A 5-gallon bucket is full of pure water. Suppose we begin dumping salt into the bucket at a rate of 1/4 pounds per minute. Also, we open the spigot so that 1/2 gallons per minute leaves the bucket, and we add pure water to keep the bucket full. If the salt water solution is always well mixed, what is the amount of salt in the bucket after:
a. 1 minute?
b. 10 minutes?
c. 60 minutes?
d. 1000 minutes?
e. a very very long time?

Answers

Answer 1

Answer and explanation:

1. In one minute, there would be zero pounds of salt in the bucket because there's 0.25 pounds of salt in one minute and 0.5 gallons of water leaves the bucket in same minute, eliminating the 0.25 pounds of salt.

2. In ten minutes there would be zero pounds of salt because theres 0.25×10= 2.5 pounds of salt and 0.5×10=5 gallons of water would leave the bucket, eliminating the salt.

3. In 60 minutes there would still be zero salt because water leaves the bucket more than salt enters

4. Zero salt too after bucket leaks

5. Zero salt


Related Questions

Please help with my question

Answers

Answer:

[tex]5\frac{5}{6}[/tex]

Step-by-step explanation:

The problem above requires the use of mathematical operation with mixed fractions. In order to do this, you have to convert the mixed fractions into improper fractions first.

Let's convert.

[tex]3\frac{1}{2}[/tex] = [tex]\frac{7}{2}[/tex][tex]1\frac{2}{3}[/tex] = [tex]\frac{5}{3}[/tex]

Next, you have to multiply the fractions by multiplying the numerators with each other and the denominators with each other.

Let's solve.

[tex]\frac{7}{2}[/tex] x [tex]\frac{5}{3}[/tex] = [tex]\frac{35}{6}[/tex]

Since [tex]\frac{35}{6}[/tex] is an improper fraction and the choices above are mixed fractions, you have to convert it.

Let's convert.

[tex]\frac{35}{6}[/tex] = [tex]5\frac{5}{6}[/tex]

Therefore, the answer is [tex]5\frac{5}{6}[/tex]

Find the equation of a line perpendicular to x=−4 that contains the point (−3,4). Write the equation in slope-intercept form.

Answers

Answer:

y=4

Step-by-step explanation:

We recognize x=−4 as a vertical line, so its perpendicular will be horizontal. The equation of the horizontal line containing the point (−3,4) is given by y=4.

The slope-intercept form of a line perpendicular to x=−4 that contains the point (−3,4) is y = 4.

What is the slope of a line that is perpendicular to the other line?

The slope-intercept form of a line is y = mx + c.

Here, m = slope and c = y-intercept of the line.

The equation of the given line is x = - 4

Therefore, the given line is a vertical line.

Now, the line that is perpendicular to the line x = - 4, is a horizontal line.

Now, the horizontal line that passes through the point (- 3, 4) is y = 4.

Learn more about the slope-intercept form of a line here: https://brainly.com/question/15000427

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how can you find the area of a circle? give me a good explanation please, ty!​

Answers

Answer:

The area of a circle is pi times the radius squared (Area = pi radius²).

Step-by-step explanation:

The circumference of a circle is the linear distance of a circle's edge. It is the same as the perimeter of a geometric figure, but the term 'perimeter' is used exclusively for polygons.

The following equation describes the relation between the circumference and the radius R of a circle:

C = 2πR

Where π is a constant approximately equal to 3.14159265..

How to find the circumference of a circle

Determine the radius of a circle. Let's assume it's equal to 14 cm.

Substitute this value to the formula for circumference: C = 2 * π * R = 2 * π * 14 = 87.9646 cm.

You can also use it to find the area of a circle: A = π * R² = π * 14² = 615.752 cm².

Finally, you can find the diameter - it is simply double the radius: D = 2 * R = 2 * 14 = 28 cm.

Use our circumference calculator to find the radius when you only have the circumference or area of a circle.

Answer:

Use this formula: A = π r²

Step-by-step explanation:

A = π r²

What does A = π r² mean? :

(Area = Pi x Radius²)

π = Pi (3.14)

² = squared

Hope this helps! :)

Sasha ate 3 pieces of bacon for breakfast and ate some pieces for lunch. How many pieces of bacon did she eat today?

Answers

3+x
This is a trick question. Unless we know how much she’s eaten for lunch, we can’t figure out how much she ate.

Will give brainliest
What is the missing reason in step three?
A.SAS
B.SSS
C. Triangle sum theorem
D. CPCTC

Answers

wouldn’t it be B. SSS

8 (3x-6) = 6(4x + 8)

Answers

Answer:

There is no solution to make it true.

Step-by-step explanation:

First you expand
24x - 48 = 24x + 48
Then you cancel 24x on both sides
-48 = 48
Since -48 = 48 is false , there is no solution

PLEASE HELP ME ON THIS QUESTION!! Ren invested in two businesses in 2010. She invested $50,000 in Dawn's Flowers, which guaranteed a 7% return per year.


Her investment in Pop's Coffeeshop is represented by the function V(t)=24,500(1.06)t.


Which statements are true?


Select each correct answer.





