"The graph of f(x) has exactly two x-intercepts" - For a linear function whose domain is the set of all real numbers, this assertion cannot be accurate.
Any function with the formula f(x) = mx + b is referred to as linear.
Setting f(x) = 0, we get:
mx + b = 0
Solving for x, we get:
x = -b/m
Depending on the slope m and y-intercept b values, there are an unlimited number of x-intercepts.
What are linear functions?A linear function in mathematics is one that has either one or two variables and no exponents. It is a function with a straight line as its graph. If the function has more variables, they should all be constants or known variables in order for the function to continue to function as a linear function. A linear function is a function that, when plotted, creates a straight line. Typically, it is a polynomial function with a maximum degree of 1 or 0. Nonetheless, calculus and linear algebra are also used to represent linear functions. The function notation is the only distinction. It is also important to understand an ordered pair written in function notation.
from the questions:
A function with the formula f(x) = mx + b, where m and b are constants, is referred to as a linear function. When f(x) = 0, the point where a linear function intersects the x-axis is known as the x-intercept.
Setting f(x) = 0, we get:
mx + b = 0
Solving for x, we get:
x = -b/m
As a result, the x-intercept of a linear function is a single point, (-b/m, 0), and depending on the slope m and y-intercept b values, there may only be zero, one, or infinitely many x-intercepts.
As a result, for a linear function whose domain is the set of all real numbers, it is not possible for the statement "The graph of f(x) has precisely two x-intercepts" to be true.
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Draw and determine the equation of a trend line that modles the data set (1, 27.5), (4,35), (7,42.5), (10, 50), (13, 57.5)
Answer: To draw a trend line that models the given data set, we first need to plot the points on a graph. We can use a scale of 1 unit on the x-axis and 5 units on the y-axis to plot the points as follows:
(1, 27.5) ●
(4, 35) ●
(7, 42.5) ●
(10, 50) ●
(13, 57.5) ●
We can see that the points roughly form a straight line. To find the equation of the trend line, we can use linear regression, which involves finding the line that best fits the data.
Using a calculator or software, we can find that the equation of the trend line is:
y = 3.5x + 24
This means that for every increase of 1 unit in x, y increases by 3.5 units. The y-intercept of the trend line is 24, which represents the value of y when x = 0.
We can plot the trend line on the same graph as follows:
|
60 |-●-
| |
55 |-●-----
| |
50 |-●-------
| |
45 |-●--------
| |
40 |-●----------
| |
35 |-●------------
| |
30 |-●--------------
| |
25 |-●-----------------
| |
--------------------
1 4 7 10 13
The dots represent the original data points, and the line represents the trend line.
Step-by-step explanation:
Brainlist for quickest answer
Which of the following describes an approach used to harness tidal energy?
I. Floating platform with turbines
II. Floating ship with turning pendulum
III. Having water spin turbines attached to fence
I only
II only
I and II
I, II, and III
Sure! Tidal energy is a type of renewable energy that is harnessed from the movement of ocean tides. There are different approaches to harnessing tidal energy, but the three options given in the question are:
I. Floating platform with turbines: This approach involves anchoring a floating platform in the tidal zone, where the rise and fall of the tides can be used to turn turbines and generate electricity. The turbines are connected to generators, which convert the mechanical energy of the turning turbines into electrical energy. This approach is commonly used in commercial tidal energy projects, such as the MeyGen tidal energy project in Scotland.
II. Floating ship with turning pendulum: This approach, also known as the "pendulor" or "pendulum" system, involves a floating ship or barge that is anchored in the tidal zone. The ship is designed to swing back and forth with the movement of the tides, and this movement is used to turn a pendulum, which in turn drives a generator. The idea behind this approach is that the ship's movement can be used to generate more energy than just the up-and-down motion of a floating platform with turbines. However, this approach is still in the experimental phase and has not yet been deployed on a commercial scale.
III. Having water spin turbines attached to fence: This approach involves installing turbines directly in the flow of tidal currents. The turbines are attached to a fence-like structure, which guides the flow of water and increases the speed of the current as it passes through the turbines. The spinning turbines generate electricity, which is then sent to a generator and converted into usable power. This approach is also known as "barrage" or "fence" technology, and it has been used in a few commercial tidal energy projects, such as the La Rance tidal power plant in France.
