A chemist has three different acid solutions,
The first solution contains 20 % acid, the second contains 35 % acid, and the third contains 55%
acid.
She created 108 liters of a 40 % acid mixture, using all three solutions. The number of liters of
55 % solution used is 3 times the number of liters of 35 % solution used.
How many liters of each solution was used?
The chemist used
liters of 20% solution,
liters of 35 % solution, and
liters of 55 % solution.
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Answers

Answer 1

9514 1404 393

Answer:

36 liters of 20%18 liters of 35%54 liters of 55%

Step-by-step explanation:

Let a, b, c represent the quantities of 20%, 35%, and 55% solutions, respectively. Then for the given mix, we have ...

  a + b + c = 108 . . . . . total number of liters

  .20a +.35b +.55c = 0.40·108 . . . . . liters of acid

  0a - 3b + c = 0 . . . . . 55% solution was 3 times 35% solution

__

Solving these three equations by your favorite method gives ...

  (a, b, c) = (36, 18, 54)

The chemist used 36 liters of 20%, 18 liters of 35%, and 54 liters of 55%.

_____

Comment on alternate approach

Since the ratio of 55% to 35% is 3 : 1, that mix will have an acid content of ...

  (3(.55) +1(.35))/4 = 0.50 = 50%

So, the final mix is equivalent to some quantity of 50% mix being added to some quantity of 20% mix. The fraction that is 50% mix* will be (40-20)/(50-20) = 2/3 of the total, or (2/3)(108 L) = 72 L.

Now we know that (1/3)(108 L) = 36 L of 20% solution is needed and (1/4)(72 L) = 18 L of 35% solution is needed. 3 times that is 54 L of 55% solution.

__

* After you work a few mixture problems, you can see the pattern. If we start with an equation for x = fraction of 50% to use with 20% to make 40%, we get ...

  x(50%) +(1 -x)(20%) = 40%

  x(50% -20%) = 40% -20% . . . . . subtract 1(20%) and factor out x

  x = (40% -20%)/(50% -20%)

The key here is to see where the numbers 20%, 40%, and 50% show up in the fraction.


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Step-by-step explanation:

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Answer:

Hey!

Your answer is 11cm!

Step-by-step explanation:

So to get the radius from the Circumference we need both the Circumference and the value of pi...3.14

Radius = [tex]\frac{C}{2\pi }[/tex] ... (that's the formula)

WE SUBSTITUTE IN:

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I HOPE THIS HELPED YOU!

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Step-by-step explanation:

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Answer:

Kindly check explanation

Step-by-step explanation:

Given that:

Jacinda = 16 baskets

Greta = 4 baskets

The number of baskets Jacinda made is how many times more than the number of baskets Greta made?

To obtain this :

Number of baskets Jacinda made / Number of baskets Greta made

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Hence, Number of basket Jacinda made is 4 times more than that made by Greta

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Answers

Answer:

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Step-by-step explanation:

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Determine the intercepts of the line.
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y-intercept:
X-intercept:


Need to know NOW

Answers

Answer:

y = 12

x = 10/3

Step-by-step explanation:

y = -3.6x + 12

From this equation, which is in slope intercept form (y = mx+b), we already know that b represents the y-intercept, so that means the y-intercept is 12.

To find the x-intercept, we need to make y equal 0 to find x. So:

0 = -3.6x + 12

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Answer:
x-intercept: 10/3
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Steps:
Finding x
y=-3.6x+12
0= -3.6x+12
3.6x=12
x=10/3

Finding y
y=-3.6x+12
y=-3.6(0)+12
y=12

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Answer:

Step-by-step explanation:

b. 27

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e 20

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Answer:

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Step-by-step explanation:

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Ok so what you need to do is you need to get all the numbers and see which one is the right number so...

A. y = 11.2 that is wrong

B. y = 25 is wrong

C. y = 5 is right

D. y = 15 is wrong.

C is right because it would be 5 times 5 times 5. SO 5 times 5 is 25, and then u times it by 5 and you get 125!

C is correct

Hope this helps!!

Answer:

This is actually a cube root, since you need a cube root to cancel out the cube.

