One inlet pipe can fill an empty pool in 12 hours, and a drain can empty the pool in 20 hours. How long will it take the pipe to fill the pool if the drain is left open?

Answers

Answer 1

Final answer:

If one inlet pipe can fill the pool in 12 hours and the drain can empty it in 20 hours, the combined rate of the two is 1/30 pools per hour. Therefore, it will take 30 hours to fill the pool with the drain open.

Explanation:

The question addresses a common concept in mathematics, which is rates and work problems. To determine the time it takes for the inlet pipe to fill the pool with the drain open, we first have to figure out the rates at which the pipe fills and the drain empties the pool.

If an inlet pipe can fill the pool in 12 hours, its rate of work is 1/12 pool per hour. Similarly, if the drain can empty the pool in 20 hours, then its rate is 1/20 pool per hour.

When both the inlet and drain are open, their combined rate will be the fill rate minus the drain rate, which is (1/12) - (1/20) = 1/30 pool per hour.

Therefore, at the combined rate, it will take 1 divided by 1/30 = 30 hours to fill the pool with the drain open.

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Answer 2

Final answer:

When both the inlet pipe and drain are open, it will take 30 hours to fill the pool, computed by dividing the total work done (1 pool) by the net rate (1/30 pool/hour).

Explanation:

In mathematics, problems such as these are usually solved by working with the concept of rates. In this scenario, we have two rates: the inlet pipe, and the drain. The rate of the inlet pipe is 1 pool per 12 hours, or 1/12 pool/hour. The rate of the drain is 1 pool per 20 hours, or 1/20 pool/hour. The net rate when both are open is thus (1/12 - 1/20) pool/hour, which simplifies to 1/30 pool/hour. To find out how long (t) it will take to fill the pool with both the inlet and drain open, we would use the fact that Rate x Time = Work Done. The Work Done in this case is 1 (equivalent to one pool), and the rate we’ve calculated as 1/30 pool/hour.

So, solving for time, we get:

t = Work Done / Rate = 1 pool / (1/30 pool/hour) = 30 hours.

So, it would take 30 hours to fill the pool with the inlet pipe and the drain open.

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Related Questions

What is the remainder of 4^31 when divided by 10

Answers

We start with

[tex]4^1 \equiv 4 \ (\text{mod} \ 10)[/tex]

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

Square both sides

[tex]4^1 \equiv 4 \ (\text{mod} \ 10)[/tex]

[tex](4^1)^2 \equiv 4^2 \ (\text{mod} \ 10)[/tex]

[tex]4^2 \equiv 16 \ (\text{mod} \ 10)[/tex]

[tex]4^2 \equiv 6 \ (\text{mod} \ 10)[/tex]

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

Square both sides again

[tex]4^2 \equiv 6 \ (\text{mod} \ 10)[/tex]

[tex](4^2)^2 \equiv 6^2 \ (\text{mod} \ 10)[/tex]

[tex]4^4 \equiv 36 \ (\text{mod} \ 10)[/tex]

[tex]4^4 \equiv 6 \ (\text{mod} \ 10)[/tex]

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

Square both sides again

[tex]4^4 \equiv 6 \ (\text{mod} \ 10)[/tex]

[tex](4^4)^2 \equiv 6^2 \ (\text{mod} \ 10)[/tex]

[tex]4^8 \equiv 36 \ (\text{mod} \ 10)[/tex]

[tex]4^8 \equiv 6 \ (\text{mod} \ 10)[/tex]

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

Square both sides again

[tex]4^8 \equiv 6 \ (\text{mod} \ 10)[/tex]

[tex](4^8)^2 \equiv 6^2 \ (\text{mod} \ 10)[/tex]

[tex]4^{16} \equiv 36 \ (\text{mod} \ 10)[/tex]

[tex]4^{16} \equiv 6 \ (\text{mod} \ 10)[/tex]

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

So far we have found that,

[tex]4^1 \equiv 4 \ (\text{mod} \ 10)[/tex]

