The range is expressed in interval notation as (-1, ∞)
How to find the function (f+g)(x)?To find the linear function f(x), let us use the table given.
A linear function with the following equation that passes through the points (a, g(a)) and (b, g(b)):
[tex]g(x) - g(a) = \frac{g(b)-g(a)}{b-a} (x-a)[/tex]
Because the g(x) line crosses through points (-6, 14) and (-3, 8), we have:
a = -6, g(a) = 16, b = -3 and, g(b) = 10
Therefore g(x)
[tex]g(x) - (16) = \frac{10-16}{-3-(-6)} (x--(6))\\g(x) - 16 = \frac{10-16}{-3+6} (x+6)\\g(x) - 16 = \frac{-6}{3} (x+6)\\g(x) - 16 = -2(x +6)\\g(x) = -2x -12+16\\g(x) = -2x+4[/tex]
now find the (f+g)(x).
[tex](f+g)(x) = f(x) + g(x) = x^{2} + 2x -5 -2x + 4\\(f+g)(x) = f(x) + g(x) = x^{2} - 1\\[/tex]
(f+g)(x) = (x-1)(x+1), therefore we get the values x = 1 and x = -1
The parabola's vertice has x-coordinate 0 (the midway between the roots). At x = 0, we get:
[tex](f +g)(x) = 0^{2} - 1 = -1[/tex]
Furthermore, because the coefficient of [tex]x^{2}[/tex] is 1, which is positive, this function indicates a parabola that has been opened upwards.
As a result, the function's minimal value is y = -1. As a result, the function's range includes all real numbers equal to or greater than -1.
The range is expressed in interval notation as (-1, ∞)
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At a local play, student tickets cost $6 each and adult tickets cost $11 each. If ticket sales were $3,000 for 400 tickets, how many students attended the play?
120
180
220
280
Answer:
If ticket sales were $3,000 for 400 tickets then 280 students attended the play.
Step-by-step explanation:
Given cos A = 3/10 and tan A < 0 , find sin A .
Answer: Since we know that cos A = 3/10, we can use the Pythagorean identity to find sin A:
sin^2 A + cos^2 A = 1
sin^2 A = 1 - cos^2 A
sin A = sqrt(1 - cos^2 A)
Substituting cos A = 3/10, we get:
sin A = sqrt(1 - (3/10)^2)
sin A = sqrt(1 - 9/100)
sin A = sqrt(91)/10
Since we also know that tan A < 0, we know that the sine and tangent of A have opposite signs, and therefore sin A is negative.
Therefore:
sin A = -sqrt(91)/10
Step-by-step explanation:
Which is NOT the same as asking:
What is the logarithm of 1,296 if the base is 6?
1. You go to the ice cream shop with your friends and you can choose an ice cream, a topping
and sprinkles. How many different sundaes can you make when you order one flavor of ice
cream, one topping and one color of sprinkles from the chart below? Show all possible
outcomes in a tree diagram.
Ice Cream
Chocolate
Vanilla
Strawberry
Topping
Fudge
Marshmallow
Sprinkles
Chocolate
Rainbow
How many sample spaces are there? HINT: How many possible combinations?
b. P (Chocolate, Fudge, Rainbow)
Answer:
Step-by-step explanation:
Answer:
You can make 12 possible sundaes with these toppings.
Step-by-step explanation:
Chocolate, Vanilla, and Strawberry all have 4 possible outcomes:
1. Fudge & Chocolate Sprinkles
2. Fudge & Rainbow Sprinkles
3. Marshmallow & Chocolate Sprinkles
4. Marshmallow & Rainbow Sprinkles
-------------------------------------------------------------------------------------------------------------
4 x 3 will equal 12, the total possible sundaes you can make with these toppings and ice cream flavors.
On the Y axis, we have the profit from the trucking company and on the X axis, we have the miles the truck has traveled. The company decided that they needed to start paying for a driver at a price of 0.25 cents a mile. After this change what will happen to the x and y axis/slope?
A. Y intercept will be less and X will be less
B. Y intercept will be less and X intercept will be greater
C. Y intercept will be greater and X will be greater
D. Y intercept will be greater and X will be less
The correct answer is: A. Y intercept will be less and X will be less.
