A swimming pool can be filled by either or both of two pipes of different diameters. it takes the smaller pipe twice the time that the larger pipe takes to fill the pool. if water flows through both pipes it take 213 hours to fill the pool. how long will it take the larger pipe to fill the pool? [hint: let x be the amount of the pool filled by the small pipe in one hour]

Answers

Answer 1

By large pipe only it will take 319.5 hours to fill the pool.

Step-by-step explanation:

Let r₁ be the rate of filling of small pipe, r₂ be the rate of filling of large pipe and V be the volume of swimming pool.

[tex]\texttt{Rate of small pipe},r_1=\frac{V}{t_1}\\\\\texttt{Rate of large pipe},r_2=\frac{V}{t_2}=\frac{V}{0.5t_1}=2r_1[/tex]

If both pipes are combined it takes 213 hours, that is

[tex]t=\frac{V}{r_1+r_2}\\\\213=\frac{V}{r_1+2r_1}\\\\V=639r_1[/tex]

Now we need to find how much time it takes to fill the pool by large pipe,

That is

[tex]t_2=\frac{V}{r_2}=\frac{639r_1}{2r_1}=319.5hours[/tex]

By large pipe only it will take 319.5 hours to fill the pool.

Related Questions

A number sentence is said to be true if both numerical expressions are

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if both expressions are equivalent (that is when both evaluate to the same number)

F= 9/5C + 32, solve for F please.

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I believe u would do it this way if it's wrong please let me know hope I helped and don't srew u up

When the factors ofa trinomial are (x+ p) and (x + q) then the coefﬁcient ofthe x- term in the trinomial is:?

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the sum of p and q for apex

What is the definition of proof in geometry

Answers

I'm guessing just to show that you did your work to get the answer.

A geometric proof involves writing reasoned, logical explanations that use definitions, axioms, postulates, and previously proved theorems to arrive at a conclusion about a geometric statement. hope this helped:)

Ohhhhh! I have a Brainliest!

Answers

answers: 1.) 37 & 2.) 1 2/3

1. 4.5+8.75+9.5+10+4.25=37

2. 4 1/3

hope this helps please give brainliest and 5 stars and a thank you

2+1/6y=3x+4 solve for y

Answers

2+1/6y=3x+4 solve for y

Answer y=18x+12

2 + 1/6y = 3x + 4
× 6y throughout
12y + 1 = 18xy + 24y
Send 12y to the other side
12y + 18xy = 1
Y is common
y (12 + 18x) = 1
y = 1/ (12 + 18x)

Hope it helped!

Suppose you are going to make a sandwich. You have mayonnaise and mustard to spread on the bread. You have white, wheat, and rye bread. You have ham, turkey, and pastrami. How many different sandwiches can you make using one spread, one type of bread, and one type of meat?

Answers

18 samiches
m8 thats alot of samiches

2 spreads

3 breads

3 meats

2 * 3 *3 = 18

18 different sandwiches....now I'm hungry

The length of a rectangle is 3 meters less than twice the width. if the area of the rectangle is 527 square meters, find the dimensions.

Answers

The rectangle is 17 meters wide and 31 meters long. To solve this problem, first work out the equation for the length of the rectangle. Using the information given, we find that length (L) is given by L=2W-3. Next we setup the formula for the area of a rectangle, A=(W)(L). We are told that the area is 527 sq. meters, so our equation is 527=(W)(L). We also know that L=2W-3, so we can plug that into the equation for area as well which gives us 527=W(2W-3), which can be written 0=2(W^2)-3W-527. We now need to solve this equation for W. Factoring the left side we get, 0=(W-17)(2W+31). Thus, either (W-17)=0 or (2W+31)=0 must equal zero. Solving these two equations, we get W=17 or W=-15.5. Since we are looking for the width (which is a length), we know it cannot be negative and therefore the width must be 17 meters. Now that we know the width, we can plug W=17 back into the equation for length (L=2W-3). Doing this give us L=2(17)-3 which is equal to 31. Thus the length is 31 meters.

Answer:

w=17

l=31

Step-by-step explanation:

correct

You have 6 green marbles, 23 blue marbles, and 18 red marbles. what is the probability of choosing a red marble. express your answer as a fraction in lowest terms.