[tex]4^2 \equiv 6 \ (\text{mod} \ 10)[/tex]

[tex]4^4 \equiv 6 \ (\text{mod} \ 10)[/tex]

[tex]4^8 \equiv 6 \ (\text{mod} \ 10)[/tex]

[tex]4^{16} \equiv 6 \ (\text{mod} \ 10)[/tex]

Multiply out all of the left sides of those equations above. Multiply out the right sides as well to balance things out

[tex](4^1)*(4^2)*(4^4)*(4^8)*(4^{16}) \equiv 4*6*6*6*6 \ (\text{mod} \ 10)[/tex]

[tex]4^{1+2+4+8+16} \equiv 24*36*6 \ (\text{mod} \ 10)[/tex]

[tex]4^{31} \equiv 4*6*6 \ (\text{mod} \ 10)[/tex]

[tex]4^{31} \equiv 24*6 \ (\text{mod} \ 10)[/tex]

[tex]4^{31} \equiv 4*6 \ (\text{mod} \ 10)[/tex]

[tex]4^{31} \equiv 24 \ (\text{mod} \ 10)[/tex]

[tex]4^{31} \equiv 4 \ (\text{mod} \ 10)[/tex]

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

The final answer is 4

Final answer:

The remainder of 4^31 when divided by 10 is 4, determined by examining the repeating last-digit pattern of powers of 4.

Explanation:

To find the remainder of 4^31 when divided by 10, we can use the concept of powers and properties of numbers related to modulo arithmetic. Specifically, we look at the last digit pattern that emerges when calculating powers of 4, since the remainder when dividing by 10 depends solely on the final digit of the number.

The powers of 4 have a cycle: 4^1 ends with 4, 4^2 ends with 6, 4^3 ends with 4 again, and so on. This cycle repeats every two powers, so we only need to consider the power of 4 modulo 2 to determine the last digit of 4^31. Since 31 is an odd number, we know that 4^31 will end with a 4. Hence, the remainder of 4^31 divided by 10 is 4.

A rectangle has a length of 8 cm and breadth 6cm . What is the perimeter in cm of the rectangle

Answers

8+8+6+6=__cm
8+8+6+6=28cm

The formula for the perimeter of rectangle is 2*( length+breadth)
So we have to do 2*(8+6)=2*14=28
So the perimeter is 28

PLEASE HELP!!!
WILL GIVE BRAINIEST TO FIRST ANSWER

Which of the following inequalities is graphed on the coordinate plane?

A. y > 1/2x - 1/2
B. y is less than or equal to 1/2x - 1/2
C. y is greater than or equal to 1/2x - 1/2
D. y < 1/2x - 1/2

Answers

The answer is a if the line is dotted/dashed. The answer is c if the line isn't dotted/dashed.

Answer:

Option C

Step-by-step explanation:

Equation of any line is of the form y=mx+b where m is the slope and b the y intercept.

The given line has y intercept [tex]\frac{-1}{2}[/tex] and slope as [tex]\frac{1}{2}[/tex]

Hence equation of given line is :

[tex]y= \frac{1}{2}x-\frac{1}{2}[/tex]

Taking point (0,0) to check the inequality we have:

0≥[tex]\frac{-1}{2}[/tex]

The statement is true so option C [tex]y\geq \frac{1}{2} x-\frac{1}{2}[/tex] is right .

If f(x) = + 8, what is f(x) when x = 10?

Answers

f(x) = (x/2) + 8
f(10) = (10/2) + 8 ... replace every x with 10; now use PEMDAS
f(10) = 5 + 8
f(10) = 13

We plugged in x = 10 as the input to get the output of f(x) = 13

Answer: 13

Answer:

Step-by-step explanation:

it correct

Please help! Create a set of five positive numbers (repeats allowed) that have a median of 10 and a mean of 14. What thought process did you use to create your numbers?

