Aja's favorite cereal is running a promotion that says 111-in-444 boxes of the cereal contain a prize. Suppose that Aja is going to buy 555 boxes of this cereal, and let XXX represent the number of prizes she wins in these boxes. Assume that these boxes represent a random sample, and assume that prizes are independent between boxes. What is the probability that she wins at most 111 prize in the 555 boxes
Answers
Using the binomial distribution, there is a 0.6328 = 63.28% probability that she wins at most 1 prize.
For each box, there are only two possible outcomes, either it has a prize, or it does not. The probability of a box having a prize is independent of any other box, hence, the binomial distribution is used to solve this question.
Binomial probability distribution
\(P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}\)
\(C_{n,x} = \frac{n!}{x!(n-x)!}\)
The parameters are:
x is the number of successes. n is the number of trials. p is the probability of a success on a single trial.In this problem:
She buys 5 boxes, hence \(n = 5\)1 in 4 boxes has a prize, hence \(p = \frac{1}{4} = 0.25\)The probability is:
\(P(X \leq 1) = P(X = 0) + P(X = 1)\)
Hence:
\(P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}\)
\(P(X = 0) = C_{5,0}.(0.25)^{0}.(0.75)^{5} = 0.2373\)
\(P(X = 1) = C_{5,1}.(0.25)^{1}.(0.75)^{4} = 0.3955\)
Then
\(P(X \leq 1) = P(X = 0) + P(X = 1) = 0.2373 + 0.3955 = 0.6328\)
0.6328 = 63.28% probability that she wins at most 1 prize.
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Related Questions
PLEASE HELP ASAP!!!!!
Answers
Given:
The side lengths of two cubes are 2.5 yd and 2 yd.
To find:
The side length of third cube.
Solution:
From the given figure it is clear that the cubes are inclined to each other in such a way so that they form a right angle triangle and side length of third cube is the base.
Let x be the side length of the third cube.
Using Pythagoras theorem, we get
\(Hypotenuse^2=Base^2+Perpendicular^2\)
\((2.5)^2=(x)^2+(2)^2\)
\(6.25=x^2+4\)
\(6.25-4=x^2\)
\(2.25=x^2\)
Taking square root on both sides, we get
\(x=\pm\sqrt{2.25}\)
\(x=\pm 1.5\)
Side cannot be negative. So,
\(x=1.5\)
Therefore, the side length of the third cube is \(x=1.5\) yd.
A large bag contains 7/12 pound of nails. How many 1/9 pound bags can be filled with this amount of nails?
Answers
We need to use cross multiplication to solve the problem. The number of 1/9 pound bags that can be filled with 7/12 pound of nails is 5.
In the given question we have a large bag that has 7/12 pound of nails. We need to find how many 1/9 pound bags will be required to contain 7/12 pound of nails. We can consider the number of bags to be x, and we can say that the total weight of all those bags will be 7/12 pound. We need to equate the total weight of the 1/9 pound bags to 7/12 and cross multiply to get the number of bags.
x/9=7/12
x=7x9/12=5.25≈5
Therefore the number of 1/9 pound bags required to fill 7/12 pound nails is approximately 5.
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Find the equation of the perpendicular bisector of AB where A and B are the points (3,6) and (-3,4) respectively. Also find its point of intersection with (i) x-axis and (ii) y-axis.
Answers
The point of intersection with x - axis is (5/3,0) and the point of intersection with y - axis is (0,5).
Any point on AB's perpendicular bisector, P(x,y), shall be considered. Then, PA = PB.
√(x-3)²+(y-6)² = √(x+3)²+(y-4)²
(x-3)²+(y-6)² = (x+3)²+(y-4)²
x² -6x+ 9 + y²- 12y + 36 = x² +6x+ 9 + y²- 8y + 16
12x + 4y -20 = 0
3x+ y-5 =0 ---(1)
Consequently, 3x+y-5=0 is the equation for the perpendicular bisector of AB.
We know that the coordinates of any point on x-axis are of the form (x,0). In other words, any point on the x-axis has a y-coordinate of zero. Thus, if we enter y = 0 in (1), we get
3x -5 = 0
x = 5/3
Thus, the x-axis is cut by the perpendicular bisector of AB at (5/3, 0).
