Mathematics Middle School

One pump can fill a swimming pool in 8 hours and another pump can fill it in 10 hours. If both pumps are opened at the same time, how many hours will it take to fill the pool?

Answers

Answer 1

Answer: It will take [tex]\dfrac{40}{9}=4\dfrac{4}{9}[/tex] hours to fill the pool.

Step-by-step explanation:

Since we have given that

Number of hours first pump takes = 8 hours

Number of hours second pump takes = 10 hours

If both pumps are opened at the same time,

Work done by first pump = [tex]\dfrac{1}{8}[/tex]

Work done by second pump = [tex]\dfrac{1}{10}[/tex]

According to question,we get that

[tex]\dfrac{1}{8}+\dfrac{1}{10}\\\\=\dfrac{5+4}{40}\\\\=\dfrac{9}{40}[/tex]

So, it will take [tex]\dfrac{40}{9}=4\dfrac{4}{9}[/tex] hours to fill the pool.

Related Questions

Alec is trying to find the surface area of a shoe box. What unit will he use?
A) cubic feet
B) square feet
C) cubic inches
D) square inches

Answers

D) Square inches.
"Square" is used when measuring area and inches are more suited for measurement due to the size of the box.

can someone help me with these 3

Answers

I can;t see the picture is burry :)

What is the change in temperature from -8°F to 14°F?

Answers

the change is 22
8+1=22
put off the negative sign.
22 degrees to get to 0 is 8 and then 14+ 8 is 22

A laboratory culture contains 150 bacteria. After twenty minutes, the culture contains 300 bacteria. After one hour, the culture contains 1200 bacteria. Make a conjecture about the rate at which the bacteria increases

Answers

the answer is C..!! 
see.. at t=0 the culture had 150 bacteria.. 
at t=20 the culture had 300 bacteria. 
at t=60 the culture had 1200. 
so if u go by the second option... at t=40 the bacteria would be 600..!! and it makes sense because it fits the sequence...!! 
i am just telling you the logic..!! if u have to formally solve it.. use the concept of sequences and series... :)
Final answer:

The bacteria in your culture appear to be experiencing exponential growth, doubling in population size every 20 minutes. This is common in organisms that reproduce by binary fission like bacteria, but the growth rate can be influenced by various environmental factors.

Explanation:

Based on your data, the number of bacteria in your culture seems to double every 20 minutes. This type of growth pattern is known as exponential growth, which is common in prokaryotes and other organisms that reproduce by binary fission.

For example, if you were to start with 1000 bacteria in a nutrient-rich environment, after one hour (or three 20-minute intervals), each bacterial cell would've divided several times, increasing the total population size from 1000 to 8000. This is based on the principle that in exponential growth, the number of new organisms added to the population in each round of division (or generation) increases as the population size increases. This results in a 'J-shaped' growth curve when plotted over time, illustrating the increasing rate of population growth.

However, please note that in reality, bacterial growth is influenced by several factors including nutrient availability and environmental conditions and the growth rate may not remain constant over time. For a more accurate analysis, you could take readings at more frequent intervals and plot a graph of population size versus time to observe the growth pattern.

Learn more about Exponential Growth here:

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The floor of the commons room at King Middle School is in the shape of a square with side lengths of x^2 y^3 feet. New tile is going to be put on the floor of the room. Find the area of the floor.

Answers

The useful hint here is the shape of the area which is square. By definition, a square is a two-dimensional figure that consist of two parallel sides have the same equal measure. The only given dimension of a square is its side. The area is equal to the square of the side. Since the side has a measure of x²y³,

A = s² = (x²y³)²
By the laws of exponents, for this problem, just simply distribute the outer exponent to each of the inner exponent.
A = x⁴y⁶

I got stuck on this one

Answers

The answer is the one on the bottom left, because since it's a less than sign, you use a dotted line for the graph, and also you shade the left of the line since x is less than two.

In a 50-question test, the highest score in the class is three times the lowest score minus four. The difference between the highest score and the lowest score is 30. What is the highest score?

Answers

that's hard to answer to be honest with you.
Final answer:

The highest score on the test is 47, found by setting up and solving a system of equations based on the information given in the question.

Explanation:

The problem described in the question can be solved using algebra. Let's denote the highest score as H and the lowest score as L. According to the question, we have two equations:

H = 3L - 4 H - L = 30.

We can solve this system of equations step by step. Since both equations have H, they can be set equal to each other: 3L - 4 = 30 + L. If you simplify this equation by subtracting L from both sides, you get 2L - 4 = 30. Then add 4 to both sides to isolate 2L on one side: 2L = 34. Divide both sides by 2, to solve for L: L = 17. Then substitute L into one of your original equations (H = 3L - 4), so H = 3*17 - 4 = 51 - 4 = 47. So, the highest test score is 47.