Dawn's Flowers earned a greater rate of return than Pop's Coffeeshop.


​​In 2020, the Pop's Coffeeshop investment will have a greater value than the Dawn's Flowers investment.


Ren's initial investment in Dawn's Flowers was greater than her initial investment in Pop's Coffeeshop.


​In 2015, the Pop's Coffeeshop investment had a greater value than the Dawn's Flowers investment.

Answers

Answer:

Dawn's Flowers earned a greater rate of return than Pop's Coffeeshop

Ren's initial investment in Dawn's Flowers was greater than her initial investment in Pop's Coffeeshop.

How do I find the volume of this pyramid

Answers

Answer:

10*10*12 = 120 ÷ 3 = 40

Step-by-step explanation:

The formula to find a pyramid's volume is

V = [tex]\frac{l*w*h}{3}[/tex] (length 'times' width 'times' height, divided by 3)

A set of equations is given below:

Equation S: y = x + 9
Equation T: y = 2x + 1

Which of the following steps can be used to find the solution to the set of equations? (4 points)

x = 2x + 1
x + 9 = 2x
x + 1 = 2x + 9
x + 9 = 2x + 1

Answers

it’s the first one! hope i helped if it’s wrong i’m sorry :(

Simplify the expression below.
5(7x+4y+1)+2(8x+3y+6)
help plz!

Answers

Answer:

51x+26y+17

Step-by-step explanation:

Answer:

51x + 26y + 17

Step-by-step explanation:

distribute

5(7x) + 5(4y) + 5(1) + 2(8x) + 2(3y) + 2(6)

35x + 20y + 5 + 16x + 6y + 12

51x + 26y + 17

What best describes the expression y over 4? (5 points)
a. Some number divided by 4
b. Some numbers times 4
c. 4 more than some number
d. 4 less than some number

I prefer you 100% know the answer and not “think” this is very important!!

Answers

A because it would be y divided by 4 and you would solve for what y is

Answer:

a

Step-by-step explanation:

Which is an example of figurative language? 10 points

Question 13 options:

1)

Definition

2)

Evidence

3)

Metaphor

4)

Claim

Answers

Answer:

Metaphor

Step-by-step explanation:

Figurative Language: Simile, Metaphor, Personification, Hyperbole

A metaphor is an example of figurative language

HURRY!! 8.1=8w- 17.5. Solve for w​

Answers

W= 3.2

Need explaining?
8.1=8w-17.5 solve for W=3.2

A profit of a football club after a takeover is modeled by p(t) = t3 - 14t2 + 20t + 120, which t is the number of years after the takeover. In which years was the club making loss?

Answers

t = 5, so after 5 years
p(t) = t^3 - 14t^2 + 20t + 120

Take derivative to find minimum:
p’(t) = 3t^2 - 28t + 10

Factor to solve for t:
p’(t) = (3t - 2)(t - 5)
0 = (3t - 2)(t - 5)

0 = 3t - 2
2 = 3t
2/3 = t

Plug 2/3 into original equation, this is a maximum. We want the minimum:

0 = t - 5
5 = t

Plug back into original:
5^3 - 14(5)^2 + 20(5) + 120
125 - 14(25) + 100 + 120
125 - 350 + 220
- 225 + 220
p(5) = -5

The club losses during the years 4.89 years<t<11.29 years.

What is Graph?

Graph is a mathematical representation of a network and it describes the relationship between lines and points.

Given,

Profit of a football club after a takeover is modeled by p(t) = t³ - 14t² + 20t + 120,

t is the number of years after the takeover

We need to find in which  years was the club making loss

p(t) = t³ - 14t² + 20t + 120,

the profit is negative when the club is in loss.

Plot the cubic equation

The profit p(t) is negative in the interval (4.89,11.29)

The number of years t cannot be a negative number

Hence the club lost during the years 4.89 years<t<11.29 years.

To learn more on Graph click:

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A family goes to a restaurant. When the bill comes, this is printed at the bottom of it:
Gratuity Guide showing 15%=4.89, 18%=5.87, and 20%=6.52

How much was the price of the meal?

Someone help I need the answer immediately.

Answers

The price of the meal is $32.60 I think
15% of x = $4.89
0.15x = 4.89
x = $4.89/0.15 = $32.60

Elena went 60 meters in 15 seconds. Noah went 50 meters in 10 seconds. Elena and Noah both moved at a constant speed. Who went faster?

Answers

Answer:

Noah went faster.

Step-by-step explanation:

Elena: 60 divided by 15 = 4

Noah: 50 divided by 10 = 5.

5 meters per second is greater than 4 meters per second, making Noah faster than Elena.

y= x/5 +3
a line perpendicular to this line would have a slope of

Answers

-5 I believe!!!!!!!!!

In a first-aid kit the ratio of large bandages to
small bandages is 5 to 3. Based on this ratio,
how many large bandages are in the kit if there
are a total of 80 bandages?
A. 50
B. 48
C. 16
D. 40

Answers

The answer is A. 50
Hope this helps :)


Plz guys help I need help

Answers

The answer would be 56 pounds
56 pounds your welcome

Can someone help me with these 2 questions please???

Answers

Answer:

See step-by-step explanation.

