Answer:Therefore, the answer is D. 16.
Step-by-step explanation:
The expression 4 + (f + 7) simplifies to 11 + f. When f = 5, the value of the expression is:
11 + 5 = 16
Therefore, the answer is D. 16.
Malik can spend no more than $24 to buy pecans and cashews. He will pay $6 per pound for pecans and $8 per pound for cashews. Which graph best represents the number of pounds of pecans and the number of pounds of cashews Malik can buy?
Answer:
Graph D
Step-by-step explanation:
We can look at the number of pounds of pecans and cashews, shown on the x- and y-axis, respectively.
All of the graphs have an x-intercept of (4, 0), meaning that the number of pecans being bought is 4 lbs.
Since pecans cost $6 per lb, we can multiply the cost by 4 in order to make sure that the total cost is not exceeding $24.
$6 · 4 lbs = $24
Let's look at the y-axis to see how many lbs of cashews Malik can buy. The y-intercept is (0, 3) for all graphs, meaning that 3 lbs of cashews are being bought.
Since cashews cost $8 per pound, we can multiply the cost by 4 in order to make sure that the total cost is not exceeding $24.
$8 · 3 lbs = $24
The shaded area represents the values that can be used in the problem. Since we want $24 or less, the shaded region has to be below the line.
Malik can spend no more than $24, so the line should be solid since this means that the values the line touches are inclusive. 4 lbs of pecans and 3 lbs of cashews should be inclusive.
The graph that has all of these properties is Graph D.
a bird leaves its nest, and flies back and forth from its nest to a nearby ditch to gather worms. the distance between the nest and the ditch is 200 meters. in one and a half hours, the bird manages to bring worms to its nest 15 times. what is the speed of the bird in kilometers per hour?
Therefore, the speed of the bird is approximately 1.001 kilometers per hour.
We can start by calculating the total distance the bird flew, which is the distance between the nest and the ditch multiplied by the number of round trips:
total distance = 2 × distance between nest and ditch × number of round trips
total distance = 2 × 200 meters × 15
total distance = 6000 meters
Next, we can calculate the bird's average speed by dividing the total distance by the time it took to make the trips:
average speed = total distance ÷ time
average speed = 6000 meters ÷ (1.5 hours × 3600 seconds/hour)
average speed = 0.278 meters/second
To convert this to kilometers per hour, we can multiply by the conversion factor of 3.6:
average speed = 0.278 meters/second × 3.6 kilometers/meter
average speed = 1.001 kilometers/hour
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find the general solution to the system x ' = ax where a is the given matrix.
The general solution to the system x' = Ax, where A is the given matrix, can be expressed as x(t) = Ce^(At), where C is a constant matrix and e^(At) is the matrix exponential of At. This solution represents a linear combination of exponential functions, where each component of x(t) is determined by the corresponding component of C and the matrix exponential of At.
To find the general solution to the system x' = Ax, we can express the solution in terms of the matrix exponential. The matrix exponential of At, denoted as e^(At), is defined as the power series expansion of the exponential function applied to the matrix At. It can be computed using various techniques, such as diagonalization, Jordan decomposition, or power series.
The general solution to the system x' = Ax can then be written as x(t) = Ce^(At), where C is a constant matrix. This solution represents a linear combination of exponential functions, where each component of x(t) is determined by the corresponding component of C and the matrix exponential of At.
The matrix exponential e^(At) has properties that are analogous to those of the scalar exponential function. It satisfies the initial condition e^(A * 0) = I, where I is the identity matrix, and it can be used to find solutions for different initial conditions by appropriately choosing the constant matrix C.
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A square, with sides of length x cm, is inside a circle.
Each vertex of the square is on the circumference of the circle.
The area of the circle is 64 cm².
Work out the value of x.
Give your answer correct to 3 significant figures.
The value of x will be 6.383cm.
