Answer:
y = 1/12 (x − 5)²
Step-by-step explanation:
We can solve this graphically without doing calculations.
The y component of the focus is y = 3. Since this is above the directrix, we know this is an upward facing parabola, so it must have a positive coefficient. That narrows the possible answers to A and C.
The x component of the focus is x = 5. Since this is above the vertex, we know the x component of the vertex is also x = 5.
So the answer is A. y = 1/12 (x−5)².
But let's say this wasn't a multiple choice question and we needed to do calculations. The equation of a parabola is:
y = 1/(4p) (x − h)² + k
where (h, k) is the vertex and p is the distance from the vertex to the focus.
The vertex is halfway between the focus and the directrix. So p is half the difference of the y components:
p = (3 − (-3)) / 2
p = 3
k, the y component of the vertex, is the average:
k = (3 + (-3)) / 2
k = 0
And h, the x component of the vertex, is the same as the focus:
h = 5
So:
y = 1/(4×3) (x − 5)² + 0
y = 1/12 (x − 5)²
Answer:
P(X = 0) = 0.1897
P(X = 1) = 0.3910
P(X = 2) = 0.3021
P(X = 3) = 0.1038
P(X = 4) = 0.0134
Step-by-step explanation:
For each owner, there are only two possible outcomes. Either they are insured against an earthquake, or they are not. The probability of a homeowner being insured against an earthquake is independent of other homeowners. So the binomial probability distribution is used to solve this question.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
In which 
is the number of different combinations of x objects from a set of n elements, given by the following formula.
And p is the probability of X happening.
Suppose that in one metropolitan area, the chance a homeowner is insured against an earthquake is 0.34.
This means that 
A sample of four homeowners are to be selected at random.
This means that 
(a) Find the probability mass function of X. (Round your answers to four decimal places.)
The pmf is the probability of each outcome.
So
Step-by-step explanation:
the volume of any pyramid is
base area × height / 3
so, since we know the base area (a square with 23 mm side length), the only trick we need to do is to get the inner height (straight up in the middle from the base area to the top of the pyramid).
because this is a regular pyramid (the top of the pyramid is right above the middle of the base area), we can use Pythagoras for right-angled triangles
c² = a² + b²
with c being the Hypotenuse (the baseline of the triangle opposite of the 90° angle) and in our case the outer height along a side area triangle (24 mm).
the legs of that right-angled triangle are half of a base area side length (remember, the top of the pyramid is right over the middle of the base area square) and the inner height to the top.
so, we have
24² = 12.5² + height²
height² = 24² - 12.5² = 576 - 156.25 = 419.75
height = 20.48780125... mm
so, the volume of the pyramid is then
23² × 20.48780125... / 3 = 3,612.682287... mm³ ≈
≈ 3,612.7 mm³
