Use the figure to the right to find the value of PT. T is the midpoint of PQ.
2 answers:
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Answer:
There are a total of 23 cars with air conditioning and automatic transmission but not power steering
Step-by-step explanation:
Let A be the cars that have Air conditioning, B the cars that have Automatic transmission and C the cars that have pwoer Steering. Lets denote |D| the cardinality of a set D.
Remember that for 2 sets E and F, we have that
Also,
|E| = |E ∩F| + |E∩F^c|
We now alredy the following:
|A| = 89
|B| = 99
|C| = 74
|(A \cup B \cup C)^c| = 24
|A \ (B U C)| = 24 (This is A minus B and C, in other words, cars that only have Air conditioning).
|B \ (AUC)| = 65
|C \ (AUB)| = 26
We want to know |(A∩B) \ C|. Lets calculate it by taking the information given and deducting more things
For example:
99 = |B| = |B ∩ C| + |B∩C^c| = 11 + |B∩C^c|
Therefore, |B∩C^c| = 99-11 = 88
And |A ∩ B ∩ C^c| = |B∩C^c| - |B∩C^c∩A^c| = |B∩C^c| - |B \ (AUC)| = 88-65 = 23.
This means that the amount of cars that have both transmission and air conditioning but now power steering is 23.
So this is going to be an exponential equation, which the format is 
, in which a is the initial value and b is the growth/decay rate.
In this case, a is going to be 340,000 and b is going to be 107%, or 1.07, since the population is going to be increasing by 7% and the equation is now
.
Now replace x with 12 and solve.
Solve
, and then if you don't round that answer and multiply it with 340000 you get 
.
In this case, a is going to be 340,000 and b is going to be 107%, or 1.07, since the population is going to be increasing by 7% and the equation is now
Now replace x with 12 and solve.
Solve