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:
1. z = -1.91429
The z score tells us that the head circumference of the girl with the down syndrome ( 44.5 cm) is 1.91429 standard deviations below the mean or average head circumference
2. 2.7792%
Step-by-step explanation:
1. Relative to the WHO data, what is this girls z-score?
z score formula is:
z = (x-μ)/σ, where
x is the raw score = 44.5 cm
μ is the population mean = 47.18cm
σ is the population standard deviation = 1.40cm
z = 44.5 - 47.18/1.40
z = -1.91429
What does the z score tell us?
The z score tells us that the head circumference of the girl with the down syndrome ( 44.5 cm) is 1.91429 standard deviations below the mean or average head circumference
2. Using the WHO data in a normal model, what percentage of the girls has a head circumference that is smaller than the girl with Down's Syndrome?
z score = -1.91429
Probability value from Z-Table:
P(z =-1.91429) = P(x<44.5) = 0.027792
Converting to percentage = 0.027792 × 100
= 2.7792%
Answer:
D. no solution
Step-by-step explanation:
h-z=3(1)
h=3+z(minus z from both side)
put in the second equation
-3h,+3z=6(2)
-3(3+z)+3z=6
-9-3z+3z=6
-9=6( not true)
so the equation doesn't have a solution.
It’s the first answer choice... the translation was 5 units to the right (horizontal movement so it affects the x) and it’s to the right (which makes it a positive 5). It didn’t move up or down so the y stays the same
Hope it helps
Answer: 15.7659
Explanation: the column the 4 is in is the ten thousandths column. Since the number after it is 8, which is bigger than 5, you round up to make is 15.7659
