New car owners were asked to evaluate their experiences in buying a new car during the past 12 months. In the survey, the owners
2 answers:
Answer:
When ranking the dealers, the total possible outcomes are 6.
Step-by-step explanation:
It is given that the owners were most satisfied with their experiences at the following three dealers (in no particular order): Subaru, Honda, and Buick.
We need to find the total possible outcomes when ranking the dealers.
It means we need to arrange these 3 dealers.
According to permutation, the total possible ways to arrange n items is
Total possible ways to rank three dealers is
The total possible outcomes are 6. The list of possible ranking in ascending order is
1. Subaru, Honda, and Buick
2. Subaru, Buick, and Honda
3. Honda, Subaru, and Buick
4. Honda, Buick, and Subaru
5. Buick, Honda, and Subaru
6. Buick, Subaru, and Honda
Therefore, the total possible outcomes are 6.
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Answer:
We want to find a solution of the system:
x^2 + y^2 > 49
y ≤ –x^2 – 4
Here we do not have any options, so let's try to find a general solution.
First, we can remember that the equation of a circle centered in the point (a, b) and of radius R is:
(x - a)^2 + (y - b)^2 = R^2
If we look at our first inequality, we can write it as:
x^2 + y^2 > 7^2
So the solutions of the first inequality are all the points that are outside (because the symbol used is >) of the circle of radius R = 7 centered in the origin.
From the other equation, we would get:
y ≤ –x^2 – 4
This is parabola, anything that is in the graph of the parabola or below will be a solution for this inequality.
Then the solutions of the system, are the ones that are in the region of solutions for both inequalities.
You can see the graph below, where both regions are graphed. The intersection of these regions is the region of the solutions for the system of inequalities:
by looking at the graph, we can see a lot of points that are solutions, like:
(0, -10)
(0, -15)
(2, -10)
etc.
