The interquartile range (IQR) is 5 minutes. Any values below 19.5 minutes or above 39.5 minutes would be considered outliers. In this data set, both the minimum time of 15 minutes and the maximum time of 50 minutes are outliers.
Explanation:
The question is whether there are any outliers in the finish times of a group of runners based on the IQR definition. To determine this, we first calculate the interquartile range (IQR), which is the range of the middle 50 percent of the data. Q1 = 32 min - 2 For this data set, we calculate the IQR by subtracting the first quartile (Q1) from the third quartile (Q3). Here, IQR = Q3 - 7 min = 5 min.
Next, we multiply the IQR by 1.5, which is our test for outliers. This gives 1.5 * IQR = 1.5 * 5 min = 7.5 min.
An outlier is defined as a data point that is below Q1 - 1.5 * IQR or above Q3 + 1.5 * IQR. So, any time less than 27 min - 7.5 min = 19.5 min or greater than 32 min + 7.5 min = 39.5 min would be considered an outlier.
Given the five-number summary: min=15 min, Q1=27 min, median=31 min, Q3=32 min, max=50 min, we can clearly see that the minimum time of 15 min is an outlier because it's less than 19.5 min. Also, the maximum time of 50 min is an outlier because it's greater than 39.5 min.
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The minimum time is 15 minutes and below the lower bound of 19.5 minutes, there is at least one outlier in the given data set.
To determine if there are any outliers using the 1.5 * IQR (interquartile range) definition, we need to calculate the IQR first. The IQR is the difference between the third quartile (Q3) and the first quartile (Q1).
Given:
- Q1 = 27 minutes
- Q3 = 32 minutes
We can calculate the IQR as follows:
[tex]\[ IQR = Q3 - Q1 = 32 - 27 = 5 \text{ minutes} \][/tex]
Now, we can use the 1.5 * IQR rule to find the lower and upper bounds for potential outliers:
Lower Bound: Q1 - 1.5 * IQR
Upper Bound: Q3 + 1.5 * IQR
[tex]\[ \text{Lower Bound} = 27 - 1.5 \times 5 = 27 - 7.5 = 19.5 \text{ minutes} \]\[ \text{Upper Bound} = 32 + 1.5 \times 5 = 32 + 7.5 = 39.5 \text{ minutes} \][/tex]
Any finish times below 19.5 minutes or above 39.5 minutes would be considered potential outliers according to the 1.5 * IQR rule.
Since the minimum time is 15 minutes and below the lower bound of 19.5 minutes, there is at least one outlier in the data set.
The formula for glue says to add 45mL of hardener to each container of resin. How much hardener should be added to 18 containers of resin?
Evaluate the following expression. 10−9×5+6×(−2)
How do you subtract 7.6 from 20.39
How do the number line graphs of the solutions sets of mc011-1.jpg and mc011-2.jpg differ? One graph uses an open circle, but the other graph uses a closed circle. Also, the rays use arrows that point in opposite directions, but they have the same endpoint. They use arrows that point in opposite directions, the rays have different endpoints, and both graphs use open circles. One graph uses an open circle, but the other graph uses a closed circle. Also, the rays have different endpoints, but they use arrows that point in the same direction. They use arrows that point in opposite directions, the rays have different endpoints, and both graphs use closed circles
Answer:A. One graph uses an open circle, but the other graph uses a closed circle. Also, the rays use arrows that point in opposite directions, but they have the same endpoint.
Find the four real zeros of the polynomial. f(x) = x4 + 6x3 - 3x2 -52x - 60
A. 2, -2, -5, -3
B. -2, -2, -5, 3
C. -2, -2, 5, 3
D. 2, -2, -5, 3
To find the zeros of the polynomial f(x) = x^4 + 6x^3 - 3x^2 -52x - 60, we can test different values and find that x = 2, -2, -5, -3 are the four real zeros.
Explanation:To find the zeros of the polynomial f(x) = x^4 + 6x^3 - 3x^2 -52x - 60, we need to solve the equation f(x) = 0. We can do this by factoring or using synthetic division. By testing different values, we find that x = 2, -2, -5, -3 are the four real zeros of the polynomial. Therefore, the correct answer is A. 2, -2, -5, -3.
A colony of bacteria triples in link every 10 minutes. It's length is now 1 mm. How long will be in 40 minutes
what is the answer to 15/4 in improper fraction s
Sara set off on a bicycle trip at 6:30 am at an average rate of 24 miles per hour. Her friend, Jayne, promised to bring her some lunch, and she set off by motorcycle 2 hours after Sara left, driving at an average speed of 40 miles per hour. At what time did Jayne catch up with Sara?
Sari has 3 times as many pencil erasers as Sam. Together they have 28 erasers. How many erasers does Sari have?
please help me differentiate this
A curve is defined by the parametric equations
x=t^2 and y=t^3
show that the equation of the tangent to the curve at the point P (p^2, p^3) is
2y-3px+p^3=0
Earth travels about 10^9 kilometers in its year-long orbit around the sun. About how far does it travel in 100 years?
