A parent has washed some nappies in a strong bleach solution and wishes to rinse them so that they contain as weak a bleach solution as possible. By wringing out, the nappies can be made to contain just half a litre of solution. Show that two thorough rinses, such that the solution strength is uniform, the first using 12 litres of water and the second using 8 litres of water, reduces the strength of the
1 425
If 20 litres of clean water is all that is available and the parent is prepared to do only two rinses, how best should the water be divided between the two rinses?

Answers

Answer 1

Answer:

a) Two thorough rinses gives;

1/25 × 1/2 × 2/17 strong bleach/L = 1/425 strong bleach/L

b) The water should be divided into two quantities of 10 liters each

Step-by-step explanation:

The given parameters are;

The initial volume of strong bleach solution in the nappies = 1/2 Liters

The volume of water first used to rinse = 12 liters

The volume of water used in the second rinse = 8 liters

Therefore, we have;

The total volume of the water and the concentrated bleach in the first rinse = 1/2 + 12 = 12.5 Liters

The new concentration of the bleach in the first rinse water = (1/2 strong bleach)/12.5 L = (1/2 strong bleach)/25/2 L = 1/2×2/25 = 1/25 strong bleach/L

The volume of the first rinse introduced in the second rinse = 1/2 Liters

The concentration of the bleach introduced in the second rinse = The new concentration of the bleach in the first rinse water = 1/25 strong bleach/L

The volume of water added in the second rinse = 8 liters

The total volume of the water and the bleach in the second rinse = (8 + 1/2) liters = 8.5 liters

The concentration of bleach in the second rinse = (The concentration of the bleach introduced in the second rinse × (Volume of bleach solution introduced in the second rinse))/(The total volume of the water and the bleach in the second rinse)

The concentration of bleach in the second rinse = (1/25 strong bleach/L × 1/2 L)/(8.5 Liters)

The concentration of bleach in the second rinse = (1/25 strong bleach/L × 1/2 L)/(17/2 Liters) = 1/25 × 1/2 × 2/17 strong bleach/L = 1/425 strong bleach/L

b) The the quantity of water in the first rinse = x

The amount of water in the second rinse = 20 - x

The concentration of bleach in the first rinse = 1/2/(x + 1/2) = 1/(2·x + 1)

The concentration introduced in the second rinse = 1/2 × 1/(2·x + 1) = 1/(4·x + 2)

The total volume of water and bleach introduced in the second rinse = (20 - x + 1/2) = 20.5 - x

The concentration of bleach in the second rinse = 1/(4·x + 2)/(20.5 - x)

The minimum value for the concentration can be found from taking the derivative of the function for the concentration and equation to zero as follows;

[tex]\dfrac{\mathrm{d} \dfrac{1}{\left ( 4\cdot x + 2 \right )\cdot \left ( 20.5 - x \right )}}{\mathrm{d} x} = \dfrac{2\cdot \left ( x - 10 \right )}{\left ( 2\cdot x + 1 \right )^{2}\cdot \left ( 20.5 - x \right )^{2}} = 0[/tex]

2·(x - 10) = 0

x = 0/2 + 10 = 10

x = 10

The the quantity of water in the first rinse = x = 10 liters

The the quantity of water in the first rinse = 10 liters

The amount of water in the second rinse = 20 - x = 20 - x = 20 - 10 = 10 liters

The amount of water in the second rinse = 10 liters

The water should be divided into two quantities of 10 liters each

Therefore, the water should be divided into two quantities of 10 liters each to give a final bleach solution concentration of 1/(4·x + 2)/(20.5 - x) = 1/(4×10 + 2)/(20.5 - 10) = 1/42 × 1/10.5 = 1/441 concentration/liter.

Answer 2

Answer: a) Two thorough rinses gives;

1/25 × 1/2 × 2/17 strong bleach/L = 1/425 strong bleach/L

b) The water should be divided into two quantities of 10 liters each


Related Questions

write an equation of a line passing through point p(-2, 6) that is parallel to the line x= -5​

Answers

Answer:

x= -2

Step-by-step explanation:

x = -5 is a vertical line, so a line parallel would also have to be a vertical line

It goes through the point ( -2,6)

The x coordinate -2

So a line parallel would be x= -2

Answer:

x= -2

Step-by-step explanation:

Luke is a dog walker. He gets $10 per day for walking his neighbor's dogs. He recently snapped his surfboard and wants to buy a used surfboard for $325. If he has $142 in the bank, how many days will he have to walk the dogs to earn enough for the board?