So, to answer the question, the correct answer is "I and III" since both involve using turbines to generate electricity from the movement of ocean tides.
Floating platform with turbines and Having water spin turbines attached to fence best describes an approach used to harness tidal energy.
What is Energy?Energy is the capacity to do work
The approach used to harness tidal energy is described by option I and III.
I. Floating platform with turbines - This involves placing turbines on floating platforms that are anchored to the seabed.
As the tide comes in and out, the water flows through the turbines, generating electricity.
III. Having water spin turbines attached to fence - This involves building a fence-like structure across a tidal inlet.
As the tide comes in and out, the water flows through the fence and spins turbines, generating electricity.
Option II, floating ship with turning pendulum, does not describe an approach used to harness tidal energy.
Therefore, floating platform with turbines and having water spin turbines attached to fence best describes an approach used to harness tidal energy.
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How can you use a math keyboard on your phone
Answer:
Once you have the cable, it will be simple to connect your phone to your laptop. On your phone, go to Settings and then the System page. Scroll down until you find the section entitled “OTG storage,” and turn on the option. When you connect the USB OTG cable to the physical keyboard, you will be able to use the keyboard to type on your phone.
Step-by-step explanation:
Please help me :( I would appreciate it.
use the Remainder Theorem and synthetic division please
Answer:
f (3) = 142
Step-by-step explanation:
#CarryOnLearning
What is the value of 40-2n, when n=2?
18
36
38
44
10 points
Answer: 36
Step-by-step explanation: plug in 3 for n.
40-2(2)= 36
Consider parallelogram ABCD below.
Use the information given in the figure to find x, m
Answer:
x = 3 ; ∠m B = 85° ; ∠m BAC = 34°
Step-by-step explanation:
Opposite sides of a parallelogram are equal. If 2x = 6, then x must be equal to 3. The same idea goes for angles. Since angle D measures 85°, angle B must as well. Using the formula 180°(n-2), where n = number of sides, it is seen that there are 180°(2) = 360° in a four sided shape. Knowing two of them, we can subtract 85*2 from 360 to find the rest of the degrees. 360° - 170° = 190°. Since the other two angles are equal as well, 190°/2 = 95°. Since ∠m DAC = 61°, ∠m BAC must equal 95°-61°, which is equal to 34°
Can someone help me with this question
Answer:
I think z>1.5 because it is not bold and underlined
Malik plans to make changes to his yard. He wants to double the lengths of the sides
of the garden, using the right angle vertex as the center of dilation. His garden will
then be rotated 180° about the right angle vertex and moved 11 feet to the right and
13 feet up.
Answer:
48.2 degrees
Step-by-step explanation:
look at photo
Thomas loves tomatoes. He plans to fill the container shown below with soil to grow his own tomato plants. The dimensions of the container are shown in inches.
How much soil will the container hold?
Either enter an exact answer in terms of \piπpi or use 3.143.143, point, 14 for \piπpi.
The required container can hold approximately 1570.8 cubic inches of soil.
Explain about Container.By enclosing units in containers—that is, by circling, boxing, or otherwise enclosing units—container numbers indicate magnitude. The worth of each container's contents is multiplied by the number system's fundamental unit. Typically, the basis is either 2 or 10 (the decimal system) (the binary system).
According to question:To find the volume of the container, we can use the formula for the volume of a cylinder:
[tex]$$ V = \pi r^2 h $$[/tex]
where r is the radius of the base (half the diameter) and $h$ is the height of the cylinder.
In this case, the diameter of the container is 10 inches, so the radius is half that, or 5 inches. The height is given as 20 inches. Substituting these values into the formula, we get:
[tex]$$ V = \pi (5\text{ in})^2 (20\text{ in}) = \pi (25\text{ in}^2)(20\text{ in}) \approx 1570.8 \text{ in}^3 $$[/tex]
Therefore, the container can hold approximately 1570.8 cubic inches of soil.