Answers

The probability of choosing a red marble is 18/47.

How do you write 100, in an exponential form

How do write 100,000, in an exponential form

And how do you write 10,000 ,in an exponential form

Answers

1. 10^2

2. 10^5

3. 10^4

Hope this helped!

Nate

Final answer:

Numbers can be written in exponential form with a base of 10. For example, 100 is written as 10^2, 100,000 as 10^5, and 10,000 as 10^4.

Explanation:

To write numbers in exponential form, you need to understand the concept of exponential notation which is a way to express a number as a base raised to a power. In each of the given cases, the base is 10.

For 100, there are two zeros following the 1. This means that 100 can be written as 10 to the power of 2, or 10^2.

Similarly, for 100,000, there are five zeros following the 1. This would be written as 10 to the power 5, or 10^5.

Lastly, 10,000, has four zeros following the 1. This would be written as 10 to the power of 4, or 10^4.

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Find four consecutive integers with the sum of 54

Answers

54/4 = 13.5

take the 2 whole numbers below 13.5 and the 2 whole numbers above 13.5

12 + 13 + 14 + 15 = 54

Cynthia besch wants to buy a rug for a room that is 18 ft wide and 30 ft long. she wants to leave a uniform strip of floor around the rug. she can afford to buy 220 square feet of carpeting. what dimensions should the rugâ have?

Answers

Since the strip around the outside of the rug will be uniform, the dimensions of the rug will have the form (18 - x) in width and (30 - x) in length, where x is equal to twice width of the strip. We can use this data to set up an equation. (18 - x) (30 - x) = 220 x^2 - 48 x + 540 = 220 x^2 - 48 x + 320 = 0 (x - 8) (x - 40) = 0 x = 8 or x = 40 Since x = 40 is too wide for the strip, the correct solution is x = 8 The width of the rug is: 18 - x = 10 feet The length of the rug is: 30 - x = 22 feet The dimensions of the rug are 10 feet x 22 feet. Note that the area is equal to 220 square feet.

two cruise ships are sailing towards each other from caribbean islands that are 264 km apart, one ship travels 4 km/h faster than the other. if they both started at the same time. and meet after 6h. how fast is the other ship travelling?

Answers

Final answer:

The slower ship is traveling at a speed of 21 km/h, while the faster ship is traveling at a speed of 25 km/h.

Explanation:

This is a mathematics problem that involves solving for unknown speeds with the given conditions. Lets assume the speed of the slower ship is x km/h. Thus, the speed of the faster ship is x+4 km/h. They are moving towards each other, thus their combined speed is (x+x+4) km/h. As speed is distance over time, we can set up the equation: (2x+4)*6 = 264. Solving this equation, we end up with x=21 km/h as the speed of the slower ship, and hence the speed of the faster ship is 25 km/h.

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What is the square root of 83 to the nearest tenth?

Answers

Knowing the squareroot of 81 is 9, we can easily know that square root of 83 is close to 9.

9 to the closest tenth is 10.

Hope I helped :)

Based on the information given the square root of 83 to the nearest tenth is 9.1.

Square root:

To determine the square root to the nearest tenth we will have to find the square root of the given number which is 83.

Hence,

Square root=√83

Square root= 9.1104335791443

Square root=9.1 nearest tenth

Inconclusion the square root of 83 to the nearest tenth is 9.1.

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The larger of two numbers is one more than four times the smaller number. if the sum of the numbers is 106, find the numbers.

Answers

Call the numbers x and y. According to the first sentence, x = 4y + 1. According to the second sentence, x + y = 106. You can combine these two equations to find the values of these variables:

x + y = 106
4y + 1 + y = 106
5y = 105
y = 21

We have y, so now we can solve for x using either original equation:

x + y = 106
x + 21 = 106
x = 85

Final answer:

To solve the problem, create two equations based on the information given, then solve these equations step-by-step. After calculation, the two numbers are 21 and 85.

Explanation:

Given the problem, we can translate and create two equations which are:

The larger number is one more than four times the smaller number. We can express this as: L = 4S + 1 The sum of the numbers is 106. We can express this as: L + S = 106

Step 1: From the first equation, we know that L = 4S + 1. We can substitute this into the second equation in place of L, giving us 4S + 1 + S = 106.

