The Sanders family and the Wright family each used their sprinklers last summer. The Sanders family's sprinkler was used for 20 hours. The Wright family's sprinkler was used for 35 hours. There was a combined total output of 1025L of water. What was the water output rate for each sprinkler if the sum of the two rates was 40L per hour?
Answers
The water output rate for the Sanders family's sprinkler was 25 liters per hour, and for the Wright family's sprinkler was 15 liters per hour.
Let the water output rate as "x" liters per hour and the water output rate for the Wright family's sprinkler as "y" liters per hour.
Given that the combined total output of water from both sprinklers was 1025L, we can set up the following equation:
20x + 35y = 1025
We also know that the sum of the two rates is 40L per hour:
x + y = 40
x = 40 - y
Substituting this value of x into the first equation:
20(40 - y) + 35y = 1025
800 - 20y + 35y = 1025
15y = 225
y = 15
Substituting this value of y back into the second equation:
x + 15 = 40
x = 25
Therefore, the water output rate for the Sanders family's sprinkler was 25 liters per hour, and for the Wright family's sprinkler was 15 liters per hour.
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Related Questions
Marina walks from the police station at (-10, -4) to her friend Marissa’s house at (3, -8). She stops half way at a fast food restaurant to buy a soda. What are the coordinates where she stops?
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What is (f * g * h)(x) Refer the the image below.
Answers
If µ = 400 and s = 100 the probability of selecting at random a score less than or equal to 370 equals ____.
Answers
The probability of selecting at random a score less than or equal to 370 is approximately 0.3821.
To find the probability of selecting at random a score less than or equal to 370 from a normal distribution with a mean [tex](\( \mu \))[/tex] of 400 and a standard deviation [tex](\( s \))[/tex] of 100, we can use the z-score formula and the standard normal distribution table.
The z-score formula is given by:
[tex]\[ z = \frac{x - \mu}{s} \][/tex]
Where:
- x is the value of the random variable (370 in this case)
- [tex]\( \mu \)[/tex] is the mean (400)
- s is the standard deviation (100)
Substituting the given values into the formula:
[tex]\[ z = \frac{370 - 400}{100} = -0.3 \][/tex]
Now, we look up the probability corresponding to z = -0.3 in the standard normal distribution table. The probability of selecting a score less than or equal to 370 is the cumulative probability up to z = -0.3.
From the standard normal distribution table, the cumulative probability corresponding to z = -0.3 is approximately 0.3821.
Therefore, the probability of selecting at random a score less than or equal to 370 is approximately 0.3821.
a store buys a baseball cap for $5 and sells it for $20. what is the profit
Answers
20-5
You want to place a towel bar that is 10 1⁄4 inches long in the center of a door that is 26 1⁄3 inches wide. How far should you place the bar from each edge of the door?
Answers
bar is 10 1/4" so center would be 10 1/4 / 2 = 5 1/8"
door is 26 1/3" so center would be 26 1/3 / 2 =13 1/6
13 1/6 - 5 1/8 = 8 1/24 inches from the edge
Please help.. I got stuck on this question please help and explain
Sam earned $150 last week. Jay earned $130 last week. They combined their money and decided to donate ¼ of their total amount to a charity. Then, they spent 40% of the remaining amount at an amusement park. Jay claims that they only have 35% of their original combined total left.
Is jay right or wrong?
Answers
they donated 1/4 of the total amount....1/4(280) = 280/4 = 70....so now they have 280 - 70 = 210
then they spent 40%.....210 - 0.4(210) = 210 - 84 = 126..what they have left
35% of 280 = 0.35(280) = 98
Jay is not correct
Evaluate 11x -4 when x = -4
Answers
11x - 4, x = -4
11(-4) - 4 = -44 - 4 = -48
Hope it helped!
11x-4=-44
A 25-foot-long footbridge has two diagonal supports that meet in the center of the bridge. Each support makes a 65∘ angle with a short vertical support.
Answers
What is a polynomial with a single root at x = -8 and a double root at x = -2?