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Complete question:
Thomas loves tomatoes he plans to fill the container with soil to grow his own tomato plant the diameter of the container is 10 inch and height 20 inch how much soil will the container hold.
ordered pairs of x=7y+2
Answer: The equation x = 7y + 2 is a linear equation in two variables, x and y. To find ordered pairs of x and y that satisfy this equation, we can choose values of y and then solve for x.
For example, if we choose y = 0, then:
x = 7y + 2
x = 7(0) + 2
x = 2
Therefore, the ordered pair (2, 0) satisfies the equation x = 7y + 2.
Similarly, if we choose y = 1, then:
x = 7y + 2
x = 7(1) + 2
x = 9
Therefore, the ordered pair (9, 1) satisfies the equation x = 7y + 2.
We can continue in this manner to find more ordered pairs. However, note that there are infinitely many ordered pairs that satisfy this equation, as the equation represents a line with a slope of 7 and a y-intercept of (0, 2). Therefore, we can choose any value of y and obtain a corresponding value of x that satisfies the equation.
Step-by-step explanation:
If a ball is thrown upward at 128 feet per second from the top of a building that is 140 feet high, the height of the ball is given by
S = 140 + 128t − 16t2 feet
t=
According to given information the correct answer is [tex]$t =[/tex] [tex]\frac{5}{4}$[/tex] seconds.
What is Equations?An equation is a mathematical statement that asserts the equality of two expressions. It typically consists of two expressions separated by an equals sign (=), with the expression on the left side equal to the expression on the right side. The equals sign indicates that the two expressions have the same value for some or all values of the variables involved.
The equation that gives the height [tex]($S$)[/tex] of the ball at time [tex]($t$)[/tex] is:
[tex]$$S = 140 + 128t - 16t^2$$[/tex]
To find the time [tex]($t$)[/tex] when the ball is at a certain height, we can set the equation equal to that height and solve for [tex]t$.[/tex]
For example, if we want to find the time when the ball is at a height of 200 feet, we would set [tex]$S = 200$[/tex] and solve for [tex]t$:[/tex]
[tex]$$200 = 140 + 128t - 16t^2$$[/tex]
Rearranging and simplifying, we get:
[tex]$$16t^2 - 128t + 60 = 0$$[/tex]
Dividing both sides by 4, we get:
[tex]$$4t^2 - 32t + 15 = 0$$[/tex]
We can solve for [tex]$t$[/tex] using the quadratic formula:
[tex]$$t[/tex]= [tex]\frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$$[/tex]
where [tex]a = 4$, $b = -32$,[/tex] and [tex]c = 15$.[/tex]
Plugging in these values, we get:
[tex]$$t[/tex] = [tex]\frac{-( -32) \pm \sqrt{(-32)^2 - 4(4)(15)}}{2(4)}$$[/tex]
Simplifying, we get:
[tex]$$t =[/tex] [tex]\frac{32 \pm \sqrt{484}}{8}$$[/tex]
[tex]$$t =[/tex][tex]\frac{32 \pm 22}{8}$$[/tex]
Therefore, the possible values of [tex]$t$[/tex] are:
[tex]$$t =[/tex] [tex]\frac{7}{2} \quad \text{or} \quad t = \frac{5}{4}$$[/tex]
Since the ball is thrown upward, the time when the ball is at a height of 200 feet is the time it reaches the height of 200 feet on its way up, not on its way down.
Therefore, according to given information the correct answer is [tex]$t =[/tex] [tex]\frac{5}{4}$[/tex] seconds.
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the 2 expressions below are equivalent expressions. is isaac correct? explain your reasoning. - 2(3x - 5) and - 6x - 10
Answer: Isaac is unfortunately incorrect.
Step-by-step explanation: We want to determine if -2(3x-5)=-6x-10. We can apply the distributive property to the parentheses on the left side of the equation to see if this statement is true.
-2(3x-5)=-2*3x+-2*-5=-6x+10
The left side simplifies to -6x+10 which is not equivalent to -6x-10.
Hope this helps!
d) El automóvil de Julián recorre aproximadamente 12 km por
cada litro de gasolina. ¿Cuántos litros necesitaría para re-
correr 180 km?
