The graph of f ′ (x), the derivative of f of x, is continuous for all x and consists of five line segments as shown below. Given f (–3) = 6, find the absolute maximum value of f (x) over the interval [–3, 0].
Graph of line segments increasing from x equals negative 4 to x equals negative 3, decreasing from x equals negative 3 to x equals 0, increasing from x equals 0 to x equals 3, constant from x equals 2 to x equals 4 and decreases from x equals 4 to x equals 5. x intercepts at x equals negative 4, x equals 0, x equals 5.
3
4.5
6
10.5
Answers
Answer
10.5
Step-by-step explanation:
The other answer is correct until solving for C. f(-3) = 6, not -6. So C = 21/2. This makes f(0) = 10.5. Local Max should occur at x intercepts on the f'(x) graph.
Answer: 10.5
Step-by-step explanation: The other answer is correct until solving for C. f(-3) = 6, not -6. So C = 21/2. This makes f(0) = 10.5. Local Max should occur at x intercepts on the f'(x) graph. A fraction is a number that shows how many equal parts there are. When we write fractions, we show one number with a line above (or a slash next to) another number. For example, 14, 1⁄4 and 1/4.are different ways of writing the same fraction (in this case a quarter). The top number tells us how many parts there are, and the bottom number tells us the total number of parts. The top part of the fraction is called a numerator. The bottom part of the fraction is called a denominator. For example, for the fraction 14 the 1 is the numerator, and the 4 is the denominator.
Related Questions
An isosceles triangle with angles measuring 50°, 50°, and 80° undergoes a translation, rotation, and reflection.
Determine whether the angle measures of the image of the triangle are 50°, 50°, and 80° after each transformation.
Select Yes or No for each transformation.
{Translation}
Yes?
or
No?
{Rotation]
Yes?
or
No?
{Reflection}
Yes?
or
No?
Answers
Translation will be the similar as that of the pre image, that means they will retain the same value of 50, 50 and 80.
The answer is yes.
Rotation will be similar to that of the preimage. This is because rotation of the figure will only affect the position of the original figure and not the size of the figure. Therefore the size of the angles will be 50, 50 and 80.
Reflection will be the same as that of the preimage, reason being the reflected figure always has the same size as the object and it is always same distance as the preimage is in front of the mirror.
For the isosceles triangle undergoing transformations, the angle measures will change for translation but remain the same for rotation and reflection.
No for Translation because translations do not change angle measures.
Yes for Rotation because rotations preserve angle measures.
Yes for Reflection because reflections preserve angle measures.
The volume of right circular cylinder a is 22 cubic centimeters. what is the volume, in cubic centimeters with twice the radius and half the height?
Answers
[volume of right circular cylinder]=pi*r²*h
Vo=pi*r²*h--------------> original volume
Vo= 22 cm³
if twice the radius and half the height
r1=2*r
h1=h/2
then
V1=pi*ri²*h1
substituting
V1=pi*(2*r)² *(h/2)----------->V1= pi*4*r² *h/2-----------> V1=2*pi*r² *h
V1=2*[pi*r² *h]------------> V1=2Vo
V1=2*22=44 cm³
the answer is 44 cm³
To find the volume of the new cylinder with twice the radius and half the height, use the formula for the volume of a cylinder and substitute the new values. The volume of the new cylinder is also 22 cubic centimeters.
Explanation:To find the volume of the new cylinder with twice the radius and half the height, we can use the formula for the volume of a cylinder: V = πr2h.
First, we double the radius of the original cylinder. Let's say the original radius is r. The new radius would be 2r.
Next, we halve the height of the original cylinder. Let's say the original height is h. The new height would be h/2.
Substituting these values into the volume formula, we get the volume of the new cylinder as V = π(2r)2(h/2)=4πr2(h/2)=2πr2h.
So, the volume of the new cylinder is also 22 cubic centimeters.
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What is the cosecant of angle y?
Answers
The cosecant of angle y is z/y.
What is Trigonometry?The area of mathematics that deals with particular angles' functions and how to use those functions in calculations. There are six popular trigonometric functions for an angle. Sine (sin), cosine (cos), tangent (tan), cotangent (cot), secant (sec), and cosecant are their respective names and acronyms (csc).