Answers
The polynomial equation will be x³ +12x² +36x+32 =0
What are the roots of a polynomial Equation ?The roots of a polynomial equation is the value at which it will satisfy the quadratic equation , i.e. function (x) = 0 at the root .
It is given that x = -8 is a single root and
x = -2 is double root
x+8 = 0
(x+2 )(x+2)=0 (double root)
The polynomial equation will be
(x+8)(x+2 )(x+2 )=0
(x+8)( x² +4+4x) = 0
x³ +4x+4x²+8x²+32+32x = 0
x³ +12x² +36x+32 =0
Therefore the polynomial equation will be x³ +12x² +36x+32 =0
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Typographic errors in a text are either nonword errors (as when "the" is typed as "teh") or word errors that result in a real but incorrect word. Spell-checking software will catch nonword errors but not word errors. Human proofreaders catch 70% of word errors. You ask a fellow student to proofread an essay in which you have deliberately made 10 word errors. What is the smallest number of misses m with P(X ≥ m) no larger than 0.05? You might consider m or more misses as evidence that a proofreader actually catches fewer than 70% of word errors.
Answers
The probability that a proofreader who catches 70% of the word errors misses exactly 7 out of 10 will be 0.3504.
How to calculate the probability?It should be noted that this is a binomial distribution.
From the information given, the human proofreaders catch 70% of word errors and a student was asked to proofread an essay in which you have deliberately made 10 word errors.
Here, n = 10
p = 0.3,
q = 1 - 0.3 = 0.7.
The probability will be:
= 1 - (10C0 × 0.3ⁿ × 0.7^10 + 10C1 × 0.3 × 0.7^9 + 10C2 × 0.3² × 0.7^8 + 10C3 × 0.3³ × 0.7^7)
= 1 - 0.6496
= 0.3504
In conclusion, the probability is 0.3504.
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How did the forces of liberalism and nationalism affect events in the united states during the 1800s?
Answers
6578 divided 34
20\5
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6578 by 34, and in the other you divide 6589 by 25.
I arbitrarily choose to focus on the second:
______________
25 / 6589
25 goes into 65 twice, with a remainder of 15:
______2_____
25 / 6589
50
-------------
158 25 goes into 158 6 times, with a remainder of 8.
Can you now finish this long division?
Find 10-3 write the substraction fact two ways
Answers
13-7
the substraction fact two ways.
And 10 + (-3) = 7
56of the 90pets in the pet show are cats 4/5of the cats are calico cats. What fraction of the pets are calico cats?
Answers
In a sample of 200 students, what is the probability that over 31% of the sample has ap credit?
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Evaluate the line integral, where c is the given curve. (x + 9y) dx + x2 dy, c c consists of line segments from (0, 0) to (9, 1) and from (9, 1) to (10, 0)
Answers
The first line segment can be parameterized by [tex]\mathbf r_1(t)=\langle0,0\rangle(1-t)+\langle9,1\rangle t=\langle9t,t\rangle[/tex] with [tex]0\le t\le1[/tex]. Denote this first segment by [tex]C_1[/tex]. Then
[tex]\displaystyle\int_{C_1}\langle x+9y,x^2\rangle\cdot\mathbf dr_1=\int_{t=0}^{t=1}\langle9t+9t,81t^2\rangle\cdot\langle9,1\rangle\,\mathrm dt[/tex]
[tex]=\displaystyle\int_0^1(162t+81t^2)\,\mathrm dt[/tex]
[tex]=108[/tex]
The second line segment ([tex]C_2[/tex]) can be described by [tex]\mathbf r_2(t)=\langle9,1\rangle(1-t)+\langle10,0\rangle t=\langle9+t,1-t\rangle[/tex], again with [tex]0\le t\le1[/tex]. Then
[tex]\displaystyle\int_{C_2}\langle x+9y,x^2\rangle\cdot\mathrm d\mathbf r_2=\int_{t=0}^{t=1}\langle9+t+9-9t,(9+t)^2\rangle\cdot\langle1,-1\rangle\,\mathrm dt[/tex]
[tex]=\displaystyle\int_0^1(18-8t-(9+t)^2)\,\mathrm dt[/tex]
[tex]=-\dfrac{229}3[/tex]
Finally,
[tex]\displaystyle\int_C(x+9y)\,\mathrm dx+x^2\,\mathrm dy=108-\dfrac{229}3=\dfrac{95}3[/tex]
To evaluate the given line integral, you need to parameterize the curve composed of two segments. Then, you solve the integrals along the two separate segments and take the sum.