We will see that the car needs 15 liters to travel the 180 km.
How many liters would he need to travel 180 km?We know that this car travels 12 km for each liter of gasoline, so we must see how many times there are 12 kilometers in 180 km, then we must take the quotient:
180km/12km = 15
And for each one of those times, the car consumes one liter, so in total there are 15*1 l = 15 l
The car needs 15 liters to travel 180 km.
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Write the following number in words: 3 811 459
Answer: three million eight hundred eleven thousand four hundred fifty nine
1 000 000 = million
100 000 = hundred thousand
10 000 = ten thousand
1 000 = one thousand
100 = one hundred
10 = ten
1 = one
When I would look at questions like this I would use this chart and replace the numbers and I found that this really helped
Find the value of x.
Given:-
[tex] \rm \: (3x+9)°[/tex][tex] \: [/tex]
[tex] \rm(4x +3) \degree[/tex][tex] \: [/tex]
Solution:-
[tex] \rm \: (3x+9)=(4x+3)[/tex][tex] \: [/tex]
[tex] \rm \: 3x + 9 = 4x + 3[/tex][tex] \: [/tex]
[tex] \rm \: 3x - 4x = 3 - 9[/tex][tex] \: [/tex]
[tex] \rm \: -1x = -6.[/tex][tex] \: [/tex]
[tex] \rm \: x = \cancel \frac{ - 6}{ - 1} [/tex][tex] \: [/tex]
[tex] \boxed{ \underline{\rm \purple{ \: \: x = 6 \: \: }}}[/tex][tex] \: [/tex]
Therefore , the value of x is 6 !
━━━━━━━━━━━━━━━━━━━━━━━
hope it helps! :)
Determine if the 3 lengths make a triangle. If they do, classify as acute, right, or obtuse.
a. 5, 6, 7
b. 1.6, 1.8, 3.1
c. 7, 9, 15
d. 4, 5, 10
e. 15, 20, 25
(45 points)
Answer: Your welcome!
Step-by-step explanation:
a. Yes, this makes a triangle. It is an acute triangle.
b. Yes, this makes a triangle. It is an acute triangle.
c. Yes, this makes a triangle. It is an obtuse triangle.
d. No, this does not make a triangle. The side lengths do not add up to more than the other two sides combined.
e. Yes, this makes a triangle. It is an obtuse triangle.
Answer: Its C
Step-by-step explanation:
0.0001 ÷ 28,0000 help
Answer:
3.5?
Step-by-step explanation:
sorry that's all i can do..
Answer: 3.5714286e^-10 or 0.00000000035714286 or 3.5714286 × 10^-10
Step-by-step explanation:
First, we divide 0.0001 by 28, which equals 3.5714286e-6.
And since we added 4 zeros to the equation, the negative (e) will be pushed by -4. So, it should look like this: 3.5714286e-10, and the equation is complete.
It is reported on the local weather broadcast that the day's temperatures will stay between –4° and 4°. Which of these represents a series of temperatures that could occur during the day?
Answer:
Any series of temperatures between -4° and 4° could occur during the day, as long as they stay within that range. For example, the temperature could start at -3°, then rise to 1°, fall to -2°, and rise again to 3°, and so on. Another example could be the temperature staying constant at 0° throughout the day. Therefore, there are many possible series of temperatures that could occur during the day, as long as they stay within the given temperature range.
WILL GIVE BRAINLIEST
(Theoretical Probability MC)
A set of 3 cards, spelling the word ADD, are placed face down on the table. Determine P(A, D) if two cards are randomly selected with replacement.
O
ها فيا
W|N
O
2/9
69
Answer:
Option 4 4/9
Step-by-step explanation:
What is the area of triangle ABC?
The area of the triangle ABC is (c) 36√3 square units
How to determine the area of triangle ABC?From the question, we have the following parameters that can be used in our computation:
Side length, l = 12 units
Triangle type = Equilateral triangle
The side lengths of an equilateral triangle are congruent, and the area of a triangle is equal to half of the product of the base and the height of the triangle.
