Since f(x, y) = 1 + y2 and ∂f/∂y = 2y are continuous everywhere, the region R in Theorem 1.2.1 can be taken to be the entire xy-
1 answer:
You might be interested in
Answer:
y = -1/10x^2 +2.5
Step-by-step explanation:
The distance from focus to directrix is twice the distance from focus to vertex. The focus-directrix distance is the difference in y-values:
-1 -4 = -5
So, the distance from focus to vertex is p = -5/2 = -2.5. This places the focus 2.5 units below the vertex. Then the vertex is at (h, k) = (0, -1) +(0, 2.5) = (0, 1.5).
The scale factor of the parabola is 1/(4p) = 1/(4(-2.5)) = -1/10. Then the equation of the parabola is ...
y = (1/(4p))(x -h) +k
y = -1/10x^2 +2.5
_____
You can check the graph by making sure the focus and directrix are the same distance from the parabola everywhere. Of course, if the vertex is halfway between focus and directrix, the distances are the same there. Another point that is usually easy to check is the point on the parabola that is even with the focus. It should be as far from the focus as it is from the directrix. In this parabola, the focus is 5 units from the directrix, and we see the points on the parabola at y=-1 are 5 units from the focus.
Answer:
a) 56.67% probability that the student is a woman
b) 16.67% probability that the student received an A
c) 63.33% probability that the student is a woman or received an A.
d) 83.33% probability that the student did not receive an A.
Step-by-step explanation:
A probability is the number of desired outcomes divided by the number of total outcomes.
We have that:
30 students
13 men
17 women
2 men that got an A and 11 men that did not get an A.
3 women that got an A and 14 women that did not get an A.
a. Find the probability that the student is a woman.
30 students, of which 17 are women.
56.67% probability that the student is a woman
b. Find the probability that the student received an A.
30 students, of which 5 received an A
16.67% probability that the student received an A
c. Find the probability that the student is a woman or received an A.
30 students, of which 17 are women and 2 are men who received an A. So
63.33% probability that the student is a woman or received an A.
d. Find the probability that the student did not receive an A.
30 students, of which 25 did not receive an A.
83.33% probability that the student did not receive an A.