Given:
Hypotenuse = z
Perpendicular = y
Base = x
As, Cosecant is the ratio of Hypotenuse to perpendicular
Using Trigonometry
cos y = H/ P
cos y = z/ y
Hence, the cosecant of y is z/y.
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Solve the inequality and then graph its solution: 7s + 12 > 46 - 10s
Answers
Add 10s to both sides:
17s + 12 > 46
Subtract 12 to both sides:
17s > 34
Divide 17 to both sides:
s > 2
The inequality graphed would have an open dot on 2 and the arrow would be going to the right.
Paul has a coupon for $2.50 off a box of name brand cereal that normally costs $12.78 the store brand cereal costs $10.98 how much will Paul save if he uses his coupon and buys the name brand cereal instead of the store brand cerial
Answers
1.Name brand cereal: $12.78 and Store brand cereal: $10.98.
2. Coupon for $2.50 off on the name brand.
What the question is asking is how much would he save if he used the coupon. So you would need to know how much it will be after the coupon is used. Here is the following steps to this question:
Step1 find out the price after coupon:
Regular price 12.78－Coupon worth 2.50 = 10.28
Now after knowing the price after coupon we need to find how much she saved
Step2 finding how much Pual saved after using to coupon and buy the named brand
Store brand price 10.98 －The price after discount 10.28 = $0.70
So Pual saved $0.70 by using the coupon and buying the named brand cereal.
Hope it helps!
Which of the following is a radical equation?
Answers
Answer:
D) [tex]7\sqrt{x} = 14[/tex]
Step-by-step explanation:
If x is under a radical symbol, then it is called radical equation.
For example, [tex]\sqrt{x} = 2[/tex]
[tex]\sqrt{x-2} = 5[/tex]
From the given equations, we have to find in which equation x under radical.
x + [tex]\sqrt{5} = 12[/tex], here x is not under radical.
[tex]x^{2} = 16[/tex], here also x is not under radical.
3 + x√7 =13, here x is not under radical
7[tex]\sqrt{x} = 14[/tex]
Here x is under the radical symbol.
Therefore, the answer is [tex]7\sqrt{x} = 14[/tex]
12. triangle KMP is isosceles with KM = KP. MX and PY are angle bisectors.
a. Is there enough information to prove triangle WMP is an isosceles
triangle? Explain.
b. Can you conclude that MX and PY are medians?
c. What one additional piece of information would allow you to prove
that MX and PY are altitudes?
triangle below
Answers
B: Yes, because the angle bisectors of MX and MP would also bisect the sides making them both medians.
C to prove that they were Altitudes we would need to know that the base angles of KMP are 60 degrees. if they are 60 degrees they would create two 30-60-90 triangles with the 90 degrees going from the center of the side directly up, perpendicularly to the altitude. (this would also make the triangle an equilateral triangle)
Which of the following best describes an unpredictable event
A. The outfit a person will wear on a particular day 3 years from now
B. The moment a car runs out of gasoline
C. The grade a student gets in a class on a final report card
D. The amount of money in a savings account
Answers
A standard number cube is rolled two times. What is the probability that the sum of the two rolls is 13?
Answers
What is the hypothesis in the following conditional statement? "If it is a Friday then Josie will receive her paycheck." A. It is a Friday. B. It is not a Friday. C. Josie will receive her paycheck. D. Josie will not receive her paycheck.
Answers
Answer:
C. Josie will receive her paycheck.
Step-by-step explanation:
The hypothesis is that Josie will have her paycheck.
The conditional thing of that hypothesis is that she needs to wait until Friday and then, she can have her paycheck.
You can see this because the main here is to get the paycheck.
And the thing that can change, without changing the main hypothesis, is the day she will receive that check.
5.1x10^-1 as an ordinary number?
Answers
so its 5.1 * 0.1 = 0.51 Answer
Convert [tex]\( 5.1 \times 10^{-1} \)[/tex] to an ordinary number, the, [tex]\( 5.1 \times 10^{-1} \)[/tex] as an ordinary number is 0.51.
To convert [tex]\( 5.1 \times 10^{-1} \)[/tex] to an ordinary number:
1. Identify the exponent: The exponent is -1.
2. Understand the meaning: [tex]\( 10^{-1} \)[/tex] means "divide by 10".
3. Apply the operation: Divide 5.1 by 10.
4. Move the decimal point: To divide by 10, shift the decimal point in 5.1 one place to the left.
5. Result: Moving the decimal point one place to the left changes 5.1 to 0.51.
Thus, [tex]\( 5.1 \times 10^{-1} = 0.51 \)[/tex].