Answers

Alright, since there are 5 numbers, and the mean (or average) is (sum)/(amount of numbers), we have (sum)/5=14. Multiplying both sides by 5, we have the sum being 80. The median of 10 means that in a, b, c, d, e, 10 has to be c and the numbers have to be in ascending order. A and b must be 10 or lower, while d and e must be 10 or higher. Putting some random numbers in, we can have 1, 1, 10, 15, and e. We left e there because the sum needs to be 80, and since 1+1+10+15=27, 80-27=53=e. This, however, would not work if e was less than 10 and we therefore would have needed to make some numbers lower to compensate for this. Our answer is therefore 1, 1, 10, 15, 53

Help me solve this please...in detail.

Answers

n+6 = 2*7
n+6 = 14
n= 14-6
n=8

60 POINTS!!

What are the missing parts that correctly complete the proof?

Answers

2. definition of bisector
3.definition of perpendicular
4.∠AXP=~∠AXQ
6.SAS congruence postulate
7.Corresponding parts of congruent triangles are congruent

the guy below/above is correct

brainiest to best answer!

The deepest part of the Mariana trench (the deepest trench in the world’s oceans) is at an elevation of -11.033 kilometers. The elevation of the deepest part of the Atacama trench is -8.065 kilometers. What is the net change in elevation from the Atacama trench to the Mariana trench?
19.098 kilometers
2.968 kilometers
-2.968 kilometers
-19.098 kilometers

Answers

if you subtract -11.033--8.065 that will give you -2.968, so -2968 would be your answer. I hope this helps, good luck.

The net change in elevation from the Atacama trench to the Mariana trench is 2.968km.

What is the net change in elevation from the Atacama trench to the Mariana trench?

We know that the deepest part of Mariana trench is at -11.033 km, while the deepest part of the Atacama trench is -8.065km.

To find the net change, we need to find the difference between the largest value and the smallest value.

So we get:

D = -8.065km - (-11.033 km) = 2.968km

Then the correct option is the second one.

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48 out of 120 equals what percent

Answers

48/120 = 40%

48 * 2,5 = 120

np ;)

The answer i got was 40 because you multiply 100 to 48 and then divide by 120.

Tali started a pool cleaning business. She purchased cleaning supplies and charged the same amount for each pool cleaned. The expression −243+24x represents the profit Tali has earned from cleaning pools.

Which expression represents the total amount Tali earns from pool cleaning?

24x

24

−243

x

Answers

Answer:

24x

Step-by-step explanation:

The variable x is used to represent the independent variable in a situation. In this situation, the independent variable would be the number of pools cleaned; this means that x represents the number of pools cleaned.

24x would then indicate that Tali charges $24 per pool cleaned; this makes 24x her total earnings from cleaning pools.

Answer:

A. [tex]24x[/tex]

Step-by-step explanation:

We have been given an expression [tex]-243+24x[/tex], which represents he profit Tali has earned from cleaning pools. We are also told that Tali purchased cleaning supplies and charged the same amount for each pool cleaned.

Upon looking at our expression we can see that [tex]-243[/tex] is constant term and it is negative, so it will represent the amount spent by Tali on supplies.

The term [tex]24x[/tex] contains independent variable [tex]x[/tex], which represents the number of pools cleaned and 24 represents Tali's earning from each pool.

Since Tali cleaned [tex]x[/tex] pools, so total amount of Tali's earning from cleaning [tex]x[/tex] pools will be [tex]24x[/tex] and option A is the correct choice.

Based on research by barsh and colleagues (2000), _____ genes appear to be related to body weight regulation.

Answers

The answer is more than 40 genes. According to their research, these genes are transcripted into the DNA during the translation.One of these genes is called CYP19. Having more than one strand of this gene can possibly be the reason why people are slightly larger than the others.

Tom usually earns $40.85 per hour. he has a 6% pay raise. which keys must he press on his calculator?

Answers

Pay raise= 6%
total pay raise= (6/100)x40.85
Total pay raise= $2.450

This can be a final answer. Your question is incomplete I think.

"+" & "=" button key Tom will press in the calculator.

What is multiplication?