Explanation:To evaluate the line integral where the curve c consists of line segments from (0, 0) to (9, 1) and from (9, 1) to (10, 0) for the function (x + 9y) dx + x² dy, we need to parameterize the curve and solve the integral.
First, we parametrize the line segments. For the segment from (0, 0) to (9, 1), we have x = 9t and y = t for t in [0, 1]. For the segment from (9, 1) to (10, 0) let x = 9 + s and y = 1 - s for s in [0, 1].
Then, we integrate along the first and second segments separately with respect to t. For the first segment, the integral is ∫(9t + 9t) d(9t) + ∫(81t²) dt = ∫18t dt + ∫81t² dt. For the second segment, the integral is ∫(9 + s + 9(1 - s)) ds + ∫(81 + 2 * 9 * s + s²) d(1 - s) = ∫ds + ∫s² ds.
We then evaluate these integrals over the respective bounds, sum them up and that gives the line integral along the path described.
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find value of m=30 and n=18. m-n÷3=8
Answers
30 - n/3 = 8
-n/3 = -22
-n = -66
n = 66
when n = 18
m-18/3 = 8
m - 6 = 8
m = 8 + 6
m = 14
hope this helps
paige mows 1/6 acre in 1/4 hour.How many acres does paige mow per hour?
Answers
---- x ----- = ------- = ------ acres
6 1 6 3
Hope this helps! :)
Divide 1/6 acre by 1/4 hour. I noticed right away that multiplying "1/4 hour" by 4 results in 1. So, I multiplied both sides of this rate by 4, obtaining
4/6 acre per 1 hour, or 2/3 acre per hour, or 2/3 acre/hr.
Of all numbers whose difference is 4, find the two that have the minimum product.
Answers
The two numbers whose difference is 4 will be +2 and -2. The two have the minimum product is -4.
What is the number?A number is a mathematical entity that can be used to count, measure, or name things. For example, 1, 2, 56, etc. are the numbers.
It is given that, there are two numbers whose difference is 4 and it must have a minimum product.
We have to apply arithmetic operation operations in which we do the addition of numbers, subtraction, multiplication, and division. It has basic four operators that are +, -, ×, and ÷.
Suppose one number is x and the other x−4.
The minimum product is,
=x(x−4)
=x²−4x
Differentiate both sides to obtain minimum value,
=2x-4
2x=4
x=2
The other number is,
=x−4
=2-4
=-2
Thus, the two numbers whose difference is 4 will be +2 and -2. The two have the minimum product is -4.
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You received 1⁄3 pound of candy from your grandmother, 1⁄2 pound of candy from your sister, but your best friend ate 1⁄5 pound of candy. How much candy do you have left?
Answers
1/3 + 1/2 = 2/6 + 3/6 = 5/6
5/6 - 1/5 = 25/30 - 6/30 = 19/30 pounds left
What is the reflection image of R across the y-axis?
(3, 2)
(–2, 0)
(0, 2)
(–3, –2)
Answers
answer
(3, 2)
Answer: (3,2)
Step-by-step explanation:
From the given picture , it is given that the point R = (-3,2)
We know that the rule of reflection across y axis is :
[tex](x,y)\rightarrow\ (-x,y)[/tex] i.e.the polarity of x coorinate changes.
Therefore, the reflection image of R across the y-axis will be :-
[tex](-3,2)\rightarrow\ (3,2)[/tex]
Hence, the reflection image of R across the y-axis =(3,2)
HECTOR PLANTED 185 FLOWERS IN 2 DAYS THERE WERE 5 VOLUNTEERS INCLUDING HECTOR WHO EACH PLANTED ABOUT THE SAME NUMBER OF FLOWERS ABOUT HOW MANY FLOWERS DID THEY PLANT
Answers
Marisol is preparing a care package to send to her brother. The package will include a board game that weighs 4 lb and several 14 lb snack packs. The total weight of the care package must be less than 25 lb.
