Function 2 has the larger maximum at (2, 5).
Hence the correct option is (C).
Given the first function is,
Function 1: f(x) = x² + 8x - 15
Differentiating the function with respect to 'x' we get,
f'(x) = 2x + 8
f''(x) = 2
Now, f'(x) = 0 gives
2x + 8 = 0
2x = -8
x = -8/2
x = -4
At x = -4 the value of f''(-4) = 2 > 0
So there is minimum at x = -4.
Second function is:
Function 2: f(x) = -x² + 4x + 1
Differentiating the function with respect to 'x' we get,
f'(x) = -2x + 4
f''(x) = -2
Now, f'(x) = 0 gives
-2x + 4 = 0
2x = 4
x = 4/2
x = 2
At x =2 the value of f''(2) = -2 < 0
So at x = 2 the function has maximum value.
max f(x) = f(2) = - 2² + 4*2 + 1 = - 4 + 8 + 1 = 5
So function 2 has the larger maximum at (2, 5).
Hence the correct option is (C).
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AABC DEF. What sequence of transformations will move AABC onto ADEF?
A. A dilation by a scale factor of 2, centered at the origin, followed by
a 90° clockwise rotation about the origin
B. A dilation by a scale factor of, centered at the origin, followed by
the translation (x, y) - (x+4, y-2)
C. A dilation by a scale factor of, centered at the origin, followed by
a 180° clockwise rotation about the origin
D. A dilation by a scale factor of 2, centered at the origin, followed by
a reflection over the y-axis
Answer:
C. Dilation by 1/2, rotation 180°
Step-by-step explanation:
You want the sequence of transformations that moves ∆ABC to ∆DEF.
PointsWe note that the coordinates of corresponding points are ...
A = (-2, 2)D = (1, -1)Comparing these, we find that D = (-1/2)·A.
The scale factor of -1/2 is equivalent to a dilation by a factor of 1/2 and reflection across the origin. Reflection across the origin is equivalent to a rotation of 180°.
SequenceThe sequence of transformations that moves ∆ABC to ∆DEF is ...
C. A dilation by a factor of 1/2 centered at the origin, followed by a 180° clockwise rotation about the origin.
__
Additional comment
The direction of rotation is irrelevant when the rotation angle is 180°. When the center of dilation is unspecified, it is assumed to be the origin.
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incent borrowed $500 from Mitchell for six months. How much interest will Mitchell earn if he charges Vincent a simple interest rate of 3 percent?
simple interest = P × r × t
A.
$7.50
B.
$15
C.
$75
The amount of interest Mitchell earn is $7.50.
We have,
P= $500
R= 3%
T= 6 month
= 6/12
= 1/2 year
Using Simple Interest
= (P x R x T)/ 100
= (500 x 3 x 1)/ 2 x 100
= 5x 3 /2
= 15/2
= 7.5
Thus, the simple interest is $7.5
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Question 4 of 8
A runner charted how long it took her to run certain distances. Here is the
information she gathered:
Minutes O 8 16 24
Miles 0 1 2 3
At this pace, how long will it take her to run 6 miles?
Step-by-step explanation:
she runs 1 mil in each 8 minute
so you can easily find the answer by multiplying 6 with 8
6 • 8 = 48
Subtract. Write your answer in simplest form.
9 1/14 - 3 6/7
A. 6 1/14
B. 5 3/14
C. 5 11/14
D. 6 11/14
only for I Brainly Expert
Difference of the given fractions is [tex]5\frac{3}{14}[/tex]. Therefore, option B is the correct answer.
The given fractions are [tex]9\frac{1}{14}[/tex] and [tex]3\frac{6}{7}[/tex].
Here, [tex]9\frac{1}{14}[/tex] = 127/14 and [tex]3\frac{6}{7}[/tex] = 27/7
So, the difference is
127/14 - 27/7
= 127/14 - 27/7 ×2/2
= 127/14 - 54/14
= (127-54)/14
= 73/14
= [tex]5\frac{3}{14}[/tex]
Therefore, option B is the correct answer.