The fundamental concept of repeatedly adding the same number is represented by the process of multiplication. The results of multiplying two or more numbers are known as the product of those numbers, and the components that are multiplied are referred to as the factors.

To calculate Tom's pay raise, he can perform the following calculation on his calculator:

= 40.85 x 0.06

= 2.4510

So Tom's pay raise is $2.45 per hour.

To calculate Tom's new hourly rate, he can perform the following calculation:

= 40.85 + 2.45

= 43.30

So Tom's new hourly rate is $43.30.

Here is how the calculation can be done on most calculators:

Enter 40.85 and then press the "+" button.

Enter 2.45 and then press the "=" button.

The result should be 43.30, which is Tom's new hourly rate with a 6% pay raise.

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How do you solve cot^2x + cscx= 1
(0,2pi)

Answers

[tex]\bf 1+cot^2(\theta)=csc^2(\theta)\implies cot^2(\theta)=csc^2(\theta)-1 \\\\\\ csc(\theta)=\cfrac{1}{sin(\theta)} \\\\ -------------------------------\\\\ cot^2(x)+csc(x)=1\implies csc^2(x)-1+csc(x)=1 \\\\\\ csc^2(x)+csc(x)-2=0\implies [csc(x)-2][csc(x)+1]=0\\\\ -------------------------------\\\\[/tex]

[tex]\bf csc(x)-2=0\implies csc(x)=2\implies \cfrac{1}{sin(x)}=2\implies \cfrac{1}{2}=sin(x) \\\\\\ sin^{-1}\left( \frac{1}{2} \right)=\measuredangle x\implies \frac{\pi }{6}~~,~~\frac{5\pi }{6}=\measuredangle x\\\\ -------------------------------\\\\ csc(x)+1=0\implies csc(x)=-1\implies \cfrac{1}{sin(x)}=-1 \\\\\\ \cfrac{1}{-1}=sin(x) \implies -1=sin(x)\implies sin^{-1}(-1)=\measuredangle x\implies \frac{3\pi }{2}=\measuredangle x[/tex]

Critical thinking write a recursive rule for a sequence where every term is the same.

Answers

To do this, let f(1) = 5 and f(n) = f(n-1) for n greater than 1. This is recursive rule and each term is the same because it eventually becomes f(1), which is 5.

Jonah and his friends went to the movie theater. He bought a movie ticket, and he split the cost of a giant popcorn with his friends. Jonah's costs are represented by the expression 11+15/x . What do the different parts of the expression model? Drag the parts of the expression into the boxes to match each description. Cost of movie ticket Total cost of popcorn Jonah's portion of popcorn cost

Answers

11 equals the cost of the movie ticket, 15 equals the cost of the popcorn, and x equals the amount of friends he is dividing the cost of the popcorn by.

Answer:

Cost of movie ticket = 11

Total cost of popcorn = 15

Jonah's portion of popcorn cost = 15/x

Step-by-step explanation:

1. I

2. Took

3. The

4. Test

What classification best represents a triangle?

Answers

c^2 = 15^2 = 225
a^2 + b^2 = 10^2 + 12^2 = 100 + 144 = 244

c^2 < a^2 + b^2
Triangle is acute triangle

answer is A.
acute because 10^2 + 12^2 > 15^2

whats 10 minutes plus 7minutes plus 48minutes plus 1 hour and 29 minutes equal?

Answers

2 hours and 34 minutes

Answer: 2 hours and 34 minutes

Step-by-step explanation:

10 minutes plus 7 minutes plus 48 minutes plus 60 minutes plus 29 minutes equals 154 minutes. 154 minutes equals 2 hours and 34 minutes.

Joseph’s garden is 9 feet wide and 12 feet long. Alana’s garden is 7 feet wide and 25 feet long.

How much greater is the area of Alana’s garden than Joseph’s garden?
Please help!! Will give 15 points!