Using the above as a guide, we have the following:
Area = 1/4√3 * l^2
Substitute the known values in the above equation, so, we have the following representation
Area = 1/4√3 * 12^2
Evaluate
Area = 36√3
Hence the area is 36√3
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CAN SOMEONE PLEASE HELP ME WITH THIS QUESTION?
The trigonometric ratio for the cosine of the angle W derived as 48.18712, is equal to 0.6667.
What is trigonometric ratios?The trigonometric ratios is concerned with the relationship of an angle of a right-angled triangle to ratios of two side lengths.
The basic trigonometric ratios includes;
sine, cosine and tangent.
cos W = 10/15 {adjacent/hypotenuse}
cos W = 2/3
W = cos⁻¹(2/3) {cross multiplication}
W = 48.18712
cos W = cos 48.18712
Therefore, the cosine of the angle W is equal to using the trigonometric ratio.
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5. My sisters were having a
lemonade stand. They
made 2 gallon of
lemonade. If they divided it
equally into 6 cups, how
much lemonade was in
each cup?
there are 3 cups of lemonade in each cup
Brad is standing on a hill which places him at the same height as a nearby flagpole. The flagpole is 15 ft. high and Brad is 20 ft. horizontally from the top of the pole. Brad can see the bottom of the flag pole.
What is the length in feet of Brad's "line of sight" to the base of the flagpole?
Record your answer and fill in the bubbles on your answer document. Be sure to use the correct place value.
Answer:
your ans please mark me brainiest
a machine can produce article A in 12 minutes or article B in 16 minutes. If it is planned to produce twice as many of A as B in a working week of 40 hours how many of each will be produced. Assuming that the machine is working nonstop.
In a working week of 40 hours, 120 articles A and 60 articles B will be produced.
What is a numerical expression?A numerical expression is a mathematical statement written in the form of numbers and unknown variables. We can form numerical expressions from statements.
Let, 'a' be the number of articles A produced and 'b' be the number of articles B produced.
Therefore, From the given information the equation can be modeled as,
12a + 16b = 60×40.
12a + 16b = 2400, and a = 2b.
12×2b + 16b = 2400.
24b + 16b = 2400.
40b = 2400.
b = 60 and hence a = 120.
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1. Is b greater than or less than 2? Explain how you know. 2. Write an equation that defines g. Show your reasoning. 3 f and g represent the number. In thousands. Of social media followers of two organizations as a function of years since 2010. What does the intersection of f and g mean in this context?
The variable b is greater than 2
The equation that defines g is g(x) = 3(4)^xThe intersecting of f and g is the year the they have equal followersHow to determine if b is greater or less than 2The graph (see attachment) represents the given parameter
The function g is given as
g(x) = a * b^x -- the red line
Using the points on the graph, we have
b = 12/3
b = 4
So, b is greater than 2
Equation that defines gIn (a), we have
g(x) = a * b^x -- the red line
Where
a = g(x) when x = 0
So, we have
a = 3
The function becomes
g(x) = 3(4)^x
The meaning of the intersecting of f and gBased on the function definitions, the intersecting of f and g represent the year when the organizations have the same number of followers
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HELP PLEASE FAST!!! How do I do this???
If a catapult launches a boulder at an initial height of 15ft and it hits the ground after 6.7 seconds.
a) What was the boulder's initial velocity?
b) What was the maximum height reached by the boulder?
The boulder's maximum height is 242.6 feet.
It takes the boulder 3.79 seconds to reach its maximum height
What is Motion?Motion is the phenomenon in which an object changes its position with respect to time. Motion is mathematically described in terms of displacement, distance, velocity, acceleration, speed.
here, we have,
From the question, we are to determine the maximum height of the boulder
First, we will calculate the time it took the boulder to reach its maximum height
Using the formula,
v = u - gt
Where v is the final velocity
u is the initial velocity
g is the acceleration due to gravity (g = 32.1741 ft/s²)
and t is the time
From the given information
u = 122 ft/s
At maximum height, v = 0 ft/s
Putting the parameters into the equation, we get
0 = 122 - 32.1741t
32.1741t = 122
t = 3.79 s
This means it takes the boulder 3.79 seconds to reach its maximum height.