Complete question:- What is [tex]5.1 * 10^{- 1[/tex] as an ordinary number?
A parking lot space is in the shape of a rectangle. If the space has a length of 23 feet and a width of 12 feet, what is the area of the parking space?
Answers
A=23*12
A=276 <the answer
Given is a parking space in the shape of rectangle with length = 23 feet and width = 12 feet. It says to find the area of parking lot.
We know the formula for area of rectangle is given by :-
Area = Length x Width
We can plug the given values in the above formula and find the answer.
Area = 23 feet x 12 feet
Area = 276 squared feets
So the area of parking space would be 276 squared feets.
Hence, final answer is 276 squared feets.
A line has a slope of 0 and passes through the point
(7, 7). What is its equation in slope-intercept
form?
Answers
The equation of a line in slope-intercept form is [tex] y=mx+c [/tex].
Where [tex] m [/tex] is slope and [tex] c [/tex] is y-intercept.
Since [tex] m=0 [/tex], the equation of the line is [tex] y=(0)x+c\\ y=c [/tex].
Since this line passes through [tex] (7,7) [/tex]. The equation of the line is
[tex] y=7 [/tex]
The equation of a line in slope-intercept form is y=mx+c .
Where m is slope and c is y-intercept.
Since m=0 , the equation of the line is y=(0)x+c\\ y=c .
Since this line passes through (7,7) . The equation of the line is
y=7
Amare wants to ride a Ferris wheel that sits four meters above the ground and has a diameter of 50 meters. It takes six minutes to do three revolutions on the Ferris wheel. Complete the function, h(t), which models Amare's height above the ground, in meters, as a function of time, t, in minutes. Assume he enters the ride at the low point when t = 0.
Answers
Final answer:
To model Amare's height above the ground as a function of time, use the equation h(t) = 2 + 2 * sin((2 * pi * t) / 6)
Explanation:
To determine a function to model Amare's height above the ground as a function of time, we can use the equation of motion for circular motion. The height of Amare above the ground can be calculated using the equation:
h(t) = r + R * sin(theta)
Where:
h(t) is the height above the ground at time t
r is the radius of the wheel (half the diameter)
R is the maximum height above the ground (given as 4 meters)
theta is the angle in radians, which is related to time by the formula theta = (2 * pi * t) / T, where T is the time for one revolution (given as 6 minutes)
Putting all these values into the equation, we get:
h(t) = 2 + 2 * sin((2 * pi * t) / 6)
helppppppppppppppppppp
Answers
y = (x + 2) ^ 3
y = x ^ 2 + 3
Then, we see the behavior of the functions:
blue: y = (x + 2) ^ 3
red: y = x ^ 2 + 3
answer:
2 units rigth and 3 units up
(option 3)
See attached graph.
I really need help ASAP
Answers
.. tan(a) = 78'/36'
.. a = arctan(78/36) ≈ 65.22°
You also know that
.. a = c = k = j
and that
.. a +c +e = 180°
.. e = g = 180° -2a = 49.55°
f = h = 180° -e = 130.45°
Of course the other corner angles are
.. b = d = i = l = 90° -a = 24.78°
_____
One bit of trigonometry and the rest is arithmetic.
I need help checking my work. MEDALS!!! will be awarded. I chose C.
Kidneys process nitrogenous wastes by
A) seperating water from nitrogenous wastes by passive diffusion.
B) using cells to actively pump water across a membrane.
C) storing the wastes as uric acid until they can be eliminated.
D) pumping ions across membranes to separate water from waste products.
Answers
What is the value of x? Enter your answer in the box. x = A triangle with midsegment parallel to the base. the left side is labeled 72 cm below the midsegment and 9 cm above the midsegment. the right side is labeled 56 cm below the midsegment and 3 x minus 20 above the midsegment.
Answers
72/9 = 56/(3x -20)
We can multiply by (3x -20)/8 to get
3x -20 = 7
3x = 27
x = 9
72/9 = 56/(3x -20)
We can multiply by (3x -20)/8 to get
3x -20 = 7
3x = 27
x = 9
6. The cost C of joining FitFast Gym includes an initial membership fee of $127, plus a monthly
fee, m, of $28.
a. The cost of going to the gym is a function of the number of months of membership. Find a
rule for the function.
b. Find the cost of using the gym for 9 months
Answers
The cost of gym membership for 9 months then would be f(9)=127+28(9)=127+252=$379.
