Within 9 hours, the number of stars seen went from 190 to 33 as the sun started to rise. Find out how many stars are getting hid
1 answer:
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I actually just learned this. I think this is the right answer.
Answer:
The answer is below
Step-by-step explanation:
Given that the minimum monthly requirements are 840 pounds of phosphoric acid, hence:
35 pounds of phosphoric acid mix A + 14 pounds of phosphoric acid mix B ≥ 840 pounds of phosphoric acid
35x + 14y ≥ 840
The minimum monthly requirements are 540 pounds of nitrogen, hence:
15 pounds of nitrogen mix A + 18 pounds of nitrogen mix B ≥ 540 pounds of nitrogen
15x + 18y ≥ 540
The minimum monthly requirements are 768 pounds of potash, hence:
16 pounds of potash mix A + 64 pounds of potash mix B ≥ 768 pounds of potash
16x + 64y ≥ 768
Also, x ≥ 0 and y ≥0.
Therefore the equations are:
35x + 14y ≥ 840
15x + 18y ≥ 540
16x + 64y ≥ 768
x ≥ 0 and y ≥ 0
Plotting with geogebra gives the graph below.
The point are (0,60), (48,0), (18,15), (32,4)
Answer:
- $20,000 at 8.5%
- $10,000 at 10%
Step-by-step explanation:
There are a number of ways to solve mixture problems like this. Some are simple enough you can almost write down the answer. One I like uses a diagram to help you find the ratios of the components of the mix. You can do the same thing with a formula (without the diagram).
The basic idea is that you compute a ratio between two differences. The numerator is the difference between the average interest rate and the lower interest rate. Here, the average interest rate is 2700/30,000 = 0.09 = 9%. Then the numerator is 9% -8.5% = 0.5%
The denominator is the difference between the two interest rates of the investments: 10% -8.5% = 1.5%. And the ratio of these two values is ...
0.5%/1.5% = 1/3
This is the fraction of the total investment that was invested at the higher interest rate:
(1/3)×$30,000 = $10,000 . . . . was invested at 10%
Then the remaining amount, $20,000, was invested at 8.5%.
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If you would prefer an equation, you can let x represent the amount invested at the higher rate. (That is the most convenient assignment of variables, as it keeps all of the numbers positive.) Then (30,000 -x) is the amount invested at the lower rate. The total amount of interest is ...
10%(x) +8.5%(30,000 -x) = 2700
x(10% -8.5%) = 2700 -8.5%(30000) . . . . . subtract 8.5%(30,000)
x = (2700 -8.5%(30,000))/(10% -8.5%) . . . . divide by the coefficient of x
We have purposely left the expression unevaluated so that you can compare it to the math we described above. If you factor out 30,000 from the numerator of this fraction, you see the ratio that we described in words:
This tells us $10,000 was invested at 10%, and $20,000 was invested at 8.5%.