Answer: The range is 7
Step-by-step explanation: To find the range you should find the lowest and the highest numbers in the number set. In this case they are 9 and 2, and subtract the smallest from the largest.
The answer will therefore be 7.
Computing inverse laplace transforms. Determine the function of time, x(t), for each of the following laplace transforms
1/(s2 + 9), Re {s} >0
The function of time x(t) corresponding to the Laplace transform 1/(s^2 + 9), Re{s} > 0, is x(t) = (1/3π) sin(3t) e^(st).
To compute the inverse Laplace, transform of 1/(s^2 + 9), we can use the formula for the inverse Laplace transform of a rational function:
L^-1{F(s)} = (1/2πi) ∫γ+σ-iγ+σ+ iF(s)e^(st) ds
where γ is a real number greater than the real part of all singularities of F(s), σ is a positive real number such that the contour of integration lies to the right of all singularities of F(s), and the contour of integration γ+σ is a line parallel to the imaginary axis.
In this case, the Laplace transform of 1/(s^2 + 9) is:
F(s) = L{1/(s^2 + 9)} = 1/[(s + 3i)(s - 3i)]
which has singularities at s = ±3i. Since Re{s} > 0, we can choose γ = 0 and σ > 3. Then, the inverse Laplace transform of F(s) is:
L^-1{F(s)} = (1/2πi) ∫γ+σ-iγ+σ+ iF(s)e^(st) ds
= (1/2πi) ∫γ+σ-iγ+σ+ i [1/((s + 3i)(s - 3i))] e^(st) ds
We can use partial fraction decomposition to express F(s) as:
F(s) = A/(s + 3i) + B/(s - 3i)
where A = 1/(2(3i)), B = -1/(2(3i)), and we get:
L^-1{F(s)} = (1/2πi) [∫γ+σ-iγ+σ+ i A/(s + 3i) e^(st) ds + ∫γ+σ-iγ+σ+ i B/(s - 3i) e^(st) ds]
= (1/2πi) [A e^(-3it) ∫γ+σ-iγ+σ+ i e^(su) du + B e^(3it) ∫γ+σ-iγ+σ+ i e^(sv) dv]
= (1/2πi) [(A e^(-3it) + B e^(3it)) ∫γ+σ-iγ+σ+ i e^(su) du]
where u = s - 3i, v = s + 3i, and we can evaluate the integral using the residue theorem:
∫γ+σ-iγ+σ+ i e^(su) du = 2πi Res[e^(su)/(u + 3i), u = -3i]
= 2πi e^(-3it)/(2(3i))
= -i/3 e^(-3it)
Therefore, we have:
x(t) = L^-1{F(s)} = (1/2πi) [(A e^(-3it) + B e^(3it)) ∫γ+σ-iγ+σ+ i e^(su) du]
= (1/2πi) [(1/(2(3i)) e^(-3it) - 1/(2(3i)) e^(3it)) (-i/3) e^(st) ds]
= (1/6π) [e^(-3it) - e^(3it)] e^(st) ds
= (1/3π) sin(3t) e^(st)
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A rectangular paperboard measuring 27 in long and 17 in wide has a semicircle cut out of it, as shown below. What is the perimeter of the paperboard that
remains after the semicircle is removed? (Use the value 3.14 for pie, and do not round your answer. Be sure to include the correct unit in your answer.)
Answer:
97.69 in
Step-by-step explanation:
You want the perimeter of a 17 in by 27 in rectangle that has a semicircular end.
PerimeterThe perimeter of the figure is the sum of the side lengths. The length of the curved side is half the circumference of the circle with the same diameter:
1/2 C = 1/2(πd) = (3.14/2)·(17 in)
The full perimeter is the sum of the lengths of the straight sides and this length of the curved side:
P = 17 + 27 + 17(3.14/2) + 27
P = 2(27) +17(1 +3.14/2) = 97.69 . . . . inches
The perimeter of the figure is 97.69 inches.
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what is the answer to 2x0.5x9
Answer:
9
Step-by-step explanation:
A conic storage unit has a radus of 8 feet and a height equal to its diameter.
