Two pay as you go which company offered the best deal

A boy thinks he has discovered a way to drink extra orange juice without alerting his parents. For every cup of orange juice he

mina [271]

Answer:

x=4.8473 cups

Step-by-step explanation:

Concentration of Liquids

It measures the amount of substance present in a mixture, often expressed as %. If there is an volume x of a substance in a total volume mix of y, the concentration is given by

$\displaystyle C=\frac{x}{y}$

It we take a sample of that mixture, we must consider that we are getting only the substance, but all the mixture (assumed it has been uniformly mixed). For example, if we take a glass of liquid from a 80% mixture of juice, the glass will also have a 80% of juice.

Let's solve the problem sequentially. At first, let's assume all the container is full of x cups of juice. Its concentration is 100%. Now let's take 1 cup of pure juice and replace it by 1 cup of pure water. The new amount of juice in the container is

x-1 cups of juice.

The new concentration is

$\displaystyle \frac{x-1}{x}$

The boy takes a second cup of liquid, but this time it's not pure juice, it has a mixture of juice and water with a concentration computed above. Now the amount of juice is

$\displaystyle x-1-\frac{x-1}{x}$ cups of juice.

Simplifying, the cups of juice are

$\displaystyle \frac{\left (x-1\right)^2}{x}$

The new concentration is

$\displaystyle \frac{\left (x-1\right)^2}{x^2}$

For the third time, we now have

$\displaystyle \frac{\left (x-1\right)^2}{x}-\frac{\left (x-1\right)^2}{x^2}$ cups of juice.

Simplifying, the final amount of juice is

$\displaystyle \frac{\left (x-1\right)^3}{x^2}$

And the final concentration is

$\displaystyle \frac{\left (x-1\right)^3}{x^3}$

According to the conditions of the question, this must be equal to 50% (0.5)

$\displaystyle \frac{\left (x-1\right)^3}{x^3}=0.5$

Taking cubic roots

$\displaystyle \sqrt[3]{\frac{\left (x-1\right)^3}{x^3}}=\sqrt[3]{0.5}$

$\displaystyle \frac{\left (x-1\right)}{x}=\sqrt[3]{0.5}$

Operating and joining like terms

$\displaystyle x-\sqrt[3]{0.5}\ x=1$

Solving for x

$\displaystyle x=\frac{1}{1-\sqrt[3]{0.5}}$

$x=4.8473\ cups$

Let's test our result

Final concentration:

$\displaystyle \frac{\left (4.8473-1\right)^3}{4.8473^3}=0.5$

6 0

3 years ago

La la laaaaa don't answer just for the points -_-

Amiraneli [1.4K]

Answer:

$\sf C=21.99~ft.$

__________

$\sf Steps$

$\sf Given~the~diameter~is~7~ft...$

$\sf We~know~we~must~use~diameter-to-circumference~formula$

$\sf Formula:$ $\pi d = \pi * (diameter) = [Circumference]$

__________

$\sf Solve$

$\pi * 7 = 21.99~ft.$

6 0

2 years ago

Read 2 more answers

Helpppppppp pleaseeeeee

telo118 [61]

F(5) = -4(25) - 3 = -100 -3 = -103
answer
f(5) = -103

g(-5) = 3(-5) - 1 = -15 -1 = -16
answer
g(-5) = -16

3 0

3 years ago

Please help me as soon as possible

Ksju [112]

Base x height x length

the first one if not the fourth

3 0

2 years ago

Read 2 more answers

Company B: starting salary-28,000 Yearly salary increase-2,400

Naya [18.7K]

Answer:

Sharla, 4400

Step-by-step explanation:

Paul's Salary:

Paul started at company B. Starting salary of company B is $ 28,000 with a yearly increase of $ 2,400. Paul's Salary in first year will be 28,000. In second year his salary will be 28000 + 2400, in 3rd year his salary will be: 28000 + 2(2400) and so on.

Since, the increase in Paul's salary every year is $ 2400, the increase in his salary after 10 years or in 10th year would be = 2400 x 9 = $ 21,600

So, his total salary in 10th year would be = 28000 + 21600 = $ 49,600

Sharla's Salary:

Sharla started at company C. Starting salary of company C is $ 36,000 with a yearly increase of $ 2,000.

Since, the increase in Sharla's salary every year is $ 2000, the increase in her salary after 10 years or in 10th year would be = 2000 x 9 = $ 18,000

So, her total salary in 10th year would be = 36000 + 18000 = $ 54,000

Conclusion:

Sharla earned more in 10th year an amount equal to $ 4400. So the answer is:

In the last year, Sharla earned $4,400 more.

5 0

3 years ago