Step 2: Add up, and we get 5S + 1 = 106. Subtract 1 from both sides and we get 5S = 105.

Step 3: Divide both sides by 5 to solve for S, we get S = 21.

Step 4: Substitute S = 21 into the equation L = 4S + 1, you can calculate and find L = 85.

Therefore, the two numbers are 21 and 85.

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At a toy factory, toy cars are produced on an assembly line. It takes 8.216 seconds to attach the wheels. It takes 3.652 seconds to attach the hood. How long does it take to attach the wheels and hoods on 42 toy cars

Answers

the answer is 11.868 hopes this helps

At a toy factory, it takes 498.456 seconds to attach the wheels and hoods on 42 toy cars.

We have been given that toy cars are manufactured on an assembly line in a toy factory. Attaching the wheels takes 8.216 seconds. Attaching the hood takes 3.652 seconds.

What are Arithmetic operations?

Arithmetic operations can also be specified by subtracting, dividing, and multiplying built-in functions. The operator that performs the arithmetic operation is called the arithmetic operator.

* Multiplication operation: Multiplies values on either side of the operator

For example 12×2 = 24

To determine the time it takes to attach the wheels and hoods on 42 toy cars

According to the given condition, the arithmetic form would be as

⇒ 42 × (8.216 + 3.652)

Calculate the sum of the difference to get,

⇒ 42 × (11.868)

Apply the multiplication operation, and we get

⇒ 498.456

Therefore, it takes 498.456 seconds to attach the wheels and hoods on 42 toy cars.

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1) Write the sum or difference in the standard form a + bi. (2 points)
( 7 + 5i) - ( -9 + i)

a) 16+4i
b) -16-4i
c) 16-4i
d) -2+6i

2) Write the product in standard form. (2 points)
( 7 + 7i)( 6 + 7i)

a) -7 + 91i
b) 49i2 + 91i + 42
c) 91 - 7i
d) -7 - 91i

3) Find the product of the complex number and its conjugate. (2 points)
1 + 3i

a) 1 + 9i
b) 10
c) -8
d) 1-9i

4) Write the expression in standard form. (2 points)
three divided by quantity three minus twelve i.

a) - one divided by seventeen. + four divided by seventeen. i
b) one divided by seventeen. - four divided by seventeen. i
c) - one divided by seventeen. - four divided by seventeen. i
d) one divided by seventeen. + four divided by seventeen. i

5) Find the real numbers x and y that make the equation true. (2 points)
5 + yi = x + 3i

Answers

When performing addition and multiplication with constant numbers, we treat i as we would treat any variable x in an expression, with the same rules and properties of addition and multiplication.

1)

[tex]( 7 + 5i) - ( -9 + i)=7+5i+9-i=(7+9)+(5i-i)=16+4i[/tex]

2)
Distribute 7+7i over 6 and 7i:

[tex]( 7 + 7i)( 6 + 7i)=( 7 + 7i)\cdot6+( 7 + 7i)\cdot7i=42+42i+49i+49i^2[/tex]

collecting similar terms, and substituting [tex]i^2[/tex] with -1 we have:

42+91i-49=-7+91 i

3)

The conjugate of a complex number a+bi is a-bi;
the conjugate of 1+3i is 1-3i.

Thus, using the difference of squares formula we have

[tex](1+3i)(1-3i)=1^2-(3i)^2=1-9i^2=1-9(-1)=1+9=10[/tex]

4)

To write a rational expression ( with a complex number in the denominator) in the standard form, we multiply by the conjugate of the denominator both the numerator and the denominator:

[tex]\displaystyle{ \frac{3}{3-12i}= \frac{3(3+12i)}{(3-12i)(3+12i)}= \frac{9+36i}{3^2-(12i)^2} [/tex]

[tex]=\displaystyle{ \frac{9+36i}{9+144}= \frac{9+36i}{153}= \frac{9}{153}+ \frac{36}{153}i [/tex]

simplifying by 9, the complex number is finally written as

[tex]\displaystyle{ \frac{1}{17}+ \frac{4}{17}i [/tex]

5)

2 complex numbers a+bi, and c+di are equal only if a=c, and b=d. (Where a, b, c, d are real numbers.)