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a 5 55-meter ladder is sliding down a vertical wall so the distance between the bottom of the ladder and the wall is increasing at 6 66 meters per minute. at a certain instant, the top of the ladder is 3 33 meters from the ground. what is the rate of change of the area formed by the ladder at that instant (in square meters per minute)?
The rate of change of the area formed by the ladder at this instant is 11.1 m²/min.
At a certain instant, we are given that the top of the ladder is 3.33 m from the ground. This means that h = 3.33 m. We also know that the distance between the bottom of the ladder and the wall is increasing at a rate of 6.66 m/min. In other words, we can say that dx/dt = 6.66 m/min.
Our goal is to find the rate of change of the area formed by the ladder at this instant. Let's denote the area of the triangle by A. We know that:
A = (1/2) x L x h
To find the rate of change of A, we need to take the derivative of A with respect to time t:
dA/dt = (1/2) x (dL/dt x h + L x dh/dt)
We know that dh/dt is zero because the height of the triangle is not changing. We also know that the ladder is sliding down the wall, which means that dL/dt is negative. Therefore, we can rewrite the equation as:
dA/dt = (1/2) x (-dL/dt x h)
Substituting the given values, we get:
dA/dt = (1/2) x (-(-6.66) x 3.33) = 11.1 m²/min
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how are binary categorical variables included in multiple linear regression?
Binary categorical variables are typically included in multiple linear regression models using a technique called "dummy coding" or "indicator coding".
These dummy variables are then included in the multiple linear regression model as additional predictor variables, along with the continuous predictor variables. The coefficient estimates for the dummy variables represent the differences in the intercept or slope between the two categories of the binary categorical variable.
It is important to note that when using dummy coding, one of the categories of the binary categorical variable must be chosen as the reference category, and the coefficient estimates for the other categories are interpreted relative to the reference category. The choice of reference category can affect the interpretation of the coefficient estimates and should be chosen based on the research question and the goals of the analysis.
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A package of fruit bars contains one of each flavor: apple, berry, cherry, and pear. Chris chooses 2 bars at random. She makes a probability model to represent the probability of each pair of fruit bars. Complete the statements about the probability model.
The probability model has
✔ 6
outcomes, and the probability for each outcome is about
✔ 0.167
.
Since there are six potential combinations and each has an equal chance of being picked, each result has a probability of 1/6, or around 0.167.
What is probability?The likelihood that an event will occur or that a proposition is true is determined by a field of mathematics known as probability theory. An event's probability is expressed as a number between 0 and 1, where 1 indicates certainty and roughly 0 indicates how likely it is that the event will occur. A probability is a numerical expression of the likelihood or potentiality of a given event. Probabilities can alternatively be stated as integers between 0 and 1, percentages between 0% and 100%, or as percentages between 0% and 100%. the fraction of times that all equally probable alternatives occur compared to all potential outcomes.
The probability model includes 6 possible outcomes, and each one has an exact chance of 0.167, or 1/6. List all potential pairs of fruit bars that demonstrate this:
berries and apples
cherries and apples
Apple and pears, berries and cherries, pears and apples
Since there are six potential combinations and each has an equal chance of being picked, each result has a probability of 1/6, or around 0.167.
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Tom bought 750 shares of a company's stock for 11.06/share. He pays a broker a commission of $12 to buy and sell stock. After one year, Tom sold all his shares, when they were worth 10.24/share.
How much did it cost Tom to buy the stock?
What was Tom's net gain or loss?
What was Tom's annual rate of return?
It cost Tom $8,334 to buy the stock.
Tom's net gain or loss is $-666.
Tom's annual rate of return is -8.0%.
We have,
To calculate Tom's cost to buy the stock, we multiply the number of shares by the cost per share and then add the commission paid to the broker:
Cost = (750 * 11.06) + 12 = $8,322 + $12 = $8,334
To calculate Tom's proceeds from selling the stock, we multiply the number of shares by the price per share and then subtract the commission paid to the broker:
Proceeds = (750 * 10.24) - 12 = $7,680 - $12 = $7,668
To calculate Tom's net gain or loss, we subtract the cost from the proceeds:
Net gain/loss = $7,668 - $8,334 = -$666
Tom has a net loss of $666, meaning he lost money on this investment.
