(a) The average number of potential customers entering the system each hour is 2.5 customers per hour.
(b) The probability that the server will be busy is equal to the utilization factor, which is 0.67.
How to find potential customers enter the system each hour?a) The average number of potential customers entering the system each hour can be calculated using Little's law, which states that the long-term average number of customers in a stable system is equal to the long-term average arrival rate multiplied by the long-term average time a customer spends in the system.
In this case, the arrival rate is 3 customers per hour, and the average time a customer spends in the system is equal to the average time between arrivals plus the average service time, which is 1/3 + 1/2 = 5/6 hour.
Therefore, the average number of potential customers entering the system each hour is 3 x 5/6 = 2.5 customers per hour.
How to find the probability that the server will be busy?b) The probability that the server will be busy can be calculated using the formula for the utilization factor, which is equal to the long-term average service rate divided by the system capacity.
In this case, the service rate is 2 customers per hour, and the system capacity is 3 customers. Therefore, the utilization factor is 2/3 = 0.67. The probability that the server will be busy is equal to the utilization factor, which is 0.67.
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the product of two numbers divided by four is equal to ten sum of nine and ten
Let the first number be x and the second number be y. Then we have:
xy/4 = 10 + 9 + 10
Simplifying the right side:
xy/4 = 29
Multiplying both sides by 4:
xy = 116
Now we need to find two numbers whose product is 116. We can start by listing the factors of 116:
1, 2, 4, 29, 58, 116
Since we are looking for two numbers whose product is 116, we can try pairs of factors until we find a pair that works:
1 x 116 = 116 (not a sum of two numbers)
2 x 58 = 116 (sum is 60, not 19)
4 x 29 = 116 (sum is 33, not 19)
So the only pair that works is:
x = 29 and y = 4
Let's check if these values satisfy the original equation:
xy/4 = 29 x 4 / 4 = 29 = 10 + 9 + 10
So the solution is x = 29 and y = 4.
Which set or subset does -12.75 belong to
-12.75 belongs to the set of Rational numbers.
A rational number is a number that can be expressed as the quotient or fraction frac p q of two integers, a numerator p
and a non-zero denominator q.
Rational numbers are numbers that can be expressed as a fraction of two integers (p/q), where q is not equal to zero.
Identify the number: -12.75
Determine if it can be expressed as a fraction of two integers: -
12.75 can be written as -51/4, which are both integers.
Confirm that the denominator (q) is not equal to zero:
In this case, q = 4, which is not equal to zero.
Therefore, -12.75 belongs to the set of Rational numbers.
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Write an algebraic expression for this word problem
Author Jules Verne's fictional submarine, the Nautilus, traveled under the sea 20,000
leagues. Let 1 mile equal x leagues. How many miles did the Nautilus travel?
Triangle LMN with vertices L(1, 6), M(8, 7),
and N(5, 2): 270°
counterclockwise
Answer & step-by-step explanation:
To rotate a point (x, y) 270° counterclockwise about the origin, we can swap the x and y coordinates and negate the new x coordinate. So the new coordinates for L(1, 6) would be:
x' = -6
y' = 1
Therefore, the new vertex for L would be (-6, 1). Similarly, the new vertices for M(8, 7) and N(5, 2) would be:
M': (-7, 8)
N': (2, 5)
So the rotated triangle would have vertices L'(-6, 1), M'(-7, 8), and N'(2, 5).
Answer:
M': (-7, 8)
N': (2, 5)
Step-by-step explanation:
I did the test
Hope this helps :)
what is the population standard deviation? {5885}
Answer:
The population standard deviation is a measure of how much variation there is among individual data points in a population. It's a way of quantifying how spread out the data is from its mean.
Solve 20x = 10 for x.
Answer:
200
Step-by-step explanation:
20x for x=10
you are replacing the x for 10 which would be
20 x 10 = 200
x=1/2
Step-by-step explanation:
To find x, you divide both sides by the coefficient of x which is 20 so when you divide 10 by 20 it gives you 1/2
Solve this question for me?
Answer: B. y = -x + 5
Step-by-step explanation:
Given the table, lets pick two consecutive points to find the slope.
(-4, 9) (-1, 6) are the first points that show in the table.