Answers

Answer:

10$

Step-by-step explanation:

two solutions to the inequality p ≤ 16.

Answers

Answer:

The inequality says p is equal to 16 and less than 16.

So from under 16 (even negative), you can give a solution.

Examples: -3; 2

Hope this helps!

1, 2, 3, 4, 5, 6, 7 are all possible answers. Any number less than or equal to 16.

Donte simplified the expression below. 4 (1 + 3 i) minus (8 minus 5 i). 4 + 3 i minus 8 + 5 i. Negative 4 + 8 i. What mistake did Donte make?

Answers

Answer:

He didn't expand properly.

This part: 4(1 + 3i)

Step-by-step explanation:

4(1 + 3i) - (8 - 5i)

Expand:

4 + 12i - 8 + 5i

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Step-by-step explanation:

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Given the points: (-2, 0) and (4,8) find the slope

Answers

Answer:

1&1/3

Step-by-step explanation:

(y2 - y1) / (x2 - x1)

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8/6

1 1/3

Hi if you can answer this i'll mark u brainllest and give you MORE points
What are three equivalent decimals for the number -4.2323?

Answers

Answer:

-4.23230, -4.232300, -4.2323000

Answer:

1) -4.23230 2)-4.232300 3)-4.2323000

Step-by-step explanation:

Where is my brainliest and my points :)

Choose the correct written expression for: (9 x 4) divided by 6.

Options:

he quotient of 9 and 4 times 6

divided by the product of 9 and 4

the product of 9 and 4 divided by 6

9 times 4 divided by 6

Answers

Answer:

the product of 9 and 4 divided by 6

Lauren's vet commented that her puppy gained 10% in weight since the first visit. Write an expression that could be evaluated to show the puppy's current weight. Use a variable to represent the weight of the puppy at the first visit. Write the expression in simplified form. If the puppy gains another 10% in weight from the current visit to a future visit, how much will the puppy weigh? Write an expression that could be evaluated to show the puppy's future weight. Write the expression in simplified form.

Answers

Answer: expression to show puppy's current weight = x+ 0.1x, simplified form = 1.1x

Expression that for puppy's future weight= 1.1x + 0.1(1.1x), simplified form = 1.21 x

Step-by-step explanation:

Let x= Puppy's weight in the first visit.

If it gained 10% in weight from the first visit, then his current weight = (weight in first visit)+10% of (weight in first visit)

= x+ 0.1x

i.e. expression to show puppy's current weight = x+ 0.1x

In simplified form it will be

x+ 0.1x = x(1+0.1)

=x(1.1)

=1.1 x  (simplified form )

If puppy gains another 10% in weight, then its future weight = (current weight)+10% of (current weight)

= 1.1x+10% of 1.1x

= 1.1x + 0.1(1.1x)

Expression that for puppy's future weight= 1.1x + 0.1(1.1x)

= 1.1x(1+0.1)

= 1.1x(1.1)

=(1.1)²x

= 1.21x  (simplified form)

Raza works at a flea market selling sunglasses. He is paid $7.50/h plus a 75¢ commission for every pair of sunglasses he sells.
Write an equation to model Raza’s earnings. (1 mark)


Find Raza’s earnings if he sells 25 pairs of sunglasses during a 6-h shift. (2 marks)




How many pairs of sunglasses must he sell to earn $90 in 8 h? (2 marks)

Answers

Answer:

7.50h+0.75s        63.75       30

Step-by-step explanation:

7.50 x how many hours + 0.75 x how many sunglasses he sold

7.50 x 6 + 0.75 x 25= 63.75

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Answers

Answer:

630/49

Step-by-step explanation:

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Answers

Answer:

2af+bf = 2af+bf

Step-by-step explanation

f(x) = 4x2 – 3x. =  x(4x−3)

The point (3,5) has been translated three right and three down. What are
the coordinates of the image?

Answers

Answer:

If you mean the coordinates of the point, then its coordinates will be (6,2)

Step-by-step explanation:

Add 3 to your x-value (3 right), and subtract 3 from your y-value (3 down). You will then get (6,2). Hope this helped :D

The coordinate of the new point will be (6, 2).