What is slope?A linear function's slope is a gauge of how steep the line is. Between any two points on the line, it is the ratio of the change in the y-coordinate to the change in the x-coordinate. The formula is used to compute it:
slope equals (y2 - y1)/. (x2 - x1)
where any two points on the line (x1, y1) and (x2, y2) are.
The company's expenses will rise once it begins paying a driver at a rate of 0.25 cents per mile, which means its profit will decline. The profit curve on the y-axis will go vertically downward as a result of this. But, because the cost of paying the driver is fixed per mile and has no impact on the profit per mile, the slope of the line—which reflects the profit per mile—will stay the same.
Hence, A. Y intercept will be less and X will be less is correct.
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coordinate plane with points at A 0 comma 2 and B 2 comma 0 intersected by line f Dilate line f by a scale factor of one half with the center of dilation at the origin to create line f′. Where are points A′ and B′ located after dilation, and how are lines f and f′ related? The locations of A′ and B′ are A′ (0, 2) and B′ (0, 0); lines f and f′ intersect at point A. The locations of A′ and B′ are A′ (0, 1) and B′ (1, 0); lines f and f′ are parallel. The locations of A′ and B′ are A′ (0, 0) and B′ (2, 0); lines f and f′ intersect at point B. The locations of A′ and B′ are A′ (0, 2) and B′ (2, 0); lines f and f′ are the same line.
The answer of the given question based on the graph is , The locations of A′ and B′ are A′ (0, 1) and B′ (1, 0); lines f and f′ are parallel.
What is Scale factor?A scale factor is a number that scales, or multiplies, a quantity by some factor. It is used in mathematics to describe the relationship between corresponding measurements of two similar figures, such as triangles or rectangles.
To dilate line f by scale factor of one half with center of dilation at origin, we multiply coordinates of each point on line f by 1/2.
The equation of line f can be found by using the points A and B:
slope of line f = (0 - 2)/(2 - 0) = -1
y-intercept of line f = 2
Therefore, the equation of line f is y = -x + 2.
To find the coordinates of A' and B' after dilation, we can apply the dilation factor to each point:
A' = (0, 2)*1/2 =(0, 1)
B' = (2, 0)*1/2 =(1, 0)
So A' is located at (0, 1) and B' is located at (1, 0) after dilation.
Now let's analyze the relationship between lines f and f'. The dilation was centered at the origin, so the origin is a fixed point of the dilation. This means that the point where lines f and f' intersect must be the origin.
If we plug in x = 0 into the equation of line f, we get y = 2. This means that point A is located at (0, 2) and intersects with line f at y = 2. After dilation, point A' is located at (0, 1), which means that lines f and f' intersect at point A.
To determine the relationship between lines f and f', we can compare their equations. The equation of f' can be found by using the points A' and B':
slope of f' = (0 - 1)/(1 - 0) = -1
y-intercept of f' = 0
Therefore, the equation of f' is y = -x.
Comparing the equations of f and f', we can see that they have the same slope of -1, which means they are parallel. Therefore, the correct answer is: The locations of A′ and B′ are A′ (0, 1) and B′ (1, 0); lines f and f′ are parallel.
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Let u = 4i-j, v = 5i + j. and w=i+6j.
Find the specified scalar
U*V+U*W
To find the specified scalar, we need to first find the dot product of U and V, and then the dot product of U and W, and add these two dot products together:
U·V + U·W
where U·V denotes the dot product of U and V, and U·W denotes the dot product of U and W.
The dot product of two vectors a = (a1, a2) and b = (b1, b2) is given by:
a · b = a1b1 + a2b2
Using this formula, we can find the dot product of U and V:
U · V = (4i - j) · (5i + j) = 4i · 5i + 4i · j - j · 5i - j · j = 20i^2 + (4i · j - 5i · j) - j^2 = 20 + (-i · j) - 1 = 19 - i · j
Next, we can find the dot product of U and W:
U · W = (4i - j) · (i + 6j) = 4i · i + 4i · 6j - j · i - j · 6j = 4i^2 + (4i · 6j - j · i) - 6j^2 = 4 + (24i · j) - 6 = -2 + 24i · j
Now we can substitute these values into the original expression:
U·V + U·W = (19 - i·j) + (-2 + 24i·j) = 17 + 23i·j
Therefore, the specified scalar is 17 + 23i·j.
