Answers
Divide 44 by 11 you get 4
Same with 52 and 13
Multiply 4 and 4
Related Questions
Triangle FGH is similar to triangle A B C
Answers
Answer:
x is 12
Step-by-step explanation:
» From scalar properties:
\({ \tt{ \frac{FG}{FH} = \frac{AB}{AC} }} \\ \\ { \tt{ \frac{9}{6} = \frac{18}{x} }} \\ \\ { \tt{x = \frac{18 \times 6}{9} }} \\ \\ { \boxed{ \tt{ \: x = 12 \: }}}\)
write an algebraic description for the sequence of Transformations that will map the preimage onto the image to show that the two circles are similar first transformation dilate the orgin (x,y) and (kx,ky)
Answers
The first transformation is a translation one unit up.
The second transformation is a translation of four units left.
The scale factor is 2.5.
According to the transformations above, the circles are similar, they are related with a scale factor of 2.5.
The equation of the preimage is
\(x^2+y^2=1\)The equation of the image is
\((x+4)^2+(x-1)^2=(2.5)^2\)Lin has a drawing with an area of 20 square inches. If she increases all the sides by a scale factor of 4, what will the new area be in square inches?
Answers
Answer:
100 square inches
Step-by-step explanation:
20*4=100
Please help me I've been stumped on this problem
Answers
The measure of ∠CFE is 40°
How do we find ∠CEF?To solve for triangle ∠CEF, we know that
Parallel to DE is BC
Arc length BD = 58°
Arc length DE = 142°
We can then draw a diameter across the center of the circle and give it a name as the first step. The diameter in this situation is line ZT.
The arcs BD and DE are split in half by the line ZT.
Which is:
Arc SC = 1/(1/2(arc BC) = 1/(58)
Arc SC = 29°
142 = 1/2(arc DE) + arc TE
Arc TE = 71°
Sum of the angles of a semicircle is 180 degrees: Arc SC + Arc CE + Arc TE
29° + Arc CE + 71° = 180°
Arc CE + 100° = 180°
Arc CE = 180-100
Arc CE = 80°
Angle inscribed equals half of angle intercepted
CFE = 1/2 of Arc CE
<CFE = 1/2(80)
< CFE = 40°
The above answer is based on the full question below;
In circle A shown, BC || DE , mBC=58° and mDE=142°. Determine the measure of ZCFE . Show how you arrived at your answer
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Stephanie owned a very large painting that she inherited from her grandfather after he passed. Her grandfather advised her that the painting was very valuable because it was painted by Van Gogh. Stephanie had the painting examined by an art expert who advised that it looked like Van Gogh painted the painting, but it was actually his student. If Van Gogh actually painted the painting it would have been worth $100,000.00. Stephanie decided to sell the painting and sold it to Charlie for $15,000.00. Charlie had a hunch that the expert was wrong and that it was actually Van Gogh. Six months after the sale, a scholar identified and proved that it was a Van Gogh.
Assume that the Court determined that there was a unilateral mistake. Could Stephanie rescind the contract?
a. Yes, because all unilateral contracts can be rescinded.
b. Yes, because there was not a "meeting of the minds."
c. No, because consideration was exchanged.
d. No, because Stephanie made the mistake, and it was not a bilateral mistake.
Answers
Stephanie would not be able to rescind the contract because she made a unilateral mistake, and it was not a bilateral mistake.
In contract law, a unilateral mistake occurs when one party to a contract is mistaken about a material fact related to the agreement. However, the general rule is that unilateral mistakes do not provide grounds for rescission of a contract. The reason for this is that contract law places a higher emphasis on the principle of enforceability and preventing one party from unilaterally avoiding their obligations based on their own mistake.
In this case, Stephanie's mistaken belief that the painting was directly painted by Van Gogh, rather than his student, constitutes a unilateral mistake. It is important to note that the art expert's opinion, though incorrect, did not induce Stephanie's mistake or misrepresent the nature of the painting. Stephanie made the decision to sell the painting to Charlie based on her own belief and understanding of its value.
Option d is the correct choice: No, because Stephanie made the mistake, and it was not a bilateral mistake. Stephanie's mistake was unilateral, meaning it was her own error in judgment. A bilateral mistake, on the other hand, occurs when both parties to a contract share a common misunderstanding or mistake about a material fact. In such cases, the contract may be voidable by either party since there was no true "meeting of the minds."