Answers

area of Josephs garden = 9*12 = 108 square feet

area for Alana's garden = 7 *25 = 175 square feet

175/108 = 1.62

Alan's garden is 1.62 times larger

In a rhombus, which of the following are always equal? Select all that apply.

opposite angles
diagonals
opposite sides
consecutive angles

Answers

opposite sides
opposite angles

hope it helps

opposite side and opposite angles would be the answers

If 5x + 5 =25 + 3x then x = ? (im in pre algebra)

Answers

Salutations!

[tex]5x+5 = 25+3x[/tex]

Isolate the variables

[tex]5x -3x = 25 -5[/tex]

[tex]7x = 21[/tex]

[tex]x=21/7[/tex]

[tex]x=3[/tex]

Hope I helped (:

Have a great day!

Final answer:

To solve the equation 5x + 5 = 25 + 3x, subtract 3x from both sides, subtract 5 from both sides, and divide by 2 to find x = 10.

Explanation:

To solve the equation 5x + 5 = 25 + 3x, you need to isolate the variable x. First, subtract 3x from both sides of the equation to combine like terms: 5x - 3x + 5 = 25. Simplify: 2x + 5 = 25. Next, subtract 5 from both sides of the equation to isolate the variable: 2x = 20. Finally, divide both sides of the equation by 2 to solve for x: x = 10.

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1. what are some different types of numbers that you have herd of before?

2. why do you think it is important to classify (sort) different types of numbers

Answers

natural, whole

you need the different classifications that way it is easier to tell someone what you are talking about.

1. Some types of numbers I've heard about are: whole numbers, fractions, negative numbers, infinite numbers, irrational numbers, rational numbers, improper fractions, imaginative numbers, radical numbers, unknown numbers, etc.

2. I think it important to group or separate numbers out in order to apply them to the categories they apply to.

Need help ASAP real quick ????????????

Answers

The answer is 54. (36+72=108. 108/2 = 54)

The length of the base of a triangle is twice its height. if the area of the triangle is 100 square kilometers, find the height.

Answers

10km

a=1/2b·h

If h=x
b=2x

a=1/2(2x)·x
a=x²
100=x²
x=10
h=x=10

Work out the value of 3x + 2y when x=4 and y=-5

Answers

3x + 2y =

3*4 + 2*-5=

12 + -10 = 2

Just substitute the equation with the given

The given are
x = 4 and y = -5
the equation is
3x + 2y
3 (4) + 2 (-5) = 12 - 10 = 2

An athlete eats
60
grams of protein per day while training. How much is this in milligrams?
Be sure to include the correct unit in your answer.

Answers

it is 60,000 milligrams

what is the square root of 49

Answers

7 is the square root of 49.
7^2 = 49

The answer is 7. Hope this helps!

Find the slope of a line parallel to the line through the given points. P(-2, 4), Q(6, -2) 4/3 3/4 -3/4

Answers

Attached the solution and work.

Answer:

Option 3 - [tex]m=-\frac{3}{4}[/tex]

Step-by-step explanation:

Given : P(-2, 4), Q(6, -2)

To find : The slope of a line parallel to the line through the given points?

Solution :

First we find the slope of the line passes through given points P(-2, 4), Q(6, -2)

The slope formula is

[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]

[tex]m=\frac{-2-4}{6-(-2)}[/tex]

[tex]m=\frac{-6}{8}[/tex]

[tex]m=-\frac{3}{4}[/tex]

When two lines are parallel then there slope are equal.

Therefore, The slope of a line parallel to the line through the given points is

[tex]m=-\frac{3}{4}[/tex]

So, Option 3 is correct.

If a set of data is in the direction of a downward line, which of the following would be the best model for this data?
Quadratic regression model
Exponential regression model
Linear regression model
None of the above

Answers

I'm not too sure about this, but I feel that it's a linear regression. A quadratic one eventually reverses direction, and an exponential one levels off and stops decreasing.

Simplify 5(a - b) + 6(a + b) - 7(a - 2b)

Answers

The answer is 4a + 15b

the simplified answer is 4a+15b

Graph the equation 5x+2y=10

Answers

Desmos graphing calculator is a very helpful tool!

5x+2y=10: Displayed in the image below

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