PLEASE HELP
1 answer:
F(x) = x³ - 18x² + 107x - 210
X - Intercept: f(x) = x³ - 18x² + 107x - 210
0 = x³ - 18x³ + 107x - 210
0 = x³ - 7x² - 11x² + 77x + 30x - 210
0 = x²(x) - x²(7) - 11x(x) + 11x(7) + 30(x) - 30(7)
0 = x²(x - 7) - 11x(x - 7) + 30(x - 7)
0 = (x² - 11x + 30)(x - 7)
0 = (x² - 6x - 5x + 30)(x - 7)
0 = (x(x) - x(6) - 5(x) + 5(6))(x - 7)
0 = (x(x - 6) - 5(x - 6))(x - 7)
0 = (x - 5)(x - 6)(x - 7)
0 = x - 5 or 0 = x - 6 or 0 = x - 7
+ 5 + 5 + 6 + 6 + 7 + 7
5 = x or 6 = x or 7 = x
Solution Set: {5, 6, 7}
Y - Intercept: f(x) = x³ - 18x² + 107x - 210
f(x) = (0)³ - 18(0)² + 108(0) - 210)
f(x) = 0 - 18(0) + 0 - 210
f(x) = 0 - 0 - 210
f(x) = 0 - 210
f(x) = -210
Shape of the Graph: Odd Degree Polynomials With a Positive Leading Coefficient
X - Intercept: f(x) = x³ - 18x² + 107x - 210
0 = x³ - 18x³ + 107x - 210
0 = x³ - 7x² - 11x² + 77x + 30x - 210
0 = x²(x) - x²(7) - 11x(x) + 11x(7) + 30(x) - 30(7)
0 = x²(x - 7) - 11x(x - 7) + 30(x - 7)
0 = (x² - 11x + 30)(x - 7)
0 = (x² - 6x - 5x + 30)(x - 7)
0 = (x(x) - x(6) - 5(x) + 5(6))(x - 7)
0 = (x(x - 6) - 5(x - 6))(x - 7)
0 = (x - 5)(x - 6)(x - 7)
0 = x - 5 or 0 = x - 6 or 0 = x - 7
+ 5 + 5 + 6 + 6 + 7 + 7
5 = x or 6 = x or 7 = x
Solution Set: {5, 6, 7}
Y - Intercept: f(x) = x³ - 18x² + 107x - 210
f(x) = (0)³ - 18(0)² + 108(0) - 210)
f(x) = 0 - 18(0) + 0 - 210
f(x) = 0 - 0 - 210
f(x) = 0 - 210
f(x) = -210
Shape of the Graph: Odd Degree Polynomials With a Positive Leading Coefficient
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71.57% of student heights are lower than Darnell's height
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 question, we have that:
Darnell has a height of 161.4 centimeters. What proportion of student heights are lower than Darnell's height?
This is the pvalue of Z when X = 161.4.
has a pvalue of 0.7157
71.57% of student heights are lower than Darnell's height
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