What is the volume of the storage unit?
Answer:
Step-by-step explanation:
he height of the storage unit is equal to twice its radius (since the diameter is twice the radius), so the height is 2 x 8 = 16 feet.
The storage unit is in the shape of a cylinder, so we can use the formula for the volume of a cylinder, V = πr^2h, where r is the radius and h is the height:
V = π(8^2)(16)
V = π(64)(16)
V = 3,218.69 cubic feet (rounded to two decimal places)
Therefore, the volume of the storage unit is approximately 3,218.69 cubic feet.
Jacque is using a soup can for a school project and wants to paint it. If the can is 11 cm tall and has a diameter of 9 cm, at least how many square centimeters of paint is needed? Approximate using π = 3.14.
374.45 cm2
139.50 cm2
699.44 cm2
438.03 cm2
The approximate amount of paint needed = 438.03 cm²
The correct answer is an option (D)
We know that the formula for the surface area of the cylinder is :
A = 2πrh + 2πr²
Here, the diameter of the can is 9 sm
So, the radius of the can would be,
r = d/2
r = 9/2
r = 4.5 cm
And the height of the can is h = 11 cm
Since the can is cylindrical, we use above formula of surface area of the cylinder to find the amount of paint needed.
Using above formula,
A = 2πrh + 2πr²
A = 2π(4.5)(11) + 2π(4.5)²
A = 311.02 + 127.01
A = 438.03 cm²
Therefore, the correct answer is an option (D)
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Can someone help me please?
What fraction does the red dot represent on the number line above?
Answer:
The answer would be Option C. [tex]\frac{1}{8}[/tex]
Step-by-step explanation:
A bag contains 10 red marbles, 15 yellow marbles, 5 green marbles, and 20 blue marbles. Five marbles are drawn
from the bag.
What is the approximate probability that exactly two of the five are blue?
1%
36%
40%
Mark this and return
Save and Exit
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Submit
The probability that exactly two of the five are blue is 36 %
Given data ,
Probability = (number of favorable outcomes) / (total number of outcomes)
The total number of outcomes is the number of ways to choose 5 marbles from 50 marbles is by combination
50 choose 5 = (50!)/(5!(50-5)!) = 2,118,760
To find the number of favorable outcomes, we need to count the number of ways to choose exactly 2 blue marbles out of 20 blue marbles, and 3 non-blue marbles out of the remaining 30 marbles
(number of ways to choose 2 blue marbles out of 20) (number of ways to choose 3 non-blue marbles out of 30)
C = (20 choose 2) (30 choose 3)
C = (20!)/(2!(20-2)!) (30!)/(3!(30-3)!)
C = 190 ( 4060 )
C = 771,400
Therefore, the probability of drawing exactly 2 blue marbles is:
Probability = (number of favorable outcomes) / (total number of outcomes)
P = 771,400 / 2,118,760
P = 0.3642
Hence , the probability is P = 36 %
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what is 3125 divided by 25
Answer:
125
Step-by-step explanation:
By using normal division method,
3125÷25 goes as 125
A. Write true or false after each sentence. If the sentence
is false, change the underlined word or words to make
it true.
1. The order of the numbers in an ordered pair is not important.
2. The horizontal axis is called the x-axis.
3. The point where the coordinate axes cross is called the center.
1. True
2. True
3. False. The point where the coordinate axes cross is called the origin.
need help due really soon….
Answer:
the answer is A
Step-by-step explanation:
Answer: A
Step-by-step explanation:
You can plug in calc
[tex]\frac{\sqrt{9} }{3} =1[/tex]
2[tex]\pi[/tex] = 6.28
a. [tex]\pi /9 = .35[/tex] this is not between
b. 3.14 this is
c. 3 this is
d. 1.09
from independent surveys of two populations, 90% confidence intervals for the population means are constructed. what is the probability that neither interval contains the respective population mean? that both do?
The probability that neither interval contains the respective population mean is 0.01 and the probability that both intervals contain their respective population means is 0.81.