To calculate Tom's annual rate of return, we need to know how long he held the stock. Let's assume he held the stock for one year. Then, his rate of return is:
Rate of return = (Proceeds - Cost) / Cost * 100% * (1 / Time)
where Time is the time period for which the rate of return is being calculated (in years).
Plugging in the values we have:
Rate of return = (-$666 / $8,334) * 100% * (1 / 1) = -8.0%
Tom's annual rate of return is -8.0%, meaning he lost 8% of his investment over the course of one year.
Thus,
It cost Tom $8,334 to buy the stock.
Tom's net gain or loss is $-666.
Tom's annual rate of return is -8.0%.
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Which of the following best describes the figure with vertices:
(-2,0), (-2, 8), (9, 8) and (9, 0)
Answer:
Step-by-step explanation:
If we connect the four points (-2,0), (-2, 8), (9, 8) and (9, 0), we get a rectangle.
A rectangle is a quadrilateral with four right angles. It has two pairs of parallel sides. The opposite sides of a rectangle are equal in length.
Task
In the picture below & and k are parallel:
m
Show that the four angles marked in the picture are congruent.
Help please I’m stuck
The four angles marked in the picture are equal, so they are congruent.
What are congruent angles?Congruent angles are angles that have the same measure or value. That is, two angles are congruent if they have the same angle measure.
When two angles are congruent, they have the same shape and size.
Let's call each of the angles formed by line L "a" and "b"
Let's call each of the angles formed by line K "c" and "d"
From the given parallel lines;
angle a = angle b (vertical opposite angles are equal)
angle c = angle d (vertical opposite angles are equal)
angle b = angle c (alternate angles are equal)
angle a = angle d (alternate angles are equal)
So angle a, angle b, angle c and angle d are equal, hence they are congruent.
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At a particular location on the Atlantic coast a pier extends over the water. The height of the water on one of the supports is 5. 4 feet, at low tide (2am) and 11. 8 feet at high tide, 6 hours later. (Let t = 0 at midnight) a) Write an equation describing the depth of the water at this location t hours after midnight
If height of water on supports is "5.4 feet", at "low-tide" and 11.8 feet at "high-tide" which is 6 hours later, then the equation for depth of water at this location "t" hours after midnight is d(t) = 1.9×t + 5.4.
We assume that the depth of the water changes linearly with time
At the "Low-Tide", (2 a.m.) the height of water is 5.4 feet,
At the "High-Tide", the height of water is 11.8 feet,
Let d(t) denote the depth of the water at time "t".
By, using "slope-intercept" form of a linear-equation,
We get : d(t) = m×t + b,
where m is = slope and b is = y-intercept,
To find the slope, we use the two points (0, 5.4) and (6, 11.8);
⇒ m = (11.8 - 5.4) / (6 - 0) = 1.0666.. ≈ 1.1,
Now, to find the y-intercept, we use the point (0, 5.4),
We get, d(t) = 1.1×t + 5.4,
Therefore, the equation describing the depth of the water is d(t) = 1.9×t + 5.4.
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editors preparing a report on the economy are trying to estimate the percentage of businesses that plan to hire additional employees in the next 60 days. they are willing to accept a margin of error of ​% but want ​% confidence. how many randomly selected employers will they need to​ contact?
Rounding up, the editors will need to contact at least 385 randomly selected employers to estimate the percentage of businesses that plan to hire additional employees in the next 60 days with a margin of error of ​% and a confidence level of ​%.
