Answer:
g/f = {(-1, 2)}
domain of g/f = {-1}
Step-by-step explanation:
Given,
f = {(-1, 4),(1, 9),(4, 0)},
g = {(-1, -8),(2, -7),(4, 8),(5, -9)}
So, Domain of f = {-1, 1, 4},
Domain of g = {-1, 2, 4, 5}
Since,
Thus, domain of g/f = Domain of f ∩ Domain of g = {-1, 4}
If x = -1,
If x = 4,
Hence, the domain of g/f = {-1}
And, g/f = {(-1, 2)}
Answer:
(1) There were fewer than 110 boxes in the warehouse before the 60 additional boxes arrived. (2) There were fewer than 120 boxes in the warehouse after the 60 additional boxes arrived.
Step-by-step explanation:
Given that all the boxes in a certain warehouse were arranged in stacks of 12 boxes each, with no boxes left over.
This implies that boxes are in multiples of 12
i.e. 12, or 24, or 36 or....
Let us say this as 12m for m an integer
Now additional boxes arrived =60
Total number of boxes now =
This when arranged in stacks of 14,nothing left out
Or this is multiple of 14
for some positive integer n.
By trial and error we find that if 60 is to be divided by 14, 24 should be added and 24 is a multiple of 12.
So we say originally 24 boxes were there now 84 boxes there.
Hence both options are right.
(1) There were fewer than 110 boxes in the warehouse before the 60 additional boxes arrived. (2) There were fewer than 120 boxes in the warehouse after the 60 additional boxes arrived.
Answer:
The correct option is D. 2/7
Step-by-step explanation:
Consider the provided information.
There are 8 volunteers including Andrew and Karen, 4 people are to be selected at random to organize a charity event.
We need to determine the probability Andrew will be among the 4 volunteers selected and Karen will not.
We want to select Andrew and 3 others but not Karen in the group.
Thus, the number of ways to select 3 member out of 8-2=6
(We subtract 2 from 8 because Andrew is already selected and we don't want Karen to be selected, so subtract 2 from 8.)
The required probability is:
Hence, the correct option is D. 2/7