Moreover, the exchange of consideration further strengthens Charlie's position as a bona fide purchaser. Charlie purchased the painting for $15,000.00, and consideration is a fundamental element in the formation of a contract. Once consideration is exchanged, it signifies that the parties have entered into a binding agreement, and it may limit the grounds for rescission.
In conclusion, based on the unilateral nature of Stephanie's mistake and the presence of consideration, Stephanie would not be able to rescind the contract. Therefore, option d is the correct choice.
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Members of a softball team raised $1525.50 to go to a tournament. They rented a bus for $1075.50 and budgeted $37.50 per player for meals. Write and solve an equation which can be used to determine x, the number of players the team can bring to the tournament.
Answers
The number of players the team can bring to the tournament is 12
What is algebraic expression?
The appropriate algebraic expression in this case is the one that considers the cost of renting the bus of $1075.50 as well as the budgeted meal cost for all players that played in the softball team.
In other words, there is fixed charge which is the rent and meal costs which increase as the number of players increases
TC=a+bX
TC=total amount raised for the tournament=$1525.50
a=cost of renting the bus= $1075.50
bX=cost per meal per player*number of players=$37.50*X
$1525.50=$1075.50+$37.50*X
$1525.50-$1075.50=$37.50*X
$450.00=$37.50*X
X=$450.00/$37.50
X=12 players
The team can only bring a team of 12 players to the tournament.
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A poll shows that 64% of Americans personally worry a great deal about federal spending and the budget deficit. a. Mean b. Proportion
Answers
The proportions are expressed as a ratio, such as 64%, which designates the portion of respondents who answered the poll question affirmatively.
A proportion is the answer the poll question is asking as it is expressing the percentage of people who answered the question. It is asking what fraction or percentage of people report worrying a great deal about federal spending and the budget deficit. Proportions are expressed as a ratio, such as 64%, which designates the portion of respondents who answered the poll question affirmatively.
Mean is not the appropriate answer because it involves calculating the average of a set of numbers, such as a list of individual responses, not percentages. Calculating the mean is not possible in this situation because the poll question does not provide individual responses but rather presents the data in a summed format (i.e., 64%), which cannot be averaged.
Therefore, the proportions are expressed as a ratio, such as 64%, which designates the portion of respondents who answered the poll question affirmatively.
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Jose's car used 1 1/3 gallons to travel 23 miles. At what rate does the car use gas, in miles per gallon? Please i need help
Answers
Unit rate is the quantity of an amount of something at a rate of one of another quantity.
The rate at which the car uses gas is 17.25 miles per gallon.
What is a unit rate?It is the quantity of an amount of something at a rate of one of another quantity.
In 2 hours, a man can walk for 6 miles
In 1 hour, a man will walk for 3 miles.
We have,
The car:
\(1\frac{1}{3}\) gallons for 23 miles
This can be written as,
\(1\frac{1}{3}\) gallons = 23 miles
4/3 gallons = 23 miles
Multiplying 3/4 on both sides.
3/4 x 4/3 gallons = 3/4 x 23 miles
1 gallons = 69/4 miles
1 gallon = 17.25 miles
Thus,
The rate at which the car uses gas is 17.25 miles per gallon.
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Describe the transformations that map the
function y = 8* onto each function.
b) y = 84x
d) y = 8-2x
a) y = ( 1⁄2 8×18x
c) y = -8x
Answers
In the first function have vertical compression by 1/2, in second function have horizontal compresion by 1/4, in third compression have Vertical reflection and in fourth function have Horizontal reflection and horizontal compression by 1/2.
In the given question we have to find the transformations that map the function y = \(8^x\) onto each function.
Since we have to find the transformation, so we know that in a transformation;
The transformation from the first equation to the second one can be found by finding a, h and k for each equation.
\(y=ab^{x-h}+k\)
The horizontal is define by the value of h. The horizontal shift is defined as:
g(x)=f(x+h) - The graph is shifted to the left h units.
g(x)=f(x−h) - The graph is shifted to the right h units.
Horizontal Shift: None
The vertical shift define on the value of k. The vertical shift is defined as:
g(x)=f(x)+k - The graph is shifted up k units.
g(x)=f(x)−k - The graph is shifted down k units.