To calculate the sample size, the editors can use the following formula:
n = (Z^2 * p * q) / E^2
where:
- n is the required sample size
- Z is the Z-score corresponding to the desired confidence level (for example, if the desired confidence level is 95%, the Z-score would be 1.96)
- p is the estimated proportion of businesses that plan to hire additional employees (this value is unknown and will be estimated based on past data or other sources)
- q is 1 - p
- E is the desired margin of error
Assuming the editors want a 95% confidence level and a margin of error of ​%, let's say they estimate that 50% of businesses plan to hire additional employees. Plugging these values into the formula, we get:
n = (1.96^2 * 0.5 * 0.5) / (0.05^2)
Simplifying, we get:
n = 384.16
They have a desired margin of error and a desired confidence level, and you need to determine the number of randomly selected employers they must contact.
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plsssssssssss help state testing is coming up !!!!!
Answer:
Step-by-step explanation:
sorry, kinda messy cuz i was using my mouse to write
OFF TOPIC QUESTION (i think) if I have 74 algebra 1 lessons on ixl how many should I do a day before may 15
Here is an identity.
a(4x 10) = 24x + 5b
Work out the values of a and b.
i know a is equal to 6 but im stuck with b
Answer:
b = 12
Step-by-step explanation:
If we substitute a = 6 and simplify the given equation, we get:
6(4x 10) = 24x + 5b
Simplifying the left-hand side, we get:
24x + 60 = 24x + 5b
Subtracting 24x from both sides, we get:
60 = 5b
Dividing both sides by 5, we get:
12 = b
Therefore, the values of a and b are a = 6 and b = 12.
if axis deviation is present, which leads that normally have positive qrs complexes will have negative qrs complexes?
If there is an axis deviation, it can result in a reversal of the QRS complex polarity in certain leads. Leads that normally have positive QRS complexes may have negative QRS complexes, and vice versa.
For example, if there is a left axis deviation, leads I and aVL, which normally have positive QRS complexes, may have negative QRS complexes.
Axis deviation refers to the direction in which the electrical activity is traveling through the heart. If the electrical activity is deviated from its normal pathway, it can cause a change in the orientation of the QRS complex, which is a graphical representation of the electrical activity generated by the ventricles during the cardiac cycle.
The change in polarity occurs because the direction of the electrical activity is now opposite to what it would be in a normal heart. This change in polarity can be used to help diagnose the location and type of axis deviation. Understanding the significance of the polarity changes can help healthcare providers determine appropriate treatment plans for patients.
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let x be a connected subset of metric space m. if x is connected. is the interior of x necessarily connected?
NO, the interior of x is not necessarily connected.
A connected subset is one that cannot be expressed as the union of two non-empty separated sets.
The interior of x may not have this property. For example, consider the subset of the real line given by the closed interval [0,1]. This set is connected, but its interior, (0,1), is not. It can be expressed as the union of the two separated sets (0,1/2) and (1/2,1). Therefore, the interior of a connected subset may not be connected.
1. A connected subset X of a metric space M means that there is no separation of X into two disjoint non-empty open sets.
2. The interior of X refers to the set of all interior points of X, which are points where every neighborhood of the point lies entirely within X.
3. However, the interior of X may have a different connectivity structure than X itself. It is possible for the interior of X to be disconnected, meaning it can be separated into two disjoint non-empty open sets.
4. As a result, the interior of a connected subset X is not guaranteed to be connected.
Hence, The main answer is: No, the interior of a connected subset X of a matrix space M is not necessarily connected.
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Question in image, please help!
i don't know how to solve this problem. please help.
Answer:
$2.71 + 4j = $6.75
j = $1.01
Step-by-step explanation:
$2.71 + 4j = $6.75
4j = 6.75 - 2.71 = 4.04
j = 4.04/4 = $1.01
Answer:
$6.75 = $2.71 + 4j
j = $1.01
Step-by-step explanation:
The total amount of money Ava spent was $6.75. We can make this one side of an equation.
The other side of the equation can be what Ava bought for that $6.75. We know that she bought $2.71 of oranges and 4 juice bottles, so we can add these on the other sides of the equation.
[tex]\$6.75 = \$2.71 + 4j[/tex]
To solve this equation for [tex]j[/tex], we can first subtract $2.71 from both sides.
