A swimming pool already contains
a small amount of water when you start filling it at a
constant rate. The pool contains 45 gallons of water after
5 minutes and 120 gallons after 30 minutes. Find the
average rate of change and use it to write a linear model
that relates the amount of water in the pool to the time.
Answers
Answer:
Rate of change = 3 gallons/minute
Starting volume = 30 gallons
Step-by-step explanation:
A graph of the pool's water level would be useful. The slope of the line would represent the rate of change for filling the pool. It will also help us determine the amount of water that was in the pool to start. Although it is tempting to say the rate of fill is 45gallons/5 minutes, or 9 gallons/minute, it is not correct. The pool already started with an unknown volume of water. The rate of change after 5 minutes, however, can be used. The problem states it is being added at a constant rate. Let's find an equation for a line, in the format of y=mx+b, where m is the slope (rate of change) and b is the y-intercept.
We'll let y represent the volume of water in the pool, and x will be the time in minutes. The y-intercept will give us the amount of water in the pool at the start (x = 0).
The slope can be determined between the two given points:
(5,45) and (30,120):
Slope = Rise/Run [The change in y divided by the change in x].
Rise = (120 - 45) = 75
Run = (30-5) = 25
Slope = 75/25 or 3
The line, so far, becomes y=3x + b
The slope of 3 has units of gallons/minute. It is the rate at which the pool is being filled.
We can find b, the starting volume of water, by using one of the two points in the equation and solving for b:
y=3x + b [I'll use (5,45)]
45 = 3*(5) + b
b = 30 gallons
The pool had 30 gallons to start (at x = 0(minutes))
See the graph of the line, attached.
Related Questions
A laser printer prints 9 pages per minute. Martha refilled the paper tray after it had printed 92 pages. In how many more minutes will there be a total of 245 pages printed?
Answers
17 minutes
hope this helps!
What is the sum of 7/13 and 11/26? Please help!!
Answers
Answer:
The sum of 7/13 and 11/26 is 25/26.
Step-by-step explanation:
7/13 + 11/26
The common denominator is 26
7/13 *2/2 +11/26
14/26 + 11/26
25/26
noah does half as many push-ups as joseph. joshua does 3 times as many push-ups as joseph. they complete 324 altogether. How many push-ups does joshua complete?
Answers
Answer:
112
Step-by-step explanation:
Anna saved $20 in a jar each month for 2 1/2
years. She spent 75% of her savings on a computer. How much money did Anna have left in the jar?
Answers
Answer:
20*2.5=50
50*0.75=37.5
Hope This Helps!!!
Answer:270
Step-by-step explanation:
I'll mark you brainlest if you answer this correctly please help
Answers
Answer:
Step-by-step explanation:
Answer:
D
Step-by-step explanation:
Determine which number is greater and tell how many times as great. 7×1012 and 3.5×109
Answers
need help with this asap………
Answers
Answer:
y= 32
Step-by-step explanation:
HOPE THIS HELPS :)
Choose the correct transformation.
Answers
Answer:
A
Step-by-step explanation:
First they flipped it, then they slid it.
#1: Find the value of X. (GEOMETRY)
I will give brainliest to BEST answer! fake answers will be reported.
refer to attachment!
Answers
Answer:
x = 14
Step-by-step explanation:
1. We know that all angle measures in a triangle sum to 180 degrees.
This means that 7x - 11 + 5x - 2 + 2x - 3 = 180.2. (Solving)
Step 1: Combine like terms.
[tex](7x+5x+2x)+(-11-2-3)=180[/tex] [tex]14x -16 = 180[/tex]Step 2: Add 16 to both sides.
[tex]14x - 16 + 16 = 180 + 16[/tex] [tex]14x = 196[/tex]Step 3: Divide both sides by 14.
[tex]\frac{14x}{14}=\frac{196}{14}[/tex] [tex]x = 14[/tex]Step 2: Check if solution is correct.
[tex]7(14)-11+5(14)-2+2(14)-3=180[/tex] [tex]98-11+70-2+28-3=180[/tex] [tex]180=180[/tex]Therefore, the answer is x = 14.
Q). The sum of four consecutive natural numbers is 166. What are the numbers?
