Answer:
question 1 and 3
Step-by-step explanation:
Let

represent the number of bacteria after

hours.
so

is the number of bacteria after 0/2 = 0 hours

is the number of bacteria after 1/2 hours

is the number of bacteria after 2/2 = 1 hours and so on
so if we list a few terms of this sequence, we have:





so clearly,

, the number of bacteria after

hours, is equal to

.

is the number of bacteria after

hours.
Thus, we calculate

, which is

.
Answer: the number of bacteria after 24 hours is

.
Answer:
Cluster analysis
Step-by-step explanation:
Cluster analysis or clustering is the task of grouping a set of objects in such a way that objects in the same group (called a cluster) are more similar (in some sense) to each other than to those in other groups (clusters).
FYI: https://en.wikipedia.org/wiki/Cluster_analysis
Answer:
3:4
4:5
Step-by-step explanation:
The ratios are ...
short side : long side = 12 : 16 = 3 : 4
and for the other rectangle, ...
short side : long side = 8 : 10 = 4 : 5
_____
To reduce the ratio to lowest terms, divide each number by their greatest common factor. 12 and 16 have a common factor of 4: 12=4·3, 16=4·4. 8 and 10 have a greatest common factor of 2.