Solution to Circle Geometry problem
Point to note
The diameter of the circle is the diagonal of the squareEach half of the square formed a right angle triangleWe can use the Pythagorean theorem to find the length of the diagonal which is same as diameter
diameter² = side² + side²
diameter² = 2 * x²
diameter = √(2 * x²)
Since the diameter is equal to twice the radius, we have:
diameter = 2 * radius
radius = diagonal / 2
radius = √(2 * x²) / 2
Recall that area of the circle is given by:
area = πr²
where r is the radius
Substituting the expression for the radius, we get:
64 cm² = π * (√(2 * x²) / 2)²
64 cm² = π * (2 * x² / 4)
64 cm² = π * (x² / 2)
128 = π * x²
Solving for x, we get:
x² = 128 / π
x = √(128 / π)
x = 6.383
Therefore, the value of x is approximately 6.383cm.
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the average number of shoppers at a particular grocery store in one day is 505, and the standard deviation is 115. the number of shoppers is normally distributed. for a random day, what is the probability that there are between 200 and 400 shoppers at the grocery store? the answer should be typed as a decimal with 4 decimal places.
This means that on a random day, there is a 16.78% chance that the number of shoppers at the grocery store will fall between 200 and 400.
Using the normal distribution formula, we can calculate the z-scores for 200 and 400 shoppers:
z(200) = (200 - 505) / 115 = -2.65
z(400) = (400 - 505) / 115 = -0.91
Next, we can use a standard normal distribution table or calculator to find the area between these two z-scores. The probability is:
P(-2.65 < z < -0.91) = 0.1678
Therefore, the probability that there are between 200 and 400 shoppers at the grocery store is 0.1678.
To calculate the probability that there are between 200 and 400 shoppers at the grocery store, we first need to determine the z-scores for those values. We can then use a standard normal distribution table or calculator to find the area between those two z-scores. The result is the probability of interest. In this case, the probability that there are between 200 and 400 shoppers at the grocery store is 0.1678.
The probability that there are between 200 and 400 shoppers at the grocery store is 0.1678. This means that on a random day, there is a 16.78% chance that the number of shoppers at the grocery store will fall between 200 and 400.
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The position (in meters) of a particle per respect to time (in seconds) is defined by the following function: s(t) = t^4 - 16t^3 + 72t^2 +5. Find the maximal and minimal value for the speed of the particle on domain of t being [1,7[
Answer:
Max at t=2, 128 m/s
Min at t=6, 0 m/s
Step-by-step explanation:
Given the position function of a particle with respect to time, find the minimum and maximum velocity the particle travels over the interval [1,7].
[tex]s(t)=t^4-16t^3+72t^2+5[/tex]
(1) - Find the velocity function of the particle
The velocity function is a derivative of the position function.
[tex]s'(t)=v(t)\\\\s(t)=t^4-16t^3+72t^2+5\\\\\Longrightarrow s'(t)=\frac{d}{dx}[t^4-16t^3+72t^2+5] \\\\\text{Use the derivative rules.}\\\\\boxed{\left\begin{array}{ccc}\text{\underline{Power Rule:}}\\\\\frac{d}{dx}[x^n]=nx^{n-1} \end{array}\right} \ \ \boxed{\left\begin{array}{ccc}\text{\underline{Constant Rule:}}\\\\\frac{d}{dx}[k]=0 \end{array}\right} \\\\\\\Longrightarrow s'(t)=(4)t^{4-1}-16(3)t^{3-1}+72(2)t^{2-1}+0\\\\\Longrightarrow s'(t)=4t^{3}-48t^{2}+144t\\\\[/tex]
[tex]\therefore \boxed{v(t)=4t^{3}-48t^{2}+144t}[/tex]
(3) - Take the derivative of v(t)
[tex]v(t)=4t^{3}-48t^{2}+144t\\\\\Longrightarrow v'(t)=12t^2-96t+144[/tex]
(4) - Let v'(t)=0 and solve for "t," these are the critical points
[tex]v'(t)=12t^2-96t+144\\\\\Longrightarrow 0=12t^2-96t+144\\\\\Longrightarrow 0=12[t^2-8t+12]\\\\\Longrightarrow 0=t^2-8t+12\\\\\Longrightarrow (t-6)(t-2)=0\\\\\therefore \text{The critical points are} \ \boxed{t=6 \ \text{and} \ t=2}[/tex]
(5) - Find the max/min values (in this case these values represent the particle's velocity) by plugging the critical points into v(t)
[tex]\text{Recall that} \ v(t)=4t^{3}-48t^{2}+144t \ \text{and} \ t=6, \ t=2\\\\\text{\underline{When t=6:}}\\\\\Longrightarrow v(6)=4(6)^{3}-48(6)^{2}+144(6)\\\\\Longrightarrow \boxed{v(6)=0 \ m/s}\\\\\text{\underline{When t=2:}}\\\\\Longrightarrow v(2)=4(2)^{3}-48(2)^{2}+144(2)\\\\\Longrightarrow \boxed{v(6)=128 \ m/s}[/tex]
Thus, at time, t=6, the particle's velocity is smallest, 0 m/s. And at time, t=2, the particle's velocity is greatest, 128 m/s.
