Present Value of Money Flow Each function in Exercise represents the rate of flow of money (in dollars per year) over the given
1 answer:
You might be interested in
Answer:
Yes, it is true that is a factor of
.
Step-by-step explanation:
Let us try to factorize
Let us try to make a whole square of the given terms:
--------------
Formula used above:
In the above equation, we had .
--------------
Further solving the above equation, taking common out of
Taking common out of the above term:
So, the two factors are .
The statement that
is a factor of
is <em>True.</em>
1. Remarks:
f(x) to f(x)-3 is the whole graph of f(x), shifted 3 units down.
f(x) to -2f(x):
The effect of "multiplication by -" is that the whole graph is reflected with respect to the x axis, so it is turned upside down.
The effect of "multiplication by 2" is that every point is "stretched vertically by a factor of 2" . So for example the point (-1, -4) in the original function, becomes (-1, -8) in the second one. Or (2, 5) would become (2, 10).
The only points that do not change (are not streched vertically) are the roots. For example if (4,0) is an x-intercept (a root) in the original function, (4,0) is still a root in the second one because 2 times 0 is still 0.
2. Consider the polynomial function of degree n:
a. Y-intercept
The y - intercept is the value of the polynomial function at x=0.
So it is f(0)=
, that is, the constant term of f(x)
in f(x)-3 the y intercept is shifted 3 units down as any other point, so it becomes
In -2f(x), the y-intercept becomes 
b. Regions of f decreasing or increasing
f(x)-3 is f(x) just shifted down 3 units, so they are both increasing and decreasing in the same intervals of x
-2f(x) is f(x) turned upside down, so -2f(x) is increasing in all intervals f(x) is decreasing and it is decreasing in all intervals f(x) is increasing.
c. End behaviors
By now it is clear that end behaviors of f(x) and f(x)-3 are same, and f(x) with -2f(x) are opposite
d. Evenness, oddness
If f(x) is even, then f(x)=f(-x)
Let g(x)=f(x)-3
g(x)=f(x)-3=f(-x)-3=g(-3), so in this case f(x)-3 is even
If f(x) is odd, then f(-x)=-f(x)
g(x)=f(x)-3=-f(-x)-3,
so -g(x)=f(-x)+3
g(-x)=f(-x)-3,
so g(-x) is not equal to -g(x). Which means f(x)-3 is not odd if f(x) is
Consider f(x)=-2f(x)
If f(x) is even, f(x)=f(-x)
g(x)=-2f(x)=-2f(-x)
g(-x)=-2f(-x)
So g(x)=g(-x), which means -2f(x) is even if f(x) is even
If f(x) is odd, f(x)=-f(-x)
let g(x)=-2f(x)=-2(-f(-x))=2f(-x)
g(-x)=-2f(-x)=-2(-f(x))=2f(x)
so g(-x) is not equal to -g(x), thus -2f(x) is not odd if f(x) is odd.
The conclusions about oddness and evenness can be also derived from the discussions about the graphs.
f(x) to f(x)-3 is the whole graph of f(x), shifted 3 units down.
f(x) to -2f(x):
The effect of "multiplication by -" is that the whole graph is reflected with respect to the x axis, so it is turned upside down.
The effect of "multiplication by 2" is that every point is "stretched vertically by a factor of 2" . So for example the point (-1, -4) in the original function, becomes (-1, -8) in the second one. Or (2, 5) would become (2, 10).
The only points that do not change (are not streched vertically) are the roots. For example if (4,0) is an x-intercept (a root) in the original function, (4,0) is still a root in the second one because 2 times 0 is still 0.
2. Consider the polynomial function of degree n:
a. Y-intercept
The y - intercept is the value of the polynomial function at x=0.
So it is f(0)=
in f(x)-3 the y intercept is shifted 3 units down as any other point, so it becomes
In -2f(x), the y-intercept
b. Regions of f decreasing or increasing
f(x)-3 is f(x) just shifted down 3 units, so they are both increasing and decreasing in the same intervals of x
-2f(x) is f(x) turned upside down, so -2f(x) is increasing in all intervals f(x) is decreasing and it is decreasing in all intervals f(x) is increasing.
c. End behaviors
By now it is clear that end behaviors of f(x) and f(x)-3 are same, and f(x) with -2f(x) are opposite
d. Evenness, oddness
If f(x) is even, then f(x)=f(-x)
Let g(x)=f(x)-3
g(x)=f(x)-3=f(-x)-3=g(-3), so in this case f(x)-3 is even
If f(x) is odd, then f(-x)=-f(x)
g(x)=f(x)-3=-f(-x)-3,
so -g(x)=f(-x)+3
g(-x)=f(-x)-3,
so g(-x) is not equal to -g(x). Which means f(x)-3 is not odd if f(x) is
Consider f(x)=-2f(x)
If f(x) is even, f(x)=f(-x)
g(x)=-2f(x)=-2f(-x)
g(-x)=-2f(-x)
So g(x)=g(-x), which means -2f(x) is even if f(x) is even
If f(x) is odd, f(x)=-f(-x)
let g(x)=-2f(x)=-2(-f(-x))=2f(-x)
g(-x)=-2f(-x)=-2(-f(x))=2f(x)
so g(-x) is not equal to -g(x), thus -2f(x) is not odd if f(x) is odd.
The conclusions about oddness and evenness can be also derived from the discussions about the graphs.
Answer:
a) 0.2316 = 23.16% probability that 0 carry intestinal parasites.
b) 0.4005 = 40.05% probability that at least two individuals carry intestinal parasites.
Step-by-step explanation:
For each trout, there are only two possible outcomes. Either they carry intestinal parasites, or they do not. Trouts are independent. This means that 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.
You know that in a specific population of rainbow trout 15% of the individuals carry intestinal parasites.
This means that
Assume you obtain a random sample of 9 individuals from this population:
This means that
a. Calculate the probability that __ (last digit of your ID number) carry intestinal parasites.
Last digit is 0, so:
0.2316 = 23.16% probability that 0 carry intestinal parasites.
b. Calculate the probability that at least two individuals carry intestinal parasites.
This is
In which
So
0.4005 = 40.05% probability that at least two individuals carry intestinal parasites.