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4 years ago

How many liters of a 10% alcohol solution must be mixed with 90 liters of a 60% solution to get a 30% solution?

1 answer:

4 0

Since 10% = 0.10 by moving the decimal two spots to the left, we can say that 0.10L is the amount of alcohol with 10% concentration in L liters. Similarly, 0.60L is 60% for L liters and 0.30L is the amount of liters with 30%. If the amount of 10% alcohol solution in liters is x and the 60% in y, we get 0.10x+0.60y=0.30L due to that the liters add up to get a 30% amount of alcohol (this equation represents the amount of alcohol). Next, x+y=L. Since we know that we have 90 liters of 0.60, y=90 and we have
0.10x+54=0.30L
x+90=L. Plugging x+90 for L, we get 0.10x+54=0.3(x+90)=0.3x+27. Subtracting 27 and 0.1x from both sides, we get 0.2x=27. Next, we can multiply both sides by 5 (since 1/0.2=5) to get x=135 liters

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A rectangular lap pool measures 80 feet long by 20 feet wide if it needs to be filled to 48 and each cubic foot hose 7.5 gallons

zmey [24]

Answer: it will take 576000 gallons to fill the lap pool.

Step-by-step explanation:

The formula for determining the volume of water in the rectangular pool is expressed as

Volume = length × width × height

The rectangular lap pool measures 80 feet long by 20 feet wide if it needs to be filled to 48. It means that the volume of water that would be pumped inside the pool is

Volume = 80 × 20 × 48 = 76800 cubic feet

1 cubic foot = 7.5 gallons

76800 cubic feet = 76800 × 7.5 = 576000 gallons

5 0

3 years ago

50 points! I understand A. and B. but I would really appreciate help with C.

FromTheMoon [43]

Answer:

$51.72\text{ cells per hour}$

Step-by-step explanation:

So, the function, P(t), represents the number of cells after t hours.

This means that the derivative, P'(t), represents the instantaneous rate of change (in cells per hour) at a certain point t.

So, we are given that the quadratic curve of the trend is the function:

$P(t)=6.10t^2-9.28t+16.43$

To find the instanteous rate of growth at t=5 hours, we must first differentiate the function. So, differentiate with respect to t:

$\frac{d}{dt}[P(t)]=\frac{d}{dt}[6.10t^2-9.28t+16.43]$

Expand:

$P'(t)=\frac{d}{dt}[6.10t^2]+\frac{d}{dt}[-9.28t]+\frac{d}{dt}[16.43]$

Move the constant to the front using the constant multiple rule. The derivative of a constant is 0. So:

$P'(t)=6.10\frac{d}{dt}[t^2]-9.28\frac{d}{dt}[t]$

Differentiate. Use the power rule:

$P'(t)=6.10(2t)-9.28(1)$

Simplify:

$P'(t)=12.20t-9.28$

So, to find the instantaneous rate of growth at t=5, substitute 5 into our differentiated function:

$P'(5)=12.20(5)-9.28$

Multiply:

$P'(5)=61-9.28$

Subtract:

$P'(5)=51.72$

This tells us that at exactly t=5, the rate of growth is 51.72 cells per hour.

And we're done!

7 0

3 years ago

A quadrilateral with 90 degree angles is shown. The lengths of the left and right sides are 10 and 2 y + 4. The lengths of the t

notka56 [123]

Answer: y=3

Step-by-step explanation:

Since the quadrilateral has 90 degree angles, it must be a a square or a rectangle. This means the measure of sides left and right are the same and the measure of sides top and bottom are the same.

To get the measure of y, you can use left and right or top nd bottom.

I'll use left and right. 10=2y+4 => 10-4=2y => 6=2y => y=3

You can check it by substituting. 2(3)+4=10 The answer is the measure of the right side, which is the same as the measure of the left side.

I hope this helps you!

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3 years ago

You spend $40 on 5 Pounds of concreate what is the 1 unit rate in dollars

Umnica [9.8K]

Answer:

Step-by-step explanation:

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2 years ago

Read 2 more answers

The answer and how to solve the problem

SVETLANKA909090 [29]

A
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3 years ago