how many gallons each of 25% alcohol and 5% alcohol should be mixed to obtain 20 gal of 8% alcohol?

How Many Gallons Each Of 25% Alcohol And 5% Alcohol Should Be Mixed To Obtain 20 Gal Of 8% Alcohol?

Answers

Answer 1

[tex]\begin{array}{lcccl} &\stackrel{solution}{gallons}&\stackrel{\textit{\% of }}{amount}&\stackrel{\textit{gallons of }}{pure~alcohol}\\ \cline{2-4}&\\ \textit{25\% solution}&x&0.25&0.25x\\ \textit{5\% solution}&y&0.05&0.05y\\ \cline{2-4}&\\ mixture&20&0.08&1.6 \end{array}~\hfill \begin{cases} ~\hfill x + y &= 20\\\\ 0.25x+0.05y&=1.6 \end{cases} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\stackrel{\textit{using the 1st equation}}{x+y=20\implies \underline{y = 20-x}} \\\\\\ \stackrel{\textit{substituting on the 2nd equation}}{0.25x~~ + ~~0.05(\underline{20-x})~~ = ~~1.6}\implies 0.25x+1-0.05x=1.6 \\\\\\ 0.20x+1=1.6\implies 0.2x=0.6\implies x=\cfrac{0.6}{0.2}\implies \boxed{x=3}[/tex]


Related Questions

Alyssa is enrolled in a public-speaking class. Each week she is required to give a speech of
greater length tharr the speech she gave the week before. The table below shows the
lengths of several of her speeches.
Alyssa's Speeches

Answers

Answer: this question search it up because i don't think and know if anyone knows this even i don't know so sorry

Step-by-step explanation:

if 2x2 is 4 then why is 2+2 5????

Answers

Answer:

Simple it's not

Step-by-step explanation:

Answer:

wait.... 2x2 is 4 2 + 2 = 4?

Step-by-step explanation:

Corey deposits $3500 a bank which pays 3%
interest per year. How much money will John have in
his account after 10 years?

Answers

Answer:

35,000

Step-by-step explanation:

Answer:

Corey will have $4550.00 in is account after 10 years.

Step-by-step explanation:

This is simple interest. Here is the formula for simple interest.

[tex]A=P(1+r*t)[/tex]

A = Final Amount

P = Principal Amount

R = Interest Rate

T = Time

We are given values for P, r, and t. Lets solve for A.

To get 3 percent as a decimal divide it by 100. We get 0.03.

[tex]P=3500[/tex]

[tex]r=0.03[/tex]

[tex]t=10[/tex]

[tex]A=3500(1+0.03*10)[/tex]

[tex]A=3500(1+0.30)[/tex]

[tex]A=3500(1.30)[/tex]

[tex]A=4550[/tex]

The ratio of a basketball player's completed free throws to attempted free throws is 4 to 7. If she completed 12 free
throws, find how many free throws she attempted.
a 3 free throws
c. 21 free throws
b. 7 free throws
d. 4 free throws


B
С
D
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Answers

Answer:

21

Step-by-step explanation:

I noticed that 4 times 3 equals 12, which is the number of free throws she completed. I multplied 3 by 7 and got 21

mhm so basically if you this about it the number of letters in the rainbow is also the color of your dog WAKE UP WAKEUP WAKEUP and if your dog's color matches the blue sky the answer is b

The price of an item has risen to $228 today. Yesterday it was $95. Find the percentage increase.

Answers

Answer:

140% increase

Step-by-step explanation:

Percent increase = [(final - initial) ÷ initial] · 100

[(228 - 95) ÷ 95] · 100

[133 ÷ 95] · 100

1.4 · 100

140

BRAINLIEST please if this helped!