Answer:
Step-by-step explanation:
The function rule would be f(m)=127+28m. This is because the membership fee, $127, is added to the monthly cost, which is given by 28×m, the number of months.
The cost of gym membership for 9 months then would be f(9)=127+28(9)=127+252=$379.
solve the following system of equations: -2x+y=1
-4x+y=-1
A)(3,1)
B)(-1,3)
C)(-1,-3)
D)(1,3)
Answers
.. (-2x +y) -(-4x +y) = (1) -(-1)
.. 2x = 2 . . . . . . . . . . . . . . . . . . . simplify
.. x = 1 . . . . . . . . . . . . . . . . . . . . . divide by 2
This corresponds to selection D) (1, 3).
The radius and height of a right cylinder are each multiplied by 2. what is that change in the total surface area of the cylinder
Answers
The total surface area is multiplied by 4.
When both the radius and height of a right cylinder are multiplied by 2, the change in the total surface area is 4 times the original surface area.
Explanation:
The total surface area of a right cylinder is given by the formula A = 2πrh + 2πr², where r is the radius and h is the height. When both the radius and height are multiplied by 2, we can calculate the change in the total surface area:
The new radius is 2r, so the new area of the bases is 4πr².The new height is 2h, so the new area of the lateral surface is 2π(2r)(2h) = 8πrh.Therefore, the total surface area of the new cylinder is A' = 4πr² + 8πrh = 4(πr² + 2πrh) = 4A.Learn more about Total surface area of a cylinder here:https://brainly.com/question/35459045
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f(x) = x4 − 4x3 − 4x2 + 36x − 45. This function has roots
Answers
x=3 is root of this function
Answer:
the answer is 4 not three
Please help
Part 1.] Match these items.
1.) The positive integers
2.) An ordering of quantities
3.) 2, 4, 8, 16, . . ., 256
4.) 1, 3, 5, 7, . . .
5.) No first term is available
A.) An example of a finite sequence
B.) A sequence
C.) The reason the numbers . . . -4, -2, 0, 2, 4, . . . are not a sequence
D.) The natural numbers
E.) An example of an infinite sequence
Part 2.] Write the first five terms of the sequence. [tex] a_{n}= n^{2}+2[/tex]
A.] 3,6,11,18,27
B.] 3,6,9,12,15
C.] 2,3,6,11,18
Part 3.] Write the first five terms of the sequence. [tex] a_{n}= -1( \frac{1}{3})^{n-1}[/tex]
A.] -1,-3,-9,-27,-81
B.] -1,[tex] \frac{-1}{3},\frac{-1}{9},\frac{-1}{27},\frac{-1}{81} [/tex]
C.] -1,[tex] \frac{1}{3},\frac{-1}{9},\frac{1}{27},\frac{-1}{81} [/tex]
Part 4.] In two or more complete sentences, explain whether the sequence is finite or infinite. Describe the pattern in the sequence if it exists, and if possible find the sixth term. [tex]2a,2a^{2}b,2a^{3}b^{2},2a^{4}b^{3}...[/tex]
Answers
1) The positive integers -----------> D.) The natural numbers
2.) An ordering of quantities -----------> B.) A sequence
3.) 2, 4, 8, 16, . . ., 256 -----------> A.) An example of a finite sequence
4.) 1, 3, 5, 7, . . . -----------> E.) An example of an infinite sequence
5.) No first term is available -----------> C.) The reason the numbers . . . -4, -2, 0, 2, 4, . . . are not a sequence
Part 2
[tex]a_n=n^2+2\\ a_1=1+2=3\\ a_2=4+2=6\\ a_3=9+2=11\\ a_4=16+2=18\\ a_5=25+2=27 [/tex]
The answers is A.
Part 3
[tex]a_n=-1(\frac{1}{3})^{n-1} \\ a_1=-1(\frac{1}{3})^{1-1}=-1\\ a_2=-1(\frac{1}{3})^{2-1}=-\frac{1}{3}\\ a_3=-1(\frac{1}{3})^{3-1}=--\frac{1}{9}\\ a_4=-1(\frac{1}{3})^{4-1}=--\frac{1}{27}\\ a_5=-1(\frac{1}{3})^{5-1}=--\frac{1}{81}\\ [/tex]
The answers is B.