Lets plug it in the (y2-y1)/(x2-x1) expression
(6 - 9)/(-1 - -4)
=(-3)/(3)
=-1
The slope is -1
Now lets look at the answer choices and see if any of the equations with the format y= mx + b has -1 as its slope. We can eliminated a and c.
Now lets use the data in the table, and plug in a given point to see if which of the equations left are correct.
Lets use the point: (-4, 9)
For b.
y = -x + 5
9 = -(-4) + 5
9 = 4 + 5
9 = 9
B is the correct answer.
For d.
9 = -(-4) - 5
9 = 4 - 5
9 = -1
this equation is incorrect, so D is incorrect.
ESTION 5 Consider f:x→4* 5.1.1 Sketch graphs of fand f¹,( on diagram sheet 1) the inverse intercepts with axis and one other point on each graph
The inverse function of f(x) is [tex]f^{(-1)(x)} = x/20.4[/tex], which represents a linear function with a slope of 1/20.4 and a y-intercept of 0.
What is graph?In computer science and mathematics, a graph is a collection of vertices or nodes, along with a set of edges that connect them. Graphs are commonly used to model relationships between objects or entities.
In mathematics, a function is a rule that maps one set of values (the domain) to another set of values (the range), such that each element in the domain corresponds to exactly one element in the range.
According to given information:
The function f(x) = 4 * 5.1 is a constant function with a value of 20.4. The graph of f is a horizontal line passing through the point (0, 20.4) with no intercepts on the x or y axis.
The inverse function of f(x) is [tex]f^{(-1)(x)} = x/20.4[/tex], which represents a linear function with a slope of 1/20.4 and a y-intercept of 0.
To sketch the graph of [tex]f^{(-1)(x)}[/tex], plot the point (0,0) on the coordinate plane, which represents the y-intercept. Then plot another point by choosing any x-value and finding the corresponding y-value using the formula [tex]f^{(-1)(x)}[/tex] = x/20.4.
To summarize:
The graph of f(x) is a horizontal line passing through the point (0, 20.4) with no intercepts on the x or y axis.
The graph of [tex]f^{(-1)(x)[/tex] is a line passing through the origin with a slope of 1/20.4 and intercepting the x-axis at x = 20.4.
One point on the graph of f(x) is (0, 20.4).
One point on the graph of [tex]f^{(-1)(x)[/tex] is (0, 0), and another point can be found by choosing any x-value and using the formula [tex]f^{(-1)(x)[/tex] = x/20.4 to find the corresponding y-value.
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investment of $2,000 at 10% simple interest for 3 years
on saturday, zoe is playing in the royal arena chess tournament. based on her competitors' rankings, she estimates she has a 50% chance of winning each match. zoe will play 8 matches and needs to win at least 5 of them to make it to the finals on sunday. how likely is it that zoe will make it to the finals? zoe simulates the situation by rolling a six-sided die 8 times. each time an even number appears, it represents zoe winning a match. this table shows the results of 200 trials: number of even numbers012345678 number of trials02184961421891 based on zoe's results, what is the probability that she will make it to the finals?
20 trials may not be enough to get a reliable estimate of the probability, especially if the true probability is close to 0.5.
Based on Zoe's results,
The probability that she will make it to the finals of the Royal Arena Chess Tournament is 96.2%.
Here's how to solve the problem:
Zoe must win at least 5 matches out of 8 to make it to the finals.
There are different ways to solve the problem, but one way is to use the binomial probability formula:
P(X = k) = (n choose k) * [tex]P^{k}[/tex] * [tex]q^{n-k}[/tex]
where:
P(X = k) is the probability of getting exactly k successes out of n trialsn is the number of trialsp is the probability of success in one trialq is the probability of failure in one trial is the probability of getting k successes q^(n-k) is the probability of getting n-k failures(n choose k) is the binomial coefficient, which represents the number of ways to choose k objects out of n distinct objects without regard to order (n choose k) = n! / (k! * (n-k)!)
The binomial probability formula is used to calculate the probability of getting a specific number of successes in a fixed number of independent trials, each with the same probability of success.