Drag and drop the answer into the box.
Question Answer
Which statement describes the solution to this inequality?
Marisol must send less than 1 snack pack.Marisol must send fewer than 21 snack packs.Marisol must send fewer than 84 snack packs.Marisol must send fewer than 100 snack packs.
Answers
1/4s < 25 - 4
1/4s < 21
s < 21 / (1/4)
s < 21 * 4/1
s < 84
Marisol must send fewer then 84 snack packs <=
writing it out like this
4 1/4 25 those are the numbers where those go are like this
4x - 1/4 < 25 then move on to the next line on here we write out
4x + 1/4 - 1/4 < 25 + 1/4 (The reason why i put + 1/4 is because you have to isolate the variable by doing addition as well And i always find it easier to convert the fractions to decimals then after you make that line you make the next one like this you have to add 1/4 to 4x then take it away (which is 4x) then put that to the side like this 4x ? ? then we need to find those two ?s by adding 25 and 1/4 (or o.25) which is 25.25 then we need to add that to the second answer 4x ? 25.25 when you have this you need to find out which one is bigger so it is 4x<25.25 (or 25 1/4) then we need to divide 4 and 25.25 to get 6.25 so
the answer is x < 6.25 so c is your awnser
Which quantity is proportional to 15⁄3?
Answers
The answer is 5 because 15/3=5
Product of prime factors for 60 = 2x2x3x5
How do i write this in index form?
I have tried by simplifying so it is 2 to the power of 2 x 3 x 5
It stills says it is incorrect, anyone know?
Answers
60 = 2,2,3,5
Index Form = [tex]2^2 \times 3 \times 5[/tex]
They might want something like below for the index form
[tex]2^2 \times 3^1 \times 5^1[/tex]
The correct index form for the product of prime factors of 60, which is 2x2x3x5, is 2^2 x 3 x 5.
Explanation:The product of prime factors for 60 is indeed 2x2x3x5. To write this in index form, we group the same numbers together and count how many there are. Then we use the base and exponent form to write it. Here, 2 is repeated twice. So, 2x2 can be written as 2^2. The primes 3 and 5 are each given once, so, we do not write powers for them. Therefore, the correct index form is 2^2 x 3 x 5.
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HELP ASAP PLEASE!!!!!!!!!!!!!!
Answers
The answers are given in Figure 2 which is also attached.
===================================================================================================================
Focus on the first Magic Square for now (the one in the top row, left side).
The middle row has 9+6+3 = 18 as the magic constant (aka magic sum). Every row, column and diagonal must add to this constant
A = 7 because the first column of values must add to 18
A+9+2 = A+11 = 18 leads to A = 7
----------
C = 10 since that solves 2+6+C = 18 (northeast diagonal)
----------
Solve the equation A+6+E = 18 for E to get E = 5 (plug in A = 7)
As a check, note how C+3+E = 10+3+5 = 18
----------
We know that A = 7 and C = 10 so B must be B = 1 since A+B+C = 7+1+10 = 18
----------
Similarly, 2+D+E = 18 and E = 5, so D must be 11.