Now, substitute the value of t into the function that gives the height of the boulder
From the given information,
The height of the boulder is given by
H(t)= -16t² + 122t + 10
Then,
H(3.79) = -16(3.79)² + 122(3.79) + 10
H(3.79) = -229.8256 + 462.38 + 10
H(3.79) = 242.5544
H(3.79) ≅ 242.6 ft
Hence, the boulder's maximum height is 242.6 feet.
It takes the boulder 3.79 seconds to reach its maximum height
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Point a,b, and c are collinest. Point b is between a and c. AC = -3 + 6x, AB = 3x - 3, and BC = 9. Find x.
Therefore , the solution of the given problem of equation comes out to be x has a value of 4.
Define equation.The equation y=mx+b is the basis of a linear regression model. B is the slope, and m is the y-intercept. The aforementioned sentence is repeatedly alluded to as a "math problem with two variables," despite the fact that y and y are distinct parts. In bivariate linear equations, there are only two variables. The application regions for linear equations have no definitive solutions.
Here,
We could use segment addition principle to write: since B is situated between A and C.
=> AB + BC = AC
Inputting the numbers provided yields:
=> -3 + 6x = 3x - 3 + 9
When we simplify the solution, we get:
=> 6x - 3x = 9 + 3
=> 3x = 12
=> x = 4
Consequently, x has a value of 4.
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When Leslie first moved to Lime County one year ago, it had a population of about 711,500.
Today, the population in the county is about 697,270, and it is expected that the population
will continue to decline each year.
Write an exponential equation in the form y = a(b)* that can model the population of Lime
County, y, x years after Leslie moved there.
Use whole numbers, decimals, or simplified fractions for the values of a and b.
y =
The exponential equation that models the population of Lime County would be: y = 711,500(0.979)^x
How to find the values of a and b?We can use the information from the question. When Leslie moved to Lime County, the population was 711,500, i.e.:
When y=711,500, x=0.Currently, the population is around 697,270, that is: When y=697,270, x=1.Let's then use this information to set up two equations:
711,500=a(b)^0a=711,500697,270=a(b)¹b=697,270/aLet's now substitute the value of a into the second equation:
b=697,270/711,500=0.979Therefore, we find the exponential equation that models the population of Lime County, which is:
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Need help with math problem
The measure of angle WUX is 78⁰.
option D.
What is the measure of angle WUX?
The measure of angle WUX is calculated by applying the following triangle principles.
∠ VUX + ∠VXU = 90 ( complimentary angles )
7x + 11 + 11x + 7 = 90
18x + 18 = 90
18x = 72
x = 72/18
x = 4
The measure of angle VXU is calculated as;
∠VXU = 11x + 7
= 11 x 4 + 7
= 51⁰
The measure of angle UWV is calculated as;
∠ UWV = 6x + 27
= 6 x 4 + 27
= 51⁰
The measure of angle WUX is calculated as;
∠ WUX = 180 - ( 51 + 51 ) ( sum of angles in a triangle )
∠ WUX = 180 - 102
∠ WUX = 78⁰
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Suppose that the relation H is defined as follows.
H = {(−3, 8) , ( 0, -3) , (1, 3) , (1, -1)}
Give the domain and range of H.
Write your answers using set notation.
Domain = ?
Range = ?
The highest value and lowest value of x is domain, here domain is [1, -3]
The highest value and lowest value of y is range, here range is [8, -3].
What is domain and range?Mathematical operations are comparable to those of a soda vending machine. You can choose from a variety of sodas when you deposit a certain sum of money. Similar to how we input different numbers into functions, we also receive new numbers as the outcome. The two main characteristics of functions are domain and range.
A soda can be purchased with quarters and one dollar bills. If pennies are put into the machine, no soda flavour will be provided. As a result, the domain represents the possible inputs, which are quarters and one-dollar bills. No matter how much you pay, a soda machine won't give you a cheeseburger. The range represents the potential outputs we can have in this situation, that is, the flavors of soda in the machine.
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