It is a discrete probability distribution that describes the probability of X successes in n trials.For this problem:P(X >= 5) = P(X = 5) + P(X = 6) + P(X = 7) + P(X = 8)where:P(X >= 5) is the probability of getting at least 5 successes out of 8 trialsP(X = 5) is the probability of getting exactly 5 successes out of 8 trialsP(X = 6) is the probability of getting exactly 6 successes out of 8 trialsP(X = 7) is the probability of getting exactly 7 successes out of 8 trialsP(X = 8) is the probability of getting exactly 8 successes out of 8 trials
T[tex]0.5^{5}[/tex]he probabilities can be calculated using the binomial probability formula with n = 8 and p = 0.5
Since Zoe estimates she has a 50% chance of winning each match
P(X = 5) = (8 choose 5) * [tex](0.5)^5[/tex]* [tex](0.5)^{(8-5)[/tex] = 56 * 0.03125 * [tex]0.5^3[/tex]
= 0.21875P(X = 6)
= (8 choose 6) * [tex](0.5)^6[/tex] * [tex](0.5)^{(8-6)[/tex]
= 28 * 0.015625 * [tex]0.5^2[/tex]
= 0.109375P(X = 7)
= (8 choose 7) * [tex](0.5)^7[/tex] * [tex](0.5)^{(8-7)[/tex]
= 8 * 0.0078125 *[tex]0.5^1[/tex]
= 0.03125P(X = 8)
= (8 choose 8) * [tex](0.5)^8[/tex] * [tex](0.5)^{(8-8)[/tex]
= 1 * 0.00390625 * [tex]0.5^0[/tex]
= 0.00390625P(X >= 5)
= 0.21875 + 0.109375 + 0.03125 + 0.00390625
= 0.36328125
Therefore, the probability that Zoe will make it to the finals of the Royal Arena Chess Tournament is approximately 36.3%.
However, Zoe simulates the situation by rolling a six-sided die 8 times.
The simulation gives an estimate of the probability, which may be different from the exact probability calculated using the binomial probability formula.
The simulation results may also depend on the sample size (i.e., the number of trials).
In this case, 200 trials may not be enough to get a reliable estimate of the probability, especially if the true probability is close to 0.5.
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Based on Zoe's 200 trials in the simulation the probability that she will make it to the finals means 22% chance.
The probability of her making it to the finals can be calculated by looking at the number of trials where she won at least 5 matches.
According to the table, she won 5, 6, 7, or 8 matches in 14, 21, 8, and 1 trials, respectively.
To find the probability,
1. Add up the number of trials where Zoe won at least 5 matches: 14 + 21 + 8 + 1 = 44 trials
2. Divide this sum by the total number of trials (200): 44/200
In the simulation,
Each even number represents a win for Zoe.
Therefore, we can calculate the probability of Zoe winning at least 5 matches by adding up the probabilities of getting 5, 6, 7, or 8 even numbers in 8 rolls of a six-sided die.
Using the table provided, we can see that there are 218 trials out of 200 where Zoe gets 5 or more even numbers. Therefore, the probability of Zoe winning at least 5 matches is:
218/200 = 1.09 or 109%
This means that based on the simulation, Zoe is more likely than not to make it to the finals.
However,
It is important to note that the simulation assumes that each match has a 50% chance of being won by Zoe, which may not be accurate in real life.
The actual probability of Zoe making it to the finals may be different from the simulation results.
So, based on Zoe's results, the probability that she will make it to the finals is 44/200 or 0.22, which means a 22% chance.
This is based on her simulation using a six-sided die, not her actual 50% chance of winning each match.
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What is the range of the graph ?
from the graph we can clearly see that range along x axis is (-2π,2π) and along y axis is (4,-4)
what is range ?
In statistics, the range is a measure of the spread or dispersion of a set of data. It is the difference between the maximum and minimum values in a dataset.
In the given question,
from the graph we can clearly see that range along x axis. the range is a measure of the spread or dispersion of a set of data. It is the difference between the maximum and minimum values in a dataset.
the start point and end point of wave is (-2π,2π) and along y axis the start point and end point of wave is (4,-4)
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Median of a group of 20 distinct numbers was
found to be 55. If largest 8 numbers are increased by 10, then what is the median of the new group?
55
The median basically means the average of the tenth and eleventh numbers as if the 20 numbers were "cut in half" to find the number in the middle. The median is all based on the order of the numbers from least to greatest. If the largest 8 numbers are increased by ten, that basically means that the tenth and eleventh numbers are unaffected and the order still stays the same from least to greatest. The median would still be 55.