Answers
Answer:
see that attachment
I hope it's help you
Let the four consecutive natural numbers are X,X+1,X+2,X+3
Their sum = X+X+1+X+2+X+3 = 4X+6
According to the given problem
Their sum = 166
⇛ 4X+6 = 166
⇛4X = 166-6
⇛4X = 160
⇛X = 160/4
∴ X = 40
X+1 = 40+1 = 41
X+2 = 40+2 = 42
X+3 = 40+3 = 43
The four consecutive natural numbers are 40,41,42,43
also read similar questions: The sum of two prime numbers is 85, what is the product of these two prime numbers? A. 85 B. 91 C. 115 D. 166
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Please I need Help!!! Solve this equation by factoring by grouping x^2-4x=12. All work must be shown and no other method will be accepted.
Answers
x² - 4x = 12
x² - 4x - 12 = 0
x² + (2x - 6x) - 12 = 0
x² + 2x - 6x - 12 = 0
x (x + 2) - 6 (x + 2) = 0
(x - 6) (x + 2) = 0
Then the solutions are x = 6 or x = -2.
help please anybody Mhm
Answers
Answer:
B
Step-by-step explanation:
Answer:
Your answer would be C
Step-by-step explanation:
Because its a ratio of integers with a nonzero denominator.
what is the value of 5/6 divded by 1/2 helpi am bad at math
Answers
Answer:
5/3 or 1 2/3
Step-by-step explanation:
when you multiply fractions, you must 'multiply by the reciprocal'
you keep the first fraction the same, then you change the operation to multiplication, and finally you flip the second fraction so the denominator becomes the numerator and vice versa
5/6 ÷ 1/2 is the same as 5/6 × 2/1 = 10/6
always reduced to lowest terms when you can . . .
10/6 equals 5/3
Answer:
1.6667 as a decimal
Step-by-step explanation:
Hope this helps! Have a great rest of your day!
I rlly don’t understand due today please help!
Answers
Answer:
a) 2x+4
b)x=8
Step-by-step explanation:
a) x+x+4 =2x +4
b) 2x+4= 20
2x = 16
x=8
Jay bought 8 packets of Chips
c) Jay: 8 x 60
=£4,80
Lauren : 12 × 60
= £7,2
Gia started to solve the equation 3(x − 10) − 5x = 2x − 26 below. They want to move the variables to the left side of the equation for their next step.
Fill in Line 4 and give the property.
Line 1: 3(x − 10) − 5x = 2x − 26 Original Problem
Line 2: 3x − 30 − 5x = 2x − 26 Distributive Property
Line 3: -2x − 30 = 2x − 26 Collect Like Terms
Line 4:
please helpp
Answers
Answer:
Subtract 2x from each side, Subtraction Property
Step-by-step explanation:
[1(23x5)]/2
Solve this questionssss
sdfghfght
Answers
Which of the following lines are perpendicular to the line y= -1/2x +4 ? (you may choose more than one answer)
A. 2x - y = 1
B. y = 2x
C. 2x + y = 1
D. 1/2x - y =2
E. 2x - y = 3
Answers
Answer:
ABE
Step-by-step explanation:
Perpendicular means the slope of the line and the answer are reciprocal to each other.
The slope of the line is -1/2, which means the slope of the answer should be 2.
From A we got: y=2x-1
B:y=2x
C:y=-2x+1
D:y=-1/2x-2
E:y=2x-3
So the answer is ABE
If f(x)=-4x+1, what is f(-x/2)?
Answers
Answer:
[tex]f(-\frac{x}{2})=-2x+1[/tex]
Step-by-step explanation:
[tex]f(x)=-4x+1[/tex]
[tex]f(-\frac{x}{2})=-4(\frac{x}{2})+1[/tex]
[tex]f(-\frac{x}{2})=-2x+1[/tex]
Last year, a website had 40,000 visitors and this year there is 37,000 visitors what is the percent change of the visitors
Answers
Answer:
-7.5 %
Step-by-step explanation:
Percent change can be calculated as
(change)/(original number) * 100, with the * 100 representing a change from decimal (which is what we get from dividing) to percent.
Here, change is (final - original) = 37000-40000 = -3000. Divide this by the original number, 40000, to get -3000/40000 = -0.075. Multiply this by 100 to get -7.5 % as our answer
Alexa has set up a lemonade stand outside her house and sells small cups and large cups of lemonade. Each small cup holds 8 ounces of lemonade and each large cup hold 16 ounces of lemonade. Alexa used 320 ounces of lemonade and sold twice as many small cups as large cups. Determine the number of small cups sold and the number of large cups sold.
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Answer:
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Step-by-step explanation:
Sarah work as a receptionist in a busy dental office she made $350.15 after 23.5 hours of work how much was Sarah paid per hour
Answers
Answer: $14.9/hr
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Solve the following compound inequality. Graph the solutions. x <2 and x> -1 Solve the compound inequality. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The solutions are enter your response here. (Simplify your answer. Type an inequality or a compound inequality.) B. The solutions are all real numbers. C. There is no solution.