Assuming that the two populations are independent, we can use the fact that the confidence interval is constructed such that there is a 90% probability that the true population mean falls within the interval.
Let's denote the two populations as Population A and Population B, and the confidence intervals for their respective means as CI_A and CI_B.
The probability that neither interval contains the respective population mean can be calculated as the complement of the probability that at least one interval contains its respective population mean.
P(neither interval contains its respective population mean) = 1 - P(at least one interval contains its respective population mean)
To calculate the probability of at least one interval containing its respective population mean, we can use the fact that the probability of an event A or B occurring is equal to the sum of their individual probabilities minus the probability of both events occurring simultaneously:
P(A or B) = P(A) + P(B) - P(A and B)
In this case, the event A is the event that CI_A contains the true population mean for Population A, and event B is the event that CI_B contains the true population mean for Population B.
Using this formula, we can calculate:
P(at least one interval contains its respective population mean) = P(CI_A contains true mean for Population A) + P(CI_B contains true mean for Population B) - P(both intervals contain their respective population means)
Since the two populations are independent, the events of each interval containing its respective population mean are also independent. Therefore, the probability of both intervals containing their respective population means can be calculated as the product of their individual probabilities:
P(both intervals contain their respective population means) = P(CI_A contains true mean for Population A) * P(CI_B contains true mean for Population B)
Now we have all the information we need to calculate the probability of interest:
P(neither interval contains its respective population mean) = 1 - P(at least one interval contains its respective population mean)
= 1 - [P(CI_A contains true mean for Population A) + P(CI_B contains true mean for Population B) - P(CI_A contains true mean for Population A) * P(CI_B contains true mean for Population B)]
Note that we don't have any specific information about the probabilities of the intervals containing their respective population means, so we can't calculate this probability exactly. However, we do know that the confidence intervals are constructed such that there is a 90% probability that the true population mean falls within the interval. This means that the probability of each interval containing its respective population mean is 0.9.
Using this information, we can calculate:
P(neither interval contains its respective population mean) = 1 - [0.9 + 0.9 - 0.9 * 0.9]
= 1 - 0.99
= 0.01
Therefore, the probability that neither interval contains the respective population mean is approximately 0.01, assuming that the confidence intervals were constructed using a 90% confidence level.
Similarly, the probability that both intervals contain their respective population means can be calculated as:
P(both intervals contain their respective population means) = P(CI_A contains true mean for Population A) * P(CI_B contains true mean for Population B)
= 0.9 * 0.9
= 0.81
Therefore, the probability that both intervals contain their respective population means is approximately 0.81, assuming that the confidence intervals were constructed using a 90% confidence level.
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the tennis team wins 73% of their games. if they play 10 games, what is the probability that they win nine games?
The Probability that the tennis team won 9 games is 1.35% , under the given condition that the tennis team wins 73% of their game, if they play 10 games.
Therefore, probability of winning nine games out of ten with a 73% win rate can be evaluated using the binomial distribution formula
[tex]P(X=k) = (n choose k) * p^k * (1-p)^{(n-k)}[/tex]
Here
P(X=k) = probability of winning k games out of n games
n = total number of games played (n=10)
k = number of games won (k=9)
p = probability of winning a single game (p=0.73)
Staging the values in the formula
[tex]P(X=9) = (10 choose 9) * 0.73^9 * (1-0.73)^{(10-9)}[/tex]
= ( 10 - 9) x (0.05) x ( 0.27)¹
= 1 x 0.05 x 0.27
= 0.0135
Converting into percentage
0.0135 x 100
= 1.35%
The probability that the tennis team won 9 games is 1.35% , under the given condition that the tennis team wins 73% of their game, if they play 10 games.
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IF 4 dice are thrown, what is the probability of getting
i.exactly 3sixes
ii.exactly2sixes
iii.no sixes.