Regroup the amounts so that each person has the same amount. What is the amount?
Tickets earned by friends playing an arcade game: 0,0,0,1,1,2,3
The amount of tickets earned by friends playing an arcade game is 1 ticket .
what is meaning of term amount ?
The term "amount" generally refers to a quantity or a sum of something, often related to a numerical value. It can refer to the total value or quantity of something, such as the amount of money in a bank account
what is arcade game?
An arcade game is a type of video game that was originally designed to be played in public places, such as arcades, malls, and restaurants. These games has gameplay mechanics
In the given question,
To regroup the amounts so that each person has the same amount, we need to find the total number of tickets earned and divide by the number of friends.
Total number of tickets earned = 0 + 0 + 0 + 1 + 1 + 2 + 3 = 7
Number of friends = 7
Each person will have the same amount of tickets if we divide the total number of tickets earned by the number of friends:
7 tickets ÷ 7 friends = 1 ticket per person
Therefore, each person should receive 1 ticket.
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The kid's meals at a fast food restaurant include one of three toys, selected at random. Each toy has an equal chance of being selected. Which simulation tool(s) could be used to find the experimental probability that it will take at least five kid's meals to collect all three toys?
random number list
dice
colored discs
coin
(it lets me pick more than one option)
Answer: coin
Step-by-step explanation: because the dice has to many outcomes
The surface area of the prism is___square units.
Answer:
96
Step-by-step explanation:
SOMEONE, PLEASE HELP ME!!
Answer:
c 96%
Step-by-step explanation:
What is the measure of arc bec in circle d? 134° 150° 209° 210°
Arc BEC measures 210°.
Hence, option (d) 210° is the correct answer.
The measure of arc BEC in circle D is 210°.
Given,
The figure is as follows.
The measure of arc BEC in circle D is to be found.
We see that the arc BEC is subtended by the angle BAC.
We can find the measure of this angle by using the fact that it is the average of the two arcs that it subtends (i.e. arcs BC and DE).
∠BAC = 1/2 (arc BC + arc DE)
= 1/2 (74° + 346°)
= 210°
option (d) 210° is the correct answer.
Now, the measure of arc BEC is equal to the measure of the angle BAC.
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Given the 4 points below, identify what shape is formed and how you found your answer.
Answer:
The shape formed is rectangle.
please help solve questions 4 ( the whole thing)
the call charges for 300 minutes on this contract are R300.
the monthly cost of talking for 300 minutes on this contract is R500.
How determine the call charges for 300 minutes ?To determine the call charges for 300 minutes on this contract, we first need to find out how many minutes are above the 50 free minutes.
300 - 50 = 250 minutes above the free minutes.
The call charges for these 250 minutes are:
250 x R1.20 = R300
Therefore, the call charges for 300 minutes on this contract are R300.
To determine the monthly cost of talking for 300 minutes on this contract, we need to add the subscription fee to the call charges:
Monthly cost = Subscription fee + Call charges
Monthly cost = R200 + R300
Monthly cost = R500
Therefore, the monthly cost of talking for 300 minutes on this contract is R500.
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Two trains are traveling at a constant
speed toward each other on different
tracks. The trains are 252 miles apart
when they start traveling. They pass each
other 4 hours later. One of the trains is
traveling at 253 miles per hour. What is
the speed of the other train?
I need the math shown too!
When we solve for train speed we get: -190 mph
It is clear that this is impossible because speed cannot be negative. Thus, the problem statement must contain a mistake.
what is speed?The rate at which an object travels a distance is called speed.
This is a well-known algebraic puzzle. Let's use "x" for the other train's speed. The first train travels 1012 miles in 4 hours, or 253 miles multiplied by 4.
The second train travels 4 hours' worth of distance, or x * 4 miles. They will have travelled a total of 252 miles when they cross paths. Thus, we can create the following equation:
1012 + 4x = 252
When we solve for x, we get:
x = (252 - 1012) / 4 = -190 mph
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A rock has a mass of 27.54 grams. Since it can't be measured to find its volume, water displacement is used. It is placed in a graduated cylinder with 20 mL of water. Once the rock is in the cylinder, the liquid level is 29.5 mL. What is the volume of the rock?
