Answer:
150 minutes (2.5 hours)
Step-by-step explanation:
We must consider that the total time that the radio program lasted represents the 100%.
Of that 100% we are told that 20% is dedicated to commercials. So the 30 minutes of commercials correspond to 20% of the air time, which can be represented in the following table:
Percentage of time time
20% ⇒ 30min
and we are looking for how long the show was on the air (the 100%).
So updating the table( I will call x the total time on the air):
Percentage of time time
20% ⇒ 30min
100% ⇒ x
This reationship between three values can be solve by the<u> rule of three</u>: multiply the cross quantities on the table (100 by 30) and divide by the remaining amount (20):
x = 100*30 / 20
x= 3000 / 20
x = 150 minutes
The radio show was 150 minutes (2.5 hours) long.
Answer:
E
Step-by-step explanation:
If you add 22 onto the sum of all the points and divide by the amount of games (6), you get 12.
Answer:
![\left\{\begin{array}{l}y=-\dfrac{1}{9}x^2 +\dfrac{2}{9}x+\dfrac{89}{9}\\ \\y=\dfrac{1}{8}x^2 -7\end{array}\right.](https://tex.z-dn.net/?f=%5Cleft%5C%7B%5Cbegin%7Barray%7D%7Bl%7Dy%3D-%5Cdfrac%7B1%7D%7B9%7Dx%5E2%20%2B%5Cdfrac%7B2%7D%7B9%7Dx%2B%5Cdfrac%7B89%7D%7B9%7D%5C%5C%20%5C%5Cy%3D%5Cdfrac%7B1%7D%7B8%7Dx%5E2%20-7%5Cend%7Barray%7D%5Cright.)
Step-by-step explanation:
1st boat:
Parabola equation:
![y=ax^2 +bx+c](https://tex.z-dn.net/?f=y%3Dax%5E2%20%2Bbx%2Bc)
The x-coordinate of the vertex:
![x_v=-\dfrac{b}{2a}\Rightarrow -\dfrac{b}{2a}=1\\ \\b=-2a](https://tex.z-dn.net/?f=x_v%3D-%5Cdfrac%7Bb%7D%7B2a%7D%5CRightarrow%20-%5Cdfrac%7Bb%7D%7B2a%7D%3D1%5C%5C%20%5C%5Cb%3D-2a)
Equation:
![y=ax^2 -2ax+c](https://tex.z-dn.net/?f=y%3Dax%5E2%20-2ax%2Bc)
The y-coordinate of the vertex:
![y_v=a\cdot 1^2-2a\cdot 1+c\Rightarrow a-2a+c=10\\ \\c-a=10](https://tex.z-dn.net/?f=y_v%3Da%5Ccdot%201%5E2-2a%5Ccdot%201%2Bc%5CRightarrow%20a-2a%2Bc%3D10%5C%5C%20%5C%5Cc-a%3D10)
Parabola passes through the point (-8,1), so
![1=a\cdot (-8)^2-2a\cdot (-8)+c\\ \\80a+c=1](https://tex.z-dn.net/?f=1%3Da%5Ccdot%20%28-8%29%5E2-2a%5Ccdot%20%28-8%29%2Bc%5C%5C%20%5C%5C80a%2Bc%3D1)
Solve:
![c=10+a\\ \\80a+10+a=1\\ \\81a=-9\\ \\a=-\dfrac{1}{9}\\ \\b=-2a=\dfrac{2}{9}\\ \\c=10-\dfrac{1}{9}=\dfrac{89}{9}](https://tex.z-dn.net/?f=c%3D10%2Ba%5C%5C%20%5C%5C80a%2B10%2Ba%3D1%5C%5C%20%5C%5C81a%3D-9%5C%5C%20%5C%5Ca%3D-%5Cdfrac%7B1%7D%7B9%7D%5C%5C%20%5C%5Cb%3D-2a%3D%5Cdfrac%7B2%7D%7B9%7D%5C%5C%20%5C%5Cc%3D10-%5Cdfrac%7B1%7D%7B9%7D%3D%5Cdfrac%7B89%7D%7B9%7D)
Parabola equation:
![y=-\dfrac{1}{9}x^2 +\dfrac{2}{9}x+\dfrac{89}{9}](https://tex.z-dn.net/?f=y%3D-%5Cdfrac%7B1%7D%7B9%7Dx%5E2%20%2B%5Cdfrac%7B2%7D%7B9%7Dx%2B%5Cdfrac%7B89%7D%7B9%7D)
2nd boat:
Parabola equation:
![y=ax^2 +bx+c](https://tex.z-dn.net/?f=y%3Dax%5E2%20%2Bbx%2Bc)
The x-coordinate of the vertex:
![x_v=-\dfrac{b}{2a}\Rightarrow -\dfrac{b}{2a}=0\\ \\b=0](https://tex.z-dn.net/?f=x_v%3D-%5Cdfrac%7Bb%7D%7B2a%7D%5CRightarrow%20-%5Cdfrac%7Bb%7D%7B2a%7D%3D0%5C%5C%20%5C%5Cb%3D0)
Equation:
![y=ax^2+c](https://tex.z-dn.net/?f=y%3Dax%5E2%2Bc)
The y-coordinate of the vertex:
![y_v=a\cdot 0^2+c\Rightarrow c=-7](https://tex.z-dn.net/?f=y_v%3Da%5Ccdot%200%5E2%2Bc%5CRightarrow%20c%3D-7)
Parabola passes through the point (-8,1), so
![1=a\cdot (-8)^2-7\\ \\64a-7=1](https://tex.z-dn.net/?f=1%3Da%5Ccdot%20%28-8%29%5E2-7%5C%5C%20%5C%5C64a-7%3D1)
Solve:
![a=-\dfrac{1}{8}\\ \\b=0\\ \\c=-7](https://tex.z-dn.net/?f=a%3D-%5Cdfrac%7B1%7D%7B8%7D%5C%5C%20%5C%5Cb%3D0%5C%5C%20%5C%5Cc%3D-7)
Parabola equation:
![y=\dfrac{1}{8}x^2 -7](https://tex.z-dn.net/?f=y%3D%5Cdfrac%7B1%7D%7B8%7Dx%5E2%20-7)
System of two equations:
![\left\{\begin{array}{l}y=-\dfrac{1}{9}x^2 +\dfrac{2}{9}x+\dfrac{89}{9}\\ \\y=\dfrac{1}{8}x^2 -7\end{array}\right.](https://tex.z-dn.net/?f=%5Cleft%5C%7B%5Cbegin%7Barray%7D%7Bl%7Dy%3D-%5Cdfrac%7B1%7D%7B9%7Dx%5E2%20%2B%5Cdfrac%7B2%7D%7B9%7Dx%2B%5Cdfrac%7B89%7D%7B9%7D%5C%5C%20%5C%5Cy%3D%5Cdfrac%7B1%7D%7B8%7Dx%5E2%20-7%5Cend%7Barray%7D%5Cright.)
Answer: 9 1/4 miles
Step-by-step explanation:
3 7/10= 3.7
2 1/2= 2.5
Multiply
3.7*2.5= 9.25
Convert to mixed number
9.25= 9 1/4