Two forces, X and Y, acting on an object form a 24° angle between each other. Force X is 56 pounds, and force Y is 76 pounds. What is the approximate magnitude of the resultant force?
Answer: i think
Step-by-step explanation: -9.8 m/s^2 is not the force of gravity, it is the free fall acceleration due to gravity on Earth. According to Newton's second law, F = ma. Which means that Weight = mass * gravitational
A fair six sided die is thrown.find the possibility Of getting the following a)a3 b)a4 c) a9 d) a1 or a2
Answer:
a) 1/6. b) 1/6. c) 0. d) 1/3.
Step-by-step explanation:
it's a fair die, so probability of getting any of the 6 numbers is equal.
that is, they all have probability 1/6.
a) p(3) = 1/6
b) p(4) = 1/6
c) p(9) = 0. die only goes up to 6.
d) p(1) = 1/6. p(2) = 1/6
p(1 or 2) = 1/6 + 1/6 = 2/6 = 1/3
Aprende con un ejemplo
GH tiene puntos finales en G (1, 7) y H (1, 9). Encuentre el punto medio M de GH .
Escribe las coordenadas como decimales o enteros.
METRO =
Answer:
Therefore, the coordinates of the midpoint M are (1, 8).
Step-by-step explanation:
The midpoint formula is:
M = ((x1 + x2)/2, (y1 + y2)/2)
where (x1, y1) and (x2, y2) are the coordinates of the endpoints.
Using this formula, we have:
M = ((1 + 1)/2, (7 + 9)/2) = (1, 8)
Therefore, the coordinates of the midpoint M are (1, 8).
find the cosine of the angle between the planes x + y + z = 0 and x + 3y + 4z = 6.
So the cosine of the angle between the two planes is 8sqrt(78) / 78.
To find the cosine of the angle between two planes, we need to find the normal vectors of each plane and then use the dot product formula.
The normal vector of the first plane is <1, 1, 1>, and the normal vector of the second plane is <1, 3, 4>.
The dot product of these two vectors is:
<1, 1, 1> · <1, 3, 4> = 1(1) + 1(3) + 1(4) = 8
The magnitude of the normal vector of the first plane is:
|<1, 1, 1>| = sqrt(1^2 + 1^2 + 1^2) = sqrt(3)
The magnitude of the normal vector of the second plane is:
|<1, 3, 4>| = sqrt(1^2 + 3^2 + 4^2) = sqrt(26)
Therefore, the cosine of the angle between the two planes is:
cosθ = (normal vector of plane 1) · (normal vector of plane 2) / (magnitude of normal vector of plane 1) * (magnitude of normal vector of plane 2)
= 8 / (sqrt(3) * sqrt(26))
= 8 / (sqrt(78))
= 8sqrt(78) / 78
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find y. the number on the leg is 9.
The length of y of the triangle is y = 9√2 units
Given data ,
Let the Triangle be ΔABC , such that
For a right angle triangle
From the Pythagoras Theorem , The hypotenuse² = base² + height²
On simplifying , we get
From the trigonometric relations , we get
sin θ = opposite / hypotenuse
sin 45° = 9 / y
Multiply by y on both sides , we get
y = 9 / sin 45°
On simplifying , we get
y = 9√2 units
Hence , the length is y = 9√2 units
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Saturday Pizza Orders at Pizza Palace
Pepperoni 24
Beef 36
Sausage 21
Cheese 38
Mushroom 6
What percent
of orders were
for beef?