Step-by-step explanation:

For the first question, you simply put an EMPTY circle above 2 and draw an arrow from it all the way down to -3. The reason why we put an empty circle is because there is no equal sign below it.

For the second question, you put a FILLED circle above 4 and draw an arrow from it all the way down to -3. The reason why we use a filled circle is because x is less than OR equal to 4.

Find the measure of CD.
Round to the nearest tenth.
mCD= [?]

Answers

Answer:

The arc CD is: 114.64°

Step-by-step explanation:

The given triangle inside the circle, we can get the trigonometric ratio such as

sin x = opposite / hypotenuse

Here:

The opposite side of angle x = 36.7/2

The hypotenuse = 21.8

Thus,

sin x = [36.7/2] / [21.8]

sin x = 18.35 / 21.8

sin x  = 0.8417

x = arc sin (0.8417)

x = 57.32°

Thus, the angle formed at the center by CD is:

2 x 57.32 = 114.64°

Therefore, the arc CD is: 114.64°

Answer:

The arc CD would be 114.6°

We use- sin x = opposite / hypotenuse

In the problem the opposite side of angle x = 36.7/2 and the hypotenuse = 21.8

So:

sin x = [36.7/2] / [21.8]

sin x = 18.35 / 21.8

sin x = 0.8417

x = arc sin (0.8417)

x = 57.32°

So the angle formed at the center by CD would have to be 2 x 57.32 = 114.64°

BUT, it says to round to the nearest tenth, so the answer would therefore, the arc CD is: 114.6°

How many real and how many are imaginary
Please Explain how to do it

Answers

Answer:

no idea bud

Step-by-step explanation:

Answer:

There are no real solutions, and 2 imaginary solutions.

Step-by-step explanation:

There are no real solutions since the function never touches the x-axis and it does not have any roots. Imaginary solutions always come in pairs, and since the exponent degree of x is 2, there are 2 solutions to the problem. You can find the imaginary solutions by plugging the equation into the quadratic formula.

how many perfect square are there between 1,000,000 and 9,000,000?​

Answers

Answer:

1999

Step-by-step explanation:

The square root of 1,000,000 = 1,000.

The square root of 9,000,000 = 3,000.

This means that the number of perfect square will be every number from 1,000^2 to 3,000^2. To find how many numbers that is, just do 3000-1000 = 2000, and then subtract one because otherwise you would be counting the 3000^2 which you don't want to do (it asks how many perfect squares are between the two numbers).

2000 - 1 = 1999.

The number of perfect squares between the values 1,000,000 and 9,000,000 would be 1999

Taking the square root of the boundaries :

√1,000,000 = 1000

√9,000,000 = 3000

The number of perfect squares would be :

[(√9,000,000 - √1,000,000) - 1]

[3000 - 1000] - 1

2000 - 1

= 1999

Hence, the number of perfect squares would be 1999.

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What is the formula for circumference? а a C = (pi) bo C = 2r с C = (pi) r2​

Answers

Answer:

2(pi)r=C

Step-by-step explanation:

PLEASE PLEASE HELP!!!

Answers

Answer:

398,765 books were sold

Step-by-step explanation:

How to get the answer:

1) Identify the given

  32,300 is percentage

  8.1 % is rate

  base (b) is missing

2) Solve

   b= p/r

   b= 32,300 / 8.1% or 0.081

   b= 398,765

3) Check

   398,765 x 8.1% = 32,299.97 or 32,300

Write the set using the roster method A={a|a an even number and 15< a< =25}

Answers

Answer:

{16, 17, 18, 19, 20, 21, 22,23, 24, 25}

Step-by-step explanation:

Given the set A={a|a an even number and 15< a< =25}

The inequality 15< a< =25 mean the set A consists of all the values between 15 and 25 with 25 inclusive (due to presence of the equal to sign)

Hence the required set A are {16, 17, 18, 19, 20, 21, 22,23, 24, 25}

Note that 15 is excluded from the set of number since 15<a i.e a > 15

A triangle has two sides that measure 5 cm and 7 cm. Which of the following CANNOT be the measure of the third side? A 3 cm B 5 cm C 7 cm D 12cm

Answers

Answer:

D

Step-by-step explanation:

Saying the number of |`s is the number side and |<|||>|| then for a triangle i can say |+||>|||

1. Lois has 10 coins in quarters and dimes in their pocket. After counting, the total value is $1.45. How many of each coin did Lois have?

Answers

Answer:

5 quarters and 2 dimes

Step-by-step explanation:

5 quarters make 1.25 + 10 cents = 1.45

Answer: she had five quarters and 2 dimes

Step-by-step explanation:

Use the substitution method to solve the system of equations. choose the correct ordered pair.x+y=12 -x=-y+10

Answers

Answer:

x=1 y=11

Step-by-step explanation:

Hopefully this helps, If you need some explaining just comment

Find the third, fifth, and eleventh terms of the sequence described by the rule.
A(n) = - 6+ (n - 1)(6)
A(3)= ?

Answers

Answer:

A(3) = 6

A(5) = 18

A(11) = 54

PLS MARK AS BRAINLIEST

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