Answer:
d. (g*f)(-9)=-1
Step-by-step explanation:
In this problem, we have two functions:
and
The notation:
(f*g)(x) represents the composite function of f and g; this can be calculated by using the output of g(x) as input for f(x), in other words:
Simiarly, the notation (g*f)(x) can be calculated by using the output of f(x) as input for g(x), mathematically:
Using the definitions of f(x) and g(x), we can derive an expression for the two composite functions here:
And
Now we can analyze the given statements:
a. (f*g)(2)=2 --> FALSE, because 
b. (g*f)(2)=0 --> FALSE, because 
c.(f*g)(9)=1 --> FALSE, because 
d. (g*f)(-9)=-1 --> TRUE, because 
Answer:
The correct answer are given by (A) 
; (B) 
.
Step-by-step explanation:
Total number of entries to the sweepstakes offered by Gemini Paper Products = 175,000.
Total number of prizes to be awarded includes 1 grand prize, 3 first prizes, 25 second prizes and 400 third prizes = 1 + 3 + 25 + 400 = 429.
(A) Required Probability for a person who has put one entry to win the grand prize is given by the fraction .
(B) Required Probability for a person who has put one entry to win any prize offered is given by .
Answer:
The only one that is true is J
Step-by-step explanation:
if a is between 0 and 1, the image of the polygon is smaller than the polygon.
Since
, and you have a corresponding term in the given Riemann sum of
, you know the integral is being taken over an interval of length 5, so you can omit the second choice.
Next,
corresponds to
with
. The fact that
alone tells you that the interval of integration starts at 3, and since we know the interval has length 5, that leaves the first choice as the correct answer.
The best answer is
B) <span>It is increasing in the interval 2 < x < 3 hours.
The time in which Hanna's distance is decreasing is also the interval in which the slope is negative. This happens on the interval 2 < x < 3 hours. </span>
