In a board game, students draw a number do not replace it, and then draw a second number. Determine the probability of each even
1 answer:
The figure depicting the board game is attached below.
Answer:
Step-by-step explanation:
Kindly note that selections done without replacement.
Count of numbers on the board game = 8
Count of odd numbers = (1, 9, 1) = 3
Count of digit 6 = 3
Probability = required outcome / Total possible outcomes
P(picking an odd number) = 3 / 8
Without replacement
Numbers left on board game = 8 - 1 = 7
P(picking a 6) = 3 / 7
Hence,
P(picking an odd number then, a 6) = 3/8 * 3/7 = 9 / 56
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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.
