One pipe takes 6 hours working alone.
The other pipe takes 12 hours working alone.
This is a rate of work problem. The formula utilized is
[tex]w=r\times t[/tex]
where
[tex]w[/tex] is the work done[tex]r[/tex] is the rate of work done[tex]t[/tex] is the time taken to do the workWe are looking for how long it will take each pipe to completely fill the pool
For pipe 1 working alone to fill 1 pool, the work done is 1;
[tex]w=r\times t\\\\1 = r_1 \times t_1\\\\t_1=\frac{1}{r_1}[/tex]
For pipe 2 working alone to fill 1 pool, the work done is 1;
[tex]w=r\times t\\\\1 = r_2 \times t_2\\\\t_2=\frac{1}{r_2}[/tex]
From the question, it would take 9 hours if each pipe took turns to fill half the pool. That is;
[tex]\frac{t_1}{2}+\frac{t_2}{2}=9\\\\t_1+t_2=18[/tex]
However, if both pipes worked together, it would take 4 hours for each pipe. That is;
[tex]w_1+w_2=w\\\\r_1t_1+r_2t_2=w\\\\4r_1+4r_2=1\\\\r_1+r_2=\frac{1}{4}[/tex]
Remember that [tex]r_1=\frac{1}{t_1}[/tex] and [tex]r_2=\frac{1}{t_2}[/tex]. So,
[tex]\frac{1}{t_1}+\frac{1}{t_2}=\frac{1}{4}\\\\\frac{t_1+t_2}{t_1t_2}=\frac{1}{4}[/tex]
Also recall that [tex]t_1+t_2=18[/tex]. So,
[tex]\frac{18}{t_1t_2}=\frac{1}{4}\\\\t_1t_2=72[/tex]
The only factors of 72 that satisfy the conditions
[tex]t_1+t_2=18\\\\t_1t_2=72[/tex]
are 6 and 12.
Therefore, pipe 1 will take 6 hours, and pipe 2 will take 12 hours to fill the pool if working alone.
The link below has a similar problem on rate of work
https://brainly.com/question/21485928
You earn
$10 per hour working as a manager at a grocery store.
You are required to work at the grocery store at least
8 hours per week. You also teach music lessons for
$15 per hour. You need to earn at least $120 per week,
$
do not want to work more than 20 hours
but you
per week.
a. Write and graph a system of linear inequalities
that represents the situation.
b. Identify and interpret a solution of the system.
c. Use the graph to determine whether you can work
8 hours at the grocery store and teach 1 hour of
music lessons.
We want to get a system of inequalities that models the given situation.
The solutions are:
a) The system is:
x ≥ 8x*$10 + y*$15 ≥ $120x + y ≤ 20.y ≥ 0And the graph can be seen at the end.
b) A solution can be x = 12 and y = 2
c) x = 8 and y = 1 is not a solution.
First, we need to define two variables:
x = number of hours working as a manager.y = number of hours teaching lessons.a) First, we know that you must at least 8 hours per week in the grocery store, then:
x ≥ 8
We know that you need to earn at least $120 per week, then we have the inequality:
x*$10 + y*$15 ≥ $120
And you don't want to work more than 20 hours per week, this gives:
x + y ≤ 20.
We also add the trivial restriction:
y ≥ 0
Then the system is:
x ≥ 8x*$10 + y*$15 ≥ $120x + y ≤ 20.y ≥ 0The graph can be seen at the end.
b) The solution region is the interception of the four shaded regions (is the dark blue part).
A solution in that region can be:
x = 12
y = 2
c) The point x = 8, y = 1 is graphed, you can see that it is outside the solution region, thus, this is not a solution.
If you want to learn more about inequalities, you can read:
https://brainly.com/question/2065712
Convert .45 to a fraction help for brainlist! with explaintion
Answer: 9/20
Step-by-step explanation:
Answer:
9/20
Explanation:
0.45
Since there are two numbers after the decimal point, the denominator will be 100 (two zeroes). So, 45/100.
Simplify the fraction. Divide both the numerator and the denominator by 5.