C, y = 5

Step-by-step explanation:

125 = 5 × 5 × 5 = 5^3

5 × 5 × 5 = 25 × 5 = 125.

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It REALLY helps when you break these into factors.

[tex] \sqrt[3]{125} = 5 , \: as \: {5}^{3} \: = 125 [/tex]

This is essentially asking what multiplied by itself three times is equal to 125.

Process of elimination can be used for any number cubed that is ≠ 125

i.e : 11.2^3 ≠ 125

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Step-by-step explanation:

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The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value. Unitary method is a technique by which we find the value of a single unit from the value of multiple devices and the value of more than one unit from the value of a single unit. It is a method that we use for most of the calculations in math.

Given;

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1 point
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Step-by-step explanation:

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Step-by-step explanation:

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Answer:

Step-by-step explanation:

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Answer:

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Step-by-step explanation:

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1) Relacione o nome dos polígonos de acordo com o total de lados. a) Triângulo ( ) 8 lados. b) Quadrilatero ( ) 6 lados. c) Pentágono ( ) 7 lados. d) Hexágono ( ) 3 lados. e) Heptágono ( ) 4 lados. f) Octógono ( ) 5 lados. 2) O ângulo reto , também conhecido como ângulo de um quarto de volta mede:. a) 90° b) 180° c) 270 ° d) 360 ° 3) O ângulo que mede menos 90 ° e mais de 0° é chamado de : a) agudo b) raso c) reto d) obtuso. 4) Um teatro 64 fileiras de poltronas e cada fileira tem 35 poltronas. Qual é a lotação desse teatro? 5) André e Federico fizeram 28 pacotes contendo 180 bandeirinhas cada pacote . Quantas bandeirinhas os meninos fizeram ? 5) Calcule : a) 861 x 27= b) 798 x 45=

Answers

Answer:

1

O nome de um polígono é um nome que se deve ao número de lados que o polígono possui.

a) Triângulo = 3 lados.

b) Quadrilátero = 4 lados.

c) Pentágono = 5 lados.

d) Hexágono = 6 lados.

e) Heptágono = 7 lados.

f) Octógono = 8 lados.

2) O ângulo reto, também conhecido como ângulo de um quarto de volta, mede: a) 90 °

3) O ângulo que mede menos 90 ° e mais que 0 ° é denominado: a) agudo

4) 2240

5) 5040 sinalizadores

6) Calcule: a) 861 x 27 = 23247

b) 798 x 45 = 35910

Step-by-step explanation:

1) Liste o nome dos polígonos de acordo com o número total de lados.

a) Triângulo = 3 lados.

b) Quadrilátero = 4 lados.

c) Pentágono = 5 lados.

d) Hexágono = 6 lados.

e) Heptágono = 7 lados.

f) Octógono = 8 lados.

2) O ângulo reto, também conhecido como ângulo de um quarto de volta, mede: a) 90 ° b) 180 ° c) 270 ° d) 360 °

= a) 90°

Um triângulo ângulo reto pode ser definido como um triângulo onde um de seus 3 ângulos é equivalente a 90 graus (90°).

3) O ângulo que mede menos 90 ° e mais que 0 ° é denominado: a ) agudo b) raso c) reto d) obtuso.

Um ângulo maior que 0 ° e menor que 90 ° pode ser definido como um ângulo agudo.

= a) agudo

4) Um teatro com 64 filas de assentos e cada fila tem 35 assentos. Qual é a capacidade deste teatro?

No teatro, cada fila tem 35 lugares.

Temos 64 linhas

O número total de licenças que temos é calculado como:

1 fila = 35 assentos

64 linhas =

Multiplicação cruzada

64 filas × 35 assentos

= 2.240 assentos.

Portanto, a capacidade do teatro é de 2240.

5) André e Federico confeccionaram 28 embalagens contendo 180 bandeiras cada embalagem. Quantas bandeiras os meninos fizeram?

O número de bandeiras que os meninos fizeram é calculado como:

28 pacotes × 180 bandeiras

= 5040 sinalizadores

6) Calcule: a) 861 x 27 = 23247

b) 798 x 45 = 35910

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