Answer:
the mathematical model is : 
Step-by-step explanation:
Given that:
Let A(t) to be the amount of oil in the barrel at time t.
However; Suppose that the amount of oil is decreasing at a rate proportional to the product of the time elapsed and the amount of oil present in the barrel.
Then,


Initially the 100 -gallon barrel is half-full of oil
So, A(0) = 100/2 = 50

The variable is now being separated as:

Taking integral of both sides; we have:


However; since A(0) = 50; Then
t = 0 ; A =50 in the above equation


Thus; the mathematical model is : 
Answer: -1.78
Step-by-step explanation:
As per given description, we have
Population proportion : 
Sample size : n= 500
Sample proportion : 
Test statistic for population proportion :-

Hence, the test statistic for this hypothesis test for a proportion= -1.78
Answer:
Number of rectangles could alex draw with an area of 11cm² = 1
Step-by-step explanation:
Minimum length in centimeter grid = 1 cm
Alex is drawing rectangles with different areas on a centimetre grid.He can draw 3 different rectangles with an area of 12cm²
That is

These are the 3 different rectangles with an area of 12cm².
Now we need to find how many rectangles could alex draw with an area of 11cm².
11 = 1 x 11
So only one factorization is possible.
Number of rectangles could alex draw with an area of 11cm² = 1
Answer:
C. (18+4)
Step-by-step explanation:
The answer on ed