The volume of the rock is 9.5 mL.
What is the volume ?
To find the volume of the rock using water displacement, we need to subtract the initial volume of water (20 mL) from the final volume of water with the rock in the cylinder (29.5 mL). The difference between the two volumes represents the volume of the rock.
Volume of rock = Final volume - Initial volume
Volume of rock = 29.5 mL - 20 mL
Volume of rock = 9.5 mL
Therefore, the volume of the rock is 9.5 mL.
Volume is the amount of space occupied by an object or a substance. It is a three-dimensional quantity that can be measured in units such as cubic meters (m³), cubic centimeters (cm³), liters (L), or milliliters (mL), depending on the size of the object or substance being measured.
The formula for calculating the volume of a simple geometric shape, such as a cube or a sphere, can be found by multiplying the length, width, and height of the object. For more complex shapes, the volume can be calculated using methods such as water displacement, which involves measuring the amount of water displaced by an object when it is submerged in a container of water.
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Complete question is: A rock has a mass of 27.54 grams. Since it can't be measured to find its volume, water displacement is used. It is placed in a graduated cylinder with 20 mL of water. Once the rock is in the cylinder, the liquid level is 29.5 mL. the volume of the rock is 9.5 mL.
a visit to a hospital emergency room for something as simple as a sore throat could have a mean cost of $320. assume that this cost is normally distributed with a standard deviation of $89. what is the cut-off dollar amount if you want to be in the top 3% of the patients?
the cut-off dollar amount for being in the top 3% of patients is approximately $487.32.
To find the cut-off dollar amount for being in the top 3% of patients visiting the emergency room for a sore throat, we need to use the normal distribution with a mean of $320 and a standard deviation of $89.
Find the z-score for the top 3%
To find the z-score, we can use a z-table, which provides the area under the curve of the standard normal distribution. Since we want to find the top 3%, we will look for 0.97 (1 - 0.03) in the z-table. The z-score corresponding to 0.97 is approximately 1.88.
Convert the z-score to a dollar amount
Now that we have the z-score, we need to convert it to a dollar amount using the mean and standard deviation. The formula for this is:
X = μ + (z * σ)
Where X is the dollar amount, μ is the mean ($320), z is the z-score (1.88), and σ is the standard deviation ($89).
Calculate the cut-off dollar amount
Using the formula from Step 2, we can now calculate the cut-off dollar amount:
X = 320 + (1.88 * 89)
X = 320 + 167.32
X ≈ 487.32
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Help pls, Im very confused and zoning out. Can you please explain and how to work it out. I would very appreciate it. ♥️
Answer:
36 cm
Step-by-step explanation:
a = 1/2 h(b1+b2)
So 10 + 8 = 18 18x4= 72/2 = 36 cm
Find the area. First, find the area of the triangle.
Answer:
18
Step-by-step explanation:
Remember, When finding the area of a triangle (especially a right angled one) the equation is 1/2bh or 0.5bh
Meaning we can do 6x6x0.5 = 18
A beekeeper estimates that his bee population will
grow 30% each year. Currently, he has 125 bees.
Type values into the blank spaces to write a function
that can predict the growth of the bee population
over time, where t is the time in years and B(t) is the
total bee population.
B(t) = ||
)t
(
Answer:
B(t) = 125*(1.3)^t
Step-by-step explanation:
i do not understand algebra 2 very well
The above given graph doesn't follow the property of onto-function so, it is not a onto in nature.
What about onto-function?
In mathematics, an onto function (or surjective function) is a function from one set to another in which every element in the target set is mapped to by at least one element in the domain set. In other words, an onto function maps every element in the target set to some element in the domain set.
Formally, let f: A → B be a function from set A to set B. The function f is onto if and only if for every element b in the target set B, there exists an element a in the domain set A such that f(a) = b.
An onto function is sometimes described as a function that "hits" every element in the target set. This means that the function's range is equal to its target set, or in other words, every element in the target set has a corresponding element in the range.
The concept of onto functions is important in many areas of mathematics, including analysis, algebra, and topology. It is used to study the properties of functions and to define various types of spaces and structures.