(ii) Any point's y-axis coordinates have the following format: (0,y). When we enter x = 0 in (1), we obtain
y − 5 = 0
⇒ y = 5
Thus, the y-axis is where the perpendicular bisector of AB intersects (0,5).
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What are the domain and range of the inequality y < sqrt x+3+1
I don't get it I try to solve it but I just didn't get .
Answers
Given:
The inequality is:
\(y<\sqrt{x+3}+1\)
To find:
The domain and range of the given inequality.
Solution:
We have,
\(y<\sqrt{x+3}+1\)
The related equation is:
\(y=\sqrt{x+3}+1\)
This equation is defined if:
\(x+3\geq 0\)
\(x\geq -3\)
In the given inequality, the sign of inequality is <, it means the points on the boundary line are not included in the solution set. Thus, -3 is not included in the domain.
So, the domain of the given inequality is x>-3.
We know that,
\(\sqrt{x+3}\geq 0\)
\(\sqrt{x+3}+1\geq 0+1\)
\(y\geq 1\)
The points on the boundary line are not included in the solution set. Thus, 1 is not included in the range.
So, the domain of the given inequality is y>1.
Therefore, the correct option is A.
I really need help on this, please! Thanks appreciate thanks
Answers
Answer:
4. y-intercept = -9, answer option a
3. roots are x = 4 and -6, answer option a
Step-by-step explanation:
4. definition of y-intercept: where the function intersects the y-axis
this occurs where the x-coordinate = 0
that means the y-intercept = -9, given in the table
3. roots are zeroes of the function, where it intersects the x-axis
to find, set the function = 0
0 = -3(x-4)(x+6)
the values of x that make this equal to zero can be found by setting
x-4 = 0
and
x+6 = 0
so x = 4 and -6
A fun park charges $10 for admission and then two dollars for every ride. Write a function that determines the amount of money spent, Y, based on the number of rides ridden, X.!! please help ahhh
Answers
Answer:
x is I think 5
Step-by-step explanation:
dndjdudjndndjdjdjjd
El cuadrado de la suma (x + 4)2 es
a) X2 + 8x + 8
b) X2 + 4x + 16
c) X2 + 8x + 16
d) X2 + 4x + 8
Answers
Answer:
B.
Step-by-step explanation:
sana makatulong sayo
Find the values of x and y. Show all of your work.
Answers
x= 39
y= 123
Step by step
The angle between points EC is a vertical angle to angle DF, so they are congruent or the same = x - 11
Line AB is a straight angle with a sum equal to 180 degrees.
So (x-10) + (x-11) + (3x + 6) = 180
Combine like terms
5x -15 = 180
Add 15 to both sides to isolate variable
5x -15 + 15 = 180 + 15
Simplify
5x = 195
Divide both sides by 5 to solve for x
5/5x = 195/5
x = 39
y is a vertical angle to (3x + 6) so they are congruent or equal
We know x= 39 so substitute the value of x into the equation and equal it to y.
(3x + 6) = y
3(39) + 6 = y
123 = y
FILL IN THE BLANK. Study with Quizlet and memorize flashcards containing terms like ____ are the categories by which data are grouped
Answers
Data categorization is a process of organizing and grouping data into meaningful classes or categories.
This process is often used to simplify data and make it easier to understand and analyze. Data categorization involves breaking down a large set of data into smaller, more manageable groups. For example, a company may group customers into categories based on their age, income, or location. Each group can then be analyzed separately to better understand customer behavior. Categorizing data can also help identify trends or patterns that may not be visible when looking at the data as a whole. Categorization can also be used to identify outliers or anomalies in the data. By breaking down the data into smaller groups, it becomes easier to see which elements don’t fit the pattern or are not part of the normal range. Categorizing data can be done using a variety of methods. For example, data can be divided into numerical ranges or grouped into categories such as low, medium, and high. Data can also be grouped using descriptive terms, such as customer type or product type. Once the data is categorized, calculations such as averages, medians, and modes can be used to analyze the data. This can help to identify patterns or trends that can be used to make decisions or draw conclusions.