9/20
Hope this helps! :)
0(-7) helppppppppppppppppppppp
Answer:
0
Step-by-step explanation:
anything multuplied by 0 is 0
Please help me please help mee
Write an equation in slope-intercept form of the line that passes through (0, 6) and (3, -3)
Answer:
y=-3x+6
Step-by-step explanation:
Using slope formula
[tex]\frac{y_{2} -y_{1} }{x_{2} -x_{1} }[/tex](0, 6) x1, y1(3, -3) x2, y2[tex]\frac{-3-6 }{3-0}=\frac{-9}{3}=-3[/tex]Please help and please no links..thanks ¯\_(ツ)_/¯
Answer:
[tex]\frac{c}{4} +5 = 7[/tex]
Step-by-step explanation:
The wording, "the quotient of a number and 4," can be displayed as c/4. C would be our variable for the number because the question asks specifically for it. 5 more would demonstrate that we're adding 5 more to our equation. Which would result in c/4 + 5. However, since it equals 7, just add that portion to create the following equation:
[tex]\frac{c}{4} +5 = 7[/tex]
Answer:
c / 4 + 5 = 7
Hope this helps!
Step-by-step explanation:
5 + ( more ) than the quotient ( division ) of a number and ( + ) 4 is ( = ) 7
5 + c / 4 = 7
c / 4 + 5 = 7
A bike that weighs 22 pounds and 3 ounces weighs a total of ____ounces.
Answer:
355 ounces
Step-by-step explanation:
Okay! We're going to have to use some conversion factors for this problem, since we're working with two different units (pounds and ounces). We know that there are 16 ounces in a pound - that's our first conversion factor. We can use it to write up a little equation to help us:
[tex]\frac{22lbs}{1} *\frac{16oz}{1lb} + 3 = x[/tex]
"x" is the total amount of ounces. Does everything in that equation make sense? The first multiplication part tells us how many ounces are in 22 pounds, and the second part (+ 3) adds the 3 ounces that were there from the beginning. Now, it's time to calculate.
[tex]\frac{22bs}{1} *\frac{16oz}{1lb} + 3 = x\\[/tex]
[tex]\frac{352oz}{1} + 3 = x[/tex]
[tex]352+3 = x[/tex]
[tex]x=355[/tex]
So, there are 355 ounces in a bike that weighs 22 pounds and 3 ounces. Hopefully that's helpful! :)
Find the least common multiple of: 2v^2y^7 and 11v^4y^8x^3
Answer:
2v6y719x3
Step-by-step explanation:
(1): "x3" was replaced by "x^3". 2 more similar replacement(s).
STEP 1
Equation at the end of step 1
(((2v2 • y711) • v4) • y8) • x3
STEP 2
Final result :
2v6y719x3
Heyyy , can you help me please and thank you
Answer:
18
Step-by-step explanation:
Total=70.
Last week she posted= 2/5 of 70= She posted 28 last week
So, 42 left
then, she posted 4/7 of remaining (42)
4/7 of 42 is 24
42-24= 18
She still needs to post 18 flyers
HOPE THIS HELPS!
Answer:
OK, so she started with 70 fliers.
Last week, she posted 2/5 of them. 2/5 of 70 is equal to 28, so she has 28 fliers less than she started with. 70-28=42.
This week, she posted 4/7 of the remaining fliers (42). 4/7 of 42 is equal to 24. So, she has 24 less than 42, so 42-24=18.
She still needs to post 18 fliers.
Hope this helps!!!
Which number sentence is true?
A. -4.25 > -2 4/5
B. 6/11 > 6.11
C. 7/8 > -0.78
D. 14/8 > 8.1
Answer: C. Is true 7/8>-0.78
00
A student ran a distance of 33 miles each day for 5 days. Then the student ran a distance of 4 miles each day
for the next 5 days.
What was the total distance in miles the student ran during these 10 days?
10days = ... miles
= 5days × 2
= 33 × 2
= 66miles
Amir invests £2000 into an savings account.
Amir gets 4.75% per year compound interest.
Work out how much Amir will have in the account after 9 years.