100 = 10^2
so 10^9 * 10^2 = 10^11 kilometers in 100 years
Find the length of l on the curve r(t)=5cos(3t)i-5sin(3t)j+3tk over the interval [3,7]
To find the length of the curve, use the formula for arc length and integrate over the given interval. The integrals can be calculated using the derivatives of the curve's components.
Explanation:To find the length of the curve, we need to calculate the arc length. The formula for arc length is given by:
L = ∫√(dx/dt)² + (dy/dt)² + (dz/dt)² dt
In this case, dx/dt = -15sin(3t), dy/dt = -15cos(3t), and dz/dt = 3. We can use these formulas to calculate the integrals over the interval [3, 7] and find the length of the curve.
A eighteen-sided die is rolled three times. In how many ways can this happen?
Number of ways it can happen is 5832.
What is Multiplication?Multiplication of two numbers is defined as the addition of one of the number repeatedly until the times of the other number.
a × b means that a is added to itself b times or b is added to itself a times.
We have eighteen-sided die is rolled three times.
When the die is first rolled, there are 18 possibilities of outcomes.
Again when the die is rolled, again there are 18 possibilities.
In the third rolling also, there are 18 possibilities.
Each die has 18 possibilities of numbers for a number for the other die.
Total number of sets = 18 × 18 × 18
= 5832
Hence the total number of ways that the numbers can be formed is 5832.
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Can you please explain how the answer is 24 for this Problem 60÷5(7-5)
do order of operations:
60 / 5*(7-5)=
do parenthesis first: 7-5=2
60 / 5*2 =
now do division: 60/5 =12
12*2 =
now multiply: 12 *2 = 24
answer is 24
Catherine likes to go ice fishing. She has learned from experience that she stays warm about 20 minutes for every undershirt she wears. If she wants to stay out for 120 minutes, how many undershirts should she put on?
Answer:
She need to put on 6 underpants
Step-by-step explanation:
She has learned from experience that she stays warm about 20 minutes for every undershirt she wears.
Time warmed by 1 undershirt = 20 minutes.
Total time she wants to stay out = 120 minutes
Number of underpants required [tex]=\frac{120}{20}=6\texttt{ underpants}[/tex]
So she need to put on 6 underpants
You have $37 to spend at the music store. Each cassette tape costs $10 and each CD costs $13. Write a linear inequality that represents this situation. Let x represent the number of tapes and y the number of CDs.
Emmanuel read 150 pages in 5 hours. How long would it take him to read 230 pages?
Simplify
19 - 1.67 + (-2.4)
Big Louie's Pizza house sells a 12 inch square pan pizza for $3.95 and a 24-inch square pan pizza for $14.95 which pizza is a better deal explain clearly how you know
The 24-inch pizza is a better deal because it costs slightly less per square inch compared to the 12-inch pizza.
Explanation:To determine which pizza is a better deal, we need to compare their prices per square inch. First, let's find the area of the 12-inch pizza. The formula to find the area of a square is side length squared, so the area of the 12-inch pizza is 12 x 12 = 144 square inches. Now, we can divide the price of the 12-inch pizza by its area to find the price per square inch: $3.95 / 144 = $0.0274 per square inch.
Next, let's find the area of the 24-inch pizza. The area of the 24-inch pizza is 24 x 24 = 576 square inches. Now, we can divide the price of the 24-inch pizza by its area to find the price per square inch: $14.95 / 576 = $0.0259 per square inch.
Comparing the prices per square inch, we can see that the 24-inch pizza is a better deal, as it costs slightly less per square inch compared to the 12-inch pizza.
When does a barbershop Quartet have 16 legs
A traditional barbershop quartet has 8 legs since it consists of four people. Female quartets exist alongside male quartets, with popular female groups like The Sweet Adelines International and The Chordettes. The scenario of a quartet having 16 legs is hypothetical and humorous, similar to a comedic tale from 'Only Fools and Horses' regarding a constantly replaced broom.
The question "When does a barbershop quartet have 16 legs?" seems to contain a riddle rather than a direct inquiry into the makeup of a barbershop quartet. Traditionally, a barbershop quartet comprises four individuals, each with two legs, totaling eight legs. This would shift to 16 legs if the quartet consisted of eight people. However, if we're speaking about the traditional four-person quartet, they would only have 16 legs if each member had four legs, which is not characteristic of human anatomy.
It is important to clarify that despite the common misconception that barbershop quartets are exclusively male, there are female quartets as well, such as those associated with The Sweet Adelines International or popular groups like The Chordettes. Neither of these situations normally results in 16 legs unless for comedic or hypothetical scenarios, akin to the tale shared in the comedy "Only Fools and Horses" where Trigger's broom maintains the same identity despite numerous replacements of its parts.
