Cual es el valor de 10=z-6
2 answers:
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Answer:
a) maximum; the parabola opens downward
b) positive; it must lie above the x-axis
c) x = 1.5
Step-by-step explanation:
The x-intercepts of a function are the points where the graph of the function crosses the x-axis. The y-values there are zero.
The "differences" of a function are related to the average slope between adjacent points. Second differences are related to the rate of change of the slope of the function. When <em>second differences are negative</em>, as here, the slope of the quadratic function is decreasing, becoming more negative. We say the <em>curvature</em> of the function is <em>negatve</em>, and that it <em>opens downward</em>.
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<h3>a, b.</h3>If the graph of the parabola opens downward, and it crosses the x-axis, it must have a <em>maximum</em> that is a <em>positive value of y</em>.
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<h3>c.</h3>The graph of a parabola is symmetrical about its vertex. That means points on the same horizontal line are the same distance from the line of symmetry, which must go through the vertex. The x-coordinate of the vertex will be the x-coordinate of the midpoint between the two x-intercepts:
x = (-2 +5)/2 = 3/2
The x-coordinate of the vertex is x = 1.5.
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<em>Additional comment</em>
The attachment shows a table with three evenly-spaced points on the curve. The calculations show first differences (d1) and second differences (d2). You can see that the sign of the second diffference is negative, in agreement with the given conditions.
Answer:
(a) The probability that the student made the Dean's list is 0.1655.
(b) The probability that the student came from a private high school, given that the student made the Dean's list is 0.2411.
(c) The probability that the student was not home schooled, given that the student did not make the Dean's list is 0.9185.
Step-by-step explanation:
The complete question is:
Of the entering class at a college, 71% attended public high school, 21% attended private high school, and 8% were home schooled. Of those who attended public high school, 16% made the Dean's list, 19% of those who attended private high school made the Dean's list, and 15% of those who were home schooled made the Dean's list.
a) Find the probability that the student made the Dean's list.
b) Find the probability that the student came from a private high school, given that the student made the Dean's list.
c) Find the probability that the student was not home schooled, given that the student did not make the Dean's list.
Solution:
Denote the events as follows:
<em>A</em> = a student attended public high school
<em>B</em> = a student attended private high school
<em>C</em> = a student was home schooled
<em>D</em> = a student made the Dean's list
The provided information is as follows:
P (A) = 0.71
P (B) = 0.21
P (C) = 0.08
P (D|A) = 0.16
P (D|B) = 0.19
P (D|C) = 0.15
(a)
The law of total probability states that:
Compute the probability that the student made the Dean's list as follows:
Thus, the probability that the student made the Dean's list is 0.1655.
(b)
Compute the probability that the student came from a private high school, given that the student made the Dean's list as follows:
Thus, the probability that the student came from a private high school, given that the student made the Dean's list is 0.2411.
(c)
Compute the probability that the student was not home schooled, given that the student did not make the Dean's list as follows:
Thus, the probability that the student was not home schooled, given that the student did not make the Dean's list is 0.9185.