Ann is adding water to a swimming pool at a constant rate. The table below shows the amount of water in the pool after different amounts of time.
Time (minutes) 8, 12, 16, 20
Water (gallons) 153,197,241,285
Answer the following questions.
Choose the statement that best describes how the time and the amount of water in the pool are related. Then give the value requested.
As time increases, the amount of water in the pool decreases.
gallons per minute
As time increases, the amount of water in the pool increases.
gallons per minute
(b)How much water was already in the pool when Ann started adding water?
gallons
Answers
Answer:
(a) As time increases, the amount of water in the pool increases.
11 gallons per minute
(b) 65 gallons
Step-by-step explanation:
From inspection of the table, we can see that as time increases, the amount of water in the pool increases.
We are told that Ann adds water at a constant rate. Therefore, this can be modeled as a linear function.
The rate at which the water is increasing is the rate of change (which is also the slope of a linear function).
Choose 2 ordered pairs from the table:
[tex]\textsf{let}\:(x_1,y_1)=(8, 153)[/tex]
[tex]\textsf{let}\:(x_2,y_2)=(12,197)[/tex]
Input these into the slope formula:
[tex]\textsf{slope}\:(m)=\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{197-153}{12-8}=\dfrac{44}{4}=11[/tex]
Therefore, the rate at which the water in the pool is increasing is:
11 gallons per minute
To find the amount of water that was already in the pool when Ann started adding water, we need to create a linear equation using the found slope and one of the ordered pairs with the point-slope formula:
[tex]y-y_1=m(x-x_1)[/tex]
[tex]\implies y-153=11(x-8)[/tex]
[tex]\implies y-153=11x-88[/tex]
[tex]\implies y=11x-88+153[/tex]
[tex]\implies y=11x+65[/tex]
When Ann had added no water, x = 0. Therefore,
[tex]y=11(0)+65[/tex]
[tex]y=65[/tex]
So there was 65 gallons of water in the pool before Ann starting adding water.
#a
Take 2 points
(12,197)(16,241)Slope=Rate of water flow
m=241-197/16-12m=44/4m=11The water increases with respect to time as slope is positive.
It's
11gallons/min#2
We need amount of water when time is 0
So
Let that be y and point is (0,y) and comaparing with (8,153)
153-y/8=11153-y=88y=153-88y=65gallonsRelated Questions
The length of a rectangular floor is two ft more than its width. If the area of the floor is 63 ft, find the length and the width of the floor.
Answers
Answer:
width = 7 and length = 9
Step-by-step explanation:
Let's assume width = w, and length = 2 + w
So area of a rectangle = width * length
63 ft² = w (2 + w)
63 = 2w + w²
w² + 2w - 63 = 0
Use the quadratic formula to solve this
here, a = 1, b = 2 and c = -63
w = 7 or -9
The dimensions of a rectangle cannot be negative. So we take the dimension, w = 7.
Width = 7 and Length = 7+2 = 9
Reggie has $240 in a savings account at the beginning of the summer. He wants to have at least $450 in the account by the end of the summer. He deposits $35 each week. What is the shortest amount of time Reggie needs to deposit money into his account?
Answers
Answer:
6 weeks
Step-by-step explanation:
Since Reggie has $240 in the account already we first subtract this $240 from the $450. 450 - 240 = 210. Now since he deposits $35 a week and needs to hit at least 210 to reach is goal of $450 for the summer then we need to divide 210/35 to see the amount of weeks. 210/35 = 6. So 6 weeks is the shortest time.
The volume of a sphere is V=4/3 pie r 3
where r is the radius of the
sphere. Determine the volume of the sphere where the radius is
measured at 6 inches.
a 288pie 3
b 216 pie 3
C 144 pie 3
d 48 pie 3
Answers
Answer:
A. 288pi in^3
Step-by-step explanation:
s
ee image
WILL MARK BRAINLIEST IF THERES WORK SHOWN AND ITS RIGHT PLEASE
An expression is shown below:
2x³ + 10x² - 4x2y - 20xy
Part A: Rewrite the expression by factoring out the greatest common factor
Part B: Factor the entire expression completely. SHOW THE STEPS OF YOUR WORK.
Answers
2x^3 + 10x^2 -8xy -20xy.
