a) The probability of getting exactly 5 successes is 0.1029.
b)The probability of getting 6 or more successes is 0.8497510126.
What is Probability?Probability refers to potential. A random event's occurrence is the subject of this area of mathematics.
The range of the value is 0 to 1. Mathematics has incorporated probability to forecast the likelihood of various events.
The degree to which something is likely to happen is basically what probability means.
Given:
Here, p = 0.7, q = 0.3 and n = 10
a) The probability of getting exactly 5 successes
P (x= 5) = C(10, 5) (0.7)⁵ (0.3)⁵
= 10!/ 5! 5! x 0.16807 x 0.00243
= 0.1029
b)The probability of getting 6 or more successes
P(X≥6) = 1 - P(X<6)
= 1 - P(X = 0, 1,2, 3, 4, 5)
= 1 - [ P(0) + P(1) P(2) + P(3) + P(4) + P(5)]
= 1 - [C(10, 0) [tex](0.3)^{10[/tex] + C(10, 1) (0.7) [tex](0.3)^{9[/tex] + C(10, 2) (0.7)² [tex](0.3)^{8[/tex]
+ C(10, 3) (0.7)³ [tex](0.3)^{7[/tex] + C(10, 4) [tex](0.7)^4[/tex][tex](0.3)^{6[/tex] + C(10, 4) [tex](0.7)^5[/tex]
[tex](0.3)^{5[/tex] ]
= 1 - [ 0.0000059049 + 0.000137781 + 0.0014467005 +
0.009001692 + 0.036756909 + 0.1029]
= 1 - 0.1502489874
= 0.8497510126
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Fine the area of the trapezoid
Answer: The area of the trapezoid can be found using the formula:
Area = (a + b)h/2
where a and b are the lengths of the parallel sides and h is the height (perpendicular distance between the parallel sides).
In this case, the parallel sides are 13ft and 15ft, and the height is 5ft.
Therefore, the area of the trapezoid is:
(13 + 15) * 5 / 2 = (28) * 5 / 2 = 140 / 2 = 70 ft^2
Step-by-step explanation: The area of the trapezoid is calculated by taking the sum of the parallel sides, multiplying by the height and then dividing by 2. The parallel sides are given as 13ft and 15ft, and the height is given as 5ft.
By substituting the given values in the formula we get (13+15)5/2 = 285/2 = 140/2 = 70 ft^2.
So, the area of the trapezoid is 70 ft^2.
a disabled sailboat is drifting in a straight line at 4 miles per hour. a coast guard rescue craft is trailing it by 11 miles, moving along the same path at a rate of 29 miles per hour. how long will it be before the rescue craft reaches the sailboat?
It will take the rescue craft 0.44 hours or 26.4 minutes to reach the sailboat.
The time required for the rescue craft to reach the sailboat can be calculated by using the formula for relative velocity:
Relative Velocity = Velocity of the Rescue Craft - Velocity of the Sailboat
= 29 mph - 4 mph = 25 mph
Therefore, the time required for the rescue craft to reach the sailboat is given by:
time= Distance/Relative Velocity
= 11 miles/25 mph
= 0.44 hours
Therefore, it will take the rescue craft 0.44 hours or 26.4 minutes to reach the sailboat.
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Show all work to identify the asymptotes and state the end behavior of the function f of x is equal to 4x divided by the quantity of x minus 16 end quantity.
The function f(x) = 4x/(x-16) has vertical asymptotes at x = 16.
To see this, we can factor the denominator:
f(x) = 4x/(x-16) = 4x/x - 16
As x approaches 16 from the left or right, the denominator x-16 approaches 0, but the numerator 4x does not. This means that the function approaches infinity or negative infinity as x approaches 16, indicating a vertical asymptote at x = 16.
To find the end behavior of the function, we can look at the behavior of the function as x approaches positive or negative infinity. We can see that f(x) = 4x/(x-16)
As x increases without bound, x-16 increases without bound. This means that the denominator becomes larger and larger, making the function approach 0 as x approaches positive infinity.