Answer:
£30000
Step-by-step explanation:
I used a couculator
[tex]\sqrt{5}+\sqrt{5}=?[/tex]
[tex]\sqrt 5 + \sqrt 5 \\\\=\sqrt 5(1+1) \\\\= 2 \sqrt 5[/tex]
2x-y=5
2x-5y=-31
elimation method
Answer:
y=9, x=7
Step-by-step explanation:
2x-y=5 --> equation 1
2x-5y=-31 --> equation 2
change signs of equation 1
-2x+y=-5
solving method
-2x+y=-5 (cut -2x and 2x because -2x+2x =0)
2x-5y=-31 (likewise +y-5y and -5-31)
-4y= -36 (since -4 is multiplying on right side it will divide)
y= -36/-4 (cut negative with negative and simplify equation)
y= 9
put value of y in equation 1
2x-y=5
2x-9=5
2x= 14
x=14/2
x=7
what is the pattern you notice when dividing 10,100,1000
Answer:
Step-by-step explanation:
Image result for what is the pattern you notice when dividing 10,100,1000
When dividing by ten, move the decimal point one place to the left. Place value is the value of a digit based on its location in the number. When dividing by 100, move the decimal place two places to the left. And, remember, if there's no decimal point, assume that the decimal falls at the end of the number.
Answer:
when you divide those numbers the place value shifts by 1.
Step-by-step explanation:
1000.0 to 100.00 to 10.000 to 1.0000 to .10000
which one is correct and if you chose a,b,c,d explain why
a
b
c
d
Answer:
A. √150
Step-by-step explanation:
12² = 144
13² = 169
The only value of any of the options falling between 12 and 13 is √150
how many 3/5s are in 9/10
Answer:they are only 2
Step-by-step explanation:
3/5 + 3/5 = 6/10 so you need a 6/5 + 3/5 and it will equal 9/10
Answer:
1
Step-by-step explanation:
3/5's = 6/10 and 6/10 plus 6/10 would be 12/10 so only 1 3/5's can fit.
How many solutions does 3(x + 5) - 3 = 2(3x + 1) - 3x have? Show your work.
2noop
no
ordon
dos
SOLUTION I don’t want the answer I just wanna know how to solve it cause I’m bad at math
Answer:
No solution
Step-by-step explanation:
1.Simplify
3(x+5)-3 = 2(3x+1) -3x
3x+15-3=6x+2-3x
2.Simplify
3x+12=3x+2
3. Combine like terms
3x-3x+12-2=3x-3x+-2
10 does not equal 0
No solution
Answer:
[tex]\boxed{\boxed{\sf No\:Solution}}[/tex]
Step-by-step explanation:
[tex]\sf 3\left(x+5\right)-3=2\left(3x+1\right)-3x[/tex]
Expand: Apply distributive property:
[tex]\sf 3(x+5)-3[/tex]
[tex]\sf 3x+15-3[/tex] [tex]\sf 3x+12[/tex][tex]\sf 2(3x+1)[/tex]
[tex]\sf 3x+2[/tex][tex]\sf 3x+12=3x+2[/tex]
Subtract 12 from both sides:
[tex]\sf 3x+12-12=3x+2-12[/tex]
[tex]\sf 3x=3x-10[/tex]
Subtract 3x from both sides:
[tex]\sf 3x-3x=3x-10-3x[/tex]
[tex]\sf 0=-10[/tex]
Sides are not equal, so therefore there is no Solution.
___________________________________________
NO LINKS
2. How many solutions does this system have?
2x+y=3
6x = 9 - 3y
O one
Onone
O infinite
Otwo
Answer:
D - Two.
Step-by-step explanation:I took the test and this was the correct answer.
Rachel has 16 chocolate bars . Tracy takes 4 and asks for the remaining quarter. what would she end up with?
Answer:
Rachel ends up with 9 chocolate bars.
Step-by-step explanation:
16 - 4 = 12
quater is 1/4, so
12 / 4 = 3
12 - 3 = 9
Answer:
9 chocolate bars
Step-by-step explanation:
Rachel had 16 chocolate bars and Tracy takes (minus) 4.Now she has 12.
Tracy asks for the remaining (12) quarter. A quarter is 1/4, and a quarter of 12 is 3.
That leaves Rachel with 9, because 12 - 3 is 9.