Vertical Shift: None
The value of a describes the vertical stretch or compression of the graph.
a>1 is a vertical stretch
0<a<1 is a vertical compression.
(a) The given first function is \((\frac{1}{2})8^{x}\).
y = \(8^x\)
Combine \(8^x\) and 1/2.
y = \(8^x\)/2
Assume that
y = \(8^x\) is f(x)=\(8^x\) and y= \((\frac{1}{2})8^{x}\) is g(x)= \((\frac{1}{2})8^{x}\).
On comparing the equation \(y=ab^{x-h}+k\)
The value of a, h, and k for f(x)=\(8^x\).
a=1, h=0, k=0
The value of a, h and k for g(x)=\((\frac{1}{2})8^{x}\).
a=1/2, h=0, k=0
Since the value of h and k so tnere is no horizontal and vertical shift.
SInce the value of a changes from 1 to 1/2 and 1/2 is greater that 0 but less than 1 so there is vertical compression by 1/2.
(b) The given second function is \(8^{4x}\).
y= \(8^{4x}\) is g(x)= \(8^{4x}\).
On comparing the equation \(y=ab^{x-h}+k\)
The value of a, h and k for g(x)=\(8^{4x}\).
a=1/4, h=0, k=0
Parent Function: f(x)=8^x
So, Horizontal Shift: None, Vertical Shift: None, Reflection about the x-axis: None, Vertical Compression or Stretch: None, horizontal compresion by 1/4.
(c) The given third function is \(-8^{x}\).
y= \(-8^{x}\) is g(x)= \(-8^{x}\).
The value of a, h and k for g(x)=\(-8^{x}\).
a=-1, h=0, k=0
Parent Function: f(x)=8^x
So, Horizontal Shift: None, Vertical Shift: None, Reflection about the x-axis: Reflected, Vertical Compression or Stretch: None.
Vertical reflection
(d) The given fourth function is \(8^{-2x}\).
y= \(8^{-2x}\) is g(x)= \(8^{-2x}\).
The value of a, h and k for g(x)=\(8^{-2x}\).
a=-1/2, h=0, k=0
Parent Function: f(x)=8^x
So, Horizontal Shift: None, Vertical Shift: None, Reflection about the x-axis: Reflected, Vertical Compression or Stretch: None.
Horizontal reflection and horizontal compression by 1/2.
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Consider the following primal problem: Maximize z=x
1
+4x
2
+3x
2
subject to: 2x
1
+3x
2
−5x
2
≤2
3x
1
−x
2
+6x
3
≥1.
x
1
+x
2
+x
2
=4
x
1
≥0,x
2
≤0,x
2
unrestricted in sign. Write down the dual problem of the above primal problem
Answers
To obtain the dual problem, we need to interchange the objective function coefficients with the constraint coefficients and vice versa.
The given problem is a primal linear programming problem with the objective of maximizing the expression z = x1 + 4x2 + 3x3. It is subject to three constraints: 2x1 + 3x2 - 5x3 ≤ 2, 3x1 - x2 + 6x3 ≥ 1, and x1 + x2 + x3 = 4,with specific signs and non-negativity restrictions on the variables. To obtain the dual problem, we need to interchange the objective function coefficients with the constraint coefficients and vice versa.
The dual problem of the given primal problem is as follows:
Minimize w = 2y1 + y2 + 4y3
subject to:
1. 2y1 + 3y2 + y3 ≥ 1
2. 3y1 - y2 + y3 ≥ 4
3. -5y1 + 6y2 + y3 ≥ 3
4. y1, y2 unrestricted in sign, y3 ≥ 0.
In the dual problem, the objective is to minimize the expression w, and the decision variables are y1, y2, and y3. The constraints are based on the coefficients of the primal problem's objective function and inequality constraints. The signs of the variables y1 and y2 are unrestricted, while y3 is non-negative.
The dual problem provides an alternative perspective on the original primal problem, where the roles of the objective function and constraints are reversed. The dual problem can help analyze the sensitivity of the primal problem's solution to changes in the constraint coefficients and provide additional insights into the optimization problem at hand.
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help, i will give u brainly. ASPA
Answers
Answer:
I need more information
Step-by-step explanation:
Jfjdkdjdjdndkdknskdd
Answer:
6, 24, 30, 48, 66
1, 4, 5, 8, 11
Step-by-step explanation:
Just by the first column we know that the scale ratio is 6. To find the second one we will multiply (6 * 4 = 24). To find the third one we will divide (30 / 6 = 5). To find the fourth one we will mulyiply (8 * 6 = 48). To find the fifth one we will divide (66 / 6 = 11).
