A. you are given that f(1)=5 therefore f(1) cannot also equal 1 unless it is a different equation.
The equation of the vertical parabola in vertex form is written as

Where (h, k) are the coordinates of the vertex and p is the focal distance.
The directrix of a parabola is a line which every point of the parabola is equally distant to this line and the focus of the parabola. The vertex is located between the focus and the directrix, therefore, the distance between the y-coordinate of the vertex and the directrix represents the focal distance.

Using this value for p and (3, 1) as the vertex, we have our equation
Answer: Ruth have to make 7 hats to break even.
Step-by-step explanation:
Break even point is a point where Cost = Revenue.
Let x be the number of hats sold.
Given: Cost of booth = $63
Each hat cost = $10
Selling price for each cost = $19
As per given,
Total cost = Cost of booth+ (Cost of each hat)(Number of hats)
= 63+10x
Total selling price = 19x
For break even,
63+10x=19x
9x=63
x=7
Hence, Ruth have to make 7 hats to break even.
Answer:
There is an 84.97% probability that at least six wear glasses.
Step-by-step explanation:
For each adult over 50, there are only two possible outcomes. Either they wear glasses, or they do not. This means that we use the binomial probability distribution to solve this problem.
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 combinatios of x objects from a set of n elements, given by the following formula.

And p is the probability of X happening.
In this problem we have that:

What is the probability that at least six wear glasses?

There is an 84.97% probability that at least six wear glasses.