Use the quadratic formula to solve the equation 2k(k+5)= -25

Answers

So, we need to solve the quadratic equation from quadratic formula as per the question, but before starting, let's first recall that, for any quadratic equation of the form ax² + bc + c = 0, the discriminant is given by D = b² - 4ac, and the value of x is given by :

[tex]{\boxed{\bf{x=\dfrac{-b\pm \sqrt{D}}{2a}}}}[/tex]

Also, their are no real solutions of x i.e their are only imaginary values of x iff D < 0, equal and real roots iff D = 0 and real and distinct roots iff D > 0. So, let's convert the given equation to the standard form ax² + bx + c = 0 and then we will find the discriminant and then we will be solving for k ;

[tex]{:\implies \quad \sf 2k(k+5)=-25}[/tex]

[tex]{:\implies \quad \sf 2k^{2}+10k=-25}[/tex]

[tex]{:\implies \quad \sf 2k^{2}+10k+25=0}[/tex]

Now, on comparing this with the standard equation, we will get a = 2, b = 10 and c = 25, and then D = (10)² - 4 × 2 × 25 = 100 - 200 = - 100, now as D < 0, so their will be imaginary values of k, so now solving for k will yield by using the Quadratic Formula ;

[tex]{:\implies \quad \sf k=\dfrac{-10\pm \sqrt{-100}}{2\times 2}}[/tex]

[tex]{:\implies \quad \sf k=\dfrac{-10\pm 10\iota}{2\times 2}}[/tex]

[tex]{:\implies \quad \sf k=\dfrac{2(-5\pm 5\iota)}{2\times 2}=\dfrac{-5\pm 5\iota}{2}}[/tex]

[tex]{:\implies \quad \boxed{\bf{k=\dfrac{-5+5\iota}{2}\:\:,\:\: \dfrac{-5-5\iota}{2}}}}[/tex]

This is the required answer

Solve:........................
[tex] \frac{x}{3} + 4 = \frac{4x - 1}{5} [/tex]

Answers

Answer:

[tex] \frac{x}{3} + 4 = \frac{4x - 1}{5} \\ \\ \frac{x}{3} + \frac{12}{3} = \frac{4x - 1}{5} \\ \\ \frac{x + 12}{3} = \frac{4x - 1}{5} \\ \\ 3(4x - 1) = 5(x + 12) \\ \\ 12x - 3 = 5x + 60 \\ \\ 12x - 5x = 60 + 3 \\ \\ 7x = 63 \\ \\ x = \frac{63}{7} \\ \\ x = 9[/tex]

A map of utah has scale 1cm :30 mi the southern border is about 285 mi long how long is the border on the map

Answers

Answer:

  9 1/2 inches

Step-by-step explanation:

The scale of a map is the ratio of map distance to represented distance. This can be used to write a proportion.

__

  map distance/represented distance = 1 in/(30 mi) = x/(285 mi)

where x represents the map length of the southern border.

Multiplying by 285 mi, we have ...

  x = (285 mi)(1 in)/(30 mi) = 9.5 in

The border is 9.5 inches on the map.

Super easy 7th grade math worth a lot of points

Answers

Answer:

you can find the answer in the given attachment

Step-by-step explanation:

1-P

2-G

3-T

4-O

5-S

6-E

7-D

8-C

9-A

Please help me thank u!

Answers

Answer:

The odds of drawing a heart are 13:52

Explanation: A standard deck of card contains 52 card. There are 4 types of playing cards: clubs, diamonds, hearts and spades. Every type of them has 13 cards. How do u know that? Well just divide 52 by 4 and then you get 13.

find the measure of angles 1, 2, 3, 4, 5 ,6 and 7

Answers

Answer:

angle1=70

angle2=65

angle4=115

angle7=45

angel6=45

angle5=45

Step-by-step explanation:

110+angle1 = 180

angle1 =180-70

angle1 = 70

115+angle2=180

angle2=180-115

angle2=65

angle4=115 because lines are parallel

angle1+angle2+angle7=180 because triangle

70+65+angle7=180

135+angle7=180

angle7=180-135

angle7=45

angel6=45

angle5=45

Select the correct answer.
The parallelogram has an area of 20 square inches. What are the dimensions of the parallelogram, to the nearest hundredth of an inch?
40°
4 in
h
OA. I = 2.57 in, h = 7.78 in
OB. I = 6.22 in, h = 3.23 in

Answers

The dimensions of the parallelogram to the nearest hundredth of an inch are 6.54 in and 3.06 in.

What are the dimensions of the parallelogram?

Trigonometry would be used to determine the base and the length of the parallelogram.

Base: cos 40 = adjacent /hypotenuse

0,7660 = adjacent / 4

adjacent = 4 x 0.7660 = 3.06 in

Length = area / base

20 / 3.06 = 6.54 in

To learn more about parallelograms, please check: https://brainly.com/question/15259486

Which of the following quadrilaterals is also a parallelogram?