Best of Luck!
Evaluate the following expression: \[ 1.723 \times 10^{2}+7.38 \times 10^{3} \] Type answer:
Answers
The sum of expression \(1.723 \times 10^{2}\) and \(7.38 \times 10^{3}\) is \(7.5523 \times 10^{3}\). The numbers in scientific notation are added by summing the coefficients while keeping the exponent unchanged.
In scientific notation, numbers are expressed as a coefficient multiplied by a power of 10. To add numbers in scientific notation, we need to ensure that the powers of 10 are the same.
In this case, both numbers are already in scientific notation with powers of 10. We can directly add the coefficients while keeping the exponent the same.
Adding \(1.723 \times 10^2\) and \(7.38 \times 10^3\) gives us a sum of \(7.5523 \times 10^3\). The coefficient represents the numerical value, and the power of 10 indicates the magnitude.
Thus, the expression \(1.723 \times 10^2 + 7.38 \times 10^3\) evaluates to \(7.5523 \times 10^3\), indicating a significant increase in magnitude compared to the individual numbers.
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If people prefer a choice with risk to one with uncertainty they are said to be averse to
Answers
If people prefer a choice with risk to one with uncertainty, they are said to be averse to uncertainty.
Uncertainty and risk are related concepts in decision-making under conditions of incomplete information. However, they represent different types of situations.
- Risk refers to situations where the probabilities of different outcomes are known or can be estimated. In other words, the decision-maker has some level of knowledge about the possible outcomes and their associated probabilities. When people are averse to risk, it means they prefer choices with known probabilities and are willing to take on risks as long as the probabilities are quantifiable.
- Uncertainty, on the other hand, refers to situations where the probabilities of different outcomes are unknown or cannot be estimated. The decision-maker lacks sufficient information to assign probabilities to different outcomes. When people are averse to uncertainty, it means they prefer choices with known risks (where probabilities are quantifiable) rather than choices with unknown or ambiguous probabilities.
In summary, if individuals show a preference for choices with known risks over choices with uncertain or ambiguous probabilities, they are considered averse to uncertainty.
If people prefer a choice with risk to one with uncertainty, they are said to be averse to uncertainty.
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(Will mark brainiest if 2 people answer)
Use the graph to answer the question.
Determine the line of reflection.
Reflection across the X-axis
Reflection across the Y-axis
Reflection across x = −5
Reflection across y = 3
Answers
Answer:
Reflection across x = -5
I need help ;----------;
Answers
Answer:
the answer is 54, its very easy
Step-by-step explanation:
For how many positive integers "n" does 1+2+...+n evenly divide 6n?
a) 3
b) 5
c) 7
d) 9
e) 11
Answers
(b) 5.Let's first express 1 + 2 + ... + n as the sum of an arithmetic series:
1 + 2 + ... + n = n(n+1)/2
Now, we need to find the positive integers n for which 6n is divisible by n(n+1)/2, or equivalently, for which n+1 is divisible by 3.
If n+1 is divisible by 3, then either n+1 = 3, 6, 9, ... or n+1 = 4, 7, 10, .... The first case gives n = 2, 5, 8, ... and the second case gives n = 3, 6, 9, ....
Thus, there are 5 possible values of n: 2, 3, 5, 6, and 9.
An arithmetic series is a sequence of numbers where each term is obtained by adding a constant value to the previous term. This constant value is called the common difference. For example, the sequence 2, 5, 8, 11, 14, ... is an arithmetic series with a common difference of 3. The formula for the nth term of an arithmetic series is: a_n = a_1 + (n-1)d, where a_n is the nth term, a_1 is the first term, n is the position of the term in the sequence, and d is the common difference. The sum of the first n terms of an arithmetic series can be calculated using the formula: S_n = n/2(a_1 + a_n).
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The height, h, of an object that is thrown upwards into the air can be represented as h = 0.5at2 + v0t + h0, where a represents the acceleration due to gravity (– 32 ft/s)
2), v0 represents the initial velocity, in feet per second, h0 represents the initial height of the object, in feet, and t represents time, in seconds.
