolute Maximum: (5,-25)
Absolute Minimum: (2,-52)
The graph is attached.
The absolute minimum and maximum of f(x) are (2,-52) and (5,-25) respectively.