As x decreases without bound, x-16 decreases without bound as well, this means that the denominator becomes smaller and smaller, making the function approach 0 as x approaches negative infinity.
Therefore, the function has a vertical asymptote at x = 16 and approaches 0 as x approaches positive and negative infinity.
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Answer:
f(x) =. 4x/(x-16)
4x= 0 =>x=
x-16= 0
=>x=16
Asymptotes(x) =16
Step-by-step explanation:
Is zero positive proof?
No, The number zero is neither positive nor negative.
Aryabhata, who is known as a great astronomer of the classic age of India was the one who invented the digit “0” for which he became immortal but later on is given to Brahmagupta.
The numbers to the right of zero on the number line are positive and those on the left side are negative.
Positive numbers are greater than 0 and located to the right of 0 on a number line. Negative numbers are less than 0 and are located to the left of 0 on a number line.
Positive and negative numbers are sometimes called signed numbers.
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in 1996 34% of students had not been absent from school even once during the previous month. in the 2000 survey, responses from 8302 students showed that this figure had slipped to 33%. officials would, of course, be concerned if student attendance were declining. do these figures give evidence of a change in student attendance? a) write appropriate hypotheses. b) check the assumptions and conditions.
On solving the provided question we can say that by null hypothesis There is insufficient proof to conclude that student attendance has changed.
What is null hypothesis?A null hypothesis is a kind of statistical hypothesis that asserts that a specific set of observations has no statistical significance. Using sample data, hypotheses are tested to determine their viability. Sometimes known as "zero" and symbolized by H0. Researchers start off with the presumption that there is a link between the variables. In contrast, the null hypothesis claims that there is no such association. Although the null hypothesis may not appear noteworthy, it is a crucial component of research.
This is a z-test for a proportion.
[tex]H0:p=.34 H1:p not=.34\\\alpha=0.01 ... this is a\\2-tailed test\\critical values are +2.58, -2.58\\p=.34 (given) q=1-p=.66\\p^=.33\\z=(p^-p)/sqrt(pq/n)\\z=(.33-.34)/sqrt(.34*.66/8302)\\z=-.01/.0051961\\z=-1.92[/tex]
1.96 does not fall in the reject region
There is insufficient proof to conclude that student attendance has changed.
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two cards are selected without replacement from a standard deck of 52 cards. find the probability of selecting a heart and then selecting a diamond.
Using the formula of probability without replacement, the probability of selecting a heart first is 13 / 52 and a diamond second is 13 / 51
What is Probability without replacementProbability without replacement refers to the likelihood of a specific event occurring when items are removed from a set or collection as they are selected. It differs from probability with replacement, where the items are replaced after each selection and the set remains unchanged.
To calculate probability without replacement, we use the formula:
P(Event) = Number of favorable outcomes / Number of possible outcomes
Where the number of possible outcomes is the total number of items in the set, and the number of favorable outcomes is the number of items that satisfy the conditions of the event.
In the first event;
P(heart) = 13 / 52
In the second event, the first card is not replaced and so, the number of possible outcomes is reduced by 1
p(diamond) = 13 / 51
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select all the examples of exponential function
a) y=3x-2
b) y=3^x
c) y=(1/2)^3x
d) y=3x^2
E) y=(1/2)^x
Answer:
Select all the examples of the exponential function
a) y=3x-2
b) y=3^x
c) y=(1/2)^3x
d) y=3x^2
E) y=(1/2)^x
Find the length of side X to the nearest tenth.
Answer:
4.6
Step-by-step explanation:
In a 30-60-90 triangle, the length of the side opposite the [tex]30^{\circ}[/tex] angle is [tex]\frac{1}{\sqrt{3}}[/tex] the length of the side opposite the [tex]60^{\circ}[/tex] angle.