Part A:
A ball thrown upwards from the top of a 64–ft high building with an initial velocity of 48
ft/s.Write an equation that could be used to determine the time, t, in seconds, for the ball to reach the ground. Assume ground level is at a height of 0 ft.
Part B:
Determine the time, t, in seconds, that takes the ball to reach the ground and explain how you determined your answer.
Answers
Answer:
ok so this awnser is v7a
Step-by-step explanation:
Why aren’t the two samples given in Table 1 and Table 2 exactly the same? Why do the two tables lead to slightly different results in the calculations?
Answers
Answer: they are not exactly the same because then you could just use the same answers and you wouldn't learn anything.because the numbers are slightly different
Step-by-step explanation:
Answer:
Yeah
Step-by-step explanation:
1) Evaluate the following expressions.show your work
a) 7(m - 8) for m = -4
Answers
Answer:
-84
Step-by-step explanation:
Since m=-4, we can plug -4 into the expression and use PEMDAS
7(m - 8)
7((-4)-8)
7(-12)
-84
The vertex form of the equation a parabola is y=(x-3)2+4 what is the standard form of the equation
Answers
Answer:
y = x² - 6x + 13
Step-by-step explanation:
Given
y = (x - 3)² + 4 ← expand (x - 3)² using FOIL
= x² - 6x + 9 + 4 ← collect like terms
= x² - 6x + 13 ← in standard form
What is 6.16 rounded to the nearest tenth?
Answers
Answer:
6.2
Step-by-step explanation:
Okay so in order to solve this equation you are going to have to round up the tenths place which is the space after the decimal point.
6.16 = 6.2
because 6 is above 5 you are able to round up to ten turning 6.16 to 6.2
Hope this helps you!!!
A bag contains 37 coins consisting of only dimes and quarters. The total amount of money in the bag is $6.85. How many dimes are in the bag?
Answers
Answer:
Step-by-step explanation:
its 16
Dimes is the coin which is equal to the 0.10 dollar. The number of dimes in the bag is 16.
To find the number of dimes we need to know about dimes.
What is dimes and quarter?Dimes is the coin which is equal to the 0.10 dollar. Quarter is the coin which is equal to the 0.25 dollar.
Given information-
The total number of coins bag contains is 37.
The total amount of money in the bag is $6.85.
Let the number of Dimes in the bag is \(x\) and the number of quarter in the bag is \(y\).
As the the total number of coins bag contains is 37. Thus,
\(x+y=37\\\)
Solve the equation for y,
\(y=37-x\)
Let the above equation is equation number 1.
As total amount of money in the bag is $6.85. Thus,
\(0.10x+0.25y=6.85\)
Put the value of y in the above equation as,
\(\begin{aligned}\\0.10x+0.25(37-x)&=6.85\\0.10x+9.25-0.25x&=6.85\\0.15x&=6.85-9.25\\x&=\dfrac{2.4}{0.15} \\x&=16\\\end\)
Hence, the number of dimes in the bag is 16.
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Exercise 1: In the right triangle below, calculate the measurement of the unknown side. Show your work.
Exercise 2: Calculate the height at which the kite is flying. Approach the height to the nearest integer. Show your work.
plz, help its Pythagorean Tioerm or however you spell it.
Answers
Answer:
Exercise 1:
base [b]=8cm
perpendicular [p]=6cm
hypotenuse [h]=?
By using Pythagoras law
h²=p²+b²
h²=6²+8²
h=√100
h=10cm
So another side's length is 10cm
Exercise 2:
base [b]=6m
perpendicular [p]=bm
hypotenuse [h]=8m
By using Pythagoras law
h²=p²+b²
8²=b²+6²
b²=8²-6²
b=√28=2√7 0r 5.29 or 5.3
So height of kite is√28or 2√7 0r 5.29 or 5.3 m
Step-by-step explanation:
[Note: thanks for translating]
A picture on a cave wall or a canvas differs from logographic writing in that Group of answer choices all of the above b and c logographic writing uses conventionalized symbols that may or may not look like what they represent. these symbols stand for linguistic units (words or individual morphemes). the order in which the logographic symbols are placed reflects the word order used in speech.
Answers
A picture on a cave wall or a canvas differs from logographic writing in that logographic writing uses conventionalized symbols that may or may not look like what they represent, and these symbols stand for linguistic units such as words or individual morphemes. Additionally, the order in which the logographic symbols are placed reflects the word order used in speech.