Thus, x=5, and y=3 is the solution to the equation.

Answers:

1) A
2) A
3) B
4) D
5) (x, y) =( 5, 3)

How do i factor -1/2 out of -1/2x + 6

Answers

-1/2x + 6

-1/2(x - 12)

multiply -2 to the 6 so that when you multiply -1/2 into the expression it will turn into positive 6

hope this helps

3(b-4)=5b-2 plz help I'm confused

Answers

3( b-4) = 5b - 2

3b - 12 = 5b - 2

3b - 5b = 12 - 2

-2b = 10

b = -5

hope this helps

3b-12=5b-2
-12=2b-2
-10=2b
b=-5

Ive been super sick so im a little behind. Help please .

1. A line goes through the points (8,9) and (-2,4)
(a) What is the slope of the line? Show your work
(b) Write the equation of the line in point-slope form. Show your work
(c) Write the equation of the line in slope-intercept form. Show your work.

Answers

(a) formula: (y2-y1)/(x2-x1)
(4-9)/(-2-8) = (-5)/(-10) = 0.5

(b) formula: y-y0 = m(x-x0) where x0,y0 is a point on the line and m is the slope
y - 9 = 0.5 ( x - 8 )

(c) formula: y=mx + b
Start with formula from (b)
y -9 = 0.5x - 4
Add 9 to both sides
y = 0.5x +5

Hope this helps.
The answers are in the top right corner.

If 5 people including mary and bob are arranged randomly in a line, what is the probability that mary and bob are next to one another?

Answers

There are 5! (5 x 4 x 3 x 2 x 1 = 120) potential different arrangements for 5 people picked at random. Of those, let's take a look at all of the possible arrangements with Mary and Bob next to each other:

MBXXX
BMXXX
XMBXX
XBMXX
XXMBX
XXBMX
XXXMB
XXXBM

There are 8 arrangements out of the 120 where Mary and Bob are next to each other, which means that they have an 8/120 = 1/15 chance of ending up in that situation.

What is 4,080,499 rounded to the nearest thousand?

Answers

4,080,499 rounded to the nearest thousand is 4,080,000.

ALGEBRA 2- Which equation has the solutions x = 1 ± √5 ?

A. x2 + 2x + 4 = 0
B. x2 – 2x + 4 = 0
C. x2 + 2x – 4 = 0
D. x2 – 2x – 4 = 0

Answers

A. But you can also read a book and not rely on this

D. x^2 - 2x - 4 = 0

You can solve this problem 2 different ways.
1. Plug in a value of x = 1 ± √5 into each of the possible equations and see if the result is 0.
or
2. Use the Quadratic formula to solve each of the equations and see which comes up with the correct answer.

For this case, I'll use the 2nd option.
A. x^2 + 2x + 4 = 0
a = 1, b = 2, c = 4
Upon attempting this, you'll quickly discover that you're going to try to get the square root of -12. Since there's no imaginary terms in the desired root, this equation can't be it.

B. x^2 – 2x + 4 = 0
Same issue here, trying to get the square root of a negative number. So this one doesn't work either.

C. x^2 + 2x – 4 = 0
Getting closer. Have (-2 ± sqrt(20)) / 2 = -1 ± √5
Still not it, but closer. At least not trying to get the square root of a negative number.

D. x^2 – 2x – 4 = 0
Since the other 3 are wrong, this must be right. But let's do the math anyway.
a = 1, b = -2, c = -4
The quadratic formula gets (2 ± sqrt(20)) / 2 = (2 ± 2√5)/2 = 1 ± √5
And it works out. So this is the answer.

An office uses 478 pounds of paper in one week. The paper comes in packages that hold 18 pounds of paper each. How many packages of paper does the office use each week?

Answers

To solve this, you would divide 478 by 18, which equals 26.5555556. Since you can't have half a package of paper, the answer would be 26. Hope this helps!

The office uses 26 and a half package of papers.

What is division?

Division is the process of splitting a number or an amount into equal parts.

Given that, An office uses 478 pounds of paper in one week. The paper comes in packages that hold 18 pounds of paper each.

To find the number of packages of paper, the office use each week, we will divide the total paper used in one week to paper in 1 package

Therefore, the number of packages of paper, the office use each week = 478 / 18 = 26.5

That means they are using 26 package plus a half package in one week.