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A school needs to buy new notebook and desktop computers for its computer lab. The notebook computers cost $225 each, and the desktop computers cost $250 each. How many total computers would someone buy if they get 19 notebooks and 12 desktop computers? How many total computers would someone buy if they get
n notebooks and
d desktop computers? (n+d)
Answers
Answer:
n=19
d=12
$225n+$250d=
$225(19)+$250(12)=
4275+3000
=7275
Step-by-step explanation:
which equation generates the value in the table
Answers
Answer:
A
Step-by-step explanation:
What is the value of cos (150°)?
PLEASE NO WEBSITES!
Thank you
Answers
Answer:
Cos (150) = -√3/2
Step-by-step explanation:
You can find this using a calculator. You will get −0.866025403 which is equal to -√3/2
i need to find the zeros by factoring but im stuck plss help me i think the zeros may be 0, 1, -4, and 4 but i dont know how to get them??
Answers
In this case. Factor by grouping, then you will have several parenthesis multiplied by each other. Set each to zero
The two-way table shows the estimated number of students who will enroll in three area high schools next year. A 5-column table has 4 rows. The first column has entries Mount Woodson High School, Valley High School, Riverside High School, Total. The second column is labeled Tenth grade with entries 110, 180, 160, 450. The third column is labeled Eleventh grade with entries 120, 150, 140, 410. The fourth column is labeled Twelfth grade with entries 80, 120, 200, 400. The fifth column is labeled Total with entries 310, 450, 500, 1,260. In decimal form, to the nearest tenth, what is the probability that a randomly selected Riverside High School student is in twelfth grade? 0. 2 0. 3 0. 4 0. 5.
Answers
The probability that a randomly selected Riverside High School student is in twelfth grade is 0.4 and it can be determined by using probability.
Given that,The two-way table shows the estimated number of students who will enroll in three area high schools next year.
A 5-column table has 4 rows.
The first column has entries Mount Woodson High School, Valley High School, Riverside High School, Total number of students.
The second column is labeled Tenth grade with entries 110, 180, 160, 450.
The third column is labeled Eleventh grade with entries 120, 150, 140, 410.
The fourth column is labeled Twelfth grade with entries 80, 120, 200, 400.
The fifth column is labeled Total with entries 310, 450, 500, 1,260.
We have to determine,What is the probability that a randomly selected Riverside High School student is in twelfth grade?
According to the question,The first column has entries Mount Woodson High School, Valley High School, Riverside High School, Total number of students.
The number of randomly selected Riverside High School students is in twelfth grade = 200,
And Total number of students in Riverside High School is = 500
Therefore,
The probability that a randomly selected Riverside High School student is in twelfth grade is,
[tex]\rm P(12th \ grade \students ) = \dfrac{Number \ of \ students \ in \ 12th \ grade }{Total\ number \ of \ students}\\\\ P(12th \ grade \students ) = \dfrac{200}{500}\\\\ P(12th \ grade \students )= 0.4[/tex]
Hence, The required probability that a randomly selected Riverside High School student is in twelfth grade is 0.4.
For more details about Probability refer to the link given below.
https://brainly.com/question/795909
Answer:
C
Step-by-step explanation:
please help me, i dont really understand this
Answers
Answer:To convert a mixed fraction to an improper fraction, follow these steps:
Multiply the whole number part by the fraction's denominator.
Add that to the numerator. or this might also help,
Then write the result on top of the denominator. To convert a mixed number to an improper fraction, follow these steps: Multiply the denominator of the fractional part by the whole number, and add the result to the numerator. Use this result as your numerator, and place it over the denominator you already have.
Step-by-step explanation:
Hope this help
If y varies inversely with x and y = 5 when x = 4, which equation that relates x and y?
Select one:
Answers
Hazel bought 3/5 of a kilogram of clay for the students in her pottery class. She then divided the clay evenly into pieces that were 1/5 of a kilogram. Into how many pieces did Hazel divide the clay? Write your answer as a fraction or as a whole or mixed number.
Answers
Answer:
3
Step-by-step explanation:
3/5 kg of clay are divided into 1/5 a kilogram, so how many times is 1/5 in 3/5?
equation is
[tex]=\frac{3}{5} /\frac{1}{5}\\\\=\frac{3}{5}*\frac{5}{1} \\\\=\frac{15}{5} \\=3[/tex]