Examples in Pop Culture and Misconceptions
A blend of humor and play on the concept of identity similar to the aforestated barbershop quartet conundrum is seen in the television sitcom "Only Fools and Horses," where a character humorously remarks on the extensive replacement of broom parts, posing a philosophical question of identity and perception.
An equation of the form ax+b=0 is called a __________ equation or a ________________ equation.
Answer:
Sloose intercept or a strait line
Step-by-step explanation:
simplify the following expression. one-fourth(24 – 16x)
You are working as a caterer and need 20 gallons of lemonade for an upcoming event. The bottles of lemonade you are purchasing are in liters.
You would need approximately 75.7 liters of lemonade for your event. This is calculated by using the conversion factor of 3.78541 liters per gallon.
Explanation:To calculate how many liters of lemonade you need for 20 gallons, we first need to know the conversion rate. There are about 3.78541 liters in 1 gallon. Thus, if you need 20 gallons, we can use multiplication to find this.
So, if we multiply 20 (gallons) by 3.78541 (liters per gallon), the result is approximately 75.7 liters. You would therefore need about 75.7 liters of lemonade for your event. This is a simple application of conversion factors, where the given quantity (gallons) is multiplied by a conversion factor (liters per gallon) to obtain the desired quantity (liters).
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Gunther is buying baseballs in bags of 10 he has 40 baseballs but needs a total of 70 baseballs for throwing practice.
A square pyramid has a height h and a base with side length b. The side lengths of the base increase by 50%. Write a simplified expression that represents the volume of the new pyramid in terms of b and h.
Final answer:
The volume of the new pyramid, after a 50% increase in base side length, is expressed as V = 0.75b²h. This comes from applying the formula for the volume of a square pyramid and substituting the new base length of 1.5b into the formula.
Explanation:
The student is asked to write a simplified expression for the volume of a new pyramid after the side lengths of the base increase by 50%. The formula for the volume of a square pyramid with a base side length b and height h is V = (1/3)b²h.
When the side lengths of the base increase by 50%, the new base side length becomes 1.5b. Plugging this into the volume formula, we have:
V' = (1/3)(1.5b)²h
= (1/3)(2.25b²)h
= (2.25/3)b²h
= 0.75b²h
This is the simplified expression for the volume of the pyramid after the increase in base side length.
The volume of the new pyramid is [tex]\(0.75b^2h\), where \(b\)[/tex] is the base side length and [tex]\(h\)[/tex] is the height.
To find the volume of a square pyramid, we use the formula:
[tex]\[ V = \frac{1}{3} \times (\text{area of base}) \times \text{height} \][/tex]
For a square pyramid, the area of the base is [tex]\( b^2 \), where \( b \)[/tex] is the side length of the base.
So, the volume [tex]\( V \)[/tex] of the original pyramid can be written as:
[tex]\[ V = \frac{1}{3} \times b^2 \times h \][/tex]
Now, if the side lengths of the base increase by 50%, the new side length of the base becomes [tex]\( 1.5b \)[/tex] (since increasing by 50% is the same as multiplying by [tex]\( 1.5 \))[/tex].
Therefore, the new area of the base is [tex]\( (1.5b)^2 = 2.25b^2 \).[/tex]
So, the volume \( V' \) of the new pyramid can be written as:
[tex]\[ V' = \frac{1}{3} \times (2.25b^2) \times h \][/tex]
[tex]\[ V' = \frac{2.25}{3} \times b^2 \times h \][/tex]
[tex]\[ V' = 0.75 \times b^2 \times h \][/tex]
So, the simplified expression representing the volume of the new pyramid in terms of [tex]\( b \) and \( h \) is \( 0.75b^2h \)[/tex].
What is the standard form of five and three hundred fifty- two thousandths?
simplify 5 + 4 • (8 – 6)2
Find the sum of 5m + 3n + p, -5p + 3n, and 2n - m.
Answer:
4m+8n -4p
Step-by-step explanation:
hello
you can just sum like a normal addition, just put similar terms on each other
5m + 3n +p
+3n -5p (second expression)
-m +2n ( third expression)
_____________
(5-1)m (3+3+2)n+(1-5)p = 4m+8n -4p
I hope it helps you
Have a great day
Find all real zeros of the function y=-7x+8
The zero of the function y = -7x + 8 is 8/7.
What is a function?A function is a relationship between inputs where each input is related to exactly one output.
Example:
f(x) = 2x + 1
f(1) = 2 + 1 = 3
f(2) = 2 x 2 + 1 = 4 + 1 = 5
The outputs of the functions are 3 and 5
The inputs of the function are 1 and 2.
We have,
y = -7x + 8
y = 0 to find the zeroes.
0 = -7x + 8
7x = 8
x = 8/7
Thus,
The zero of the function is 8/7.
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The sum of two numbers is 99. If three times the smaller number is subtracted from the larger number, the result is 19. Find the two numbers.