how many gallons of 20% alcohol solution and 50% alcohol solution must be mixed to get 9 gallons of 30% alcohol solution

Answers

Answer 1
The problem asks you to find how many gallons of 20% solution and 50% solution, respectively, are needed to create a 12 gallon solution that is 30% alcohol.

 

To solve this, set up the following equation using the given values: that you have some quantity of a 20% solution, a quantity of a 50% solution, and that you need to have 12 gallons of a 30% solution. We will use a variable, x, together with the "goal" quantity of 12 gallons to solve this problem with only one unknown, even though we really have two unknowns (the quantity of 20% solution and that of the 50% solution).

 

Remember that when writing out percentages, a 20% solution is also a 0.2 solution, and a 50% solution is a 0.5 solution.

 

Let x = an unknown quantity of the 20% (or 0.2) solution. We therefore have 0.2x, since we have x gallons of the 20% solution. (Remember that "of" is a key word that denotes multiplication).

Therefore, 12 - x is the other unknown and is multiplied by the 0.5 (50%) solution, since we have this quantity of the 50% solution. Really, we could say that we have 0.5y (if we want to introduce another variable; however, it is much simpler to put the other quantity in terms of x, which is easy to do, since we know that the two unknown quantities must amount to 12 gallons). Now, we must multiply our second unknown, 12 - x, by 0.5. This gives us 0.5(12 - x). 

 

Our two unknown quantities, 0.2x and 0.5(12 - x) add up to 12 gallons of a 30% solution. Putting all the words together to form an equation we get:

0.2x + 0.5(12 - x) = 0.3(12)

 

Now we expand the equation (call it distributing out the parentheses).

0.2x + 6 + 0.5x = 3.6

 

Combine like terms:

-0.3x + 6 = 3.6

 

Solve for x:

-0.3x = -2.4

x = 8

 

Plug x = 8 back into the equation to check that this is possible. 

x = 8, and 12 - x = 4

0.2(8) + 0.5(12 - (8)) = 0.3(12)

0.2(8) + 0.5(4) = 0.3(12)

3.6 = 3.6 

Check

Answer 2
Final answer:

To create 9 gallons of a 30% alcohol solution, mix 6 gallons of the 20% alcohol solution with 3 gallons of the 50% alcohol solution by setting up and solving a system of equations based on volumes and concentrations.

Explanation:

To find out how many gallons of 20% alcohol solution and 50% alcohol solution must be mixed to get 9 gallons of a 30% alcohol solution, we can set up a system of equations based on the volumes and concentrations of the solutions. Let's let x represent the volume of the 20% solution and y represent the volume of the 50% solution.

Since the total volume of the mixture should be 9 gallons, we have our first equation:

x + y = 9

Next, we consider the concentration of alcohol in the final mixture. The amount of pure alcohol from the 20% solution is 0.20x gallons, and from the 50% solution, it is 0.50y gallons. The final mixture has a concentration of 30%, so the total amount of alcohol in the 9 gallons mixture is 0.30 * 9 gallons. This gives us our second equation:

0.20x + 0.50y = 0.30 * 9

Now we have a system of two equations with two variables that can be solved using methods such as substitution or elimination. After solving, we find that x = 6 gallons and y = 3 gallons. Therefore, to obtain 9 gallons of a 30% alcohol solution, you'd need to mix 6 gallons of the 20% alcohol solution with 3 gallons of the 50% alcohol solution.


Related Questions

x−18 , if x<18. Please help asap!

Answers

If x < 18 then you can subtract both sides by 18 and you would get x - 18 < 18 - 18 = 0

So that would be x - 18 < 0.

Hope this helps.

If x < 18 then you can subtract both sides by 18 and you would get x - 18 < 18 - 18 = 0

So that would be x - 18 < 0.

Hope this helps.

Which polynomial represents the difference below?

Answers

5x² +9x+3 - (6x² - 3x) = 5x² +9x+3 - 6x² + 3x = -x²+12x +3

Correct answer is B.

The difference between given two polynomials is [tex](- x^{2} + 12x + 3)[/tex].

What is a polynomial?

"A polynomial is an expression consisting of indeterminates and coefficients, that involves only the operations of addition, subtraction, multiplication, and non-negative integer exponentiation of variables."

Given two polynomials are [tex](5x^{2} + 9x + 3)[/tex] and [tex](6x^{2} - 3x)[/tex].