When rolling a fair six-sided die, the probability of rolling a six is 1/6. Assuming that the dice are fair and independent, we can use the rules of probability to find the probability of rolling certain outcomes when 4 dice are thrown:
i. To find the probability of getting exactly 3 sixes when 4 dice are thrown, we can use the binomial probability formula:
P(exactly k successes in n trials) = (n choose k) * p^k * (1-p)^(n-k)
where n is the number of trials, k is the number of successful outcomes, p is the probability of success on each trial, and (n choose k) is the binomial coefficient.
For this problem, n = 4, k = 3, and p = 1/6.
P(exactly 3 sixes) = (4 choose 3) * (1/6)^3 * (5/6)^1
= 4 * (1/216) * (5/6)
= 5/54
Therefore, the probability of getting exactly 3 sixes when 4 dice are thrown is 5/54.
ii. To find the probability of getting exactly 2 sixes when 4 dice are thrown, we can use the same formula with k = 2:
P(exactly 2 sixes) = (4 choose 2) * (1/6)^2 * (5/6)^2
= 6 * (1/36) * (25/36)
= 25/72
Therefore, the probability of getting exactly 2 sixes when 4 dice are thrown is 25/72.
iii. To find the probability of getting no sixes when 4 dice are thrown, we can use the complement rule:
P(no sixes) = 1 - P(at least one six)
To find the probability of getting at least one six, we can use the complement of getting no sixes:
P(at least one six) = 1 - P(no sixes)
For each die, the probability of not rolling a six is 5/6. Therefore, the probability of getting no sixes on 4 dice is:
P(no sixes) = (5/6)^4
= 625/1296
Therefore, the probability of getting no sixes when 4 dice are thrown is 625/1296, and the probability of getting at least one six is 1 - 625/1296 = 671/1296.
Anna has a loyalty card good for a 7% discount at her local grocery store. What number should she multiply the prices on the tags by to find the price she would have to pay, before tax, in one step?
Anna should multiply the prices on the tags by 0.93 to find the price she would have to pay before tax in one step.
Given that Anna has a loyalty card good for a 7% discount at her local grocery store.
We have to find the number should she multiply the prices on the tags by to find the price she would have to pay, before tax
Anna should multiply the prices on the tags by 0.93 (which is 1 minus the 7% discount) to find the price she would have to pay before tax in one step.
For example, if an item costs $10 before the discount, Anna would pay $10 x 0.93 = $9.30 after the discount.
Hence, Anna should multiply the prices on the tags by 0.93 to find the price she would have to pay before tax in one step.
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Determine the number of solutions to the given system. Remember to use the format (x,y) to type in your points, and do not use spaces. If there is only one, type the point in one space and "none" in the other. If there is none, type none in both the boxes. System: {y=−x+10y=(x−5)2+6
The two solutions to the system as a whole of equations is (3, 7) as (7, 3), respectively. These locations show where a line [tex]y = x+10[/tex] with the parabola of [tex]y = (x^{5} )^{2+6}[/tex] cross.
We can change the initial equation in the second to solve a set of equations[tex]y=x+10[/tex], [tex]y = (x^{5} )^{2+6}[/tex] , yielding: [tex]−x+10 = (x^{5} )^{2+6}[/tex]
When we simplify and enlarge the right side, we obtain: [tex]x^{2} - 11x + 21 = 0[/tex]The quadratic equation is factored to yield: (x - 3)(x - 7) = 0.
x has solutions of 3 and 7. In order to determine the associated y-values, we may then enter these values back into one of the original equations. There are two possible answers: (3, 7) and (7, 3).
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Alexi's restaurant bill is $58, and he wants to leave a 20 percent tip. Which expression represents the total amount that
Alexi needs to pay?
$58(0.20) + $58
$58(0.20)
$58(20) + $58
$58(20)
Answer:
$58(0.20) + $58
Step-by-step explanation:
this is true because you would need to find what 20% of 58 is before you add it to the bill
Solve the systems of equations by substituting
4) y=6x-11
-2x-3y=-7
The value of the variables are y = 2 and x = 1
How to determine the valueFrom the information given, we have that;
y= 6x-11
-2x-3y =-7
Using the substitution method, we have;
Substitute the value of y in equation (2)
-2x - 3(6x - 11) = -7
expand the bracket
-2x - 18x + 33 = -7
collect the like terms
-20x = -7 - 33
subtract the values
-20x = -40
Make 'x' the subject
x = 2
Substitute the values of x in equation 1
y = 6(2) - 11
expand the bracket
y = 12 - 11
y = 1
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a 3 person committee is to be chosen from 14 men and 10 women. what is the probability that the committee will consist of men
The probability that the committee will consist of men is 17.95%.
