Find the equation of the parabola with focus (5,0) and directrix x =5

y²=20x

Step-by-step explanation:

Note: I'm assuming you mean x=-5 for the directrix because what you're asking isn't possible

Since we are given a horizontal directrix, the parabola must also be horizontal.

Horizontal Parabola:

(y-k)² = 4p(x-h)

Vertex: (h, k)

Focus: (h+p, k)

Directrix: x = h - p

Since the focus of the parabola is (5,0), then k=0 and h+p=5. We also know that since the directrix is x=-5, then -5=h-p. If we set these equations equal to each other, we can solve for h and p:

h+p=5

h-p=-5

2p=10

p=5

Since p=5, then h=0. Therefore, we have for our equation of the parabola:

(y-k)² = 4p(x-0)

(y-0)² = 4(5)(x-0)

y²=20x

since proposition states that a number is greater than 25, if is true then the number must actually be greater than 25.

this implies that all possible options, except 24, can be accepted

85.560%

step-by-step explanation:

conditional probability is defined as:

p(a|b) = p(a∩b) / p(b)

in other words, the probability that a occurs, given that b has occurred = the probability that both a and b occur / the probability that b occurs.

in this example:

p(turns 64 | turns 44) = p(turns 64 & turns 44) / p(turns 44).

if someone turns 64, they must have already turned 44, so:

p(turns 64 | turns 44) = p(turns 64) / p(turns 44)

on page 42, we see that of the original 100,000, 94944 turn 44, and 81234 turn 64.   therefore:

p(turns 64 | turns 44) = 81234 / 94944

p(turns 64 | turns 44) = 0.85560