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A laptop computer that you want to purchase was originally priced at $775. You will receive a 20% student discount, and the sales tax rate is 8%. How much money will you pay for the laptop? Round to the nearest cent if needed.
Answers
Answer:
669.60
Step-by-step explanation:
775 is the original price so multiply 775 by 0.2 to find 20% of 775 which is 155. Subtract 155 from 775 to find how much you are saving. Next, multiply that number with 1.08.
1. fish population in a lake grows according to the logistic law. the initial population of 100 fish and year later it was 200. after a long time fish population stabilized at 2000. a. write down the logistic equation for this problem. b. what is the maximum reproduction rate (fish/year)?
Answers
a) The logistic equation for this problem is L dP/dt = P(1 - P/L), where L = 2000 and Po = 100.
b) The maximum reproduction rate is 0.03465 times the current population.
a. The logistic equation for this problem is:
L dP/dt = P(1 - P/L)
where L is the carrying capacity of the lake, P is the current population, and dP/dt is the rate of change of the population over time.
We know that at t = 0, P = 100, and one year later at t = 1, P = 200. So we can use this information to find k, which is the growth rate coefficient:
P(t) = L / (1 + (L / Po - 1) * exp(-kt))
200 = L / (1 + (L / 100 - 1) * exp(-k))
200 = L / (1 + (L - 100) * exp(-k))
200 + 200L - 20000 = L * (1 + (L - 100) * exp(-k))
200L -\(L^2\) * exp(-k) + 200L * exp(-k) - 10000 * exp(-k) = 0
\(L^2\) - 400L + 5000 = (L - 200)^2 - 30000
\((L - 200)^2\) = 35000
L = 200 + sqrt(35000) ≈ 223.6
So L ≈ 223.6, and we can use this to find k:
2000 = 223.6 / (1 + (223.6 / 100 - 1) * exp(-k))
20000 + 2000L - 2236 = L * (1 + (L - 100) * exp(-k))
2236 - \(L^2\) * exp(-k) + 2236 * exp(-k) - 100 * exp(-k) = 0
\(L^2\) - 4472L + 220000 = 0
(L - 2000)(L - 100) = 0
So either L = 2000 or L = 100. We know that L ≠ 100, since we know that the population stabilizes at 2000 after a long time. Therefore, L = 2000, and we can solve for k:
k = -ln((L / Po - 1) / (1 + (L / Po - 1))) / t
k = -ln((2000 / 100 - 1) / (1 + (2000 / 100 - 1))) / 1
k ≈ 0.0693
Therefore, the logistic equation for this problem is:
L dP/dt = P(1 - P/L)
dP/dt = 0.0693P(1 - P/2000)
b. The maximum reproduction rate occurs when the population is halfway to the carrying capacity, or P = L/2. At this point, the equation becomes:
dP/dt = 0.0693P(1 - 0.5)
dP/dt = 0.03465P
Therefore, the maximum reproduction rate is 0.03465 times the current population. For example, if the current population is 1000, the maximum reproduction rate is 34.65 fish per year.
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Full Question : Logistic Equation: L dP dt P(1-2). P() = L - Po Po 1+ 4e ki Where A 1. Fish population in a lake grows according to the logistic law. The initial population of 100 fish and year later it was 200. After a long time fish population stabilized at 2000.
a. Write down the logistic equation for this problem.
b. What is the maximum reproduction rate (fish/year)?
Webrooming, researching products online before buying them in store, has become the new norm for some consumers and contrasts with showrooming, researching products in a physical store before purchasing online. A recent study reported that most shoppers have a specific spending limit in place while shopping online. Findings indicate that men spend an average of $270 online before they decide to visit a store. Assume that the spending limit for men is normally distributed and that the standard deviation is $19.
Required:
a. What is the probability that a male spent less than $229 online before deciding to visit a store?
b. What is the probability that a male spent between $298 and $320 online before deciding to visit a store?
c. Eighty percent of the amounts spent online by a male before deciding to visit a store are less than what value?
