Answer:
if the height of the triangle is 8 in, its side is 9.2379, and this side is also the side of the hexagon, so the perimeter is 6*9.2379 = 55.43 in
Step-by-step explanation:
As the hexagon is regular, each of those triangles will also be regular.
So if the height of one triangle is 8 inches, we can find the side of the triangle with the height formula of a regular triangle:
height = side * sqrt(3)/2
8 = side * 0.866
side = 8/0.866 = 9.2379
The side of the triangle will also be the side of the hexagon. So the perimeter of the hexagon will be:
P = 6 * 9.2379 = 55.43 inches
Answer:
0.1426 = 14.26% probability that at least one of the births results in a defect.
Step-by-step explanation:
For each birth, there are only two possible outcomes. Either it results in a defect, or it does not. The probability that a birth results in a defect is independent of any other birth. This means that 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.
The proportion of U.S. births that result in a birth defect is approximately 1/33 according to the Centers for Disease Control and Prevention (CDC).
This means that 
A local hospital randomly selects five births.
This means that 
What is the probability that at least one of the births results in a defect?
This is:

In which



0.1426 = 14.26% probability that at least one of the births results in a defect.
Answer:
D. 
Step-by-step explanation:
we are given

Firstly, it is reflected over x-axis
we know that for reflection about x-axis , we can replace y as -y
we get


now, it is vertical shift up by 4 units
so, we can add 4 to y-value
we get


Answer: 9x²-6x+5
Step-by-step explanation:
To find (gοf)(x), you want to plug f(x) into g(x). It is the same as g(f(x)).
g(f(x))=(3x-1)²+4 [distribute by FOIL]
g(f(x))=9x²-6x+1+4 [combine like terms]
g(f(x))=9x²-6x+5
Now, we know that (gοf)(x)=9x²-6x+5.