See the attached for a graph and the solution: (x, y) = (3, 0).
_____
With the availability and simplicity of the Desmos on-line graphing calculator, this is my favorite method of solving systems of equations.
Answer:
1/12
Step-by-step explanation:
<u>Needed information</u>
The sum of the probabilities of all outcomes must equal 1
<u>Solution</u>
We are told that the probability that the counter is <em>not</em> black is 3/4.
As the sum of the probabilities of all outcomes <u>must equal 1</u>, we can work out the probability that the counter <em>is </em>black by subtracting 3/4 from 1:
We are told that the probability that the counter is <em>not </em>white is 2/3.
As the sum of the probabilities of all outcomes <u>must equal 1</u>, we can work out the probability that the counter <em>is </em>white by subtracting 2/3 from 1:
We are told that there are black, white and grey counters in the bag. We also know that the sum of the probabilities of all outcomes must equal 1. Therefore, we can work out the probability the counter is grey by subtracting the probability the counter is black and the probability the counter is white from 1:
Answer:
a) True
<em> </em><em></em>
Step-by-step explanation:
<u><em>Step(i):-</em></u>
<em>Given that the definite integration</em>
<em> </em><em></em>
<em>we know that the trigonometric formula</em>
<em> sin²∝+cos²∝ = 1</em>
<em> cos²∝ = 1-sin²∝</em>
<u><em>step(ii):-</em></u>
<em>Now the integration</em>
<em> </em><em></em>
<em> = </em><em></em>
<em>Now, Integrating </em>
<em> </em><em></em>
<em> = sin π - sin 0</em>
<em> = 0-0</em>
<em> = 0</em>
<u><em>Final answer:-</em></u>
<em> </em><em></em>
<em></em>
<em></em>
1) We can determine by the table of values whether a function is a quadratic one by considering this example:
x | y 1st difference 2nd difference
0 0 3 -0 = 3 7-3 = 4
1 3 10 -3 = 7 11 -7 = 4
2 10 21 -10 =11 15 -11 = 4
3 21 36-21 = 15 19-5 = 4
4 36 55-36= 19
5 55
2) Let's subtract the values of y this way:
3 -0 = 3
10 -3 = 7
21 -10 = 11
36 -21 = 15
55 -36 = 19
Now let's subtract the differences we've just found:
7 -3 = 4
11-7 = 4
15-11 = 4
19-15 = 4
So, if the "second difference" is constant (same result) then it means we have a quadratic function just by analyzing the table.
3) Hence, we can determine if this is a quadratic relation calculating the second difference of the y-values if the second difference yields the same value. The graph must be a parabola and the highest coefficient must be 2