Then collect like terms -8-20 to get
2x^3 + 10x^2 -28xy
Then you factor out GCF which is 2x
2x(x^2) + 5x -14y which is the final answer
1. Suppose a married man and woman both carry the gene for cystic fibrosis but don't
have the disease themselves. According to the laws of genetics, the probability that
any child they have will develop cystic fibrosis is .25.
a) Explain what this probability means.
b) If the couple has 4 children, is one of them guaranteed to have cystic fibrosis.
Answers
Answer:
a) Probability is the chance or possibility that an event will occur.
b) No,
just as the question states there is a 25% chance of this event happening in a child, so no matter the number of children they have the chances of them getting cystic fibrosis is 25% for each child and it's never guaranteed.
Use the quadratic formula to solve for X.
Round your answer to the nearest hundredth.
If there is more than one solution, separate them with commas.
Answers
So you would make your answer equal to zero then plug in the proper variables and your answers would be 2.11 and -1.11 don’t forget to seperate them with commas
What is the equation for the function shown in FACTORED FORM?
Answers
Answer:
f(x) = (x + 1)(x - 4)
Step-by-step explanation:
let f be the function
FACTORED FORM of f :
f(x) = a(x - p)(x - q)
Where p and q are the roots/zeros of f
and ‘a’ is a real number.
=================================
Find p and q :
The roots of f are the x-coordinates where the graph crosses the x-axis, which can be read from the graph: x = -1 and x = 4 ⇒ p = -1 and q = 4.
then f(x) = a(x + 1)(x - 4)
Find ‘a’ :
f(3) = -4 ⇒ a((3) + 1)((3) - 4) = -4 ⇒ a(4)(-1) = -4 ⇒ -4a = -4 ⇒ a = 1
Therefore, f(x) = (x + 1)(x - 4)
Norman gave 1/3 of his money to his wife. He divided the remainder equally between his 3 children. What fraction of his money did each of his children receive?
Answers
Methamatics
I was absent the entire time my teacher taught this lesson, please help me
Answers
Answer:
1 - 4/9
2 - 1/9
3 - 5/9
Step-by-step explanation:
1 - Look on the left side for all two-letter combinations with only one R. We can see four. (YR, GR, RG, RY). Divide by the total number of outcomes (9).
2 - There is only one with two yellows, so divide 1 by 9.
3 - Same as before, we find 4 with 1 green and 1 with 2 green. We have to include the new one since it says atleast one. Add 1 and 4 and then divide by 9.
I need this asap
13 points (SHOW WORK)
Answers
Answer: 23
6*6=36 total area
3*3=9
2*2=4
9+4=13
36-13=23 shaded area
In a Crystal Light container, the ratio of strawberry flavored packages to orange flavored packages are 8 to 4. Based on this ratio, how many orange flavored packages will you find in a Crystal Light container with a total of 96 packages?
Answers
Answer:
32
Step-by-step explanation:
With the ratio 8:4 we can assign variables.
8x+4x=96
12x=96
x=8
Subsitute to ratio: 8x:4x
64:32
32 orange packages
Hope this helps
In a class of 35 students, 20 offer Physics, 18 offer Chemistry and 2 offer neither Physics nor Chemistry. i) Illustrate the information on a Venn diagram. ii) How many students offer all the two subjects? ii) How many students offer Physics? iv) How many students offer only one subject?
Answers
Answer:
Given:
35 = Total number of students20 = Physics students18 = Chemistry students2 = Neither Physics or Chemistry studentsTo construct the Venn diagram:
Draw 2 circles overlapping.Label one P (for Physics) and the other C (for Chemistry)Draw a box around the circles.
As 2 students study neither subject, place the number 2 in the box outside the circles.
Calculate the number of students who study both subjects (central overlapping section):
Physics students + Chemistry students + neither students - Total students
= 20 + 18 + 2 - 35 = 5
Place the number 5 in the central overlapping section.
⇒ Left section = Physics students - both subjects
= 20 - 5
= 15
⇒ Right section = Chemistry students - both students
= 18 - 5
= 13
i) See attachment
ii) Physics and Chemistry = 5 students
iii) Physics only = 15 students
iv) One subject only = 15 + 13 = 28 students
1. what is the product of 3.62 and 9.8?
2. Express 5/6 as a percentage
3. find 500,000 less than 1031001 ?
4. Express 75% as a fraction in the lowest term .
5. Express 2.50 as a percentage
6. simplify 18 + 0.8 - 1.293
7. find the cost of a shirt with a price tag of £29•00
8. Anna was given £50.00.she bought a mathematical set for £15.50 and an exercise book £2.30.how much change will she receive .