4. Assuming that the rectangles have whole number side lengths, why is it possible to draw two different rectangles that have an area of 30 square inches but not possible to draw two rectangles with an area of 7 square inches?
Answer:
hm
Step-by-step explanation:
The reason why it is possible to draw two different rectangles that have an area of 30 square inches is that there are multiple pairs of whole numbers that multiply to 30. For example, a rectangle with dimensions 5 inches by 6 inches has an area of 30 square inches, and so does a rectangle with dimensions 2 inches by 15 inches.
However, the number 7 is a prime number, which means it can only be divided evenly by 1 and itself. Therefore, the only way to get an area of 7 square inches for a rectangle is by multiplying 1 and 7, which means the dimensions of the rectangle would be 1 inch by 7 inches. Since there are no other pairs of whole numbers that multiply to 7, it is not possible to draw two different rectangles with an area of 7 square inches.
On the Y axis, we have the profit from the trucking company and on the X axis, we have the miles the truck has traveled. The company decided that they needed to start paying for a driver at a price of 0.25 cents a mile. After this change what will happen to the x and y axis/slope?
A. Y intercept will be less and X will be less
B. Y intercept will be less and X intercept will be greater
C. Y intercept will be greater and X will be greater
D. Y intercept will be greater and X will be less
Answer:
B.
Step-by-step explanation:
Answer:
B.
Step-by-step explanation:
the description is very confusing and lacks any hint about the behavior of the curve before the change.
but ok, let's assume that the curve (line ?) is in general going up. in other words, if the traveled miles go up, so does the profit.
I also don't know how they could drive the miles without paying the driver, but again, let's assume they did.
now they pay the driver. $0.25 per mile.
this has to come out of their profit.
so, the Y (profit) values all go down by 0.25.
therefore, the y-intercept is going down too.
that eliminates C. and D.
for this to be true they have to have some overhead costs that apply even if there are 0 miles traveled (which is the meaning of the y-intercept : the y-value when x = 0).
so, the line must be in a form
y = ax + b
with "b" <> 0.
and since we assumed the line to go up (positive slope), a "sinking" line means that the x-intercept (the break-even point, where the line goes from below the x-axis and therefore negative (y) profit up into positive profit) will move to the right (become greater).
because now that they have additional costs (paying the driver), it takes longer (more driven miles) to make a positive profit.
and that eliminates A, leaving B. as the right answer.
Write an Algebraic Equation for each problem (include a let statement) and use it to solve the world problem
On number is eight less than five times another. If the the sum of the two numbers is 28, find the two numbers.
The smaller number is __.
The larger number is __.
The smaller number is 6 .
The larger number is 22
To solve this problem
Let's let x be the smaller number and y be the larger number.
From the problem, we know that one number is eight less than five times the other, so we can write:
y = 5x - 8
We also know that the sum of the two numbers is 28, so we can write:
x + y = 28
Now we have two equations in two variables. We can solve for one of the variables in terms of the other, and substitute that expression into the other equation to eliminate one variable.
Let's solve the first equation for x
x = (y + 8)/5
Now we can substitute this expression for x into the second equation:
(y + 8)/5 + y = 28
Multiplying both sides by 5 to eliminate the fraction, we get:
y + 8 + 5y = 140
Combining like terms, we get:
6y + 8 = 140
Subtracting 8 from both sides, we get:
6y = 132
Dividing both sides by 6, we get:
y = 22
Now we can use the equation y = 5x - 8 to solve for x:
22 = 5x - 8
Adding 8 to both sides, we get:
30 = 5x
Dividing both sides by 5, we get:
x = 6
Therefore, the smaller number is 6 and the larger number is 22.
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whats the answer to 102-38x14 divided by 7+162= help plss
Answer:
-2.5
Step-by-step explanation:
follow BIMDAS.
like my answer if you find it helpful
What’s the length of side AB?
tan = 1/√3= perpendicular/ base
1/√3 = AB / AC
AB / 6 = 1/√3
AB = 6/√3
Hello, I am confused on how to answer this question.