Learn more about Mathematics Problem Solving here:

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One day, a king left his castle with a bag of silver coins to wander his kingdom. to the first peasant he met, he gave one-half of the coins plus two more. A little later, he met another peasant to whom he also gave one-half of his coins plus two more. Walking on, he met a third peasant and again gave half his coins plus two more. FInally, the king went home with two coins left in his bag. How many coins did he have to begin with? Create an algebraic equation. Please explain why.

Answers

are there any options on what type of problem u want?

Answer:

The king left his castle with 44 silver coins.

Step-by-step explanation:

A king left his castle with a bag of silver coins and he gave his coins to 3 peasants in an order. Finally he went home with two coins left.

To solve this question we calculate it in reverse order.

Finally the king has in his bag = 2 coins

Before it he met third peasant king had =

= (2+2) × 2

= 4×2 = 8

Before the king met third peasant, he had 8 coins.

Before he met Second peasant king had :

= (8+2) × 2

= 10 × 2 = 20

Before he met second peasant king had 20 coins.

Before he met first peasant he had :

= (20+ 2) × 2

= 22 × 2 = 44

Before King met first peasant he had 44 silver coins.

he Discount Hair Center has a large container of combs. Each purchase qualifies a customer to receive a free comb. The container contains 4 blue combs, 2 purple combs, 8 black combs, 3 white combs, 6 yellow combs, and 5 pink combs.

What is the probability that the next customer will pull out a blue comb?

Answers

it would be a 4 in 28 probability (or 1 in 7 if you simplify)
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 
first you add up all the number of combs together which gives you 28 combs total

the there were 4 blue combs out of the 28

so the probability it 4 in 28       or 1 in 7

Evaluate the following expression using the values given:

Find 4x − y − 2z if x = −2, y = 3, and z = −2

−15
15
−7
7

Answers

4x-y-2z
Evaluate, by substituting the values for the variables
4(-2)-(3)-2(-2)
Simplify by multiplying
-8-3+4
Add/subtract
-11+4
-7 is your answer

the answer is -7
4(-2)-(3)-2(-2)

How much will a person pay for 11.3 pounds of bananas at a price of ​$2.07 per​ pound?

Answers

All you have to do is multiply 11.3 and $2.07 and you get 23.391
$23.39. I got that by multiplying $2.07x 11.3.

How to convert 14520 millimeters to liters?Report to the nearest hundredth of a liter.

Answers

your answer would be 14.52 liters

Solve W=(5/8+7/8)*2*2

Answers

w = 6 is the answer to your question

Read the problem in the box below. Make a list to help you find the correct answer

Answers

The answer would be 
A) WP, WB, WC, PB, PC, BC.

I need help I don't understand this!!

Answers

B is 2,2 A is -1,1 c is 2,-1
Because you are dilating by 2, then you multiply 2 for all the points

b(2,2) => b (4,4)
a(0,1) => a (0,2)
c(2,0) => c (4,0)

your new points will be A' (0,2) B' (4,4) and C' (4,0)

hope this helps

just graph it on the graph

Tristan bought an orange that weighs 1/5 pound. He cut the orange into 8 slices. How much does each orange slice weigh?

Answers

A pound is 16 ounces, so you would divide 16 by 5, finding that is 3.2 you would then divide 3.2 by 8 getting your answer 0.4 of an ounce
16÷5=3.2, 3.2÷8=0.4 ounce

Answer:

1/40 pound

Step-by-step explanation:

What was the biggest decrease in time from the 1st leg to the 2nd leg?? Relay scores

Answers

I'm sorry, but you're going to have to give out the chart given or what shows the relay scores so we can answer the question.

(0,0), (1,5), (2,20), (3,45), (4,80) what's the rule?

Answers

hmm, seems to multiply by 5
wait, no

first is multiply by 5
2nd is multiply by 10
3rd is multiply by 15
4th is multiply by 20
seems to be

[tex]f(x)=x(5x)[/tex] or [tex]f(x)=5x^2[/tex]
the rule is square the input then multiply by 5

What is the missing term in the factorization?

12x^2-75=3(2x+?)(2x-5)

Can anybody help me asap please?
Thank you

Answers

3(2x+5)(2x-5), 5 is the missing term.

