Answer: ![\frac{27}{125}](https://tex.z-dn.net/?f=%5Cfrac%7B27%7D%7B125%7D)
Step-by-step explanation:
Here the total numbers are 1, 4, 3, 7, 6
Since the total number of possible arrangement =
The total number of the odd numbers in the given numbers = 3
Thus the possible arrangement that the first three digits will be odd numbers = ![3\times 3\times 3\times 5\times 5=3^3\times 5^2](https://tex.z-dn.net/?f=3%5Ctimes%203%5Ctimes%203%5Ctimes%205%5Ctimes%205%3D3%5E3%5Ctimes%205%5E2)
Thus, the probability that the first three digits of Irvings ID number will be odd numbers = the possible arrangement that the first three digits will be odd numbers / total possible arrangement =
= ![\frac{3^3}{5^3} = \frac{27}{125}](https://tex.z-dn.net/?f=%5Cfrac%7B3%5E3%7D%7B5%5E3%7D%20%3D%20%5Cfrac%7B27%7D%7B125%7D)
The water bill was 1/5 of the total, so was 0.2*$540 = $108.
Answer:
![A = \int\limits^3__-3}{9}-{x^{2}} \, dx = 36](https://tex.z-dn.net/?f=A%20%3D%20%5Cint%5Climits%5E3__-3%7D%7B9%7D-%7Bx%5E%7B2%7D%7D%20%5C%2C%20dx%20%3D%2036)
Step-by-step explanation:
The equations are:
![y = x^{2} + 2x + 3](https://tex.z-dn.net/?f=y%20%3D%20x%5E%7B2%7D%20%2B%202x%20%2B%203)
![y = 2x + 12](https://tex.z-dn.net/?f=y%20%3D%202x%20%2B%2012)
The two graphs intersect when:
![x^{2} + 2x + 3 = 2x + 12](https://tex.z-dn.net/?f=x%5E%7B2%7D%20%2B%202x%20%2B%203%20%3D%202x%20%2B%2012)
![x^{2} = 0](https://tex.z-dn.net/?f=x%5E%7B2%7D%20%3D%200)
![x_{1} = 3\\x_{2} = -3](https://tex.z-dn.net/?f=x_%7B1%7D%20%20%3D%203%5C%5Cx_%7B2%7D%20%20%3D%20-3)
To find the area under the curve for the first equation:
![A_{1} = \int\limits^3__-3}{x^{2} + 2x + 3} \, dx](https://tex.z-dn.net/?f=A_%7B1%7D%20%3D%20%5Cint%5Climits%5E3__-3%7D%7Bx%5E%7B2%7D%20%2B%202x%20%2B%203%7D%20%5C%2C%20dx)
To find the area under the curve for the second equation:
![A_{2} = \int\limits^3__-3}{2x + 12} \, dx](https://tex.z-dn.net/?f=A_%7B2%7D%20%3D%20%5Cint%5Climits%5E3__-3%7D%7B2x%20%2B%2012%7D%20%5C%2C%20dx)
To find the total area:
![A = A_{2} -A_{1} = \int\limits^3__-3}{2x + 12} \, dx -\int\limits^3__-3}{x^{2} + 2x + 3} \, dx](https://tex.z-dn.net/?f=A%20%3D%20A_%7B2%7D%20-A_%7B1%7D%20%3D%20%5Cint%5Climits%5E3__-3%7D%7B2x%20%2B%2012%7D%20%5C%2C%20dx%20-%5Cint%5Climits%5E3__-3%7D%7Bx%5E%7B2%7D%20%2B%202x%20%2B%203%7D%20%5C%2C%20dx)
Simplifying the equation:
![A = \int\limits^3__-3}{2x + 12}-({x^{2} + 2x + 3}) \, dx = \int\limits^3__-3}{9}-{x^{2}} \, dx](https://tex.z-dn.net/?f=A%20%3D%20%5Cint%5Climits%5E3__-3%7D%7B2x%20%2B%2012%7D-%28%7Bx%5E%7B2%7D%20%2B%202x%20%2B%203%7D%29%20%5C%2C%20dx%20%3D%20%5Cint%5Climits%5E3__-3%7D%7B9%7D-%7Bx%5E%7B2%7D%7D%20%5C%2C%20dx)
Note: The reason the area is equal to the area two minus area one is that the line, area 2, is above the region of interest (see image).
Answer:
The slope is 3
Step-by-step explanation:
Parallel lines always have the same slopes. This equation is in slope-intercept form, y=mx+b, m being the slope. Our m, or the slope, is 3, and because the line is parallel, it also has a slope of 3.
Answer:
The answer is 4
Step-by-step explanation:
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