Answer: x=14
Step-by-step explanation:
cb=10.
ac=14
The value of X will be 14.
This is a simple mathematics problem that can be solved by using ratios.
Given, AC : BC : AB = 7 : 5 : 8
AC = X ; BC = 10 ; AB = X + 2
AC/ BC = X/ 10 = 7/5 (Ratios can also be represented as fractions)
X/10 = 7/5
On Transposing,
5X = 70
X = 70/5
X = 14
Alternatively,
BC/AB = 5/8 = 10/ (X + 2)
5/8 = 10/ (X + 2)
On Transposing,
80 = 5X + 10
5X = 70
X = 14
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There is a 25% chance that a vowel is drawn from a bag of random letter tiles. what is the probability of drawing a vowel, placing it back in the bag, and then drawing a consonant
The probability of drawing a vowel, placing it back in the bag, and then drawing a consonant is 0.1875 or 18.75%.
The probability of drawing a vowel from the bag of random letter tiles is 25%. Since the tile is replaced after drawing, the probability of drawing a vowel on the second draw is also 25%.
The probability of drawing a vowel and then a consonant can be calculated by multiplying the probabilities of each event:
P(vowel and consonant) = P(vowel) x P(consonant)
= 0.25 x 0.75
= 0.1875
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Brenda is fishing from a small boat. Her fishing hook is 12 feet below her, and a fish is swimming at the same depth as the hook, 16 feet away. How far away is Brenda from the fish?
Answer:
We can use the Pythagorean theorem to solve this problem. Let's call the distance Brenda is away from the fish "x". Then, we have a right triangle with legs of length 12 and x, and a hypotenuse of length 16. So:
x^2 + 12^2 = 16^2
Simplifying:
x^2 + 144 = 256
x^2 = 112
Taking the square root of both sides:
x ≈ 10.6 feet
Therefore, Brenda is approximately 10.6 feet away from the fish.
Hurry please combine Leon’s results and Celia’s results to find the experimental probability of spinning a 4
The experimental probability of spinning a 4 will equals to 0.3.
How to find the experimental probability of spinning a 4?Outcome Tally Frequency
1 IIII 4
2 III 3
3 IIIIIIII 7
4 IIIIII 6
Total 20
The probability of spinning a 4:
= 6/20
= 3/10
= 0.3
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3. How many ways can you line up 7 books on a shelf?
Answer:
There are 5040 different ways to arrange the 7 books on a shelf.------------------------------
Use the formula for permutations:
n! = n × (n - 1) × (n - 2) × ... × 1, where n is the number of objects and ! denotes a factorial.The number of objects is n = 7 books.
Calculate the factorial:
7! = 7 × 6 × 5 × 4 × 3 × 2 × 1 = 5040Triangle PQR is rotated 180 degrees clockwise about the origin to produce the image Triangle P’Q’R’. Which of the following statements is TRUE abóyate Triangle P’Q’R’.
Answer:
Step-by-step explanation:
We get triangle PQR by plotting the point P (1, 4), Q (3, 1), R (2, -1) on the graph paper when rotated through 180° about the origin. The new position of the point is: P (1, 4) → P' (-1, -4) Q (3, 1) → Q' (-3, -1) R (2, -1) → R' (-2, 1) Thus, the new position of ∆PQR is ∆P’Q’R’.
What is the least whole number that rounds to 570 when rounded to the nearest ten?
What is the greatest whole number that rounds to 570 when rounded to the nearest ten?
Use the number pad to enter your answers in the boxes.
Least number:
Greatest number:
Answer:
Least: 565
Greatest: 574
Step-by-step explanation:
564 would round down to 560 and 575 would round to 580
Helping in the name of Jeus.
The least whole number that rounds to 570 when rounded to the nearest ten is 570. The greatest whole number that rounds to 570 when rounded to the nearest ten is 580.