Answers
a. The probability that a male spent less than $229 online before deciding to visit a store is approximately 1.5%.
b. The probability that a male spent between $298 and $320 online before deciding to visit a store is approximately 6.6%.
c. 80% of the amounts spent online by a male before deciding to visit a store are less than approximately $285.598.
We have,
a. To find the probability that a male spent less than $229 online before deciding to visit a store, we need to calculate the cumulative probability.
Using the normal distribution with a mean of $270 and a standard deviation of $19, we can calculate:
P(X < $229) = P(Z < (229 - 270) / 19) = P(Z < -2.158) ≈ 0.015
Therefore, the probability that a male spent less than $229 online before deciding to visit a store is approximately 0.015, or 1.5%.
b. To find the probability that a male spent between $298 and $320 online before deciding to visit a store, we can calculate the difference between the cumulative probabilities for each value.
Using the normal distribution, we have:
P($298 < X < $320) = P(X < $320) - P(X < $298)
= P(Z < (320 - 270) / 19) - P(Z < (298 - 270) / 19)
= P(Z < 2.632) - P(Z < 1.474)
≈ 0.995 - 0.929
≈ 0.066
Therefore, the probability that a male spent between $298 and $320 online before deciding to visit a store is approximately 0.066, or 6.6%.
c. To find the value below which 80% of the amounts spent online by a male before deciding to visit a store fall, we can use the inverse cumulative distribution function (also known as the Z-score).
We need to find the Z-score corresponding to the cumulative probability of 0.8:
Z = invNorm(0.8) ≈ 0.842
Now, we can use the Z-score formula to find the corresponding value:
X = mean + Z x standard deviation
= $270 + 0.842 * $19
≈ $285.598
Therefore, 80% of the amounts spent online by a male before deciding to visit a store is less than approximately $285.598.
Thus,
a. The probability that a male spent less than $229 online before deciding to visit a store is approximately 1.5%.
b. The probability that a male spent between $298 and $320 online before deciding to visit a store is approximately 6.6%.
c. 80% of the amounts spent online by a male before deciding to visit a store are less than approximately $285.598.
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Which expression would be easier to simplify if you used the associative property to change the grouping?
A. ( 50 + 50 ) + 63
B. ( 43 + 60 ) + 40
C. ( 2/5 + 3/5 ) + 7/3
D. [ - 14 + ( - 26 ) ] + 67
Answers
Answer:
probably A
Step-by-step explanation:
In the figure below, AB is a diameter of circle P.
What is the arc measure of minor arc AD in degrees?
Answers
Answer:
D
Step-by-step explanation:
Answer:
a
Step-by-step explanation:
Find area of the figure.
Answers
First the top right quart
area = 16, 4 * 4
Then the top left quart
making a 2 by 4 triangle followed with 4 additional square
making 2 * 4 * 1/2 = 4 + 4 meaning area = 8
then the bottom quart
Making a large triangle of 7 by 3
meaning 7 * 3 * 1/2 = 10.5
total area = 16 + 8 + 10.5 = 34.5
What is the distance between the points (3,10) and (7,7)?
Answers
The length of the line drawn between points (3, 10) and (7, 7) is 13.454 unit length.
The length of the line is described by the distance formula which is described as below:
d = √ ( x₂ - x₁ )² + ( y₂ - y₁ )²
where x is the x coordinates of the points
y is the y coordinates of the points
Coordinates of first point = (3, 10)
Coordinates of second point = (7, 7)
x₁ = 3
x₂ = 7
y₁ = 10
y₂ = 7
d = √ (3 - 7)² + (10 - 7)²
d = √ 16 + 9
d = √ 25
d = 5 unit length
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Solve -2x+6<20 please answer! Thank you!
Answers
Answer:
x>-7
Step-by-step explanation:
-2x+6<20
-2x+6-6<20-6
-2x<14
-2x/2<14/2
x>-7
Hope this helps:)
Answer:
x>-7 i think im so sorry if im wrong
Step-by-step explanation:
Task 2
If two figures are similar, then they are congruent.
Check all that apply
true in all cases
true in some cases
true in no cases
Answers
Answer:
pqoejbbbsvbhxncbqbqheeirowoqpnabzvxjsmqkw
Please Help 100 POINTS!!!
