Each table shows a proportional relatioship. fill in the missing values and determine k.

If you measure a tds of 1.4%, and you used a brew ratio of 15, what is the percent extraction?

sweet-ann [11.9K]

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

4 0

2 years ago

Given O A ‾ ⊥ O C ‾ OA ⊥ OC start overline, O, A, end overline, \perp, start overline, O, C, end overline m ∠ B O C = 6 x − 6 ∘

Lelu [443]

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°

7 0

2 years ago

A company needs to package 7,560 beads. A wooden container shaped like a rectangular prism can hold 180 beads. A plastic cylindr

Kobotan [32]

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.

8 0

2 years ago

Read 2 more answers

Factor both quadratic expressions. (x 4 + 5x 2 - 36)(2x 2 + 9x - 5) = 0

Sonbull [250]

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: $x^4+9x^2-4x^2-36$

Next, factor x^4 + 9x^2 and -4x^2 - 36 separately. Make sure that they have the same quantity inside of the parentheses: $x^2(x^2+9)-4(x^2+9)$

Now you can rewrite this as $(x^2-4)(x^2+9)$ , however this is not completely factored. With (x^2 - 4), we are using the difference of squares, which is $a^2-b^2=(a+b)(a-b)$ . Applying that here, we have $(x+2)(x-2)(x^2+9)$ . 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: $2x^2+10x-x-5$