Therefore, the difference between these two polynomials

[tex]= (5x^{2} + 9x + 3) - (6x^{2} - 3x)\\= (5x^{2} - 6x^{2}) + (9x + 3x) + 3\\= - x^{2} + 12x + 3[/tex]

Learn more about polynomial here:

https://brainly.com/question/21610884

#SPJ3

27 33 34 35 37 39 40 41 54 84,75,90,87,99,91,85,88,76,92,94 median: first quartile: third quartile: interquartile range:

Answers

Final answer:

For the given data, the median is 85, the first quartile is 37, the third quartile is 90.5, the interquartile range (IQR) is 53.5, and the range is 72.

Explanation:

The median in a dataset is the middle value when the values are arranged in numerical order. For the given data 27, 33, 34, 35, 37, 39, 40, 41, 54, 75, 84, 75, 90, 87, 99, 91, 85, 88, 76, 92, 94, after arranging them in ascending order, the median (Q2) is the value positioned at the center of the dataset. Since there are 21 values, the median is the 11th value, which is 85. The first quartile (Q1) is the median of the first half (lower half) of the dataset, which is the value in the 5.5th position, so we average the 5th and 6th values to get 37. Similarly, the third quartile (Q3) is the median of the second half (upper half) of the dataset, which would be the average of the 16th and 17th values, yielding 90.5. The interquartile range (IQR) is the difference between the third quartile and the first quartile, so IQR = Q3 - Q1 = 90.5 - 37 = 53.5. The range of the dataset is the difference between the maximum and minimum value which is 99 - 27 = 72.

What percent of 7 is 2?

Answers

It is 350% I think, because you are trying to find how many groups of 2 go into 7. So, you have to divide 7 by 2. You get 3.5. 3.5 in percentage form is 350%

hey can you please help me posted picture of question

Answers

I believe the answer is C, but I am not 100% sure. Though, I hope this helps.
When you subtract (x -2)² from both sides of the equation, you get
  y² = 64 -(x -2)²
  y² = 64 -(x² -4x +4)
  y² = -x² +4x +60

The answer is ...
  D. y² = -x² +4x +60

Round off 1563385 to the nearest million?

Answers

1,563,385

Look at the millions place. 1 is in the millions place. 
Now look at the number to the right of 1.
Since it is 5 or greater, round 1 up to 2.
Change all the numbers after 1 to 0.

1,563,385 rounded to the nearest million is 2,000,000.

To round 1,563,385 to the nearest million, we look at the hundred-thousands digit (5), and since it's 5 or greater, we round up to 2,000,000.

To round off 1,563,385 to the nearest million, look at the hundred-thousands digit, which is 5 in this case.

If it is 5 or greater, we round up; if it is less than 5, we round down.

Since our hundred-thousands digit is 5, we round up, so 1,563,385 rounded to the nearest million is 2,000,000.

340 students went to the first dance but only 306 went to the second. What is the percent decrease in the attendance from the first to the second dance

Answers

first find the difference that went by subtracting the 2 numbers:

340 - 306 = 34

 divide that by the number of students that went to the first dance:

34 / 340 = 0.1 = 10% decrease

Decrease = 340 - 306 = 34

Percentage decreased = 34/340 x 100 = 10%

Answer: 10%

37​% of a certain​ country's voters think that it is too easy to vote in their country. you randomly select 12 likely voters. find the probability that the number of likely voters who think that it is too easy to vote is​ (a) exactly​ three, (b) at least​ four, (c) less than eight.

Answers

The probability that the number of likely voters who think that it is too easy to vote is​:

a) exactly​ three = 0.17422

(b) at least 4 = 0.70533

(c) less than eight = 0.96406

How to use binomial probability theorem?

The general formula for binomial probability theorem is:

P(X = x) = ⁿCₓ * pˣ * (1 - p)⁽ⁿ ⁻ ˣ⁾

Where:

n = 12

p = 0.37

(a) exactly three,

P(x = 3) = ¹²C₃ * 0.37³ * 0.93⁹

= 0.17422

(b) at least 4,

P(4 ≤ x ≤ 12) = P(4) + P(5) + P(6) + P(7) + P(8) + P(9) + P(10) + P(11) + P(12)

= 0.70533

(c) less than eight.