Round to the
nearest percent.
Answer: 28.8%
Step-by-step explanation:
First, add all the pizzas together. This gives us the total; 125
Next, put 36 over the total. 36/125.
Divide 36/125. Equals .288
When doing percentage, You multiply your decimal by 100, or bounce the decimal twice to the right. This gets you 28.8%
100 points pls hurry and mark brainly
Each pail of plaster covers 95 square feet of ceiling. How many pails of
plaster would you need to buy to cover the ceiling of a room with walls 15
feet long?
Answer:
2.02
Explanation:
Each pail of plaster covers 97 Square feet of ceiling
The ceiling of the room is 14 ft long
= 14×14
= 196
Therefore the pail of plaster that will be needed to cover the rooms can be calculated as follows
= 196/97
= 2.02
Find the condition that one root of x² + sx+F= 0 May be
Five times the other
Let α be one root of the quadratic equation x² + sx + F = 0. If β is the other root, then we have: Therefore, the condition is that the sum of roots of the quadratic equation x² + sx + F = 0 must be zero.
Let α be one root of the quadratic equation x² + sx + F = 0. If β is the other root, then we have:
α + β = -s (sum of roots)
αβ = F (product of roots)
We are given that α is five times β, i.e., α = 5β. Substituting this in the first equation, we get:
5β + β = -s
6β = -s
β = -s/6
Using this value of β, we can find the corresponding value of α:
α = 5β = -5s/6
So, the condition for one root to be five times the other is:
α = 5β or -5s/6 = 5(-s/6)
s = 0
Therefore, the condition is that the sum of roots of the quadratic equation x² + sx + F = 0 must be zero.
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PROBLEM SOLVING The period of a pendulum is the time the pendulum takes to complete one back-and-forth swing. The period $T$ (in seconds) can be modeled by the function $T=1.1\sqrt{L}$ , where $L$ is the length (in feet) of the pendulum. Estimate the length of a pendulum with a period of $1.65$ seconds. Write your answer as a decimal.
Answer:
If $T=1.65$ seconds, then we can solve the equation for $L$ as follows:
$$
T=1.1\sqrt{L}
$$
$$
\frac{T}{1.1}=\sqrt{L}
$$
$$
\left(\frac{T}{1.1}\right)^2=L
$$
Substituting $T=1.65$, we get:
$$
L=\left(\frac{1.65}{1.1}\right)^2=2.25
$$
Therefore, the length of the pendulum is approximately 2.25 feet.
The sum of two numbers is 52 and the difference is 18. What are the numbers?
Answer:
17 and 35
Step-by-step explanation:
x + y = 52
x − y = 18
Add the equations together:
2x = 70
x = 35
Substitute into either equation:
y = 17
Which set of numerical values represents the minimum, lower quartile, median, upper quartile, and maximum, in that order, of the box plot of this data set?
51, 51, 53, 53, 54, 55, 55, 56, 58, 58, 58, 59, 60
51, 54, 56, 58, 60
51, 53, 56, 59, 60
53, 54, 55, 59, 60
51, 53, 55, 58, 60
The set of numerical values that represents the minimum, lower quartile, median, upper quartile, and maximum, in that order, is:
51, 53, 55, 58, 60
To determine the minimum, lower quartile, median, upper quartile, and maximum of the given data set, we can arrange the values in ascending order:
51, 51, 53, 53, 54, 55, 55, 56, 58, 58, 58, 59, 60
Arranging the values in ascending order gives us:
51, 51, 53, 53, 54, 55, 55, 56, 58, 58, 58, 59, 60
The minimum value is 51.
The lower quartile (Q1) is the median of the lower half of the data, which is 53.
The median (Q2) is the middle value of the data set, which is 55.
The upper quartile (Q3) is the median of the upper half of the data, which is 58.
The maximum value is 60.