To fathom this issue, we ought to utilize the concept of combinations. The number of ways to select a committee of 3 individuals from a add up to of 24 individuals is:
C(24,3) = 24! / (3! * 21!) = 2024
Presently, we ought to discover the number of ways to select a committee comprising of as it were men. We will select 3 men from 14 in:
C(14,3) = 14! / (3! * 11!) = 364 ways.
In this manner, the likelihood of choosing a committee comprising of as it were men is:
P(3 men) = C(14,3) / C(24,3) = 364 / 2024 = 0.1795
So the likelihood that the committee will comprise men is 0.1795, or approximately 17.95%.
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The value of a computer that originally sold for $800 can be modeled by g(x)=800(0.8^x), where x is the number of years since the computer was purchased. Describe g(x) as a translation of the parent function f(x)=0.8^x.
Answer:
Step-by-step explanation:
The parent function is f(x) = 0.8^x, which represents exponential decay. This means that as x increases, f(x) gets smaller and smaller.
The given function g(x) is obtained by multiplying f(x) by 800, which stretches the graph vertically by a factor of 800.
Also, the function g(x) has an additional translation: the entire graph of f(x) is shifted vertically upwards by 800 units. This is because the computer originally sold for $800, and g(x) represents the current value of the computer, which is $800 times the value of the parent function.
Therefore, g(x) can be described as a vertical stretch and translation of the parent function f(x) = 0.8^x.
I need helpp ASAP….please
Answer:
the formula is y=0.06x + 45
A. The rate of change is 0.06 dollars per kilometer
B. The initial cost is $45 dollars
C. The charge after 837 km is 95.22 including the initial cost
D. For $200 dollars you could drive 2583.3 km repeating.
Step-by-step explanation:
Answer:
Step-by-step explanation:
Your initial equations are: r is rate i is initial fee
59.4 = r(240) + i
74.4 = r(490) + i
solve the systems of equations. I eliminate i by multiplying both sides of top equation by -
74.4 = r(490) + i
-59.4 = -r(240) - i
15=250r
r=.06
plug r back in to get i
59.4=(.06)(240)+i
i=45
so
y=.06x+45
The functions f(x) and g(x) are shown on the graph.
The graph shows a v-shaped graph, labeled f of x, with a vertex at the origin, a point at negative 1 comma 1, and a point at 1 comma 1. The graph shows another v-shaped graph, labeled g of x, which has a wider opening than f of x, with a vertex at the origin, a point at negative 3 comma 1, and a point at 3 comma 1.
What transformation of f(x) will produce g(x)?
g of x equals one third times f of x
g of x equals negative f of one third times x
g(x) = f(3x)
g(x) = −3f(x)
The transformation that will produce g(x) from f(x) is:
g(x) = 1/3f(x)
A transformation in geometry is a function that assigns new positions, orientations, or configurations to points, lines, or forms in a plane or in space. An object's attributes, such as distance, angle, or symmetry, can be preserved while its size, shape, or location are changed.
This is so because g(x) scales down f(x) by a factor of three-quarters. To acquire the appropriate y-value of g, each y-value of f(x) is multiplied by a third (x).
The other answer choices are not correct:
It is not the same as g(x) = -f(1/3 x) to reflect f(x) across the y-axis and compress it horizontally by a factor of 3. (x).
That is not the same as g(x) = f(3x), which would expand f(x) horizontally by a factor of three (x).
The equation g(x) = -3f(x) would extend f(x) vertically by a factor of 3 and reflect it across the x-axis (x).