P(x < 8) = P(0) + P(1) + P(2) + P(3) + P(4) + P(5) + P(6) + P(7)

= 0.96406

how many problems must be answered correctly on a math test with 60 problems to get a score of 85%

Answers

You would have to answer 51 questions correctly. To get this, multiply .85 (85% as a decimal) by 60. So 51 is 85% of 60.
[tex]\begin{array}{ccc}60&-&100\%\\x&-&85\%\end{array}\\\\\text{cross multiply}\\\\100\cdot x=60\cdot85\\\\100x=5100\ \ \ |:100\\\\\boxed{x=51}[/tex]

Answer: 51 problems.

Which values are outliers?

5.8, 6.1, 4.9, 10.9, 0.8, 6.1, 7.4, 10.2, 1.1, 5.2, 5.9

Select Outlier or Not Outlier for each data point.



Data Outlier Not Outlier
0.8
1.1
10.2
10.9

Answers

The outliers are 0.8, 1.1, 10.2, and 10.9. The rest are not outliers.

A value is typically considered an outlier if it is less than Q1 - 1.5 [tex]\times[/tex] IQR or greater than Q3 + 1.5 [tex]\times[/tex] IQR.

First, we need to arrange the data in ascending order:

0.8, 1.1, 4.9, 5.2, 5.8, 5.9, 6.1, 6.1, 7.4, 10.2, 10.9

Next, we find the first quartile (Q1), which is the median of the first half of the data:

(4.9 + 5.2) / 2 = 5.05

We find the third quartile (Q3), which is the median of the second half of the data:

(6.1 + 7.4) / 2 = 6.75

Now, we calculate the interquartile range (IQR):

IQR = Q3 - Q1 = 6.75 - 5.05 = 1.7

The lower bound for outliers is:

Q1 - 1.5 [tex]\times[/tex] IQR = 5.05 - 1.5 [tex]\times[/tex] 1.7 = 5.05 - 2.55 = 2.5

The upper bound for outliers is:

Q3 + 1.5 [tex]\times[/tex] IQR = 6.75 + 1.5 [tex]\times[/tex] 1.7 = 6.75 + 2.55 = 9.3

Now we can determine which values are outliers:

0.8 is less than the lower bound (2.5), so it is an outlier.

1.1 is less than the lower bound (2.5), so it is an outlier.

10.2 is greater than the upper bound (9.3), so it is an outlier.

10.9 is greater than the upper bound (9.3), so it is an outlier.

The remaining values (4.9, 5.2, 5.8, 5.9, 6.1, 6.1, 7.4) are not outliers as they fall within the range of Q1 - 1.5 [tex]\times[/tex] IQR and Q3 + 1.5 [tex]\times[/tex] IQR.

Patrick's favorite shade of purple paint is made with 4 ounces of blue paint for every 3ounces of red paint.



Which of the following paint mixtures will create the same shade of purple?


Choose 2 answer

Blue : 4x2=8
Red : 3x2=6
Blue :4x5=20
Red:3x5=15
The following mixtures will create Patrick's favorite shade of purple:

:8ounces of blue paint mixed with 6ounces of red paint

:20 ounces of blue paint mixed with 15 ounces of red paint

Answers

The ratio of Blue to red in the purple shade that Patrick wants is:
Blue:red=4:3
The mixtures that will create the same shade of purple is:

a] 8ounces of blue paint mixed with 6ounces of red paint
because the ratio of blue to red is 4:3
and
b] 20 ounces of blue paint mixed with 15 ounces of red paint
because the ratio of blue to red is 4:3

Answer:

actually its b and d

Step-by-step explanation:

according to khan academy

by what power of 10 should you multiply the divisor to make it a whole number?


0.82÷6.232

Answers

The divisor has 3 digits to the right of the decimal point. It will be a whole number when multiplied by 10 to the power of 3.

Value of m varies directly as value of n and n=5 when m=12. What is n when m=18?

Answers

Simplify the problem down, so:

m = 12 & n = 5
m = 6 & n = 2.5 (divided each number by 20)

Now m is a factor of 18. Multiply each number by 3.
Answer: m = 18 & n = 7.5

1. A line passes through the ordered pairs (7,2) and (5,4). What is the slope? please show work

2. A sphere has a diameter od 20 cm. What would be the volume of sphere?

Answers

[tex]\bf \begin{array}{ccccccccc} &&x_1&&y_1&&x_2&&y_2\\ % (a,b) &&(~ 7 &,& 2~) % (c,d) &&(~ 5 &,& 4~) \end{array} \\\\\\ % slope = m slope = m\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{4-2}{5-7}\implies \cfrac{2}{-2}\implies -1[/tex]



since the sphere has a diameter of 20, its radius is half that, or 10.

