Asurvey conducted five years ago by the health center at a university showed that 18% of the students smoked at the time. this year a new survey was conducted on a random sample of 200 students from this university, and it was found that 50 of them smoke. we want to find if these data provide convincing evidence to suggest that the percentage of students who smoke has changed over the last five years. what are the test statistic (z) and p-value of the test?
c = 4 a
the given function p(c) = - 15 c (c-8) is actually quadratic function:
p(c) = - 15c² + 120c or parabola
the standard form of a quadratic function is:
y = ax² + bx + c
for which x is the maximum of the parabola we can find with this formula
x = - b/2a
in this case a = -15 and b = 120 and input variable is current c
c = - 120/(2 · (-15)) = - 120/ (-30) = 4 a
c = 4 a
god with !
note that (f • g) = f(x) × g(x)
f(x) × g(x) = x²(x - 4)
(f • g )(10) = 10²(10 - 4) = 100 × 6 = 600
if the equation log(6x+10)=log(1/2) x is solved by graphing, the curves intersect at approximately x=0.46