A stone is thrown vertically upwards.its height , y ,meter from the ground after x seconds is given by the formulae x=17y-2y².find the time,in seconds,when the stone is at the height of 8 meter from the ground.
Time can't be negative so we need to get absolute value of x .
A contestant on a game show spins a wheel that is located on a plane perpendicular to the floor. He grabs the only red peg on the circumference of the wheel, which is 1.5 m above the floor (the peg is) and pushes it downward. The peg reaches a min height of 0.25 m and a max height of 2.75 m above the floor. Sketch two cycles of the graph representing the height above the ground as a function of the total distance moved. Then determine the equation of the sine function
The spin of the wheel by the contestant is an illustration of a sine function whose equation is [tex]\mathbf{y =-1.25 sin(0.8x) + 0.25}[/tex]
The wheel is 1.5 m above the floor, and the peg reaches a maximum height of 2.75 m.
So, the amplitude is:
[tex]\mathbf{A = 1.5 - 2.75}[/tex]
[tex]\mathbf{A = -1.25}[/tex]
The vertical shift is the minimum height of the peg.
So, we have:
[tex]\mathbf{D = 0.25}[/tex]
The period (T) equals one circumference.
So, we have:
[tex]\mathbf{T = (max-min)\pi}[/tex]
This gives
[tex]\mathbf{T = (2.75-0.25)\pi}[/tex]
[tex]\mathbf{T = 2.5\pi}[/tex]
The frequency (B) is then calculated as:
[tex]\mathbf{B = \frac{2\pi}{T}}[/tex]
This gives
[tex]\mathbf{B = \frac{2\pi}{2.5\pi}}[/tex]
Divide
[tex]\mathbf{B = 0.8}[/tex]
A sine function is represented as:
[tex]\mathbf{y =A sin(B(x + C)) + D}[/tex]
Substitute the calculated values
[tex]\mathbf{y =-1.25 sin(0.8(x + C)) + 0.25}[/tex]
The horizontal shift (C) is 0.
So, the function becomes
[tex]\mathbf{y =-1.25 sin(0.8x) + 0.25}[/tex]
See attachment for the graph of the equation
Read more sine function at:
https://brainly.com/question/11904902
what is equivalent to |14-20|
Answer:
7/10
Step-by-step explanation:
A line passes through the point (0, -3/2) and has a slope of 1/2. what is the eqaution of the line?
Answer:
y = 1/2x - 3/2
Step-by-step explanation:
We apply our knowledge of slope intercept form:
y = 1/2 x + b
therefore, we plug in the values for x and y getting
-3/2 = 0 + b
so b = -3/2, plug it back into the equation getting
y = 1/2x - 3/2
What is (f•g)(x)?
f(x) = 4x + 6
g(x) = -5x
(f.g)(x) = (4x + 6)(-5x) = -20x^2 -30x
ok done. Thank to me :>
Suppose you want a guitar. It costs $756. About how much would you have to save every month for 6 months to be able to buy the guitar? i assume $126?
Answer:
$126 is correct
Step-by-step explanation:
Answer:
$126/month
Step-by-step explanation:
Divide the total cost ($756) by 6 (months). We get $126/month. Six months' payment (6 times $126) will produce a total savings of $756.
The lines represented by the equations 2y - 3x = 14 and y - 3/2x= 7 are
Answer:
00000
Step-by-step explanation:
24 pens in 2 boxes How many pens in 1 box?__________
find unit rate
Solve for b
Is it square root 39?
Or
Square root 89?
Answer:39
Step-by-step explanation:
Answer:
[tex]\sqrt{39}[/tex]
Step-by-step explanation:
By the Pythagorean Theorem:
[tex]b^2+5^2=8^2[/tex]
We can rearrange this equation to find b:
[tex]b^2=8^2-5^2\\\\b^2=64-25=39\\\\\sqrt{b^2}=\sqrt{39}\\\\b=\sqrt{39}[/tex]
solve pls brainliest
Answer:
192
Step-by-step explanation:
Volume of a rectangular prism = length times width times height.
For the following prism, length = 4, width = 6 and height = 8
So volume would equal 4 * 6 * 8 = 192ft²