Hence, The office uses 26 and a half package of papers.

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Hanks pickup can travel 60miles on 4gallons of gas. How many gallons will hanks pickup need to travel 30miles?

Answers

Hank can go 30 miles with 2 gallons.This is the answer because 30 is half of six so simply do 4 divided by half and get 2. Hope i helped

a boat salesperson earns a 2.5% commission on the sale of each boat Find the commision earned on a boat that sells for 18,500

Answers

100% = 1.0
2.5% = 0.025

So now we know the decimal that corresponds to 2.5%, so all we have to do is multiply the price of the boat by this value in order to find the commission earned:

18 500 x 0.025 = $462.50

Whenever you need to find the percentage OF a number (often money), you just convert that percentage to a decimal (just move the decimal to the left twice so 40% becomes 0.40, 10.5% becomes 0.105, 2% becomes 0.02, etc) and MULTIPLY that decimal by the amount/number you need to find the percentage of.

For example, find the 20% commission of a $10,000 car sale
Calculation:
0.20x$10000 = $2000
Answer:
the commission would be $2000

That’s how you do it. I hope that helps. You should be able to solve it on your own now.

Reflection : Across the line y = 1

Answers

What is the question supposed to be?

Reflecting across y = 1 means each point's position stays the same horizontally but mirrors vertically across the line.

When reflecting a point or shape across a line, y = 1,

it means that each point is mirrored on the other side of the line while maintaining the same distance from the line.

Here, the line y = 1 acts as a "mirror" or "axis of reflection."

To reflect a point (x, y) across the line y = 1, follow these steps:

Find the vertical distance between the point and the line y = 1. Let's call this distance "d."

If the point is above the line (y > 1), then d = y - 1.

If the point is below the line (y < 1), then d = 1 - y.

Move the point to the same vertical distance on the other side of the line y = 1.

If the point was above the line (y > 1), the new reflected point will be (x, 1 + d).

If the point was below the line (y < 1), the new reflected point will be (x, 1 - d).

Keep in mind that the x-coordinate remains the same in both cases since the line of reflection is vertical (parallel to the y-axis).

By repeating these steps for all points in a shape, obtain the reflection of the entire shape across the line y = 1.

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A train travels 750 miles in 15 hours. which unit rate describes the speed of the train?
a. 50 miles per hour
b. 75 miles per hour
c. 150 miles per hour
d. 350 miles per hour

Answers

The answer your looking for is A

Assume that lines that appear to be parallel are parallel. Find the value of x and the measure of angle y

Answers

What information have we been given here? From the diagram, we can see that (9x+1)° and (14x-34)° degrees are supplementary, meaning:

(9x+1)+(14x-34)=180

There, we have an equation we can fairly easily solve for x. What about y?

If we take a look at the line y° occupies, we can see that it shares a straight angle with our (14x-34)° term and - as implied by the right angle on the bottom line - a 90° angle.

All three of these should add up to 180°, so we have:

(14x-34) + y + 90 = 180

Another think to note is that, upon inspection, (14x-34)° and y° are complementary - they add up to 90° - and subtracting the 90 from both sides of our equation confirms that fact:

(14x-34) + y = 90

If you've solved for x prior to this, solving for y should be pretty straightforward.

Answer:

The answer would be (14x-34) + y = 90.

Step-by-step explanation:

Which statement is true about the difference 2√7-√28

Answers

It seems like there are answer choices but you forgot to post them. If you want to simplify then

2*sqrt(7) - sqrt(28) = 2*sqrt(7) - sqrt(4*7)
2*sqrt(7) - sqrt(28) = 2*sqrt(7) - sqrt(4)*sqrt(7)
2*sqrt(7) - sqrt(28) = 2*sqrt(7) - 2*sqrt(7)
2*sqrt(7) - sqrt(28) = (2-2)*sqrt(7)
2*sqrt(7) - sqrt(28) = (0)*sqrt(7)
2*sqrt(7) - sqrt(28) = 0

So the whole complicated expression simplifies to 0 (zero)

This is because sqrt(28) = 2*sqrt(7) when you simplify sqrt(28)

Side Note: "sqrt" is shorthand for "square root"

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