Answers

Answer:

RECTANGLE

A rectangle is a parallelogram with four right angles, so all rectangles are also parallelograms and quadrilaterals.

What is 5389 rounded off to the nearest 100?

Answers

Answer:

5400

Step-by-step explanation:

the 89 is higher then 5 so it would round the 3 up to a 4

Answer:

5389 rounded to the nearest 100 is 5400

Step-by-step explanation:

we round the number up to the nearest 100 if the last 2 digits  of the number are 50 an d over we round the number down to the nearest 100 if the last 2 digets are 49 and below

find the slope of the line (3,5) (7,3)

Answers

HOPE IT WILL HELP YOU

...............................................

Round your answer to the nearest hundredth.

Answers

Answer:

41.81°

Step-by-step explanation:

Hope this helps! Please let me know if you need more help or think my answer is incorrect. Brainliest would be MUCH appreciated. Also remember to rate answers to help other students, While leaving thanks to answers that help you. Have a great day!

Linda counted different colored leaves on a tree. She counted 8 red leaves. She also counted 3 times as many yellow leaves as red leaves. How many yellow leaves did Linda count?

Answers

to find the number of yellow leaves you'll have to multiply number of red leaves she counted by 3.

8×3

=24

Linda counted 24 yellow leaves.

Linda counts 24 yellow leaves in total

How to determine the number of yellow leaves?

The number of red leaves is given as:

Red = 8

The statement 3 times as many yellow leaves as red leaves means that:

Yellow = Red * 3

So, we have:

Yellow = 8 * 3

Evaluate the product

Yellow = 24

Hence, Linda counts 24 yellow leaves in total

Read more about products at:

https://brainly.com/question/10873737

how many faraday passes through a resistance in a circuit carrying a current of 1.68 A for 2 days (1F = 965000 (principal quantum number) is 3 A. FB. 2F C. 3F D. 4F

Answers

Answer:

b

Step-by-step explanation:

Well has -55.00 in his account if he saves $2.50 his mom gives him lunch every day, how many days will it be until he has a balance of at least $0

Answers

Answer:

22 days

Step-by-step explanation:

55 divided by 2.5=22 days

Answer: 22 Days

Step-by-step explanation:

-55.00/2.50= -22
But since you can’t have a negative answer then you have to make it positive for your amount of days! So it would take that person 22 days to have 0 in his account!

- I hope this helped! I tried my best but definitely double check with your teacher for this answer!

Justify the first step that David took in verifying that x = 5 is a solution for the equation
8x – 13 = 2x + 17.

8x – 13 = 2x + 17
8(5) – 13 = 2(5) + 17
A.
David multiplied 8 by 5.
B.
David subtracted 13 from both sides.
C.
David replaced x with 5.
D.
David added 17 to both sides.

Answers

Answer:

Step by step I don't see the correct first step.

Step-by-step explanation:

Solve for x:

8 x - 13 = 2 x + 17

Hint: | Move terms with x to the left hand side.

Subtract 2 x from both sides:

(8 x - 2 x) - 13 = (2 x - 2 x) + 17

Hint: | Combine like terms in 8 x - 2 x.

8 x - 2 x = 6 x:

6 x - 13 = (2 x - 2 x) + 17

Hint: | Look for the difference of two identical terms.

2 x - 2 x = 0:

6 x - 13 = 17

Hint: | Isolate terms with x to the left hand side.

Add 13 to both sides:

6 x + (13 - 13) = 13 + 17

Hint: | Look for the difference of two identical terms.

13 - 13 = 0:

6 x = 17 + 13

Hint: | Evaluate 17 + 13.

17 + 13 = 30:

6 x = 30

Hint: | Divide both sides by a constant to simplify the equation.

Divide both sides of 6 x = 30 by 6:

(6 x)/6 = 30/6

Hint: | Any nonzero number divided by itself is one.

6/6 = 1:

x = 30/6

Hint: | Reduce 30/6 to lowest terms. Start by finding the GCD of 30 and 6.

The gcd of 30 and 6 is 6, so 30/6 = (6×5)/(6×1) = 6/6×5 = 5:

Answer: x = 5

Can someone tell me what I did wrong here

Answers

Answer:

no roots.