Answers
Answer:
B
Step-by-step explanation:
Answer:
B. \(\frac{x^2}{3^2} +\frac{y^3}{2^2} =1\)
Step-by-step explanation:
Micro the highest score he made of his new video game as the product of 70 * 6,000 use the surgery and community property to show how mark can calculate this product mentally
Answers
Micro's highest score in his new video game is 420,000.
To calculate the highest score Micro made in his new video game, we can use the associative property of multiplication. The associative property states that the grouping of numbers being multiplied does not affect the product.
Given that Micro's highest score is the product of 70 * 6,000, we can use the associative property to break down the calculation mentally.
Step 1:
Multiply 70 by 6,000:
70 * 6,000 = 420,000
Step 2:
Now, let's apply the associative property. We can break down 6,000 into two parts: 6,000 = 100 * 60.
Step 3:
Multiply 70 by 100:
70 * 100 = 7,000
Step 4:
Multiply the result from Step 3 by 60:
7,000 * 60 = 420,000
Therefore, Micro's highest score in his new video game is 420,000.
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AABC is reflected across the x-axis and then translated 4 units up to create AA'BC. What are the coordinates of the vertices of AABC?
OA A'(-3, 3), B(-1, 1). C(-2.3)
ОВ.
A'(3.-3), B(1,-1), C(2.-3)
OC. A'(3.-5), B(1, -7), C(3.-5)
OD. A'(-3, 3), B(-1, 1), C(-2,-
Answers
Answer:
A
Step-by-step explanation:
Under a reflection in the x- axis
a point (x, y ) → (x, - y ) , then
A(- 3, 1 ) → (- 3, - 1 )
B(- 1, 3 ) → (- 1, - 3 )
C(- 2, 1 ) → (- 2, - 1 )
A translation of 4 units up means adding 4 to the y- coordinate
( - 3, - 1 ) → A' (- 3, - 1 + 4 ) → A' (- 3, 3 )
(- 1, - 3 ) →B' (- 1, - 3 + 4 ) → B' (- 1, 1 )
(- 2, - 1 ) → C' (- 2, - 1 + 4 ) → C' (- 2, 3 )
A figure lies entirely in Quadrant I. The figure is reflected in the x-axis. In which quadrant is the image?
Answers
Answer: quadrant 4 i think...
Step-by-step explanation:
Answer:
Quadrant IV (4).
Step-by-step explanation:
It will be in the quadrant below which is Quadrant IV.
I am 3 units less than -3
Answers
Hi!
your answer is 0
hope this helps!
I’ll mark you brainlist I’ll mark you brainlist write in y=mx+b form
Answers
Answer:
y=-4x+2
hope this helped
Can someone please help me? :(
Answers
Answer:
12 edges, 6 faces, and 7 vertices.
▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬
I say 12 edges because there are 12 meeting points, and an open shape.
6 faces because there are 6 highlighted points on what looks like an unfolded shape.
8 vertices because you add 2 to the number of edges and subtract by the number of faces, 6.
if the area of the quadrilateral ABCS is 924cm^2 and the length of the diagonal AC is 33cm,find the sum of lengths of the perpendicular from points B and D to AC.
please answer with full steps asap
Answers
3BE² + 3DF²- (2AC²- AB) is the answer of the following question
The calculation is as follows
Let E and F be the feet of the perpendiculars from B and D, respectively, to AC. We can use the fact that the area of a quadrilateral is equal to half the product of the diagonals multiplied by the sine of the angle between them to find the length of the diagonal BD.