Part 4
The pattern in this sequence is:
[tex]a_n=2a^nb^{n-1}[/tex]
Let's list first six terms:
[tex]a_n=2a^nb^{n-1}\\ a_1=2a^1b^0=2a\\ a_2=2a^2b^1=2a^2b\\ a_3=2a^3b^2\\ a_4=2a^4b^3\\ a_5=2a^5b^4\\ a_6=2a^6b^5\\[/tex]
This is a infinite sequence. The patern is obvious and we could find any term within the sequence.
The questions involve matching concepts related to sequences, finding the first terms of given sequences, and analyzing an infinite sequence. The correct matches were 1-D, 2-B, 3-A, 4-E, 5-C. Options C and C were correct for Parts 2 and 3, while for Part 4, the sequence was infinite, with the sixth term as [tex]2a^{6}b^{5}[/tex].
Explanation:
For Part 1, the correct matching of the items would be as follows:
1 - D (The positive integers can also be referred to as natural numbers)2 - B (A sequence is simply an ordering of quantities)3 - A (2, 4, 8, 16, ... , 256 is a finite sequence because it ends at 256)4 - E (1, 3, 5, 7, ... is an infinite sequence because it goes on indefinitely)5 - C (The numbers -4, -2, 0, 2, 4, ... can't be a sequence because there is no first term)
For Part 2, Option C is correct. The first five terms of the sequence [tex]a_{n} = n^{2} + 2[/tex] are 3, 6, 11, 18, 27, as these are the results you obtain when you plug the first five positive integers into the formula.
For Part 3, Option C is correct. The first five terms of the sequence [tex]a_{n} = -1 * (1/3)^{n-1}[/tex] are -1, 1/3, -1/9, 1/27, -1/81. Notice the alternating signs due to the factor of -1.
For Part 4, the sequence [tex]2a,2a^{2}b,2a^{3}b^{2},2a^{4}b^{3}...[/tex] is infinite since there is no last term. The pattern involves progressively increasing the powers of a and b in each term. The sixth term would be [tex]2a^{6}b^{5}[/tex] following this pattern.
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Which set of ordered pairs represent a function
Answers
Answer: second set
Step-by-step explanation:
PLEASE HELP
7.02
1. Determine whether the sequence converges or diverges. If it converges, give the limit.
60, 10, five divided by three , five divided by eighteen , ...
A) Converges; 72
B) Converges; 0
C) Diverges
D) Converges; -15540
2. Find an explicit rule for the nth term of the sequence.
1, 3, 9, 27, ...
A) an = 1 • 3n + 1
B) an = 3 • 1n - 1
C) an = 1 • 3n - 1
D) an = 1 • 3n
3. Find an explicit rule for the nth term of the sequence.
-5, -25, -125, -625, ...
A) an = -5 • 5n
B) an = 5 • -5n + 1
C) an = 5 • -5n
D) an = -5 • 5n - 1
4. Find an explicit rule for the nth term of a geometric sequence where the second and fifth terms are -6 and 162, respectively.
A) an = 2 • 3n - 1
B) an = 2 • (-3)n - 1
C) an = 2 • 3n
D) an = 2 • (-3)n + 1
5. A certain radioactive isotope has a half-life of 11 days. If one is to make a table showing the half-life decay of a sample of this isotope from 32 grams to 1 gram; list the time (in days, starting with t = 0) in the first column and the mass remaining (in grams) in the second column, which type of sequence is used in the first column and which type of sequence is used in the second column?
Answers
2. C
5.
TABLE
0 32
5 16
10 8
15 4
20 2
after 25 days ----> from 32g to 1g
first column: increments of +5; arithmetic sequence
second clmn: x5 ; geometric sequence
Answers:
1-A, 2-C, 3- D, 4- B.
I don't understand this question.
the instructions say: "In exercises 1-4,tell whether the ordered pair is a solution of the inequality."
Answers
5 - 4 > 2
1 > 2
(5, 4) is not a solution to this inequality
Jerry solved the system of equations.