[tex]\bf \textit{volume of a sphere}\\\\ V=\cfrac{4\pi r^3}{3}~~ \begin{cases} r=radius\\ -----\\ r=10 \end{cases}\implies V=\cfrac{4\pi (10)^3}{3}[/tex]

Anna plans a business model to compete with two video stores, where she hopes to draw in customers from one store but not lose money on the deal. Movie Mania charges a subscription fee of $30 and an additional $5 per movie, x. Movie Time charges a subscription fee of $25 and an additional $6 per movie, x. Based on this information, which system of inequalities could be used to determine how many movies need to be rented for a customer on Anna’s plan, y, to pay her more than they would at Movie Time, but less than they would at Movie Mania?

Answers

Movie Mania charges a subscription fee of $30 and an additional $5 per movie, x. So the total charges at Movie Mania for x movies will be:

30 + 5x

Movie Time charges a subscription fee of $25 and an additional $6 per movie, x. So the total charges at Movie Time for x movies will be:

25 + 6x

Anna wants her plan to her amount y which is more than Movie Time but Less than Movie Mania. So we can set up the equation as:

Cost at Movie Time < y < Cost at Movie Mania

Using the values, we can write:

25 + 6x < y < 30 + 5x

Using this system of inequalities Anna can determine how many movies need to be rented for a customer on her plan

Answer:D.  y<5x+30/x

y>6x+25/x

Step-by-step explanation:

got right on edmentum

if a circle has a radius of 13 and a sector defined by a 7.4 degree arc, what is the area, in cm2, of the sector? round your answer to the nearest tenth.

Answers

For this case the area of the sector is given by:
 A = (S '/ S) * (pi) * (r ^ 2)
 Where,
 S '/ S = relation of arcs
 r: radius of the circle
 Substituting values we have:
 A = (7.4/360) * (3.14) * (13 ^ 2)
 A = 10.9080111
 Rounding off we have:
 A = 10.9 cm^2
 Answer:
 the area of sector is:
 A = 10.9 cm^2


What is the correct inverse function for f(x) = e2x ?

Answers

To solve this problem you must appy the proccedure shown below:

 1. You have the following function given in the problem above:

 f(x)=e^2x

 2. You can rewrite is:

 y=e^2x

 3. Interchange the variables, as below:

 x=e^2y

 3. The inverse of an exponential function is the logarithm function. Thereforem you have:

 ln(x)=ln(e^2y)
 ln(x)=2y

 4.Then, you have:

 y=ln(x)/2

 Therefore, the answer is: 

 f^-1(x)=ln(x)/2
 

the snowfall in year 1 was 2.03 meters .the snowfall in year 2 was 1.6 meters .how many total meters of snow fell in years 1 and 2

Answers

To find the total amount of snowfall for both these years, you will add the amounts that fell each year together.

  2.03
+1.60
  3.63

It is important to line up your decimal points because when you are adding anything, you must add units that are the same.  Lining up the decimal points puts the units in order automatically!

Name the pattern block used to cover 1 third of the hexagon

Answers


See the attached figure

By sketching a hexagon and dividing it to 3 equal shapes.
we will shading one of the 3 equal shapes.
So, the shaded area is a parallelogram with equal sides which is called rhombus

The correct answer is:
The pattern block used to cover 1 third of the hexagon is rhombus







Please help me with coordinates. IT'S DO IN 3 HOURS

Answers

I cannot help you with the exact answer, but i can make the solution easier

Get graphs (standard X,Y graphs) and start placein the numbers in the following format (x,y) If they are negative, it will be placed to the left of the graph, if positive to the right of the graph

Assume that the number of watches produced every hour is normally distributed with a mean of 500 and a standard deviation of 100. what is the probability that in a randomly selected hour the number of watches produced is greater than 500

Answers

To evaluate the probability that in a randomly selected hour the number of watches produced is greater than 500 we proceed as follows:
z=(x-μ)/σ
where:
x=500
μ=500
σ=100
thus
z=(500-500)/200=0

Thus:
P(x>500)=1-P(x<500)=1-P(z<0)=1-0.5=0.5

Answer: 0.5~50%

Answer:  0.5

 

Step-by-step explanation:

Given :  The number of watches produced every hour is normally distributed with a mean of 500 and a standard deviation of 100.

i.e. [tex]\mu = 500\text{ and } \sigma= 100[/tex]

Let x be the number of watches produced every hour.