[tex]\textrm{ } \ \$6.75 = \$2.71 + 4j\\\underline{-\$2.71} \ \ \ \ \underline{-\$2.71 \ \ \ \ }[/tex]
[tex]\$4.04 = 4j[/tex]
Finally, we can divide both sides by 4.
[tex]\$4.04 = 4j\\\overline{\ \ \ 4\ \ \,} \ \ \ \ \overline{\: 4 \:}[/tex]
[tex]\$1.01 = j[/tex]
[tex]\boxed{j = \$1.01}[/tex]
Sean, a store manager earns $125. 20 for eight hours of work. How much does he earn per hour?
Answer:
$15.65 per hour
Step-by-step explanation:
125.20 / 8 = 15.65
Check
15.65 x 8 = 125.20
which of the following statements could be false?
A. The diagonals of a rectangle are congruent.
B. The diagonals of an isosceles trapezoid are congruent.
C. The diagonals of a square are perpendicular and bisect each other.
D. The diagonals of a rhombus are congruent and perpendicular to each other
in the function y=2x(4+x)-2, if x=3, what is the value of y?
(i know the answer is 40, i just need help figuring out the step by step process of solving this problem)
Answer: 40
Step-by-step explanation:
y = 2x (4 + x) - 2
Substitute x with 3:
y = 2(3) (4 + 3) - 2
Simplify:
y = 2(3) (7) - 2
y = 6(7) - 2
y = 42 - 2
y = 40
2. Identify if the following are one-to-one functions or not.
(a) People to their birthdays
(b) People to their Social Security System number
(c) People to their place of residence
[6]
List the positive factors of 100.
The positive factors of 100 are 1,2,4,5,10,20,25,50,100.
In mathematics, a factor is a divisor of a given integer that divides it fully without leaving any remainder. We can use numerous methods to find the factors of a number, such as the division method and the multiplication approach.
In real life, we employ factors to split anything into equal rows and columns, compare prices, exchange money, and so on. We can use the division and multiplication methods to get the factors of a number.
A number's factors can be good or negative. Consider the components of 8. Because 8 is divisible by 1, 2, 4, and 8, the positive factors of 8 are 1, 2, 4, and 8.
The factors of 100 are ,2,4,5,10,20,25,50,100 as they all divide the number 100 without leaving any remainder.
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a nationwide survey showed that 4% of childrean like lima beans. what is the probability that any 2 childrean will both like limabeans
The probability that any two children will both like lima beans is 0.0016 or 0.16%.
Assuming that every child's choice for lima beans is independent of the other, we will use the binomial distribution to calculate the probability that two kids out of a group of will both like lima beans.
Let p be the chance that a child likes lima beans, which we realize is 0.04 primarily based on the survey. The probability that anyone infant does no longer like lima beans is then 1 - p = 0.96.
The possibility that each children will like lima beans is given through the binomial chance mass feature:
P(X = 2) = (2 choose 2) * [tex]p^2 * (1 - p)^{(2-2)} = p^2 = (0.04)^{2 }= 0.0016[/tex]
So the chance that any two children will both like lima beans is 0.0016, or 0.16%. that is a very low probability, this means that that it is not likely that any two children selected at random will both like lima beans.
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Suppose y varies directly with x, and y = 104 when x = 8. What is the value of y when x = 18?
Answer:
Okay, let's break this down step-by-step:
y varies directly with x, meaning y is proportional to x.
This can be expressed as y = kx for some constant k.
We are given: When x = 8, y = 104.
Substituting the given values: 104 = k(8)
Solving for k: k = 104/8 = 13
Now we want to find y when x = 18. We use the proportional relationship:
y = kx
= 13(18)
= 234
Therefore, when x = 18, y = 234.
Step-by-step explanation:
A lecture class has 30 full-time students and 20 part-time students. A random sample of 10 students is drawn. Use R commands to answer the following questions: (a) What is the probability that exactly 6 of the students will be full-time? (b) What is the probability that at most 8 of the students will be full-time?
