Answer:
18 pounds of cashews are needed.
Step-by-step explanation:
Given;
A manager bought 12 pounds of peanuts for $30.
Price of peanut per pound P = $30/12 = $2.5
Price of cashew per pound C = $5
Price of mixed nut per pound M = $4
Let x represent the proportion of peanut in the mixed nut.
The proportion of cashew will then be y = (1-x), so;
xP + (1-x)C = M
Substituting the values;
x(2.5) + (1-x)5 = 4
2.5x + 5 -5x = 4
2.5x - 5x = 4 -5
-2.5x = -1
x = 1/2.5 = 0.4
Proportion of cashew is;
y = 1-x = 1-0.4 = 0.6
For 12 pounds of peanut the corresponding pounds of cashew needed is;
A = 12/x × y
A = 12/0.4 × 0.6 = 18 pounds
18 pounds of cashews are needed.
Answer:
The percent error in his estimate is<u> 16.67%</u>.
Step-by-step explanation:
Given:
Christopher estimates it will take him half an hour to complete his math homework.
He is able to complete it in 25 minutes.
Now, to find the percent error in his estimate.
Time estimates of completing homework = 30 minutes.
Time actual taken to complete homework = 25 minutes.
Error in estimate = Time estimates of completing homework - Time actual taken to complete homework.
Error in estimate = 30 minutes - 25 minutes.
Error in estimate = 5 minutes.
Now, to get the percent error:
![Percent\ error =\frac{Error\ in\ estimate}{Time\ estimates\ of\ completing\ homework} \times 100.](https://tex.z-dn.net/?f=Percent%5C%20error%20%3D%5Cfrac%7BError%5C%20in%5C%20estimate%7D%7BTime%5C%20estimates%5C%20of%5C%20completing%5C%20homework%7D%20%5Ctimes%20100.)
![Percent\ error=\frac{5}{30} \times 100](https://tex.z-dn.net/?f=Percent%5C%20error%3D%5Cfrac%7B5%7D%7B30%7D%20%5Ctimes%20100)
![Percent\ error=\frac{500}{30}](https://tex.z-dn.net/?f=Percent%5C%20error%3D%5Cfrac%7B500%7D%7B30%7D)
![Percent\ error=16.67\%.](https://tex.z-dn.net/?f=Percent%5C%20error%3D16.67%5C%25.)
Therefore, the percent error in his estimate is 16.67%.
Looking at a number in different ways can help understand it’s application better. For example, giving an answer with radicals(square roots) is precise, but it’s not practical because you really don’t know what that number means.