Answer:
A)0.8533
Step-by-step explanation:
For each person, there are only two possible outcomes. Either they are 65 or older, or they are not. The probability of a person being 65 or older is independent of any other person. So we use the binomial probability distribution 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.
14 percent of the population of Arizona is 65 years or older.
This means that 
A random sample of five persons from this population is taken.
This means that 
The probability that less than 2 of the 5 are 65 years or older is :
In which
So the correct answer is:
A)0.8533
Answer:
One possible equation is 
, which is equivalent to 
.
Step-by-step explanation:
The factor theorem states that if 
(where 
is a constant) is a root of a function, 
would be a factor of that function.
The question states that 
and 
are 
-intercepts of this function. In other words, 
and 
would both set the value of this quadratic function to 
. Thus, 
and 
would be two roots of this function.
By the factor theorem, 
and 
would be two factors of this function.
Because the function in this question is quadratic, and would be the only two factors of this function. In other words, for some constant 
(
):
.
Simplify to obtain:
.
Expand this expression to obtain:
.
(Quadratic functions are polynomials of degree two. If this function has any factor other than and , expanding the expression would give a polynomial of degree at least three- not quadratic.)
Every non-zero value of corresponds to a distinct quadratic function with -intercepts and . For example, with 
:
, or equivalently,
.
Answer:
(i) Breadth = 14 cm
(ii) Perimeter = 176 cm
Step-by-step explanation:
Given,
- Area of a rectangle =
cm²
- Length =
cm
(i) Breadth = ?
We know that, Area of a rectangle = length × breadth.
Then,
(ii) Perimeter of a rectangle = 2 (length + breadth)
Then,
Answer:
2
Step-by-step explanation:
The average rate of change from x=1 to x=2 is the same as finding the slope of a line at x=1 and x=2.
So we are going to need to corresponding y coordinates.
What y corresponds to x=1? y=3
What y corresponds to x=2? y=5
So we have the ordered pairs (1,3) and (2,5).
Line the points up vertically and subtract vertically then put 2nd difference over 1st difference.
(2 , 5)
-(1 , 3)
-----------
1 2
The average rate of change is 2/1 or just 2.
Now since we were asked to find the average rate of change given the function was a line, it really didn't matter what two points you used on that line.