Explanation:To find the least whole number that rounds to 570 when rounded to the nearest ten, we need to look at the digit in the tens place. In this case, the tens digit is 7. Since the number can only round up or down, we need to determine if rounding 570 to the nearest ten would be up or down. Since 570 is closer to 570 than to 580, we can round down to 570. Therefore, the least whole number that rounds to 570 when rounded to the nearest ten is 570 itself.
On the other hand, to find the greatest whole number that rounds to 570 when rounded to the nearest ten, we again need to look at the digit in the tens place. Since the tens digit is 7, we need to determine if rounding 570 to the nearest ten would be up or down. Since 570 is closer to 580 than to 570, we can round up to 580. Therefore, the greatest whole number that rounds to 570 when rounded to the nearest ten is 580.
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Find the value of x. Write your answer in simplest form.
Answer:
C
Step-by-step explanation:
using the sine ratio and the exact value
sin45° = [tex]\frac{1}{\sqrt{2} }[/tex] , then
sin45° = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{5}{x}[/tex] = [tex]\frac{1}{\sqrt{2} }[/tex] ( cross- multiply )
x = 5[tex]\sqrt{2}[/tex]
PLSSS HELP ME ITS DUE TOMORROW!!!!!
FIND THR CIRCUMFERENCE OF A CD THAT HAS A RADIUS OF 6 CENTIMETERS
___cm
Answer:
Hm
Step-by-step explanation:
The formula to find the circumference of a circle is:
Circumference = 2πr
Where "r" is the radius of the circle, and "π" (pi) is a mathematical constant approximately equal to 3.14.
Substituting the given value of radius, we get:
Circumference = 2 x π x 6
Circumference = 12π
Circumference ≈ 37.7 cm (rounded to one decimal place)
Therefore, the circumference of a CD that has a radius of 6 centimeters is approximately 37.7 cm.
^4√p7
in exponential form.
Answer:1111
Step-by-step explanation:
A hamster runs at a speed of 16 centimeters per second in a wheel of radius 15 centimeters.
a) What is the angular velocity of the wheel? (in radians/sec)
b) How fast will the wheel spin in revolutions per minute?
a) The angular velocity of the wheel is approximately 1.0667 radians per second. b) The wheel will spin at approximately 10.16 revolutions per minute.
What is angular velocity?Angular velocity is a measure of how quickly an object rotates or revolves around a fixed point, such as an axis or a center of rotation. It is a vector quantity that describes the rate of change of an object's angular position with respect to time, and is usually expressed in units of radians per second (rad/s) or degrees per second (deg/s).
According to given information:a) To find the angular velocity of the wheel, we can use the formula:
angular velocity = linear velocity / radius
In this case, the linear velocity of the hamster is 16 centimeters per second, and the radius of the wheel is 15 centimeters. So, we have:
angular velocity = 16 / 15
angular velocity = 1.0667 radians per second
Therefore, the angular velocity of the wheel is approximately 1.0667 radians per second.
b) To find the speed of the wheel in revolutions per minute, we need to convert the angular velocity from radians per second to revolutions per minute. There are 2π radians in one revolution, and 60 seconds in one minute. So, we can use the following formula:
angular velocity (in revolutions per minute) = angular velocity (in radians per second) * 60 / 2π
Plugging in the angular velocity we found in part (a), we get:
angular velocity (in revolutions per minute) = 1.0667 * 60 / 2π
angular velocity (in revolutions per minute) ≈ 10.16 revolutions per minute
Therefore, the wheel will spin at approximately 10.16 revolutions per minute.
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You own 23 CDs. You want to randomly arrange 5 of them in a CD rack. What is the probability that the rack ends up in alphabetical order?
The probability that the CDs are in alphabetical order is
The probability of choosing 5 CDs in alphabetical order out of a collection of 23 CDs is approximately 0.00003 or 0.003%.
What is combination?
In mathematics, a combination is a way of selecting objects from a larger group of objects, where the order of selection is not important. A combination is a subset of objects that are chosen from a larger set without regard to the order in which they are selected.
The formula is given by:
C(n, r) = [tex]\frac{n!}{r!* (n - r)!}[/tex]
The total number of ways to choose 5 CDs from a collection of 23 CDs is given by the combination formula:
C(23, 5) = [tex]\frac{23!}{5!* (23 - 5)!}[/tex]
= 33649
This means there are 33649 different ways to arrange 5 CDs out of the 23 CDs.