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What is the approximate circumference of a circle that has a diameter of 379? Use 3.14 for π and express your answer to the hundredths place.
fill in the blank
__
thank you
The circumference of a circle with diameter 379 can be found using the formula:
C = πd
where d is the diameter of the circle. Substituting the given value of d, we get:
C = 3.14 x 379
C ≈ 1191.06
Rounding to the hundredths place, the circumference is approximately 1191.06 units of length (e.g. inches, centimeters, etc.).
Therefore, the answer to fill in the blank is 1191.06.
Find the excluded values
Answer:
[tex]2 {a}^{2} - 8a = 0[/tex]
[tex]2a(a - 4) = 0[/tex]
[tex]a = 0[/tex]
[tex]a = 4[/tex]
The excluded values are a = 0 and a = 4.
Sketch a rectangular prism that has a volume of 500cm3 and sides that are whole numbers
Answer: Answers will vary
one answer is...
The dimensions are 5cm 10cm and 10cm
Step-by-step explanation:
You just have to find 3 numbers that equal 500.
Find the weighted average of the numbers −1 and 5 with two thirds of the weight on the first number and one third on the second number.
a (0)
b (1)
c (2)
d (3)
Answer:
C (2)
Step-by-step explanation:
The weighted average of -1 and 5 with two-thirds of the weight on the first number and one-third on the second number is 1.
As per the question, we have:
First number: -1
Weight on the first number: 2/3
Second number: 5
Weight on the second number: 1/3
To calculate the weighted average:
Weighted average = ((-1) × (2/3) + (5) × (1/3)) / ((2/3) + (1/3))
Simplifying the expression:
Weighted average = ((-2/3) + (5/3)) / (2/3 + 1/3)
Weighted average = (3/3) / (3/3)
Weighted average = 3/3
Thus, the weighted average of -1 and 5 with two-thirds of the weight on the first number and one-third on the second number is 1.
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Complete the table.
(Type an integer or a simplified fraction.)
please help, no links
The complete table is as follows
x y
0 -11/2
1 -3
2 -1/2
3 2
4 9/2
5 7
How to complete the tableThe table is completed by identifying the constant change
-11/2 + k = -3
k = -3 + 11/2
k = 5/2
This is used to complete the table as follows
For x = 1
-11/2 + 5/2 = -3
For x = 2
-3 + 5/2 = -1/2
For x = 3
-1/2 + 5/2 = 2
For x = 4
2 + 5/2 = 9/2
For x = 5
9/2 + 5/2 = 7
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Jensine earns $6 per hour babysitting,
She is saving to buy an MP3 player
that costs $150, but she does not yet
have enough money. If h represents
the number of hours she has spent
babysitting, which inequality describes
her situation?
507
Answer:
well maybe if Jensine gets a better f ***** job she can buy it instead she wants to waste her time to watch a annoying a *baby for 6$ a hour
Step-by-step explanation:
This is all a joke dont get mad :)
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 10, 16, 20, and 28. There are two dots above 8 and 14. There are three dots above 18. There are four dots above 12. The graph is titled Bus 14 Travel Times.
Compare the data and use the correct measure of center to determine which bus typically has the faster travel time. Round your answer to the nearest whole number, if necessary, and explain your answer.
Bus 47, with a median of 16
Bus 14, with a median of 14
Bus 47, with a mean of 16
Bus 14, with a mean of 14
The best measure of center to determine which bus typically has the faster travel time is: A. Bus 47, with a median of 16.
What is a line plot?In Mathematics and Statistics, a line plot simply refers a type of graph that is used for the graphical representation of data set above a number line, while using crosses, dots, or any other mathematical symbol.
For Bus 47, the median is given by;
4,6,14,28,10,10,12,12,18,18,22,22,16,16,16
Median of Bus 47 = 16
Mean of Bus 47 = 15.
For Bus 14, the median is given by;
10,16,20,28,8,8,14,14,18,18,18
Median of Bus 14 = 16.
Mean of Bus 14 = 16
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If it is known that a and b are positive integers and that a-b=2 evaluate the following.
Answer: 1/9
Step-by-step explanation: I do rsm it is correct from my hw
