Answer: false
Step-by-step explanation:
If f and g are increasing on I, this implies that f' > 0 on I and g' > 0 on I. That is both f' and g' have a positive slope. However,
Using product rule;
(fg)' = fd(g) + gd(f)
(fg)' = f * g' + f' * g
and although it is given that g' and f' are both positive we don't have any information about the sign of the values of the functions themselves(f and g). Therefore, if at least one of the functions has negative values there is the possibility that the derivative of the product will be negative. For example;
f = x, g = 5x on I = (-5, -2)
f' = 1 and g' =5 both greater than 0
f and g are both lines with positive slopes therefore they are increasing, but f * g = 5x^2 is decreasing on I.
Answer: 0.003757(approx).
Step-by-step explanation:
Total number of combinations of selecting r things out of n things is given by:-
Total cards in a deck = 52
Total number of ways of choosing 8 cards out of 52 = 
Total number of ways to choose 5 clubs and 3 cards with one of each remaining suit = 
[since 1 suit has 13 cards]
The required probability = 
Hence, the required probability is 0.003757 (approx).
The answer is B) it shifts up and to the right
