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Maurinko [17]
3 years ago
12

A scientist needs 4.8 liters of a 12% alcohol solution. She has available a 22% and a 10% solution. How many liters of the 22% a

nd how many liters of the 10% solutions should she mix to make the 12% solution?
Liters of 10% solution =


Liters of 22% solution =

pls someone help!!
Mathematics
1 answer:
yanalaym [24]3 years ago
5 0

Answer:

  • 4.0 L of 10%
  • 0.8 L of 22%

Step-by-step explanation:

For mixture problems, it is convenient to define a variable to represent the amount of the greatest contributor. Let x represent the amount of 22% solution in the mix. Then 4.8-x is the amount of 10% solution.

The amount of alcohol in the mix is ...

  0.22x +0.10(4.8-x) = 0.12(4.8)

Eliminating parentheses, we have ...

  0.22x -0.10x +0.10(4.8) = 0.12(4.8)

Subtracting (0.10)(4.8) and combining x-terms gives ...

  0.12x = 0.02(4.8)

  x = (0.02/0.12)(4.8) = 0.8 . . . . . divide by the x-coefficient

The scientist needs 0.8 L of 22% solution and 4.0 L of 10% solution.

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Step-by-step explanation:

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Answer:

All of these terms are dollar amounts.

Step-by-step explanation:

Here, x + y = 10 (where these numerals represent counts)

(1/2)x + (1/4)y = 4 (where (1/2), (1/4) and 4 are dollar amounts)

Let's eliminate y.  To accomplish this, mult. the 2nd eq'n by-4, obtaining

-2x - y = -16, and then combining this with the 1st equation, as follows:

-2x - y = -16

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 -x  = -6, or x = 6.  This represents the number of pens purchased by Terrance.  

Subbing 6 for x in the first equation, we get y = 4.  This represents the number of pencils he bought.

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5 0
3 years ago
In the diagram shown overline AD and intersect at point E. overline AB and overline CD are parallel . Given the segment length s
Harrizon [31]

Answer:

11.25

Step-by-step explanation:

Since AB and CD  are parallel, ∠D is congruent to ∠A and ∠C is congruent to ∠B.  Therefore the two triangles are similar by the AA postulate.  Now, the corresponding sides are in proportion

Since AE ↔ DE and AB ↔ CD

So, AE/CD = AB/CD

AE/5 = 9/4

AE = 9(5)/4

     = 45/4  = 11.25

8 0
2 years ago
The data below are the monthly average high temperatures for New York City. What is the five-number summary? 40, 40, 48, 61, 72,
yawa3891 [41]

Answer:

B) Sample minimum: 40, Sample maximum: 84

Q1: 45, Median: 63, Q3: 77

Step-by-step explanation:

The first step is to write the temperatures in crescent order:

40, 40, 42, 48, 54, 61, 65, 72, 76, 78, 84, 84,

The sample minimum is the lowest value = 40

The sample maximum is the highest value = 84.

Since there are 12 numbers, the sample median is the average between the 6th and 7th terms:

M = \frac{61+65}{2}\\ M=63

The first quartile is the average between the 3rd and 4th terms:

Q_1 = \frac{42+48}{2}\\ Q_1=45

The third quartile is the average between the 9th and 10th terms:

Q_3 = \frac{76+78}{2}\\ Q_3=77

Therefore, the answer is:

B) Sample minimum: 40, Sample maximum: 84

Q1: 45, Median: 63, Q3: 77

8 0
2 years ago
$100 is invested at 12% per year. If the amount is compounded annually, write the total amount after 2 years in exponential func
Sladkaya [172]

Answer:

A = $100(1.12)^2

Step-by-step explanation:

The standard formula for compound interest is given as;

A = P(1+r/n)^(nt) .....1

Where;

A = final amount/value

P = initial amount/value (principal)

r = rate yearly

n = number of times compounded yearly.

t = time of investment in years

For this case;

P = $100

t = 2years

n = 1

r = 12% = 0.12

Substituting the values, we have;

A = $100(1+0.12)^(2)

A = $100(1.12)^2

7 0
3 years ago
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