The probability of at most 8 of the students being full-time is approximately 0.988, or 98.8%.
To answer this question, we can use the binomial distribution function in R. The formula for the binomial distribution is:
P(X=k) = (n choose k) * p^k * (1-p)^(n-k)
where:
- P(X=k) is the probability of getting exactly k successes
- n is the total number of trials
- p is the probability of success in each trial
- (n choose k) is the number of ways to choose k items from a set of n items
(a) To find the probability that exactly 6 of the students will be full-time, we can use the following command in R:
dbinom(6, 10, 0.6)
This will give us the probability of getting exactly 6 full-time students out of a random sample of 10 students, assuming that the probability of a student being full-time is 0.6 (since there are 30 full-time students out of a total of 50 students).
The output of this command is:
[1] 0.2508227
So the probability of exactly 6 of the students being full-time is approximately 0.251, or 25.1%.
(b) To find the probability that at most 8 of the students will be full-time, we can use the following command in R:
pbinom(8, 10, 0.6)
This will give us the probability of getting 8 or fewer full-time students out of a random sample of 10 students.
The output of this command is:
[1] 0.9884969
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A company promises to release a new smartphone model every month. Each model’s battery life will be 6% longer than the previous model’s. If the current models battery life is 731.0 minutes what will the latest models Battery life be in 9 months from now
The number of months that it will take the latest model's battery life to reach 731.0 minutes would be 8 months
Each month, there is an increase by a factor of 0.06 of the past months model.
By geometric sequence formula of aₙ = ar^(n - 1),
where; a is first term
r is common ratio, aₙ is nth term
we have;
1,008.9 = 731.0 * 1.06^(n - 1)
1008.9/731.0 = 1.06^(n - 1)
In 1.504 = (n - 1) In 1.06
0.408 = (n - 1) * 0.058
n - 1 = 0.408/0.058
n = 7.03 + 1
n ≈ 8 months
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Find the exact length of the curve.x = et − 9t, y = 12et/2, 0 ≤ t ≤ 3
To find the exact length of the curve given by x = et − 9t, y = 12et/2, 0 ≤ t ≤ 3, we can use the arc length formula:
L = ∫(a to b) √[dx/dt]^2 + [dy/dt]^2 dt
Substituting the given values, we get:
L = ∫(0 to 3) √[e^t - 9]^2 + [6e^(t/2)]^2 dt
Simplifying the expression under the square root, we get:
L = ∫(0 to 3) √(e^(2t) - 18e^t + 81 + 36e^t) dt
L = ∫(0 to 3) √(e^(2t) + 18e^t + 81) dt
L = ∫(0 to 3) (e^t + 9) dt
L = [e^t + 9t] from 0 to 3
L = [e^3 + 9(3)] - [e^0 + 9(0)]
L = e^3 + 27 - 10.99
L ≈ 25.5
Therefore, the exact length of the curve is approximately 25.5 units.
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what is 3/4 / 1/2 equal to using common denominators
3/4 divided by 1/2, when written with common denominators, is equal to 3/2 or 1.5 as a decimal.
What is common denominators?In mathematics, common denominators refer to a shared multiple of the denominators of two or more fractions. When fractions have common denominators, their denominators are the same, which makes it easier to add, subtract, or compare them. For example, to add the fractions 1/4 and 3/8, we need to find a common denominator that both 4 and 8 can divide into evenly. One common denominator is 8, so we can rewrite the fractions as:
1/4 = 2/8
3/8 = 3/8.
In the given question,
To divide one fraction by another, we can multiply the first fraction by the reciprocal of the second fraction. Therefore, we can rewrite the expression 3/4 / 1/2 as:
3/4 * 2/1
To simplify this expression, we can multiply the numerators and denominators:
(3 * 2) / (4 * 1) = 6/4
We can simplify this fraction by dividing both the numerator and the denominator by their greatest common factor, which is 2:
6/4 = 3/2
Therefore, 3/4 divided by 1/2, when written with common denominators, is equal to 3/2 or 1.5 as a decimal.
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