1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
ser-zykov [4K]
3 years ago
5

A paint company mixes it's paint with water to create more paint per gallon. They currently have ten gallon jugs which contain 1

0% water. How much water must they add to create a 80/20 mix of paint to water?
Mathematics
1 answer:
Karo-lina-s [1.5K]3 years ago
5 0
<h3>Answer:  1.25 gallons</h3>

==================================

Explanation:

They currently have ten gallon jugs that contain 10% water, so this means 0.10*10 = 1 gallon of the jug is water and the other 10-1 = 9 gallons is paint. This is assuming the cans are just paint and water.

The ratio of paint to water is 90:10 which reduces to 9:1

Often it helps to reduce as much as possible, but it's actually more handy in this case to keep it at 90:10 so you can see the two parts add back up to 100%

--------------

Let x be the amount of water we add. This amount is in gallons.

We start off with 1 gallon of water and it bumps up to 1+x gallons of water.

The overall amount of 10 gallons also bumps up to 10+x gallons.

We want a ratio of 80:20 this time, so we want 20 parts water and 80 parts paint. In other words, we want 20/(20+80) = 20/100 = 20% water

Divide (1+x) over (10+x) to get (1+x)/(10+x). This represents the fraction of water. We want this fraction to be equal to 0.20, which is the 20% water amount. It is also equal to 20/100.

--------------

(1+x)/(10+x) = 20/100

100(1+x) = 20(10+x) ... cross multiply

100+100x = 200+20x ... distribute

100x-20x = 200-100

80x = 100

x = 100/80 ... divide both sides by 80

x = 1.25

You need to add 1.25 gallons of water

--------------

If you add 1.25 gallons of water, then,

amount of water = 1+x = 1+1.25 = 2.25

amount of paint&water = 10+x = 10+1.25 = 11.25

So you'll have 2.25 gallons of water out of 11.25 gallons of water&paint mix

2.25/11.25 = 0.2 = 20% water

This confirms our answer.

--------------

Extra info:

1.25 gallons = 1 gallon + 1/4 gallon

1.25 gallons = 1 gallon + 1 quart

This is because 1 gallon = 4 quarts, so 1 quart = 1/4 gallon.

You might be interested in
Rachel and Abby are trying to solve a science homework question. They need to find how much a rock that weighs 6 pounds on Earth
OverLord2011 [107]
A c e are all ancers thor you go
4 0
3 years ago
Read 2 more answers
Can someone help me out with number 2?
Norma-Jean [14]
\sin255^o=\sin(300^o-45^o)=\sin300^o\cos45^o-\cos300^o\sin45^o= \\\\=- \frac{ \sqrt{3} }{2}\cdot  \frac{ \sqrt{2} }{2}- \frac{1}{2} \cdot  \frac{ \sqrt{2} }{2}=-      \frac{ \sqrt{6} }{4} -  \frac{ \sqrt{2} }{4}=  -\frac{  \sqrt{6}+\sqrt{2} }{4}

5 0
3 years ago
in the unted states, the height of men are normally distributed with the mean 69 inches and standard deviation 2.8 inches. If 16
yaroslaw [1]

Answer:

Probability that their mean height is less than 68 inches is 0.0764.

Step-by-step explanation:

We are given that in the united states, the height of men are normally distributed with the mean 69 inches and standard deviation 2.8 inches.

Also, 16 men are randomly selected.

<em>Let </em>\bar X<em> = sample mean height</em>

The z-score probability distribution for sample mean is given by;

              Z = \frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }  ~ N(0,1)

where, \mu = population mean height = 69 inches

            \sigma = population standard deviation = 2.8 inches

            n = sample of men = 16

The Z-score measures how many standard deviations the measure is away from the mean. After finding the Z-score, we look at the z-score table and find the p-value (area) associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X.

So, probability that the mean height of 16 randomly selected men is less than 68 inches is given by = P(\bar X < 68 inches)

 P(\bar X < 68 inches) = P( \frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } } < \frac{68-69}{\frac{2.8}{\sqrt{16} } } ) = P(Z < -1.43) = 1 - P(Z \leq 1.43)

                                                           = 1 - 0.9236 = 0.0764

<em>Now, in the z table the P(Z  x) or P(Z < x) is given. So, the above probability is calculated by looking at the value of x = 1.43 in the z table which has an area of 0.92364.</em>

Therefore, probability that their mean height is less than 68 inches is 0.0764.

3 0
3 years ago
Please help!!!
Nonamiya [84]

Answer:

I belive it would be 1/5. ;;;

4 0
3 years ago
Determine the equation of the line given by the graph.
Dominik [7]
A is the correct answer!!!
5 0
3 years ago
Other questions:
  • What would you have to do to make the line y = 2x -7 steeper on the coordinate plane?
    7·1 answer
  • Write an algebraic expression to model the price s of a pair of shoes plus 5% sales tax
    8·1 answer
  • An object is dropped from a bridge and allowed to freefall to the ground. The height of the object over time can be modeled usin
    6·2 answers
  • Hey:) can you please help me posted picture of question
    11·2 answers
  • Middle school math with pozzazzi! Book C C-31 what did the football coach send in a bunch of second string players?
    14·1 answer
  • How do you solve this equation log(3x+1)=5
    11·2 answers
  • Find the cost of 20 grams of lead at 60$ per kilogram
    7·1 answer
  • 13.6% complete This is a Single Choice Question; skip ahead to question content A B C D E Confirm Difficulty Level: Moderate Som
    14·1 answer
  • 2x + 3y = -6<br> -2x + 3y = 6<br><br> How do I graph it
    6·1 answer
  • What is the approximate volume of the cone<br> below?
    7·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!