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You and your friends decide to go out to
dinner and celebrate your birthday. The
meal costs $168.34. The sales tax is 5%
and your waiter was okay so you want to
leave a 15% tip. What was the total bill?
Round to the nearest cent.
The total bill of the dinner to celebrate birthday including sales tax and tip to the nearest cent is $202.01
What was the total bill?Cost of the meal = $168.34
Sales tax = 5% of $168.34
= 0.05 × 168.34
= $8.417
Tip = 15% of $168.34
= 0.15 × 168.34
= $25.251
Total bill = Cost of the meal + Sales tax + Tip
= $168.34 + $8.417 + $25.251
= $202.008
Hence, the total bill is $202.01 to the nearest cent.
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In the diagram, ⨀R≅ ⨀S . Find m DE⌢ .
Answer:
60°
Step-by-step explanation:
ST = SW, since both are radii of the circle.
SW = WT, given.
STW is an equilateral triangle.
RED is an equilateral triangle.
Therefore, the measure of DE is 60°.
Help me please! 45 points and brainliest will be given if the option is available.
Answer:
I think it should be -2.5,-4.5
Answer: Yes the answer is -2.5 , -4.5
Step-by-step explanation:
This is not only because the X axis is always first, but also because the lines are not perfectly centered. Hope this helps! Give the other person brainliest, they answered first and they have never gotten one.
pls help!!! need help asap!!!
Answer:
parallel
Step-by-step explanation:
all horizontal lines are parallel
Answer:Parallel and all horizontal lines are parallel
Step-by-step explanation:
a bag contains 6 red marbles, 4 blue marbles, 8 yellow marbles, 10 green marbles, & 2 white marbles. find the probability of drawing a blue marble (please help right now)
The probability of selecting a blue marble is 2/15
What is the probability of drawing a blue marbleA probability event can be defined as a set of outcomes of an experiment. In other words, an event in probability is the subset of the respective sample space.
In this problem, to find the probability of drawing a blue marble, let's work with the sample space.
Probability of blue marble = number of blue marbles / total number of marbles
Total number of marbles = 6 + 4 + 8 + 10 + 2 = 30
Probability of blue marble = 4 / 30
probability of blue marble = 2/15 = 0.133
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(k + 1 )(k - 5 ) = 0 solve equation for x
Answer:
solve for k or x?
because x isnt on the equation.
i solved for k though
k = -1, 5
Step-by-step explanation:
Solved by simplifying both sides of the equation, then isolating the variable.
Please answer quickly I need it asap ill give brainiest!!!
The correct matching of the items of math in the columns is:
a number that has more factors than just 1 and itself - composite numbersmallest number that all the given denominators divide into evenly - least common denominatordata grouped using non-numerical criteria - categorical datafractions with the same numerical value; fractions that are equal to each other - equivalent fractionsa line segment that goes through the center of the circle to connect two points on the circle - diametera plane figure that is one side of a solid figure - facethe measurement of the space inside a plane figure - areaa shape or object that has been transformed - imagehaving the same exact size and shape - congruentWhat are some terms in math ?A composite number is a number that possesses additional factors besides 1 and its own value. The smallest number that can be divided evenly by all the denominators given is known as the least common denominator.
Non-numeric criteria are used to group data in categorical data. Fractions that have identical numerical values are referred to as equivalent fractions. When a line segment passes through the center of a circle and joins two points on its circumference, it is known as the circle's diameter.
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a recent study found that 30% of all opioid prescriptions are missing a documented medical justification for use. a hospital administrator wonders if a smaller proportion of patients at her hospital are missing a medical justification for their opioid prescriptions. suppose the hospital administrator conducts a review of a random sample of 25 opioid-prescribed patient files at her hospital and 5 of those files are missing a documented medical justification for the opioid prescription. a statistician carries out a significance test of the null hypothesis versus the alternative hypothesis. what is the value of the standardized test statistic for this significance test (rounded to the nearest tenth)?
The value of the standardized test statistic for this significance test is -1.3
For the standardized test statistic for this significance test, we need to compare the sample proportion to the hypothesized population proportion.