Pictures on a cave wall or a canvas are visual representations that depict objects, scenes, or ideas. They do not rely on conventionalized symbols to convey meaning, nor do they necessarily follow a specific word order. Instead, pictures communicate through visual imagery and are often open to interpretation.
In contrast, logographic writing systems, such as Chinese characters or ancient Egyptian hieroglyphs, use symbols that represent words or morphemes. These symbols are standardized and carry specific meanings. While the symbols may not always resemble the objects they represent, they are recognized within the linguistic community and follow established conventions.
Furthermore, logographic writing typically reflects the word order used in speech. The placement of the symbols within a written text aligns with the order in which the corresponding words or morphemes would be spoken in a sentence. This adherence to word order allows for effective communication and comprehension within the logographic writing system.
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What is the value of h?
0.8h = 1.12
Answers
a ____ is a procedure performed for definitive treatment rather than diagnostic purposes.
Answers
A therapeutic procedure is a procedure performed for definitive treatment rather than diagnostic purposes.
A procedure performed for definitive treatment rather than diagnostic purposes is a therapeutic procedure. These procedures are aimed at treating or curing a particular condition, disease, or illness. Therapeutic procedures are used to relieve pain, restore function, improve mobility, or even save a patient's life. Unlike diagnostic procedures that are performed to identify a problem, therapeutic procedures involve actually treating the problem. Examples of therapeutic procedures include surgeries, chemotherapy, radiation therapy, and immunotherapy. These procedures are often more invasive than diagnostic procedures and may require anesthesia or sedation. The goal of a therapeutic procedure is to improve the patient's health and well-being, and they are an essential part of modern medical care.
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In 2010, the population of a city was 88,000. From 2010 to 2015, the population grew by 4%. From 2015 to 2020, it fell by 3%. To the nearest 100 people, what was the population in 2020?
Answers
The population in 2020 is 2,240,700
What is population?A population is the set of people concentrated in a particular area.
Given that, in 2010, the population of a city was 88,000, from 2010 to 2015, the population grew by 4%. From 2015 to 2020, it fell by 3%. We need to determine the population in 2020,
For population growing we will multiply the population is 104 and for population reducing we will multiply by 97,
Therefore, the population in 2020 =
88000 × 5(104/100) × 5(97/100)
= 88000 × 5.25 × 4.85
= 2,240,700
Hence, the population in 2020 is 2,240,700
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What is the interquartile range of the set of data this box-and-whisker plot represents?
Answers
Answer:
3
Step-by-step explanation:
The interquartile range is where the 2nd and 5th dots are, on the opposite ends of the square, from 15-18.
Answer:
3
Step-by-step explanation:
The interquartile range (IQR) is the difference between the upper quartile (Q₃) and the lower quartile (Q₁).
In a box plot:
The left edge of the box represents the lower quartile.The right edge of the box represents the upper quartile.From inspection of the given box plot:
lower quartile (Q₁) = 15upper quartile (Q₃) = 18Therefore:
IQR = Q₃ - Q₁
= 18 - 15
= 3
So the interquartile range of the given box plot is 3.
please help me its algebra I
Answers
The waiting time to ride a roller coaster is 20 minutes when 150 people are in line. How long is the waiting time when 240 people are in line WRITE a proportion
Answers
Answer: The waiting time will be 32 minutes when 240 people in line.
Step-by-step explanation:
Let us assume that the waiting time is directly proportional to the number of people in the queue.
Equation of direct proportion between variables x and y : \(\dfrac{x_1}{y_1}=\dfrac{x_2}{y_2}\)
Put \(x_1=20,\ y_1=150,\ y_2=150\) to find \(x_2\).
\(\dfrac{20}{150}=\dfrac{x_2}{240}\\\\\Rightarrow\ x_2=\dfrac{20}{150}\times240\\\\\Rightarrow\ x_2=32\)
Hence, the waiting time will be 32 minutes when 240 people in line.
Answer:
32 minutes
Step-by-step explanation:
According to the scenario, computation of the given data are as follows,
For 150 people, waiting time = 20 minutes
So, for 1 minute waiting time, number of people = 150 ÷ 20
= 7.5 people per minute
So, for 240 people, waiting time = 240 ÷ 7.5
= 32 minutes.
So, the waiting time when 240 people are in line is 32 minutes.