Answer:
All in all, Jonathan's piggy bank contains 100 coins. Among these coins, only 50 are one-dollar coins. Therefore, the theoretical probability of picking one-dollar coin from the piggy bank is equal to 50/100 or 1/2.
Similarly, from the experiment, 20 coins were picked and among these there are 12 one-dollar coins. The answer to the second question is therefore 12/20 or 3/5.
Step-by-step explanation:
The vertex form of the function gives the vertex as (-6,48). The vertex of f(x)=x^2 is (0,0) so from this information, the vertex is moved LEFT 6 and UP 48. This cancels out two options. The coefficient -3 tells us that the graph is flipped or reflected over the x-axis (negative sign flips graph) and that all y-values will be 3 times as large. Larger y-values for the same x inputs makes the graph narrower.
Let us try reflecting (2,3) about x=y and across x-axis and y-axis.
If we are reflecting about y=x, that means both x,y values will be interchanged that is (2,3) will become (3,2)and this will be achieved by
.
And for reflection across x-axis,y-value will be multiplied by -1.That is (2,3) becomes (2,-3) and the matrix used to achieve it is
.
For reflection across y-axis, x-value will be multiplied by -1. That is (2,3) becomes (-2,3) when reflected across y-axis. The matrix used to achieve it will have -1 in the first place that is ![\left[\begin{array}{cc}-1&0\\0&1\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D-1%260%5C%5C0%261%5Cend%7Barray%7D%5Cright%5D)