Answers
Answer:
1. 35.476
2. 83.33%
3. 531001
4. 3/4
5. 250%
6. 17.507
7. £29•00
8. 32
Step-by-step explanation:
math is done on calculator :)
PLSSS HELP IF YOU TURLY KNOW THISS
Answers
Answer:
La respuesta es A
Step-by-step explanation:
simplemente tienes que multiplicar 7 x 3 que te da 21 y luego tienes que sumar el 2 del numerador (siempre multiplica el o los enteros por el denominador y sumale el numerador)
Answer:
A
Step-by-step explanation:
The larger number in a mixed number represents how many "wholes" of the fraction there are. The fraction in a mixed number is sort of like the "leftovers", the amount that doesn't fit into a whole number. In this case, the whole number is 7, meaning there are 7 amounts of 3/3. You would multiply the whole number by the number in the denominator of the fraction, which would equal 21. The improper fraction of the whole number would be 21/3 (21 divided by 3 equals 7). Now you would add that to the fraction 2/3. The answer would be 23/3.
I hope this makes some type of sense, I didn't explain it very well.
What is the 43rd term of a Arithmetic sequence 3, 5, 7
Answers
Answer:
87
Step-by-step explanation:
common difference = d = 2
an = a1 + (n-1)*d
a43 = 3 + 42*2 = 87
How is perimeter helpful in daily life?
Answers
Answer:
so you can know how long an objects size on the outside
Are the ratios 8:3 and 4:1 equivalent?
Answers
8/3 = 2.7
4/1 = 4
2.7 ≠ 4
Answer:
No.
Step-by-step explanation:
8:3 = 8/3
4:1 = 4/1 = 8/2
8/2 is not = 8/3
I need help, I have a test tomorrow and I didn't understand this exercise
Answers
Answer:
Step-by-step explanation:
Circumference = 2(pi)r
Radius = Circumference/2(pi)
Circumference = 37.68
Radius = 37.68/2(pi)
Radius = about 59.18760559
What is the completely factored form of f(x)=x^3+5x^2+16x+80 ?
f(x)=(x−5)(x−4i)(x+4i)
f(x)=(x+5)(x−4i)(x+4i)
f(x)=(x−5)(x−4)(x+4)
f(x)=(x+5)(x−4)(x+4)
Answers
Answer:
B) [tex]f(x)=(x+5)(x-4i)(x+4i)[/tex]
Step-by-step explanation:
[tex]f(x)=x^3+5x^2+16x+80\\\\f(x)=x^2(x+5)+16(x+5)\\\\f(x)=(x^2+16)(x+5)\\\\f(x)=(x-4i)(x+4i)(x+5)[/tex]
Thus, the second choice is correct.
pls help me classify this
Answers
First image -Pentagon(Five sides).
Second image-Equilateral triangle(All sides are equal).
Reuben has bought 30 pounds of dog food. He feeds his dog 3/5 pounds for each meal. For how many meals will the food last?
Answers
Answer:
50
Step-by-step explanation:
3*50=150. 150/5=30 pounds
Use the information in the diagram to find the length of segment AD. Round your answer to the nearest hundredth.
Answers
If the length of the side AB is 39.21 then the length of the side AD will be 21.61. Then the correct option is B.
What is a right-angle triangle?It's a form of a triangle with one 90-degree angle that follows Pythagoras' theorem and can be solved using the trigonometry function. The Pythagoras theorem states that the sum of two squares equals the squared of the longest side.
The length AD is given as
AD = AB - BD
AD = AB - 17.6
Then the value of AB will be given by the Pythagoras theorem.
AB² = BC² + CA²
AB² = 26.5² + 28.9²
AB² = 1537.46
AB = 39.21
Then the value of AD will be
AD = 39.21 - 17.6
AD = 21.61
More about the right-angle triangle link is given below.
https://brainly.com/question/3770177
#SPJ1
Find areas of the triangles.
Answers
Answer:
2.75
Explain
1 3/5 = 8/5
3 7/16 = 55/16
8/5 x 55/ 16 = 440/80
440/80 : 2 = 5.5
5.5 / 2 = 2.75
Simple as that
You can check the calculator
Answer:
2.72
Step-by-step explanation:
1 3/5 is 1.6 and 3 7/16 is 3.4 so 1.6 x 3.4=5.44 and 5.44/2 is 2.72 sq u
Write and solve an addition or subtraction equation to find the missing angle measure
Answers
Answer:
n = 60°
Step-by-step explanation:
60° + n + 60° = 180° ( straight line angles)
-> n + 120° = 180°
-> n = 180° - 120°
-> n = 60°
The measure of the missing angle can be found using the equation 120 + n = 180 and the value of n is 60°.
