Answer:
![x = \frac{1}{32} \\](https://tex.z-dn.net/?f=x%20%3D%20%20%5Cfrac%7B1%7D%7B32%7D%20%20%5C%5C%20)
Step-by-step explanation:
![{2x}^{(2 - 3)} = 64 \\ {2x}^{ - 1} = 64 \\ \frac{2}{x} = 64 \\ x \times \frac{2}{x} = 64 \times x \\ 2 = 64x \\ \frac{2}{64} = \frac{64x}{64} \\ \frac{1}{32} = x \\](https://tex.z-dn.net/?f=%20%7B2x%7D%5E%7B%282%20-%203%29%7D%20%20%3D%2064%20%5C%5C%20%20%7B2x%7D%5E%7B%20-%201%7D%20%20%3D%2064%20%5C%5C%20%20%5Cfrac%7B2%7D%7Bx%7D%20%20%3D%2064%20%5C%5C%20x%20%5Ctimes%20%5Cfrac%7B2%7D%7Bx%7D%20%3D%2064%20%5Ctimes%20x%20%5C%5C%202%20%3D%2064x%20%5C%5C%20%20%5Cfrac%7B2%7D%7B64%7D%20%20%3D%20%20%5Cfrac%7B64x%7D%7B64%7D%20%20%5C%5C%20%20%5Cfrac%7B1%7D%7B32%7D%20%20%3D%20x%20%5C%5C%20)
Answer:
-17.00 dollars.
Step-by-step explanation:
Here is the equation:
![4 \frac{1}{2} \div 1 \frac{1}{4} = a \frac{b}{c}](https://tex.z-dn.net/?f=%204%20%5Cfrac%7B1%7D%7B2%7D%20%5Cdiv%201%20%5Cfrac%7B1%7D%7B4%7D%20%3D%20a%20%5Cfrac%7Bb%7D%7Bc%7D%20%20)
When you're going to be dividing fractions, you have to keep, change, and flip. Also, make sure you make the fractions improper when it's a mixed number.
![4 \frac{1}{2} = \frac{9}{2}](https://tex.z-dn.net/?f=%204%20%5Cfrac%7B1%7D%7B2%7D%20%3D%20%5Cfrac%7B9%7D%7B2%7D%20%20%20)
![1 \frac{1}{4} = \frac{5}{4}](https://tex.z-dn.net/?f=%201%20%5Cfrac%7B1%7D%7B4%7D%20%3D%20%5Cfrac%7B5%7D%7B4%7D%20%20%20)
Now keep, change, flip
![Keep\ \frac{9}{2} \\ Change \div to\ \times \\ Flip\ \frac{5}{4} = \frac{4}{5}](https://tex.z-dn.net/?f=%20Keep%5C%20%5Cfrac%7B9%7D%7B2%7D%20%5C%5C%20Change%20%5Cdiv%20to%5C%20%5Ctimes%20%5C%5C%20Flip%5C%20%5Cfrac%7B5%7D%7B4%7D%20%3D%20%5Cfrac%7B4%7D%7B5%7D%20%20%20)
Your new equation is:
![\frac{9}{2} \times \frac{4}{5}](https://tex.z-dn.net/?f=%20%5Cfrac%7B9%7D%7B2%7D%20%5Ctimes%20%5Cfrac%7B4%7D%7B5%7D%20%20)
Multiply:
![\frac{9}{2} \times \frac{4}{5} = \frac{36}{10} = 3 \frac{6}{10} \rightarrow 3 \frac{3}{5}](https://tex.z-dn.net/?f=%20%5Cfrac%7B9%7D%7B2%7D%20%5Ctimes%20%5Cfrac%7B4%7D%7B5%7D%20%3D%20%5Cfrac%7B36%7D%7B10%7D%20%3D%203%20%5Cfrac%7B6%7D%7B10%7D%20%20%5Crightarrow%203%20%5Cfrac%7B3%7D%7B5%7D%20%20)
Your answer is:
![3 \frac{3}{5} \\ a = 3 \\ b = 3 \\ c = 5](https://tex.z-dn.net/?f=%203%20%5Cfrac%7B3%7D%7B5%7D%20%5C%5C%20a%20%3D%203%20%5C%5C%20b%20%3D%203%20%5C%5C%20c%20%3D%205%20)
Answer:
Given the information in the attached image;
The number of blue marbles is 5.
The total number of marbles is 10.
So, the probability of drawing blue as the first marble is;
![P_1=\frac{5}{10}=\frac{1}{2}](https://tex.z-dn.net/?f=P_1%3D%5Cfrac%7B5%7D%7B10%7D%3D%5Cfrac%7B1%7D%7B2%7D)
Also, since there is a replacement, the probability of drawing blue as the second marble is;
![P_2=\frac{5}{10}=\frac{1}{2}](https://tex.z-dn.net/?f=P_2%3D%5Cfrac%7B5%7D%7B10%7D%3D%5Cfrac%7B1%7D%7B2%7D)
the probability of drawing two blue marbles will be;
![\begin{gathered} P=P_1\times P_2 \\ P=\frac{1}{2}\times\frac{1}{2} \\ P=\frac{1}{4} \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20P%3DP_1%5Ctimes%20P_2%20%5C%5C%20P%3D%5Cfrac%7B1%7D%7B2%7D%5Ctimes%5Cfrac%7B1%7D%7B2%7D%20%5C%5C%20P%3D%5Cfrac%7B1%7D%7B4%7D%20%5Cend%7Bgathered%7D)
Therefore, the probability of drawing two blue marbles is;
![\frac{1}{4}](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B4%7D)