As a check, note how B+6+D = 1+6+11 = 18
----------
----------
In summary we have
A = 7
B = 1
C = 10
D = 11
E = 5
See Figure 2 for the completed magic square
----------
Check:
Row1: 7+1+10 = 18
Row2: 9+6+3 = 18
Row3: 2+11+5 = 18
Column1: 7+9+2 = 18
Column2: 1+6+11 = 18
Column3: 10+3+5 = 18
NorthEast Diagonal: 2+6+10 = 18
NorthWest Diagonal: 7+6+5 = 18
As you can see, we get the same magic constant of 18
===================================================================================================================
Second Magic Square (Top Right)
For this magic square, the magic constant isn't known. So this is mainly a guess and check type of problem. This is what I got
F = 9
G = 6
H = 10
J = 12
K = 5
See Figure 2 for the completed magic square
----------
Check:
Row 1: 11+4+9 = 24
Row 2: 6+8+10 = 24
Row 3: 7+12+5 = 24
Column 1: 11+6+7 = 24
Column 2: 4+8+12 = 24
Column 3: 9+10+5 = 24
NorthEast Diagonal: 7+8+9 = 24
NorthWest Diagonal: 11+8+5 = 24
===================================================================================================================
Third Magic Square at the very bottom
The magic constant is 12+6+7+9 = 34
----------
Bottom row: 13+3+S+16 = 34 which solves to S = 2
----------
Northeast Diagonal: 13+Q+7+4 = 34 which solves to Q = 10
----------
Second Column: 3+Q+6+M = 34 turns into 3+10+6+M = 34 after substitution and that solves to M = 15
----------
For values R, P, L and N, I couldn't figure out an algebraic way to solve for them. So I had to resort to trial and error (guess and check). This is what I got
R = 11
P = 8
L = 1
N = 14
----------
----------
In summary we have
L = 1
M = 15
N = 14
P = 8
Q = 10
R = 11
S = 2
See Figure 2 for the completed magic square
----------
Check:
Row 1: 1+15+14+4 = 34
Row 2: 12+6+7+9 = 34
Row 3: 8+10+11+5= 34
Row 4: 13+3+2+16 = 34
Column 1: 1+12+8+13 = 34
Column 2: 15+6+10+3 = 34
Column 3: 14+7+11+2 = 34
Column 4: 4+9+5+16 = 34
NorthEast Diagonal: 13+10+7+4 = 34
NorthWest Diagonal: 1+6+11+16 = 34
How many binary digits does it take to represent the decimal number 2013?
Answers
So there will be 10 + 1 = 11 digits Answer
It takes 11 binary digits to represent the decimal number 2013. Decimals are numbers that have two parts: a whole number part and a fractional part separated by a decimal point.
What is meant by decimal number?A decimal is a number with a whole and a fractional part. Decimal numbers are between integers and represent numerical value for whole plus some fraction of a whole. Decimals are numbers that have two parts: a whole number part and a fractional part separated by a decimal point. 12.5 is a decimal number, for example. (12)10 and (300)10 are two examples of decimal numbers. Thus, we can say that the Decimal Number System is the number system that uses the numbers 0 to 9 and has a base of 10, and each digit in this system has a power value of 10.Therefore, the correct option is C) 11
The complete question is:
How many binary digits does it take to represent the decimal number 2013?
a) 16
b) 8
c) 11
d) 2013
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A theater group made appearances in two cities. The hotel charge before tax in the second city was $500 lower than in the first. The tax in the first city was 3.5% , and the tax in the second city was 7.5% . The total hotel tax paid for the two cities was $347.50 . How much was the hotel charge in each city before tax?
Answers
a = charges before tax on first city
b = charges before tax on second city
how much is 3.5% of a? (3.5/100) * a, 0.035a.
how much is 7.5% of b? (7.5/100) * b, 0.075b.
the taxes for both cities, summed up to 347.50
so, 0.035a + 0.75b = 347.50
we also know that, whatever "a" may be, the second city charged $500 less, so b = a - 500.
[tex]\bf \begin{cases} \boxed{b}=a-500\\ 0.035a+0.075b=347.5\\ --------------\\ 0.035a+0.075\left( \boxed{a-500} \right)=347.5 \end{cases} \\\\\\ 0.035a+0.075a-37.5=347.5\implies 0.110a=385 \\\\\\ a=\cfrac{385}{0.11}\implies a=3500[/tex]
how much did the second city charge? well, b = a - 500.
what is 62 1/2% converted as a fraction
Answers
How do I find Primefactor of 150
Answers
2 75
3 25
5 5
5 1
2 * 3 * 5* 5
Starting with 150, determine some of the factors: 150 = 15(10)
Continue: 3 5 2 5 = {2, 3, 5} None of these can be factored, so the prime factors of 150 are {2, 3, 5}. Of course, you could include 1 as a prime factor, in which case the prime factor list would be {1, 2, 3, 5}.