What are Linear Pair of Angles?Linear pair of angles are the pair of angles formed when two lines are intersected at a point forming on a line.
Sum of the measures of angles of linear pair is supplementary.
Given is a line on which some shapes are drawn.
Clearly, it can be seen that,
The three angles 60°, n and 60° forms a linear angles since all are formed on a line.
So the sum is 180°.
60 + 60 + n = 180
120 + n = 180. is the required equation.
Solving,
n = 180 - 120 = 60°
Hence the value of n is 60 degrees.
Learn more about Linear Angles here :
https://brainly.com/question/29247673
#SPJ2
what is the value of the expression 1 cubed, 2 cubed, and 3 cubed
Answers
1³ + 2³ + 3³
1 + 8 + 27
36
hope it helps..!!!
Please help me geometry proof for trapezoid
Answers
A trapezoid is a quadrilateral that has two parallel sides with a height.
The proof for trapezoidFrom the diagram, AK = 1/2(AD-BC)
The combination of the bases of the equilateral triangle and the parallelogram is = the base of the trapezoid.
Therefore, BC = AD - 2AK
Make AK the subject of formula,
AK= 1/2 (AD -BC)
From the second equation given,KD = 1/2(AD - BC). This is wrong because of the following,
BC is parallel to KD.
Therefore length of KD = BC - AK and not KD = 1/2(AD - BC).
Learn more about trapezoid here:
https://brainly.com/question/4758162
#SPJ1
Solve these pls I will give 25 points
Answers
Answer:
108 minutes
Step-by-step explanation:
because 45/5=9 and 180/20=9 so multiply 12 by 9 12x9=108
Find the y-intercept of the line 11x - 8y = -1.
write your answer as an integer or as a simplified proper or improper fraction, not as an
ordered pair.
submit
Answers
Answer:
1/8
Step-by-step explanation:
I'd start by rearranging the terms for y:
11x-8y=-1
-8y=-1-11x
y=[tex]\frac{-1-11x}{-8}[/tex]
The x-intercept is found when x equals 0, so substitute 0 for x in this new equation to find the y-intercept:
[tex]y=\frac{-1-11x}{-8} \\y=\frac{-1-11(0)}{-8}\\ y=\frac{-1-0}{-8} \\y=\frac{-1}{-8}\\ y=\frac{1}{8}[/tex]
The y-intercept is 1/8
Solve x^2 =-25, where x is a real number.
Simplify your answer as much as possible.
If there is more than one solution, separate them with commas.
If there is no solution, click on "No solution".
Answers
Answer: x = ±5i
Step-by-step explanation:
√x2 = √−25
x = √−1 ∗ 25
x = i√25
x = ±i5
What is true about the domain and range of the function? the domain is all real numbers less than or equal to 4, and the range is all real numbers such that –3 ≤ x ≤ 1. the domain is all real numbers such that –3 ≤ x ≤ 1, and the range is all real numbers less than or equal to 4. the domain is all real numbers, and the range is all real numbers less than or equal to 4. the domain is all real numbers less than or equal to 4, and the range is all real numbers.
Answers
The domain is all real numbers, and the range is all real numbers less than or equal to 4.
How to determine the true statement?The equation of the function is given as:
f(x) = -(x + 3)(x -1)
The above function is a quadratic function, and the domain of a quadratic function is the set of all real numbers
Expand the function
f(x) = -(x² + 3x - x - 3)
f(x) = -(x² + 2x - 3)
Expand
f(x) = -x² - 2x + 3
Differentiate
f'(x) = -2x - 2
Set to 0
-2x - 2 = 0
Add 2 to both sides
-2x = 2
Divide through by -2
x = -1
Substitute x = -1 in f(x)
f(-1) = -(-1 + 3)(-1 -1)
Evaluate
f(-1) = 4
This means that the maximum value of the function is 4
Hence, the domain is all real numbers, and the range is all real numbers less than or equal to 4.
Read more about domain and range at:
https://brainly.com/question/10197594
#SPJ4
Answer: C: The domain is all real numbers, and the range is all real numbers less than or equal to 4.
Step-by-step explanation: EDGE 2022