Answer: the extraction is 18.2%.
Explanation:
Let's see few definitions:
TDS = Total Dissolved Solids = solids dissolved in the brew
PE = Percent Extraction = percent of solids extracted from the dry coffee grounds
The percent extraction can be calculated by the formula:
PE = TDS × Rm
where
Rm = ratio between the mass of the brew and the mass of dry grounds
Now, you need to consider the following facts:
1) every 1g of coffee absorbs 2g of water
2) the given brew ratio is 1:15, which means that for every 1g of grounds we use 15g of water
Let's call
x = grams of coffee grounds we want to use
Therefore the mass of the brew will be:
m(brew) = water we use - water absorbed by the coffee
= 15·x - 2·x
= 13·x
Therefore,
Rm = m(brew) / x
= 13·x / x
= 13
Hence, the percent of extraction will be:
PE = <span> TDS × Rm
= 1.4 </span>× 13
= 18.2
Answer:
m∠BOC = 40°
Step-by-step explanation:
Given O A ‾ ⊥ O C ‾ OA ⊥ OC m∠BOC=6x−6 ∘
m∠AOB=5x+8 ∘
Find m ∠ B O C:
This means that: m∠BOC and m∠AOC intersect at a right angle.
Hence:
m∠BOC + m∠AOC = 90°
Step 1
Solving for x
6x - 6 + 5x + 8 = 90°
11x -2 = 90°
11x = 90 - 2
11x = 88
x = 88/11
x = 8
Step 2
Solving for m∠BOC
m∠BOC = 6x - 8
m∠BOC = 6(8) - 8
= 48 - 8
= 40°
For the wooden box, if you do 7560 ÷ 180 you get 42. that's how many boxes you would need. multiply 42 by the cost of the wooden boxes: 42 × 0.70 you get 29.40 dollars
for the plastic container, do 7560 ÷ 126 which equals 60, the amount of plastic containers you would need. multiply 60 by the plastic containers cost: 60×40= 24 dollars.
to save money, the company should use the plastic containers because it costs less than the wooden ones.
So focusing on x^4 + 5x^2 - 36, we will be completing the square. Firstly, what two terms have a product of -36x^4 and a sum of 5x^2? That would be 9x^2 and -4x^2. Replace 5x^2 with 9x^2 - 4x^2: 
Next, factor x^4 + 9x^2 and -4x^2 - 36 separately. Make sure that they have the same quantity inside of the parentheses: 
Now you can rewrite this as
, however this is not completely factored. With (x^2 - 4), we are using the difference of squares, which is
. Applying that here, we have
. x^4 + 5x^2 - 36 is completely factored.
Next, focusing now on 2x^2 + 9x - 5, we will also be completing the square. What two terms have a product of -10x^2 and a sum of 9x? That would be 10x and -x. Replace 9x with 10x - x: 
Next, factor 2x^2 + 10x and -x - 5 separately. Make sure that they have the same quantity on the inside: 
Now you can rewrite the equation as
. 2x^2 + 9x - 5 is completely factored.
<h3><u>Putting it all together, your factored expression is

</u></h3>
Answer:
1.3
Step-by-step explanation:
20/100 x 6 5/10 =
1 3/10
Hopes this helps