Choose the best answer. according to the u. s. census, the proportion of adults in a certain county who owned their own home was 0.71. an srs of 100 adults in a certain section of the county found that 65 owned their home. which one of the following represents the approximate probability of obtaining a sample of 100 adults in which fewer than 65 own their home, assuming that this section of the county has the same overall proportion of adults who own their home as does the entire county?
(a) (10065)(0.71)65(0.29)35
(b) (10065)(0.29)65(0.71)35
(c) p⎛⎝⎜z< 0.65−0.71(0.71)(0.29)100√⎞⎠⎟
(d) p⎛⎝⎜z< 0.65−0.71(0.65)(0.35)100√⎞⎠⎟
(e) p⎛⎝⎜z< 0.65−0.71(0.71)(0.29)100√⎞⎠⎟

let's cover over the formula of the vertex:

y = a(x – h)^2 + k

in this formula, (h,k) are the vertex, always remember that the positive or negative value of the vertex is based on the sign it has.

for example, if the vertex is -3,-6 then both the x and y value would have the positive sign attached to it and if it were a positive x and y value, then a negative sign would be attached to it.

with that being said, for our problem the x value is a positive one so we are looking for a number with a negative sign next to it, in this case the first and second choice.

however, for the first answer choice it isn't quite part of the formula so we know that the answer choice correctly displays the x value.

to confirm, we can see if the -1 fits correctly with the second answer choice, and as mentioned above a negative number will have a positive sign attached to it. so, for our problem we can see that -1 has been changed to +1, so we can confirm that the second answer choice is correct.

hence, our final answer is y=(x - 1)^2 + 1

its 50 miles away from the starting point

x^2 + 81

we can factor this using difference of square binomials.

rewrite the equation:

x^2 - (-81)

factor:

(a^2 - b^2) = (√a^2 + √b^2)(√a^2 - √b^2)

(x^2 - (-81) = (x + √-81)(x - √-81)

we can remove the - from under the radical by multiplying it by i.

(x^2 - (-81) = (x + i√81)(x - i√81)

(x^2 - (-81) = (x + 9i)(x - 9i)

we can check our answer by using foil:

x^2 - 9ix + 9ix - 81i^2

x^2 - 81^2

i^2 = -1

x^2 + 81