How much is one ninth?

How many liters each of a 35% acid solution in a 80% acid solution must be used to produce 60 L of a 65% acid solution?

STALIN [3.7K]

Let x and y be the required amounts of the 35% and 60% acid solutions, respectively.

x liters of 35% acid solution contains 0.35x L of acid.

y liters of 80% acid solution contains 0.80y L of acid.

Together, a combined (x + y) L of mixed solutions contains (0.35x + 0.80y) L of acid.

You want to end up with 60 L of 65% acid solution, which means

x + y = 60

0.35x + 0.80y = 0.65 × 60 = 39

Solve for x and y :

y = 60 - x

0.35x + 0.80 (60 - x) = 39

0.35x + 48 - 0.80x = 39

0.45x = 9

x = 20

y = 40

6 0

3 years ago

3. As part of your weight training regimen, you want to consume lean sources of protein. You want consume at least 300 Calories

erastova [34]

Answer:

Let x ounce of chicken and y ounce of tofu were taken,

∵ One ounce of chicken provides 35 Calories and 8.5 g of protein,

So, in x ounces of chicken

Calories = 35x, Protein = 8.5x grams,

Now, One ounce of tofu provides 20 Calories and 2.5 g of protein.

So, in y ounces of tofu,

Calories = 20y and protein = 2.5y grams,

Thus, the total calories = 35x + 20y,

Total protein = 8.5x + 2.5y

According to the question,

35x + 20y ≥ 300 -----(1),

8.5x + 2.5y ≥ 48 ----(2),

Now, the cost of a pound for chicken = $ 5,

So, the cost of 16 ounces of chicken = $ 5 ( ∵ 1 pound = 16 ounces ),

⇒ the cost of 1 ounces of chicken = $\frac{5}{16}$ dollars,

Similarly, the cost of a pound of tofu = $ 2.5,

So, the cost of 1 ounces of tofu = $\frac{2.5}{16}$ dollars,

Thus, the total cost of x ounces of chicken and y ounces of tofu

$C=\frac{5}{16}x+\frac{2.5}{16}y$

Now, by graphing the above constraints ( by equation (1) and (2) )

We get a feasible region that shows the possible values of x and y,

The boundary points of the feasible region are,

(2.545, 10.545), (0, 19.2), (8.571, 0)

$C=\frac{5}{16}\times 2.545+\frac{2.5}{16}\times 10.545 = 2.443$

$C=\frac{5}{16}\times 0+\frac{2.5}{16}\times 19.2 = 3$

$C=\frac{5}{16}\times 8.571+\frac{2.5}{16}\times 0 = 2.678$

Hence, the minimum cost is $ 2.443,

For which 2.545 ounces of chicken and 10.545 ounces of tofu should be eaten.

3 0

3 years ago

Courtney reads about 110 words per minute she procrastinated and now has less then a week to finish her reading assignment if th

ss7ja [257]

Multiply the amount of pages by the amount of words per page:

$820 \times 350 = 287000$

There are about 287000 words remaining.

Courtney can read at a rate of 110 words per minute. Since we want to find the amount of hours she needs to finish the book, multiply this rate by 60 to convert into an hour:

$110 \times 60 = 6600$

Courtney reads at a rate of 6600 words per hour.

Divide the amount of words in the book by Courtney's reading speed in hours:

$287000 \div 6600 = \boxed{43.48}$

Courtney will need to set aside 43.48 hours to complete her assignment.

8 0

3 years ago

How do you solve this

fiasKO [112]

(((x + y) / 3) + (1 / x)) / (5 + (15 / x))
The best way is to make it one fraction.
Multiply by ((3x/3x) / (3x/3x)) to remove the other fractions.
((x(x + y)) + 3(1)) / (5(3x) + 3(15))
(x^2 + xy + 3) / (15x + 45)
Then factor to simplify
(x^2 + xy + 3) / (3(x + 15))

4 0

3 years ago

Fill in the table using this function rule. y = 2x + 5

aivan3 [116]

Just put in the x values for example
First one x = 1

y = 2(1) + 5
y= 7

I’ll tell u all the answers here in order:
7
9
15
19

4 0

3 years ago

Read 2 more answers