How many times does the graph of 4x = 32 - x2 cross the x-axis ?
2 answers:
Answer:
Step-by-step explanation:
● 4x = 32 - x^2
Add x^2 to both sides
● 4x +x^2 = 32 -x^2+x^2
● x^2 +4x = 32
Substract 32 from both sides
● x^2+4x -32 =32-32
● x^2 +4x-32=0
That is a quadratic equation
We will use the determinant method
The determinant is b^2-4ac
● a = 1
● b = 4
● c = 32
● b^2-4ac = 4^2 -4×1×(-32) = 144
144 is positive so the parabola will cross the x-axis two times
● x = (-b -/+ √(b^2-4ac))/2a
● x = (-4 +/- 12) /2
● x = 8/2 or x= -16/2
● x = 4 or x =-8
The solutions are 4 and -8
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Answer:
There is a 2.17% probability that a randomly selected person aged 40 years or older is male and jogs.
It would be unusual to randomly select a person aged 40 years or older who is male and jogs.
Step-by-step explanation:
We have these following probabilities.
A 13.9% probability that a randomly selected person aged 40 years or older is a jogger, so .
In addition, there is a 15.6% probability that a randomly selected person aged 40 years or older is male comma given that he or she jogs. I am going to say that P(B) is the probability that is a male. is the probability that the person is a male, given that he/she jogs. So
The Bayes theorem states that:
In which is the probability that the person does both thigs, so, in this problem, the probability that a randomly selected person aged 40 years or older is male and jogs.
So
There is a 2.17% probability that a randomly selected person aged 40 years or older is male and jogs.
A probability is unusual when it is smaller than 5%.
So it would be unusual to randomly select a person aged 40 years or older who is male and jogs.