[tex]\implies x=\frac{8}{\sqrt{3}} \approx 4.6[/tex]
if i had 304,770 in total. 8.3% female viewers, 91.2% male viewers, and 0.5% user-specified viewers how many female viewers would i have in numbers (without percent)
Answer:
25,295.91
Step-by-step explanation:
304,770
1%=3047.7
0.1%=304.77
8%=24,381.6
0.3%=914.31
24,381.6+914.31=25,295.91
female viewers =25,295.91
how to find midline of sinusoidal functions from equation
A function's midline is the horizontal line positioned exactly halfway between its maximum and minimum values.
what is trigonometric ratios ?Trigonometric ratios are based on the side ratio of a right-angled triangle and consist of the values of all trigonometric functions. The ratios of the sides to any acute angle in a right-angled triangle are the trigonometric ratios of that angle. You can use trigonometric ratios to determine the lengths of one (or both) of the acute angles of a right triangle if you know the lengths of its two sides.
given
A function's midline is the horizontal line positioned exactly halfway between its maximum and minimum values.
The midline is the line y = 0 for y = sin (the horizontal axis). The difference between the highest and smallest values of a function is half its amplitude.
The amplitude of the y = sin function is 1.
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How do you solve ratio problems?
A ratio is an ordered pair of numbers a and b, written a / b where b does not equal 0. A proportion is an equation in which two ratios are set equal to each other
What is an equivalent ratios?
A ratio compares two quantities named as antecedent and consequent, by the means of division. For example, when we cook food, then each ingredient has to be added in a ratio. Thus, we can say, a ratio is used to express one quantity as a fraction of another quantity.
Two ratios are equivalent to each other if one of them can be expressed as the multiple of the other. Hence, to get the equivalent ratio of another ratio, we have to multiply the two quantities (antecedent and consequent) by the same number.
Given ratios are 2:1 and 3:1
we can write it as 2/1 and 3/1.
The lcm of 2 and 3 is 6.
Multiply denominator of both ratio with 6, we get
2/6 and 3/6 And we can see both the ratios are not equal.
Hence, there are not equivalent ratios.
4:1 and 8:3 are equivalent ratios -----> is false, because 4:1 is equivalent to 8:2
11:2 and 2:11 are equivalent ratios------> is false (because, are reciprocal ratios, not equivalent ratios)
3:1 and 9:3 are equivalent ratios ------> is true
because 3:1 multiply both sides by 3 -----> 3*3:1*3=9:3
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One pipe can fill and drain the pool at a rate that is 1 more than 2 times faster than the other pipe. If both pipes are open and working properly, it will take 3.5 hours to fill the pool.
So the time taken to fill the pool by the slower pipe is 30 hours .
As mentioned about the time in the question stated below.
Let the slower pipe's time be x and the quicker pipe's time be x/2.
By slower pipe in an hour = 1/x, quicker pipe in an hour = 2/x, and by both = 1/10.
2/x+1/x = 1/10
we have to take reciprocal of the time taken by each pipes.
(1+2)/x = 1/10
=> 3/x = 10
=> x= 30
The slower pipe requires 30 hours of times to completely fill the pipe.
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Complete question:
A single pipe can fill a pool twice as quickly as a second one. The pool will be filled in ten hours once both pipes are opened. If only the slower pipe is utilized, how long would it take to fill the pool?
what do i do if the there is a number in a set of numbers that is much lower than the other when finding the average
Answer: Keep it in the calculation
Step-by-step explanation:
circles with centers at o and p have radii 2 and 4, respectively, and are externally tangent. points a and b on the circle with center o and points c and d on the circle with center p are such that ad and bc are common external tangents to the circles. what is the area of the concave hexagon aobcpd?
Area of concave hexagon = 24
To find the area of the concave hexagon, we can divide it into two triangles and a rectangle. The side lengths of the rectangle are the difference of the radii of the two circles (4-2=2) and the distance between the centers of the circles, which can be found using the Pythagorean theorem. Using that we can find the area of the rectangle and the two triangles. The area of the hexagon is the sum of the areas of these three shapes.