The null hypothesis (H₀)
H₀: The proportion of patients missing a medical justification for opioid prescriptions at the hospital is equal to 30%.
The alternative hypothesis (H₁)
H₁: The proportion of patients missing a medical justification for opioid prescriptions at the hospital is different from 30%.
The sample size is 25 and 5 of those files are missing a medical,
The sample proportion (p) can be calculated as
(p) hat = (Number of files missing justification) / (Total number of files)
(p) hat = 5 / 25
(p) hat = 0.2
The standard error is given by
SE = √[((p) hat × (1 - (p) hat)) / n]
SE = √[(0.2 × (1 - 0.2)) / 25] = √(0.16 / 25) = 0.08
For the standardized test statistic, we use the formula:
z = ((p) hat - p₀) / SE
where p₀ is the hypothesized population proportion.
p₀ = 30% = 0.3
z = (0.2 - 0.3) / 0.08 = -0.1 / 0.08 = -1.25 = -1.3
The value of the standardized test statistic for this significance test is approximately -1.3
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help help helpppppppppppppppppppppppp
Answer:
B, D, F
Step-by-step explanation:
You want the diagrams that show lines through the center of enlargement, where the smaller triangle is enlarged to form the larger triangle.
EnlargementEach point in an enlarged figure is moved toward or away from the center of enlargement along a line through that center. That is, corresponding vertices of a triangle and its enlargement will lie on a line through the enlargement center.
The diagrams of interest are those that show lines through corresponding vertices of the triangles.
Diagrams B, D, F show lines through the center of enlargement.
__
Additional comment
The center of enlargement is marked in the attachment by a blue dot. Enlargement is by a factor of 3.
Points are moved away if the scale factor is greater than 1; toward the center of enlargement for a scale factor less than 1.
<95141404393>
The great pyramid in giza, Egypt is a square-based. The length of one side of the base is 755 feet, it has a height of 481 feet and a slant height of 610 feet. About how many cubic feet are inside the great pyramid
There are 98,087,770 cubic feet inside the Great Pyramid.
To calculate the approximate volume of the Great Pyramid in Giza, we can use the formula for the volume of a pyramid:
Volume = (1/3) × base area × height
Since the Great Pyramid is square-based, the base area is equal to the length of one side squared. Given that the length of one side of the base is 755 feet, the base area is [tex]755^2[/tex] square feet.
Using the given height of 481 feet, we can substitute these values into the formula:
Volume = (1/3) × [tex]755^2[/tex] × 481
Calculating this expression, we find that the approximate volume of the Great Pyramid is:
Volume ≈ 98,087,770 cubic feet
There are approximately 98,087,770 cubic feet inside the Great Pyramid.
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Find the value of x in the figure.
if the population of san diego grows by 2.0% per year how long will it take the population to double?
It will take approximately 35 years for the population of San Diego to double if it grows at a rate of 2.0% per year.
To determine how long it will take for the population of San Diego to double, we can use the concept of exponential growth.
When a population grows by a fixed percentage, the formula to calculate the doubling time is given by:
Doubling Time = (log(2) / log(1 + growth rate))
In this case, the growth rate is 2.0% or 0.02 (expressed as a decimal). Plugging this value into the formula, we can calculate the doubling time.
Doubling Time = (log(2) / log(1 + 0.02))
Using a calculator, we can evaluate this expression:
Doubling Time ≈ 35 years
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The radius of circle O is 22, and OC = 15. The diagram is not drawn to scale. What is the length of segment AB? Round the answer to the nearest tenth.
16.1
32.2
26.7
53.3
The length of the segment AB according to the given equation as required to be determined is; 32.2.
What is the length measure of the segment AB?As evident from the task content; the length measure of segment AB is required to be determined.
The assumption is such that point C is the midpoint of AB.
Therefore, on this note, the triangle OBC is a right triangle and the since radius OB = 22 and OC = 15;
CB² = 22² - 15²
CB² = 484 - 225
CB² = 259
CB = 16.1
Therefore, since C is the midpoint of AB; AB = 2 × 16.1 = 32.2.
Ultimately, the length of segment AB is; 32.2.
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