Answer:
a) 6.68th percentile
b) 617.5 points
Step-by-step explanation:
Problems of normally distributed samples are solved using the z-score formula.
In a set with mean and standard deviation , the zscore of a measure X is given by:
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
In this problem, we have that:
a) A student who scored 400 on the Math SAT was at the ______ th percentile of the score distribution.
has a pvalue of 0.0668
So this student is in the 6.68th percentile.
b) To be at the 75th percentile of the distribution, a student needed a score of about ______ points on the Math SAT.
He needs a score of X when Z has a pvalue of 0.75. So X when Z = 0.675.
Answer: P: 6x - 6 + (pi * x/2) A: 3x^2 - 3x - (pi * (x^2)/4)
Step-by-step explanation:
The missing section is a quarter of a circle. It is the same length at 90 degrees difference following an arc. This radius is X, same as the smaller length of the rectangle. The longer length of the rectangle is 2x-3+x, or 3x-3.
Area: Rectangle area is X * (3x-3) or 3x^2 - 3x. Subtract the missing piece. The full area of the circle would be pi * x^2. Divide by 4 for a quarter circle. So the full area would be 3x^2 - 3x - (pi * (x^2)/4).
Perimeter. x + 2x-3 + 3x-3 + the arc. The arc is a quarter of the circle's circumference. pi * 2x over 4. So total perimeter would be 6x-6 + (pi * 2x/4 or pi * x/2).
Just my best guess tho
X^2 + y^2 = 9 . . . . . . . . circle
y = x + 3 . . . . . . . (linear graph)
They intersect at (-3, 0) and (0, 3)