In the given case, let the distance between the centers of the circles be 'd'.
d^2 = (4+2)^2
d = √((4+2)^2) = √(36) = 6
Area of rectangle = 26 = 12
Area of each triangle = (1/2)(2d) = (1/2)(2*6) = 6
Area of hexagon = 12 + 2*6 = 24
Area of concave hexagon = 24
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Determine the value of h in the equation h minus four sevenths equals two sevenths
Answer:
h = 6/7
Step-by-step explanation:
h minus four sevenths equals two sevenths
minus means -
equals means =
h - four sevenths = two sevenths
four sevenths means 4/7
two sevenths = 2/7
h - 4/7 = 2/7
add 4/7 to both sides to isolate h
h = 6/7
Answer: h =6/7
Step-by-step explanation: 4/7 + 2/7 = 6/7 so h - 4/7 = 2/7 h = 6/7
Solve for d: 1/4(d-2)=6
The value of d = 26.
What are Equations:A mathematical statement that maintains the equality of two expressions that are joined by the equals sign "=" is known mathematically as an equation.
A mathematical equation can be solved by adding or subtracting the same number on both sides or multiplying or dividing the same number into both sides.
Here we have
1/4(d-2) = 6
Solve the above equation as follows
=> 1/4(d-2) = 6
Multiply by the same number on both sides
=> 4[ 1/4 (d - 2) ] = 4 × 6
=> (d - 2) = 24
Add '2' on both sides
=> (d - 2) + 2 = 24 + 2
=> d = 26
Therefore,
The value of d = 26
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for some experiment, rats were put in a maze and time of completion was noted. the completion time was normally distributed with a mean of 1.5 and a standard deviation of 0.35. if 5 rats are selected, what is the probability that their total completion time in the maze for all rats is between 6 and 8 minutes? (hint: the mean and standard deviation are for one rat).
With a mean of 1.5 and a standard deviation of 0.35. if 5 rats are selected, the probability that their total completion time in the maze for all rats is between 6 and 8 minutes is 0.4455.
First, we need to convert the given mean and standard deviation from "one rat" to "five rats". The mean for five rats would be 5 x 1.5 = 7.5, and the standard deviation for five rats would be sqrt(5) x 0.35 = 0.87. Next, we need to convert the given time range of 6-8 minutes to the standard normal distribution, using the z-score formula: z = (x - mean) / standard deviation.
For 6 minutes, z = (6 - 7.5) / 0.87 = -1.72 ,For 8 minutes, z = (8 - 7.5) / 0.87 = 0.58 Finally, we can use a standard normal distribution table to find the probability that the rats will complete the maze in between 6 and 8 minutes. This is the area under the standard normal curve between -1.72 and 0.58. The probability is 0.4455.
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Help me out here pls
Answer:
x = 82°, y = 98°, z = 98°---------------------------------------
Property of a parallelogram:
Opposite angles are congruent and adjacent angles are supplementary.According to the property we have:
x = 82°y = z = 180° - 82° = 98°What is the midpoint formula in coordinate geometry class 10?
For class 10, the midpoint formula in the coordinate geometry for the endpoints ( x₁ , y₁ ) and ( x₂ , y₂ ) is given by:
( x , y ) = [( x₁ + x₂)/2 , (y₁ + y₂)/2].
As given in the question,
In the coordinate geometry of class 10,
To get the x and y coordinate of the midpoint following points need to follow:
Let us consider the endpoints of any line segment be given by ( x₁ , y₁ ) and ( x₂ , y₂ ).To get the x coordinate add x₁ and x₂ then divide it by 2.To get the y coordinate add y₁ and y₂ then divide it by 2.In standard form midpoint formula is written as ( x , y ) = [( x₁ + x₂)/2 , (y₁ + y₂)/2].Therefore, in the coordinate geometry of class 10 the midpoint formula is given by ( x , y ) = [( x₁ + x₂)/2 , (y₁ + y₂)/2].
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Please help asap!! I need help, how do you solve this??
Answer:
FIRST ONE IS 7
Step-by-step explanation:
SECOUND ONE IS 12THIRD ONME IS 2
What is the range of the following data set?