According to the given information:
x represents the input, y represent the output
According to the graph, there exists more than one x - values for at least one y - values.
So, there exists more than one input for at least one output
Hence-: No, there exists more than one input for at least one output is correct option.
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a college bookstore store sells hoodies. they want to price their hoodies to sell as many as possible during homecoming week. the table below gives the price (in $) of their hoodies and the weekly quantity they would sell at this price. find the linear regression equation that gives the quantity of hoodies sold as a function of the price. round each coefficient in the regression equation to 2 decimal places.
The linear regression equation that gives the quantity of hoodies sold as a function of the price: y = -2.6147x + 215.34
And the number of hoodies the bookstore can sell if the price is $32. = 131
To find the linear regression equation that represents the quantity of hoodies sold as a function of the price, we will use a calculator or a spreadsheet program to perform linear regression analysis on the data.
The scatter plot with the line of linear regression of the data is shown below.
The linear regression equation that gives the quantity of hoodies sold as a function of the price is:
y = -2.6147x + 215.34
here x represents the price of hoodie and y represents the quantity of hoodies.
Now we determine the number of hoodies the bookstore can sell if the price is $32.
i.e., for x = 32 we need to find the value of y
y = -2.6147(32) + 215.34
y = 131.6696
y ≈ 131
Therefore, the number of hoodies the bookstore can sell if the price is $32. = 131
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Find the complete question below.
as part of an animation the length and width of the image are decreased by 8 pixels every second. The total number of pixels in the image after t seconds is given by the function A(t)=(256-8t)(192-8t). After how many seconds will the number of pixels be reduced to 0. Answer
Answer:24 seconds
Step-by-step explanation:
Since A(t) equals the total number of pixels in the image, then to figure out when it will be zero you just need to set A(t) equal to zero. This gives you the equation
[tex]0=(256-8t)(192-8t)[/tex]
Since this equation equals zero, we know either 256-8t must equal 0 or 192-8t must since they are multiplied.
We can split this into two equations
[tex]256-8t=0[/tex]
[tex]8t=256\\t=32[/tex]
and
[tex]192-8t=0\\8t=192\\t=24[/tex]
So, after 24 and 32 seconds both the width and height equal zero. Only the height or the width need to equal zero for the total area to equal zero (A=w*h), so we go with the lesser time, 24 seconds.
Steven went to the mall with some money. He bought 3 pairs of pants for $35 dollars each and 7 shirts for $10 dollars each. Now he has $25 dollars left. How much money did Steven start with?
A hotel woth 225 rooms has 175 for doubles and 50 singles. Singles can be booked in any room, but reservations for two or more people must be booked in double rooms. Let x be the number of single reservations and y the number of reservations for two or more. Which system of inequalities represents this situation?
the system of inequalities that represents this situation is: x ≤ 50 , y ≤ 100 , 175 - y ≥ x Let's start by defining some variables:
Let x be the number of single reservations.
Let y be the number of reservations for two or more people.
Since there are 50 single rooms and x single reservations, there must be at least 50 - x double rooms available for reservations for two or more people. Since each of these double rooms can accommodate 2 or more people, the total number of people who can be accommodated in these double rooms is 2(50 - x) = 100 - 2x.
The total number of people who can be accommodated in the hotel is 2x + (100 - 2x) = 100. This means that y, the number of reservations for two or more people, must satisfy the inequality y ≤ 100.
Each reservation for two or more people requires a double room, so the total number of double rooms used for reservations for two or more people is y. Since there are 175 double rooms in the hotel, the number of double rooms available for single reservations is 175 - y. Each single reservation requires one room, so the total number of single rooms used for reservations is x.
Therefore, the system of inequalities that represents this situation is:
x ≤ 50
y ≤ 100
175 - y ≥ x
The first inequality represents the fact that the number of single reservations must be less than or equal to the number of single rooms available. The second inequality represents the fact that the number of reservations for two or more people must be less than or equal to the total number of people who can be accommodated in double rooms. The third inequality represents the fact that the number of double rooms available for single reservations must be greater than or equal to the number of single reservations.
These three inequalities together represent the constraints on the number of single and double rooms that can be used for reservations, and the number of people who can be accommodated in the hotel. Solving this system of inequalities will give us the feasible region of the problem, which will allow us to find the optimal solution
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