What is a transformation of a point?

A spatial transformation is each mapping of feature space to itself and it maintains some spatial correlation between figures.

The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This rule is used to answer the problem correctly and precisely.

Point (3,5) has been translated as three right and three down.

Add 3 in the abscissa and subtract 3 from the ordinate. Then the transformation is given as,

(x, y) ⇒ (3 + 3, 5 - 3)

(x, y) ⇒ (6, 2)

The coordinate of the new point will be (6, 2).

More about the transformation of a point link is given below.

https://brainly.com/question/27224339

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Answers

Answer:

world

Step-by-step explanation:

Answer:

world

Step-by-step explanation:

"I can show you the world shining, shimmering, splendid"

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Answers

-5p^2-11p-4/2p^2+4p-6
Hope this helps:)

Answer:

2-5p

1-p

Step-by-step explanation:

put the whole equation into one one fraction. then you simplify. first do the bottom

1. first do 3-2=1

2. then the variable numbers i forget the fancy term

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3. add together 1 - p

then do the top

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4. 2-5p

1-p

I forget if there's anymore steps but I hope this helps

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Answers

Answer:

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Step-by-step explanation:

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Answers

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Answers

Answer:

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Step-by-step explanation:

A certain hybrid car can travel 1 4/11 times as far as a similar nonhybrid car can, each one gallon of gasoline. If the nonhybrid car can travel 33 miles per gallon of gasoline, how far can the hybrid travel on 4/5 gallon of gasoline?

Answers

Answer:

On 4/5 gallon of gasoline, hybrid car will travel 36 miles of distance.

Step-by-step explanation:

Suppose, non hybrid car travel "x" distance in 1 gallon of gasoline

then, hybrid will travel " 1 4/11* x" distance in 1 gallon of gasoline

Given that, non hybrid car travel, x = 33 miles per gallon

Then, hybrid car travel, 1 4/11*x = 1 4/11* 33 = 45 miles per gallon

On 1 gallon of gasoline hybrid car travel= 45 miles

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On 4/5 gallon of gasoline, hybrid car will travel 36 miles of distance.

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Answers

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Answers

Answer:

Coefficient of x, in this case, is '2'

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Answers

Answer:

a point Is an imaginary line

Answer:

imaginary

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Answers

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Step-by-step explanation:

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Answers

Answer:

x=2

Step-by-step explanation:

-2(1-4x)=3x+8

-2*1 and -2*-4x

-2+8x=3x+8

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5x=10

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Answers

Answer:

$11.75

Step-by-step explanation:

In order to solve this problem, you divide $47.00/4. When you do that, you get $11.75

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Answers

Answer:

c

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i believe it's hard to see the graph

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Answers

Answer:

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Answers

Answer:

8p+25b

Step-by-step explanation:

Answer:

8p+25b

Step-by-step explanation:

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Which fraction is equivalent to 7/8 ?

Answers

So from 7/8 = 35/40 , 35 is the answer
Many fraction equivalent to 7/8
7/8•2=7/4
7/8•3=21/8
7/8•4=7/2
7/8•5=35/8
7/8•6=21/4
7/8•7=49/8
7/8•8=7
7/8•9=63/8
7/8•10=35/4

A jet ski company charges a flat fee of $22.00 plus $3.00 per hour to rent a jet ski. Another company charges a fee of $17.50 plus $3.75 per hour to rent the same jet ski. Write a system of equations that can be used to determine when the cost will be the same, then solve your system.

Answers

Answer: The cost will be same for 6 hours.

Step-by-step explanation:

Given: A jet ski company charges a flat fee of $22.00 plus $3.00 per hour to rent a jet ski.

Another company charges a fee of $17.50 plus $3.75 per hour to rent the same jet ski.

Let x = Number of hours

y = Total cost

Then, Total cost (in $) for first company (y) = 22+3x

Total cost (in $) for second company (y) = 17.50+3.75x

So required system of equations :

y =  22+3x

y= 17.50+3.75x

When the cost will be the same,

22+3x = 17.50+3.75x

⇒ 3x - 3.75x = 17.50- 22

⇒ - 0.75x = -4.5

⇒ x =6  [Divide both sides by -0.75]

Hence,  the cost will be same for 6 hours.

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