34 15 75 81 45 73 97 89 23
Answer: 45
Step-by-step explanation:
question 6 a data analyst at an e-commerce company is working with a spreadsheet containing last month's sales. the most expensive product their company sells costs $49.99, so they want to quickly confirm that all of the data in the sales column is $49.99 or less. what function can they use?
The required function,which best describe the problem is split function.
What is Split function?By designating one of the given string's sub-strings as the delimiter, the split() method can be used to divide a given string or line. The output is the string that comes before and comes after the substring that was supplied as a delimiter.
According to question:a data analyst at an e-commerce company is working with a spreadsheet containing last month's sales.
the most expensive product their company sells costs $49.99, so they want to quickly confirm that all of the data in the sales column is $49.99 or less.
This situation is defined for split function, which is best describe it.
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Find the length of the toothpick nearest millimeter
Answer:
85 Millimeters
Step-by-step explanation:
1 centimeter is equal to 10 millimeters. Hope this helped!
jason wants to have pizza for dinner. a large pizza costs $10.50 with no toppings other than cheese. jason wants 4 toppings on his pizza for a cost of $12.10. write an equation
On solving the provided question, we can say that the linear equation, will be 10.50x + 12.50y = 4 => x = 23.1 => y = 3.21
What is a linear equation?A linear equation is one that has the form y=mx+b in algebra. B is the slope, and m is the y-intercept. It's usual to refer to the previous clause as a "linear equation with two variables" because y and x are variables. The two-variable linear equations known as bivariate linear equations. There are several instances of linear equations: 2x - 3 = 0, 2y = 8, m + 1 = 0, x/2 = 3, x + y = 2, and 3x - y + z = 3. It is referred to as being linear when an equation has the form y=mx+b, where m stands for the slope and b for the y-intercept.When an equation has the formula y=mx+b, with m denoting the slope and b the y-intercept, it is referred to as being linear.
a large pizza costs = $10.50 with no toppings other than cheese
Jason wants 4 toppings on his pizza for a cost of = $12.10
the linear equation, will be
10.50x + 12.50y = 4
x = 23.1
y == 3.21
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In the diagram, four squares of side length 2 are placed in the corners of a square of side length 6. Each of the points $W$, $X$, $Y$, and $Z$ is a vertex of one of the small squares. Square $ABCD$ can be constructed with sides passing through $W$, $X$, $Y$, and $Z$. What is the maximum possible distance from $A$ to $P$
In this problem, you have a square with side length 6 and four smaller squares with side length 2 placed in the corners. The points W, X, Y, and Z are the vertices of the smaller squares. The goal is to find the maximum possible distance between points A and P.
[asy] size(200); pair A,B,C,D,P,W,X,Y,Z; A=(0,4); B=(4,4); C=(4,0); D=(0,0); P=(2,2); W=(0,6); X=(6,6); Y=(6,0); Z=(0,0); draw(A--B--C--D--cycle); draw(W--X--Y--Z--cycle); draw(A--P--C); label("A",A,NW); label("B",B,NE); label("C",C,SE); label("D",D,SW); label("P",P,S); label("W",W,N); label("X",X,NE); label("Y",Y,S); label("Z",Z,SW); [/asy]
The point A is located on the bottom-left corner of the square with side length 6, and the point P is the center of the square $ABCD$. To find the maximum distance from A to P, we need to find the longest diagonal of the square $ABCD$.
The longest diagonal of a square is the one that goes from one corner of the square to the opposite corner. In this case, the longest diagonal goes from point A to point C, which is a distance of 6 units. Therefore, the maximum possible distance from A to P is 6 units.
Round 1212 to the nearest hundred
Answer:
1200
Step-by-step explanation:
step 1: Locate and underline the hundreds place (2) then look at the digit to the right (1): 1212
Step 2: The digit to the right (1) is 4 or below. So, we replace it with a 0 (zero) to get 1200 as the answer.
In short: 1212 rounded to the nearest hundred is 1200.
the smith family has cats and dogs. in how many ways can these pets be placed in a row of chairs such that at least cats are next to each other?
