Answer:
4 7/8
Step-by-step explanation:
3 1/4 / 2/3
convert mixed numbers to improper fractions: 3 1/4 / 2/3
13/4 / 2/3
apply the fraction rule: a/b / c/d = a/b * d/c
= 13/4 * 3/2
multiply fractions: a/b * c/d = (a * c)/(b * d)
= (13 * 3)/(4 * 2)
multiply the numbers: 13 * 3 = 39
= 39/(4 * 2)
multiply the numbers: 4 * 2 = 8
= 39/8
convert improper fractions to mixed numbers: 39/8 = 4 7/8
= 4 7/8
Remark
So CAB is a base 16 number? I hope that's correct. I'll treat it that way. If I am incorrect, please leave a note and I'll modify my answer accordingly.
Expand
A = 10 in decimal
B = 11 in decimal
C = 12 in decimal
B is the "units" value in decimal it is 11
A is the "tens" value or 12 place and in decimal you would get 12 * 10 = 120
C is the "hundreds" value or 12^2 place and in decimal you would get 144*12 =1728
Now you need to all all three results together. 11 + 120 + 1728 = 1850
Answer
(CAB)_16 = 1850 in decimal
14+5= 19; 19-8=11. the hotel elevator is now on the 11th floor
The inclusion/exclusion principle states that
That is, the union has as many members as the sum of the number of members of the individual sets, minus the number of elements contained in both sets (to avoid double-counting).
Therefore,
will have the most elements when the sets
and
are disjoint, i.e.
, which would mean the most we can can in this case would be
(Note that
denotes the cardinality of the set
.)
One example is if you wanted to measure the height of a tall building. You'll need to measure the distance from where you're standing to the base of the building. You'll also need the angle of elevation. To get the angle of elevation, start by looking completely horizontal, then tilt upward until your eyeline reaches the top of the building. Once you have those two things (the side and angle) you can use the tangent ratio to find the height. This is because
tan(angle) = opposite/adjacent
where in this case
angle = angle of elevation
opposite = height of building
adjacent = distance from your position to the base of the building
It takes a bit of algebra, but the opposite side can be solved for. You'll most likely need a calculator to compute the tangent ratio.