Step-by-step explanation:

1)   [tex]\sqrt{8x+16}=2-8; \ - \ correct;[/tex]

2)   [tex]\sqrt{8x+16}=-6; \ - \ correct;[/tex]

note, the value after operation 'square root' cannot be negative ('-6' is on the right side!), then

3) it means, the given equation has no real roots.

Use substitution to solve the system.
- 3x+y = 14
2x + 3y = -2

Х
5
?
y = 0

Answers

Answer:

x= -4 and y=2

Step-by-step explanation:

-3x+y=14 ...eqn 1

2x+3y= -2....eqn 2

from eqn 1

-3x+y=14

y=14+3x

substitute y=14+3x into eqn 2

2x+3(14+3x) = -2

2x+ 42+ 9x = -2

11x= -2-42

11x= -44

x = -4

substitute X = -4 into eqn 1 to get y

-3x+y=14

-3(-4) +y =14

12+y= 14

y= 14-12

y =2

What is the median of the data set? -10, -5, -1, 0, 0, 3, 6, 8

A. 0
B. 0.125
C. 3
D. -1

Answer: A

Answers

Answer:

the anwer is a so 0

Step-by-step explanation:

the number that showed up the most is 0 so median is 0

solve this system of equations 2x+4y=-48

Answers

Answer:

x=-24-2y

y=-12-x/2

Step-by-step explanation:

To solve for x move everything to one side, 2x=-48-4y, then you can divide by 2 to just get x, x=-24-2y.

To solve for y move everything to one side, 4y=-48-2x, then you can divide by 4 to just get y, y=-12-x/2.

Emily wants to put trim around a square window and measures 3 ft on each side. How many feet of t r i m does she need?

Answers

Answer:

12ft trim

Step-by-step explanation:

assuming that she wants to use the same size on each side (3ft) of the window, we know that the window is a square

and a square has 4 sides

3 + 3 + 3 + 3 = 12ft

She needs 12 ft trim

What is the value found using the linear​ approximation? ln(0.93) ≈

Answers

Answer:

I think its 0.9 I believe so

I’ll give BRAINLIEST


Helen is N year old. Helen’s Brother is a year older than her.

a. Write n algebraic expression for the age of Helen’s brother
b. Find her brother’s age if Helen is age 12
C. Find her brothers age If Helen is x years old

Answers

Answer:

[tex] \fbox{ \sf A) Age of Helen’s brother = N+1} \\ \fbox{ \sf B) Age of Helen’s brother = 13 \: year \: old} \\ \fbox{ \sf C) Age of Helen’s brother = x+1} [/tex]

Step-by-step explanation:

Given:

Helen's age = N year old

Helen's brother = One year older than helen

To find:

a. Write n algebraic expression for the age of Helen’s brother

b. Find her brother’s age if Helen is age 12

C. Find her brothers age If Helen is x years old

Solution:

A)algebraic expression for the age of Helen’s brother = Helen’s age + 1 = N+1

[tex]\fbox{Age of Helen’s brother = N+1}[/tex]

B) if helen is 12 year old then, N = 12

substituting the value of N in above equation,

Age of Helen’s brother = N+1 = 12+1 = 13 y/o

[tex]\fbox{Age of Helen’s brother = \: 13 \: year \: old}[/tex]

C) if helen is x year old then, N = x

substituting the value of N in above equation,

Age of Helen’s brother = N+1 = x+1

[tex]\fbox{Age of Helen’s brother = x+1}[/tex]

Thanks for joining brainly community!

are these lines parallel or perpendicular? 2y=-3x=5 and y=3/2-6

Answers

Answer:

perpendicular because they have a positive and negative slope meaning on a graph they would be crossing each other.

The value of a car decreases linearly with time. The car was bought new for $62,000 and had a value of $41,000 after 6 years.

Answers

62000-41000=21000
21000/6=3500
3500= 5.64516129% of 62000

PLEASE HELP ILL GIVE FIVE STARS AND GIVE BRAINLIEST
Ray is x years old. His brother Ron is y years older than Ray
What is the sum of their ages now?

Answers

Answer: The sum will be x+y because their ages are variables.

Step-by-step explanation:

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