The number of ways to arrange the pets such that at least one pair of cats are next to each other is:
(n+m)!/(n!m!) - (m+n-1)!/(m!(n-1)!). Considering n as catcats and m as dogs
There are a few different ways to approach this problem, but one possible method is to use the complement principle, which states that the total number of ways to arrange the pets minus the number of ways to arrange them such that no cats are next to each other will give the number of ways to arrange them such that at least one pair of cats are next to each other.
Let n be the number of cats and m be the number of dogs. The total number of ways to arrange the pets in a row of chairs is (n+m)!/(n!m!), which is the number of ways to arrange n identical cats and m identical dogs. To arrange the pets such that no cats are next to each other, we can first arrange the cats in n! ways and then place the dogs between the cats in (m+n-1)!/(m!(n-1)!) ways, since there are m+n-1 spaces to place the m dogs and n-1 dividers between the n cats.
Therefore, the number of ways to arrange the pets such that at least one pair of cats are next to each other is:
(n+m)!/(n!m!) - (m+n-1)!/(m!(n-1)!)
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GPS Guided Problem Solving An equilateral triangle's perimeter is 27 ft. The height of the triangle is 7.8 ft. What is the triangle's area?
The area of the triangle is given by the equation A = 35.1 feet²
What is a Triangle?A triangle is a plane figure or polygon with three sides and three angles.
A Triangle has three vertices and the sum of the interior angles add up to 180°
The area of the triangle = ( 1/2 ) x Length x Base
An equilateral triangle is a triangle in which all three sides have the same length.
Let the triangle be ΔABC , and
∠A = ∠B = ∠C = 60° and AB = BC = CA
Given data ,
Let the triangle be represented as ABC
Now , the triangle ABC is an equilateral triangle
So , AB = BC = CA
The perimeter of the triangle is P = 27 feet
So , the base length of the triangle AB = 27/3 = 9 feet
The height of the triangle = 7.8 feet
Now , area of the triangle = ( 1/2 ) x Length x Base
Substituting the values in the equation , we get
The area of the triangle A = ( 1/2 ) x 7.8 x 9
The area of the triangle A = 35.1 feet²
Hence , the area of the triangle is 35.1 feet²
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describe the possible lengths of the third side of the triangle given the lengths of the other two sides. 15 inches, 37 inches
The possible length of the third side of the triangle is x>52 inches.
What is the sum of the first side and second side of any triangle?The sum of the lengths of any two sides of a triangle is always greater than the length of the third side. If the sum of the two sides is equal to the third side, then the two sides will coincide with the third side so a triangle cannot be formed. Hence, the sum of the two sides must be greater than the third side for the triangle to be formed.
Given: Sides of two sides of a triangle as 15 and 37 inches.
let the third side of the triangle be x.
then x>15+37
x>52 inches.
Hence, The possible length of the third side of the triangle is x>52 inches.
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Ekaterina’s favorite expression is 4x – 4. Alban’s favorite expression is 8x – 24. What value of x makes these two expressions equal?
Answer:
x = 5
Step-by-step explanation:
You are solving for a x that can, when plugged in, equate both given expressions. To do so, set each given expression equal to each other:
4x - 4 = 8x - 24
Isolate the variable, x. Note the equal sign, what you do to one side, you do to the other. Do the opposite of PEMDAS.
PEMDAS is the order of operations, and stands for:
Parenthesis
Exponents (& roots)
Multiplications
Divisions
Additions
Subtractions
~
First, subtract 8x and add 4 to both sides of the equation:
4x (-8x) - 4 (+4) = 8x (-8x) - 24 (+4)
4x - 8x = -24 + 4
-4x = -20
Next, divide -4 from both sides of the equation:
(-4x)/-4 = (-20)/-4
x = -20/-4
x = 5
5 is your answer.
Check:
Plug in 5 for x in both given expressions:
4x - 4
4(5) - 4
= 20 - 4
= 16
-
8x - 24
8(5) - 24
= 40 - 24
= 16
~
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