Salaries differ greatly between faculty members at public universities in the United States. Full professors (who have tenure an
d do research) earn an average of $125,572 per year with a standard deviation of $18,328. Associate professors (who are working towards tenure and do research) earn an average of $90,101 per year with a standard deviation of $12,741. Lecturers (whose primary responsibility is teaching and do not earn tenure) earn an average of $59,707 per year with a standard deviation of $7,386. Assume all three populations are normally distributed.
a. What is the probability that a randomly selected full professor makes less than $100,000 per year?
a. What is the probability that a randomly selected full professor makes less than $100,000 per year?
1 answer:
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General Idea:
If we have a quadratic function of the form f(x)=ax^{2} +bx+c , then the function will attain its maximum value only if a < 0 & its maximum value will be at x=-\frac{b}{2a} .
Applying the concept:
The height h is modeled by h = −16t^2 + vt + c, where v is the initial velocity, and c is the beginning height of the firecracker above the ground. The firecracker is placed on the roof of a building of height 15 feet and is fired at an initial velocity of 100 feet per second. Substituting 15 for c and 100 for v, we get the function as .
Comparing the function f(x)=ax^{2} +bx+c with the given function , we get
,
and
.
The maximum height of the soccer ball will occur at t=\frac{-b}{2a}=\frac{-100}{2(-16)} = \frac{-100}{-32}=3.125 seconds
The maximum height is found by substituting in the function as below:
Conclusion:
<u>Yes !</u> The firecracker reaches a height of 100 feet before it bursts.