Stan's heart rate, in beats per minute, was measured 20 times at random. The results are 82, 84, 98, 112, 97, 93, 91, 87, 112, 87, 79, 80, 72, 82, 94, 89, 89, 74, 80, and 72 beats per minute. Construct a 99% confidence interval for Stan's mean heart rate. (82.5659, 92.8341) (80.4942, 92.8341) (82.5659, 94.9052) (82.4288, 92.9712) (80.4942, 94.9052)

(80.4942, 94.9052)

Step-by-step explanation:

The sample mean is x = 87.7.

The sample standard deviation is s = 11.26.

At 99% confidence and 19 degrees of freedom, the critical value is t = 2.861.

The confidence interval is:

x ± t (s/√n)

87.7 ± 2.861 (11.26 / √20)

87.7 ± 7.2053

(80.4947, 94.9053)

if the eqn of the parabola is f(x) = (x-4)(x+2), we need to mult. this out to find the coordinates of the vertex.

then f(x) = x^2 + 2x - 4x - 8, and f(x) = x^2 - 2x - 8.

one way in which you can find the vertex is to calculate x = -b / (2a).   here, that comes to

        )

x = = 1.   f(1) = 1^2 - 2(1) - 8 = - 9.   vertex is at (1, -9).

        2(1) 

find another point on the curve:   let x=0, for which y=-8.   then (0, -8) is on the curve.   plot the vertex and this point and draw a smooth parabola thru both.

hope this

take it another