Then, the probability that in a randomly selected hour the number of watches produced is greater than 500 will be :

[tex]P(x>500)=1-P(x\leq500)\\\\=1-P(\dfrac{x-\mu}{\sigma}\leq\dfrac{500-500}{100})\\\\=1-P(z\leq0)\ \ [\because\ z=\dfrac{x-\mu}{\sigma}]\\\\=1-0.5\ \ [\text{ By z-table}]\\\\=1-0.5=0.5[/tex]

Hence, the probability that in a randomly selected hour the number of watches produced is greater than 500 =0.5.

A piece of cardboard has two circles punched out of it. What is the approximate area of the remaining cardboard? Use 3.14 for pie and round to the nearest whole number.
227 cm2
246 cm2
258 cm2
276 cm2

Answers

the complete question in the attached figure

we know that
[the approximate area of the remaining cardboard]=(area of rectangle) - 2(area of circle)

area of rectangle=14 cm* 18 cm------> 252 cm²

area of a circle=pi*r²
r=2/1----> 1 cm
area=pi*1²-----> 3.14 cm²

[the approximate area of the remaining cardboard]=252- 2*3.14
=245.72-------> 246 cm²

the answer is
246 cm²
okay so once the answer rounded it is 246 

simplify the expression (-5)2. -10 10 -25 25

Answers

(-5)² = (-5)*(-5) = 25

_____
There are an even number of negative factors, so the result is positive.

Factor completely.

3x squared + 2xy - y squared

Answers

The factors of given expression are (x-y) and (3x-y). The solution is shown below:

[tex]3 x^{2} +2xy- y^{2} \\ \\ 3 x^{2} +3xy-xy- y^{2} \\ \\ 3x(x-y)-y(x-y) \\ \\ (x-y)(3x-y) [/tex]

Hey can you please help me posted picture of question

Answers

The answer is B
F(x)= (x-1)^2+3
The parent function is G(x) = x²

First the graph is shifted right by 1 unit which can be expressed as:

(x - 1)²

Next the function is shifted up by 3 units, so the final function can be expressed as:

F(x) = (x - 1)² + 3

So, the correct answer is option B

What are the values of the variable in 37=30-x^2

Answers

Add x^2-37 to the equation and you get
  x^2 = -7
Then the values of x are
  x = ±√-7
  x = -i√7 or i√7 . . . . . . where i = √-1

hey can you please help me posted picture of question

Answers

The inverse of F(x) will contain the points in inverse order.

So x-value of F(x) will be the y-value of its inverse.
And y-value of F(x) will be the x-value of its inverse.

So, (-3, 7) on F(x) will be translated to (7, -3) on its inverse.

Thus, the correct answer is option A

Mr Walton ordered 12 pizzas,for the art class celebration one fourth of the pizza had only mushrooms. how many of the pizza has only mushrooms

Answers

You would do 12 divided by 1/4=3
So your answer is 3 pizzas

3 out of the 12. if you set it up as a proportion it  should be 1 over 4 and x over 12 cross multiply and divide.  

Hey can you please help me posted picture of question

Answers

Stretching or compression changes the shape of a function, i.e the function can be made narrower or wider by stretching/compression.

So, the correct statement will be:

To change the shape of a function you need to stretch or compress it.

Thus, option C is the correct answer.

Can someone help me with this problem? please explain.

Answers

The units attached to the numbers can help you out. They work just like variables when you go to add, subtract, multiply, or divide.

You have weight (5.76 pounds) and density (0.08 pounds/in³). The units of volume (in³) are in the denominator of the density, but we want them in the numerator of a number that gives the volume of the brick. At the same time, we want to cancel units of pounds. We can do all that by dividing weight by density.

  volume = weight/density
  volume = (5.76 pounds)/(0.08 pounds/in³) = (5.76/0.08) in³ = 72 in³

We know the volume of a rectangular prism (brick) is given by the product of its length, width, and height. We now have enough information to find the height.
  volume = length*width*height
  72 in³ = (8 in)*(2.25 in)*height . . . . . substitute known numbers
  72 in³/((8*2.25) in²) = height . . . . . .. solve for height
  72/18 in = height = 4 in . . . . . . . . . . . do the arithmetic. (in³)/(in²) = in

The height of the brick is 4 inches.
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