X-3y= 1
7x+2y=7 As the first step, he decided to solve for y in the second equation because it had the smallest number as a coefficient. Max told him that there was a more efficient way. What reason can Max give for his statement?
Answers
Answer:
A: The variable x in the first equation has a coefficient of one so there will be fewer steps to the solution.
Step-by-step explanation:
I got it right on Edge
The value of x and y is 1 and 0 for the given system of equations.
And, the reason Max gives for his statement that " the variable x in the first equation has coefficient of one so there will be fewer steps to the solution".
What is system of equations?A system of equations is a set of two or more equations with the same variables. A solution to a system of equations is a set of values for the variable that satisfy all the equations simultaneously.
What is substitution method?The substitution method can be defined as a way to solve a linear system algebraically. In this method we substitute one y-value with the other. To put it simply, the method involves finding the value of the x-variable in terms of the y-variable.
According to the given question.
We have system of equations.
x - 3y = 1
and 7x + 2y = 7
To solve the above system of equations we use substitution method.
Since, the first the corffeficient of x in first equation is 1. So we will use the value of x of equation x -3y = 1 to substitute in second equation. Because it require fewer steps to get the solution.
So,
From x - 3y = 1
We cay say that
x = 1 + 3y
Substitute the value of x in 7x + 2y = 7.
⇒ 7(1 + 3y) + 2y = 7
⇒ 7 + 21y +2y = 7
⇒ 7 + 23y = 7
⇒ 23y = 7-7
⇒ 23y = 0
⇒ y = 0
Again susbstitute the value of y in x =1 + 3y.
⇒ x = 1 + 3(0)
⇒ x = 1
Hence, the value of x and y is 1 and 0 for the given system of equations.
Therefore, the reason Max gives for his statement that " the variable x in the first equation has coefficient of one so there will be fewer steps to the solution".
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Which best describes what is happening in section C? His car is stopped. His car is speeding up. His car is slowing down. His car is traveling at a constant speed.
Answers
The best describes what is happening in section C is His car is slowing down.
What is graph?Graph is a mathematical representation of a network and it describes the relationship between lines and points. A graph consists of some points and lines between them.
As, from the speed versus time graph we can see that section C occurs in between section B and D.
In section B,
line is horizontal which means the car is at constant high speed.
In section D,
line is also horizontal which means the car is at a constant low speed.
In section C,
the line goes down to the right which shows that from section B to D there is decrease in speed of car. So, in section C the car in movement of slowed down.
Hence, in section C is car is slowing down.
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what is the value of x?
Answers
Answer:
x = 5
Step-by-step explanation:
In this figure with two similar triangles, corresponding edges are proportional. The proportion can be written several ways. One of them is ...
(x+5)/(x+1) = (x)/(x-2)
Multiplying by the product of denominators gives ...
(x -2)(x +5) = (x +1)(x)
x^2 +3x -10 = x^2 +x . . . eliminate parentheses
2x = 10 . . . . . . . . . . . . . . add 10 -x -x^2
x = 5 . . . . . . . . . . . . . . . . divide by 2
Solve this problem. Find the number of gallons of paint needed to cover all four sides four sides) of the building shown with two coats of paint if one gallon covers 350 square feet. Disregard windows and doors. Round to the nearest gallon.
Answers
1) calculate the area all four sides
A=[12+9+12+9]*8=336 ft²
if 1 gallons---------------------------- > covers 350 ft²
X------------------------------------ > 336 ft²
X=336/350=0.96 gallons
but remember
that there are two coats of paint
therefore
0.96*2----------- > 1.92------- > 2 gallons
the answer is 2 gallons
Answer: the answer is 3 gallons of paint is required to paint the building.
Step-by-step explanation:
The area to be painted is:
= 2× [Area of Rectangle with dimensions 20 ft.×10 ft.+Area of triangle with height 5 ft. and base 20 ft.+Area of rectangle with dimensions 24 ft. and 10 ft.]
=2×[20×10+(1/2)×5×20+24×10]
=2×[200+50+240]
=2×490
=980 square ft.
Hence, the area to be painted=980 square feet.
Now, amount of paint require to cover 350 square feet=1 gallon.
i.e. 1 square feet requires=1/350 gallon of paint.
⇒ 980 square feet requires=980/350=2.8 gallons of paint.
Hence, to the nearest gallon we could say that:
3 gallons of paint is required to paint the building.