Since ABCS is a quadrilateral, we have:
Area of ABCS = (1/2) * AC * BD * sin(angle between AC and BD)
Substituting the given values, we get:
924 = (1/2) * 33 * BD * sin(angle between AC and BD)
sin(angle between AC and BD) = 924 / (16.5 * BD)
Now, consider triangles ABC and ACD. Using the Pythagorean theorem, we can write:
AB² + BC² = AC² (1)
CD²+ BC² = AC² (2)
Adding equations (1) and (2), we get:
AB² + 2BC²+ CD²= 2AC²
Substituting AC = 33 and rearranging, we get:
BC² = (2AC²- AB² - CD²) / 2
We can also write:
BE²= AB²- AE² (3)
DF² = CD²- CF²(4)
Adding equations (3) and (4), we get:
BE² + DF²= AB²+ CD² - AE²- CF²
Substituting BC²from earlier, we get:
BE²+ DF² = 2AC² - BC²- AE²- CF²
We want to find BE + DF. Squaring both sides of equation (3), we get:
BE²= AB² - AE²
AE²= AB²- BE²
Similarly, squaring both sides of equation (4), we get:
DF²= CD²- CF²
CF²= CD² - DF²
Substituting these expressions into the equation for BE²+ DF², we get:
BE²+ DF² = 2AC² - BC² - (AB² - BE²) - (CD²- DF²)
Simplifying, we get:
BE² + DF²= 2AC² - BC²- AB²- CD² + 2BE² + 2DF²
Collecting like terms, we get:
BE²+ DF²- 2BE² - 2DF²= 2AC²- BC² - AB² - CD²
Simplifying, we get:
BE²- DF² = 2AC²- BC²- AB²- CD²- 2BE² - 2DF²
Substituting the values we know, we get:
BE²- DF²= 2(33)²- BC²- AB² - CD²- 2BE²- 2DF²
Rearranging, we get:
3BE²+ 3DF² - BC²- AB²- CD²= 2(33)² - 924
Substituting BC^2 from earlier, we get:
3BE²+ 3DF² - (2AC²- AB)
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graph one is linear so incorrect prolly but help ty ty
Answers
The function given is:
\(f(x)=x^3+3\)It is required to find the graph of f(5x).
Recall that the graph of f(kx) for k>1 is the horizontal compression or shrink of the graph of f(x) by k units. The graph is compressed horizontally towards the y-axis.
Graph the given function f(x)=x³+3:
Compress the graph horizontally by k=5 units as shown below:
The required graph is:
The graph that best fits this is graph 4.
The answer is gra
I am thinking of two numbers. When i add my numbers, the answer is 1 when i multiply my numbers, the answer is 0. 09 what are my numbers?.
Answers
The two numbers are either 0 and 1 or 1 and 0. This is a method of solving a system of equations called substitution method
To solve this problem you can use a mathematical one, called a system of equations. A system of equations is a set of two or more equations that contain multiple variables. In this case, we have two equations with two variables, x and y.
We know that when you add the two numbers, the result is 1. We also know that when you multiply the two numbers, the result is 0.
Given these two equations:
x + y = 1 and x*y = 0
We know that one of the numbers is 0, because when we multiply any number by 0 the result is 0.
So x=0 or y=0
Now we can use the first equation, x + y = 1, and substitute in one of the values we know:
x = 0 and y = 1
or
y = 0 and x = 1
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do anyone know the answer???
Answers
Answer:
13/15
Step-by-step explanation:
THis is because 2/3and 1/5 change 5 and 3 to 15 . And 2 to 10 and 1 to 3=13/15
Which statement is true about the ranges for the box plots? the range of the morning box plot is the same as the range of the afternoon box plot. The range of the morning box plot is 1 less than the range of the afternoon box plot. The range of the morning box plot is 1 more than the range of the afternoon box plot. The range of the morning box plot is 2 less than the range of the afternoon box plot.
Answers
The range of the Morning box plot is the same as the range of the Afternoon box plot. Therefore, the correct answer is option A.
A box and whisker plot—also called a box plot—displays the five-number summary of a set of data. The five-number summary is the minimum, first quartile, median, third quartile, and maximum. In a box plot, we draw a box from the first quartile to the third quartile. A vertical line goes through the box at the median.
Number of sales in Afternoon:
Minimum value = 4
First quartile = 8
Median = 14
Third quartile = 15
Maximum value = 16
Here, the range is 16-4=12
Number of sales in Morning:
Minimum value = 3
First quartile = 5
Median = 8
Third quartile = 12
Maximum value = 15
Here, the range is 15-3=12
Therefore, the correct answer is option A.
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