Out of these 33649 ways, only one arrangement is alphabetical. For this to happen, the first CD chosen must be the first one alphabetically, the second CD chosen must be the second one alphabetically, and so on.
The first CD can be any of the 23 CDs. However, once the first CD is chosen, there is only one CD that can be the second one alphabetically, two CDs that can be the third one alphabetically, and so on. Therefore, the probability of choosing 5 CDs in alphabetical order is:
P = 1 / C(23, 5)
P = 1 / 33649
P ≈ 0.00003
So the probability of choosing 5 CDs in alphabetical order out of a collection of 23 CDs is approximately 0.00003 or 0.003%.
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Calculate Volume of Air passing through Filter HEPA Filter 100ft/min *- Airflow 4ft 2ft Volume = Filter Area x Airflow Velocity
The volume of air passing through the filter is 800 cubic feet per minute. It is calculated by multiplying the air flow speed (100ft/min) by the area of the filter (8ft²).
Explanation:The volume of air passing through the HEPA filter can be calculated using the formula for the speed of air flow multiplied by area. The speed of the air flow is given as 100ft/min and the area of the filter is given as 4ft x 2ft, which equals 8 square feet. Therefore, the volume of the air passing through the filter can be calculated as 8ft2 x 100ft/min = 800 cubic feet per minute.
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A ski club charges $70 for a lift ticket and $20 per hour to ski. Jim paid at least $130 last week to ski. How many hours would he have skied.
Answer:
Step-by-step explanation: $130-$70 lift = $60/$20 per hour= 3 hours ski time
3√b in exponential form
what is one of the zeros of the function shown in this graph?
Answer:
x = -3 and x = 1 are the two zeroes of this function. Choose one of them for your answer.
ANSWER Quick Due in 5 minutes!!!!!!
The line plots represent data collected on the travel times to school from two groups of 15 students. A horizontal line starting at 0, with tick marks every two units up to 28. The line is labeled Minutes Traveled. There is one dot above 4,6,14, and 28. There are two dots above 10, 12, 18, and 22. There are three dots above 16. The graph is titled Bus 47 Travel Times. A horizontal line starting at 0, with tick marks every two units up to 28. The line is labeled Minutes Traveled. There is one dot above 8, 9,18, 20, and 22. There are two dots above 6, 10, 12,14, and 16. The graph is titled Bus 18 Travel Times. Compare the data and use the correct measure of variability to determine which bus is the most consistent. Explain your answer. Bus 18, with an IQR of 16 Bus 47, with an IQR of 24 Bus 18, with a range of 16 Bus 47, with a range of 24
IQR offers a more accurate indicator of consistency than range since it is less impacted by outliers.
Due to Bus 18's smaller IQR, we can infer that it is more consistent than Bus 47.
WHAT IS IQR?An indicator of statistical dispersion used to describe the variability of a dataset is the interquartile range (IQR). It is derived by subtracting a dataset's 75th percentile (Q3) from its 25th percentile (Q1). When compared to other measures of variability like range, the IQR represents the middle 50% of the data and is less susceptible to outliers.
We must contrast the measurements of variability for the two buses in order to determine which one is more reliable. We can utilize range and interquartile range as measurements of variability. (IQR).
The range of a dataset is the difference between its maximum and minimum values.
The range for Bus 18 is 16 (22 - 6), whereas the range for Bus 47 is 24. (28 - 4).
As a result, Bus 47's range is greater than Bus 18's.A measure of variability that is less impacted by outliers than the range is the interquartile range (IQR). It is determined as the difference between a dataset's third and first quartiles (Q3 and Q1, respectively).
The IQR is 16 for Bus 18 (Q3 - Q1 = 22 - 6)
The IQR for Bus 47 is 24 (Q3 - Q1 = 28 - 4"). Bus 18 therefore has a lower IQR than Bus 47.IQR offers a more accurate indicator of consistency than range since it is less impacted by outliers. Due to Bus 18's smaller IQR, we can infer that it is more consistent than Bus 47.
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