Two spinners are spun. One has 5 sections labeled Red, Orange, Purple, Yellow, and Green. The other has three sections labeled 1
, 2, and 3. Find the Sample Space.
1. Create a tree diagram to show the outcomes for these two spinners.
1. Create a tree diagram to show the outcomes for these two spinners.
1 answer:
Answer:
<em>Sample space:</em>
<em>possible outcomes</em>
<em>Tree diagram:</em>
<em>Observe the attached image.</em>
Step-by-step explanation:
For any experiment, the sample space of this experiment is the set of all the possible results of the experiment.
In this case we have two spinners. The first has 5 colors, by spinning the spinner you can get up to 5 different results. Therefore the sample space is
For the second spinner there are 3 possible results. By spinning the spinner you can get the numbers 1, 2 or 3. Then
Then, if the two spinners are rotated, the sample space would be:
possible outcomes.
The tree diagram shown in the attached image shows the 15 possible results
{R, 1} {R, 2} {R, 3} {O, 1} {O, 2} {O, 3} {Y, 1} {Y, 2} {Y, 3} {P, 1} {P, 2} {P, 3} {G, 1}
{G, 2} {G, 3}
You might be interested in
Your problem statement makes no reference to p or q, so we can only guess that "p/q" refers to the ratio of the lowest- and highest-degree coefficients:
... -6/1
Then the factors of p/q are the factors of 6, with either sign.
Factors of p/q: ±1, ±2, ±3.
There are a number of ways the factors can be tested. To test 1, simply add the coefficients. (The sum is -8.) To test -1, subtract the sum of odd-degree coefficients from the sum of even-degree coefficients. (The difference is 0.)
Knowing that -1 is a root of the function, you can use synthetic division to find the quadratic factor. (See the first attachment for the work.) Then you have ...
... f(x) = (x +1)(x² +x -6)
You can continue to test the factors of p/q, or you can factor the quadratic to get ...
... f(x) = (x +1)(x -2)(x +3)
Another way to test the factors is to program your graphing calculator to evaluate the function f(x) for those factors. The result from my TI-84 is shown in the second attachment. That shows f(x) = 0 for x = -3, -1, and +2.
Test the factors: f({-3, -2, -1, 1, 2, 3}) = {0, 4, 0, -8, 0, 24}
This tells you the x-intercepts.
X-intercepts: -3, -1, 2
Of course, the y-intercept is just the constant in the function—the value of the function when x=0.
Y-intercept: -6
As with any odd-degree polynomial with a positive leading coefficient, the overall behavior looks like "/". That is ...
End behaviors: f(x) goes to -∞ as x goes to -∞; f(x) goes to +∞ as x goes to +∞.
_____
A graph of f(x) is shown in the third attachment. (Graphing calculators make it easy to use graphing to find x-intercepts.)
