James and Cameron are watching a film. They pause it with one fifth left to watch. What is the ratio of how much they have watch
1 answer:
Answer:
The ratio of how much they have watched to how much they have left to see is 4 : 1.
Step-by-step explanation:
Consider that the total duration of the film is, 1.
It is provided that James and Cameron paused when there is one-fifth left to watch.
That is, they have already watched, th of the film.
Compute the ratio of how much they have watched to how much they have left to see as follows:
Thus, the ratio of how much they have watched to how much they have left to see is 4 : 1.
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Answer:
The solution x = 229.89 ≅ 230 (since we cannot have a decimal number of sweatshirts)implies that, the money collected from selling sweatshirts equals the money used in producing sweatshirts when 230 sweatshirts have been sold or produced.
Step-by-step explanation:
Here is the complete question
In the first equation in the system of equations, y represents the money collected from selling sweatshirts. in the second equation, y represents the money spent to produce x sweatshirts with team logos on them for a professional sports league.
y=35x; y=-0.05(x-400)²+9,492
what does the solution of the system represent in this context?
Solution
The solution of the system is obtained when both equations are equal. That is y=35x = y=-0.05(x-400)²+9,492 .
So, 35x = -0.05(x-400)² + 9,492.
Expanding the right side, we have
35x = -0.05(x² - 800x + 160000) + 9492
35x = -0.05x² -800x × -0.05 + (-0.05) × 160000 + 9492
35x = -0.05x² +40x - 8000 + 9492
35x = -0.05x² +40x + 1492
Collecting all the terms to the left side, we have
0.05x² - 40x - 1492 + 35x = 0
0.05x² - 5x -1492 = 0
Using the quadratic formula,
We choose the positive answer x = 229.83. Since we cannot have a decimal number of sweatshirts, we approximate to the nearest whole number. So, x = 229.83 ≅ 230 sweatshirts.
The solution implies that the money collected from selling sweatshirts equals the money used in producing sweatshirts when 230 sweatshirts have been sold or produced.
We confirm that by plugging in x = 229.83 in both equations.
y = 35x = 35(229.83) = 8044.05 ≅ 8044.1
y=-0.05(x-400)²+9,492 = y=-0.05(229.83-400)²+9,492 = y=-0.05(-170.17)²+9,492 = y=-0.05(28,957.8289)+9,492 = -1447.8914 + 9492 = 8044.11 ≅ 8044.1