ANSWER

The missing term is

[tex]5[/tex]


EXPLANATION


The quadratic expression given to us is

[tex]12 {x}^{2} - 75[/tex]

We factor 3 to obtain,


[tex]12 {x}^{2} - 75 = 3(4 {x}^{2} - 25)[/tex]

We rewrite the expressions in the parenthesis to obtain,

[tex]12 {x}^{2} - 75 = 3( ({2x})^{2} - {5}^{2} )[/tex]



Recall that,


[tex] {a}^{2} - {b}^{2} = (a + b)(a - b)[/tex]



We apply the difference of two squares formula for the expression in the parenthesis to obtain,

[tex]12 {x}^{2} - 75 = 3(2x + 5)(2x - 5) )[/tex]



By comparing to,



[tex]12 {x}^{2} - 75 = 3(2x + ?)(2x - 5) )[/tex]



The missing term is 5.

Write two inequalities to compare -9 and -6

Answers

-9 is less than -6

-6 is greater than -9
 Two inequalities could be: 

-9 < -6
-6 > -9

Figure ABCD is a parallelogram with point C (3, −2). Figure ABCD is rotated 90° counterclockwise to form figure A′B′C′D′. What coordinate would be the output for point C'?

Answers

Refer to the diagram below

Point C (3, -2) is rotated 90° turn anticlockwise and the image is (2, 3).
Notice the red line that is rotated 90° anticlockwise. The final position is given in green line. 

232 round to nearest ten

Answers

the nearst rounding to the tens is 230

230 because 2 is less than 5 and so it has to go to 230.

What is the greatest number of points of intersection that can occur when 2 different circles and 2 different straight lines are drawn on the same piece of paper.

Answers

8:

A line can intersect a circle twice. So, two lines intersect one circle 4 times. Two lines can intersect two circles 8 times.

Hope this helps!

Answer:

11

Step-by-step explanation:

Make a diagram. Two geometric figures intersect if they have one or more points in common. Draw two circles which intersect in  points. Draw a line which intersects the two circles in  points. Draw another line which intersects the two circles in  points and also intersects the first line. There are 11 points of intersection. 

Is this the correct answer? Am I missing anything? Do I need to delete anything?

Answers

It should be congruent angles, for "congruent angles" are angles that have the same measures

vertical angles measurements are also equal, however, you want to be as broad as possible

hope this helps

It should be congruent angles, for "congruent angles" are angles that have the same measures

vertical angles measurements are also equal, however, you want to be as broad as possible

hope this helps

I don't understand this one help me please

Answers

Well you need to find the value of x. So this is what you do. You have to isolate the variable in other words it needs to be on one side of the equation. You would need to add 11 to both sides and you would get 13x= 9x -2. Then you do the same with 9x and subtract it from boths sides and end up with 4x= -2. You divide -2 by 4 and get -1/2 as your answer. So x= -1/2. I hope this helps love! :)

Tim mixed 2 parts vinegar and 5 parts water to make a cleaning liquid. How many parts of vinegar did Tim mix with each part of water?
one over ten
one over five
two over seven
two over five

Answers

2 parts vinegar to 5 parts water so two over five

Answer:

2/5

Step-by-step explanation:

Traveling at 65 miles/hour, how many minutes will it take to drive 125 miles to San Diego?

Please break this down into parts so i can easily understand this. I take gse algebra 1 in the 8th grade and i'm having trouble with dimensional analysis word problems so I really need help with this one. We also have to use a certain chart that looks like a big fraction we use to solve problems like this, the units cancel out, and we multiply the top and bottom and then divide the top product by the bottom product. Please help. I'll also be giving the brainliest answer.

Answers

1.92307692308 Hours To San Diego

WHAT IS .115 IN EXPANDED FORM

Answers

0.115 = 0.1 + 0.01 + 0.005

hope it helps

4(g - 1 )=24
what is the answer

Answers

Hello There!

First Expand:
4g - 4 = 24
Then solve:
4g = 24 + 4
4g = 28
g = 28/4
g = 7.

Hope This Helps You!
Good Luck :) 
Hello Aneily!

[tex]4(g-1)=24 Distributive property (4)(g)+(4)(-1)=24 4g - 4 = 24 4g = 24 + 4 4g = 28 Divide both sides by 4 4g/4 = 28/4 g= 7 [/tex]


Have a beautiful day!

15 points!

Solve. 1/3r + 1 = −2/3r − 2 Drag and drop the answer into the box.

a. -3
b. -1/3
c. 2/3
d. 18

r = ???

Please help and thanks!

Answers

a. -3 
I know this because 1/3+2/3= 1 which would make the problem r+1=-2. -1+-2=-3

Answer: a -3

Step-by-step explanation:

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