Scores on a standardized test are normally distributed with a mean of 228 and a standard deviation of 18. students who score at least 2.3 standard deviations above the mean receive a certificate.

what is the minimum score required to receive the certificate?

270

Step-by-step explanation:

The mean is 228 and the standard deviation is 18.

2.3 standard deviations above the mean is:

228 + 2.3×18

228 + 41.4

269.4

Since scores are usually integers, we round up to 270.

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

$79500

step-by-step explanation: