The probability of you, Leonard, and Sheldon being chosen together is 1/1140.
Probability is calculated by the total number of ways an event can occur divided by the total number of possible outcomes.
In this case, the total number of ways three students can be drawn out of 20 is 20C3 or 1140.
The probability of selecting you, Leonard, and Sheldon out of the three spots is 1/1140, or approximately 0.000877 or 0.0877%.
Total number of students in physics department = 20.Number of student spots for a conference trip to Cancun = 3.The probability that you, Leonard, and Sheldon are chosen is equal to the total number of ways you, Leonard, and Sheldon can be chosen divided by the total number of ways 3 students can be chosen from 20 students.
The number of ways that you, Leonard, and Sheldon can be chosen is 1 since you all need to be chosen together.
The total number of ways that 3 students can be chosen from 20 students is given by 20C3 (the combination of 20 objects taken 3 at a time).20C3 = (20*19*18)/(3*2*1) = 1/140
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Question 16
SALARY Sondra just started a job with an annual salary of $45,000. Each year, her salary will increase by 7%. If Sondra continues to work at
this job, what will be her total earnings in the first 4 years, rounded to the nearest dollar?
OA) $48,359
OB) $58,986
OC) $199,797
OD) $213,783
The solution is Option C.
The total amount of earnings of Sondra after 5 years is $ 169,113
What is an Equation?
Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the annual salary of Sandra be A = $ 30,000
Now , the percentage increase in salary = 6 %
So , the equation will be
First year :
The increase in first year = annual salary of Sandra + percentage increase in salary x annual salary of Sandra
The increase in first year = 30000 + ( 6/100 ) x 30000
= 30000 + 1800
= $ 31,800
Second year :
The increase in second year = increase in first year + percentage increase in salary x increase in first year
The increase in second year = 31800 + ( 6/100 ) x 31800
= 31800 + 1908
= $ 33,708
Third year :
The increase in third year = increase in second year + percentage increase in salary x increase in second year
The increase in third year = 33708 + ( 6/100 ) x 33708
= 33708 + 2022.48
= $ 35,730.48
Fourth year :
The increase in fourth year = increase in third year + percentage increase in salary x increase in third year
The increase in fourth year = 35730.48 + ( 6/100 ) x 35730.48
= 35730.48 + 2143.8288
= $ 37,874.3088
Now , the equation is
The total earnings of Sondra is = First year salary + second year salary + third year salary + fourth year salary
The total earnings of Sondra is = 30000 + 31,800 + 33,708 + 35,730.48 + 37,874.3088
The total amount earnings of Sondra is = $ 169,112.7888
Therefore , the total amount earnings = $ 169,113
Hence , The total amount of earnings of Sondra after 5 years is $ 169,113
Answer:
C) $199,797
Step-by-step explanation:
Adding 7% of a number to the number is the same as multiplying the number by 1.07
First year: $45,000
Second year: $45,000 × 1.07 = $48,150
Third year: $48,150 × 1.07 = $51,520.50
Fourth year: $51,520.50 × 1.07 = $55,126.94
Total = $199,797.43
Answer: C) $199,797
Freshman and sophomores were surveyed during lunch about their favorite professional football team.
A bar graph with the first bar labeled Jaguars, divided into freshmen from 0 to 40 percent and sophomores from 40 to 100 percent. The second bar is labeled Dolphins, with freshman from 0 to 45 percent and sophomores from 45 to 100 percent, and the third bar is labeled Buccaneers, with freshmen from 0 to 45 percent and sophomores from 45 to 100 percent.
If 140 students selected Jaguars, how many of those students are freshman?
56 students
63 students
77 students
84 students
Answer:
56 students
Step-by-step explanation:
If 40% of students who picked Jaguars are freshmen, and the total who picked it is 140 means [tex]140\times0.4 = 56[/tex]
Hope this helps!!!
Micaela is going to invest $360 and leave it in an account for 12 years. Assuming the
interest is compounded daily, what interest rate, to the nearest hundredth of a
percent, would be required in order for Micaela to end up with $670?
The required in order for Micaela to end up with ,n = 365 , t = 12, P = $360, and A = $670
What are functions?A relation is any subset of a Cartesian product.
As an illustration, a subset of is referred to as a "binary connection from
A binary relation from A to B is made up of these ordered pairs (a,b),
A to B," and more specifically, a "relation on A."
A binary relation from A to B is made up of these ordered pairs (a,b), here the first component is from A and the second component is from B.
Every item in a set X is connected to one item in a different set Y through a connection known as a function (possibly the same set).
A function is only represented by a graph, which is a collection of all ordered pairs (x, f (x)).
Every function, as you can see from these definitions, is a relation from X.
According to our question-
r=7.5%
Thus, 7.5% would be required in order for Micaela to end up with $670.
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Candice's financial counselor asked her to compile a list of all of financial commitments. Candice gave her counselor documentation of her
mortgage payment, car loan, credit card account, and student loans. With what part of the assessment phase was Candice's counselor
helping?
assets
liability
income
O living expenses
Candice's counselor was helping with the liability part of the assessment phase by asking for documentation of her mortgage payment, car loan, credit card account, and student loans. So correct option is B.
Describe loan?A loan is a financial transaction in which one party, typically a lender, provides money or assets to another party, typically a borrower, in exchange for future repayment of the loan amount plus interest or fees. Loans are a common way for individuals, businesses, and governments to finance purchases, investments, and other expenses.
Loans can be secured or unsecured. A secured loan is backed by collateral, such as a house or car, which the lender can seize if the borrower fails to repay the loan. An unsecured loan, on the other hand, is not backed by collateral and is based solely on the borrower's creditworthiness and ability to repay.
Loans can have fixed or variable interest rates. A fixed interest rate remains the same over the life of the loan, while a variable interest rate can fluctuate based on changes in the market or other factors.
Candice's counselor was helping with the liability part of the assessment phase by asking for documentation of her mortgage payment, car loan, credit card account, and student loans.
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Prove that 5^7 + 5^6 is divisible by 60
Answer:
I think it is not ?
Step-by-step explanation:
You get a remainder at the end when you solve it and that's the opposite of what divisible means
"(of a number) capable of being divided by another number without a remainder."
Answer:
Not divisible
Step-by-step explanation:
5^7 is 78125
5^6 is 15625
15625 + 78125 = 93750
93750/60 = 1562.5
Therefore it is not fully divisible by 60.
can you pls tell me the answer for ixl
Answer:
the P is 25% for all positions
Step-by-step explanation:
P = (1/n)
P = probability
1 = the total of the whole
n = number of options
P = 1/4
P = .25
Use your knowledge of dot plots to answer the questions below.
2. The height of all 23 students in Mrs. Dani's preschool class are shown in the dot plot below.
a. What is the median height of the preschoolers?
O
00
00
00000
00
00
+111
32 33 34 35 36 37 38 39 40
HEIGHT IN INCHES
b. What is the mode height of the preschoolers?
c. What is the range in student height?
d. About what percent of preschoolers in Mrs. Dani's class were taller than the median height?
e. How does the number of preschoolers who are 38 inches or faller compare to the number of
preschoolers who are 36 inches tall?
a.The median height of the preschoolers is 36 inches.
b.The mode height is 35 inches.
c.The range in student height is 40 - 32 = 8 inches.
d.Since the median height is 36 inches, about 50% of the preschoolers in Mrs. Dani's class were taller than the median height.
e. There are 4 dots above 38 and 7 dots between 35 and 38.
What is median?The median is the middle value of a dataset when it is arranged in order from least to greatest or greatest to least. If the dataset has an odd number of values, the median is the middle value. If the dataset has an even number of values, the median is the average of the two middle values.
What is range?Range is the difference between the largest and smallest values in a set of data. In statistics, range is a measure of dispersion that indicates the spread or variability of a set of observations.
In this questions,
a. The median height is the middle value of the data when arranged in order. Since there are 23 students in the class, the median will be the average of the 12th and 13th tallest students. Looking at the dot plot, we can see that the 12th and 13th tallest students both have a height of 36 inches. Therefore, the median height of the preschoolers is 36 inches.
b. The mode height is the most common height among the students. Looking at the dot plot, we can see that the mode height is 35 inches, as there are more dots above 35 than any other value.
c. The range is the difference between the highest and lowest values in the data set. Looking at the dot plot, we can see that the shortest student is 32 inches tall and the tallest student is 40 inches tall. Therefore, the range in student height is 40 - 32 = 8 inches.
d. Since the median height is 36 inches, about 50% of the preschoolers in Mrs. Dani's class were taller than the median height.
e. There are fewer preschoolers who are 38 inches or shorter than preschoolers who are 36 inches tall. From the dot plot, we can see that there are 4 dots above 38 and 7 dots between 35 and 38.
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50 points for thorough explanation!
Which equations represent linear functions?
f(x) = 10x + 10
k(x)=10/x
m(x)=10
h(x)=1/10x
g(x)=10^x
j(x)=10x^2+10
what is the sum of the reciprocals of all positive integers greater than 1, whose only prime factors are 2's and/or 3's
The sum of the reciprocals of all positive integers greater than 1, whose only prime factors are 2's and/or 3's is 8/3.
The sum of the reciprocals of all positive integers greater than 1, whose only prime factors are 2's and/or 3's is 8/3. To prove this, we can use the following equation:
(1/2) + (1/3) + (1/4) + (1/6) + (1/8) + (1/9) + (1/12) + (1/18) = 8/3.
Here, 1/2, 1/3, 1/4, and 1/6 are all reciprocals of numbers whose prime factors are only 2's and/or 3's,
and the sum of these four fractions is 2/3.
To complete the sum, we can add the reciprocals of 8, 9, 12, and 18, which are 1/8, 1/9, 1/12, and 1/18, respectively.
The sum of these four fractions is 6/3, and the sum of 2/3 and 6/3 is 8/3.
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What is the theoretical probability of selecting a vowel from the word orange?
A. 10%
B. 75%
C. 20%
D. 50%
Answer:50%
Step-by-step explanation: Since there are 6 letters in orange, and there are 3 vowels in the word (o,a,e), that would mean there is a 3/6 chance (50%) of selecting a vowel.
I’m a bit stuck can someone help me please
Answer:
x < 6/5 and x > 32/5
Step-by-step explanation:
|x| means taking the absolute value, or the distance from 0. This means that |-8| = 8, because -8 is 8 from 0
if |14-5x|>8, 14-5x > 8, or 14-5x < -8 because the absolute value of any number less than -8 is more than 8
for 14 - 5x > 8, -5x > -6, 5x < 6, x < 6/5
for 14 - 5x < -8, -5x < -32, 5x > 32, x > 32/5
Find a fraction that is equivalent to 5/7 and the product of its numerator and denominator is 140. Pls help
Answer:
10 / 14
Step-by-step explanation:
10 × 14 = 140
When 10 / 14 is simplified, you'll get 5 / 7 because 2 will go into 10 five( 5 ) times and 2 will go into 14 seven ( 7 ) times.
What is the formula for the circumference of a circle? c = pi r squared c = 2 pi r c = 2 pi r squared c = pi r cubed
The formula for the circumference of a circle is "c = 2 pi r", where "c" represents the circumference, "pi" represents the mathematical constant pi (approximately equal to 3.14159), and "r" represents the radius of the circle.
This formula relates the distance around a circle to its size, and is useful for calculating various measurements related to circles, such as arc length and sector area. It is important to note that the formula for the circumference of a circle assumes the circle is a perfect, unbroken curve, and thus may not be accurate for circles that are not perfectly round.
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The graph of y = 4x? - 4x - 1 is shown.
Use the graph to find estimates for
the solutions
The estimates for the solutions are x = -0.25 and 1.25 when y = 0 and x = -0.5 and 1.5 when y = 2
Finding estimates for the solutionsFrom the question, we have the following parameters that can be used in our computation:
y = 4x² - 4x - 1
When y = 0, we have
4x² - 4x - 1 = 0
From the graph, we can see that
x = -0.25 and 1.25 when y = 0
When y = 2, we have
4x² - 4x - 1 = 2
From the graph, we can see that
x = -0.5 and 1.5 when y = 2
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Where does the graph of [tex]y=-2x+1[/tex] intersect the [tex]x[/tex] -axis?
Answer:
x = 1/2
Step-by-step explanation:
You want to know the x-intercept of the graph of y = -2x +1.
X-interceptThe x-axis corresponds to a y-value of 0. The graph of any relation will intersect the x-axis where the output value is 0. We can find those points by solving the relation after setting y=0.
y = -2x +1 . . . . . . . given relation
0 = -2x +1 . . . . . . . equation with y=0
2x = 1 . . . . . . . . . . . add 2x
x = 1/2 . . . . . . . . . . . divide by 2
The graph intersects the x-axis where x = 1/2.
Which of the following equations are equivalent? Select three options.
2 + x = 5
x + 1 = 4
9 + x = 6
x + (- 4) = 7
- 5 + x = - 2
Answer:
2 + x = 5 2 + x = 5 x + 1 = 4 2 + x = 5 x + 1 = 4 - 5 + x = - 2Step-by-step explanation:
2 + x = 5 2 + x = 5 x = 5 - 22x = 32x = 3x + 1 = 4 2x = 3x + 1 = 4 x = 4 - 12x = 3x + 1 = 4 x = 4 - 1x = 32x = 3x + 1 = 4 x = 4 - 1x = 3- 5 + x = - 22x = 3x + 1 = 4 x = 4 - 1x = 3- 5 + x = - 2x = -2 + 52x = 3x + 1 = 4 x = 4 - 1x = 3- 5 + x = - 2x = -2 + 5 x = 3A bag contains tiles with letters that spell the word OUTCOME. Which letter should we expect to appear more than the others when tiles are chosen from the bag?
A.) letter O
B.) letter C
C.) letter E
D.) letter T
Answer: O
Step-by-step explanation: if the bag is only filled with the letters in OUTCOME then there are more O’s than the rest
a newsletter publisher believes that 78% of their readers own a rolls royce. is there sufficient evidence at the 0.02 level to refute the publisher's claim? state the null and alternative hypotheses for the above scenario.
There is not enough information provided to determine if there is sufficient evidence at the 0.02 level to refute the publisher's claim. The null hypothesis is that proportion of readers owning a Rolls Royce is equal to 0.78 and alternative hypothesis is that proportion of readers owning a Rolls Royce is not equal to 0.78.
To determine if there is sufficient evidence at the 0.02 level to refute the newsletter publisher's claim that 78% of their readers own a Rolls Royce, we need to conduct a hypothesis test. Here are the null and alternative hypotheses for this scenario:
Null Hypothesis (H0): The proportion of readers who own a Rolls Royce is equal to 0.78 (P = 0.78)
Alternative Hypothesis (H1): The proportion of readers who own a Rolls Royce is not equal to 0.78 (P ≠ 0.78)
To test these hypotheses, follow these steps:
1. Collect a random sample of readers and record the number of Rolls Royce owners in the sample.
2. Calculate the sample proportion (p-hat) of Rolls Royce owners.
3. Calculate the test statistic using the formula: z = (p-hat - P) / sqrt(P * (1-P) / n), where P is the claimed proportion (0.78) and n is the sample size.
4. Determine the critical value for a two-tailed test at the 0.02 significance level (α = 0.02), which is approximately ±2.576 (from a z-table or calculator).
5. Compare the test statistic (z) to the critical value. If the test statistic is greater than or equal to the critical value or less than or equal to the negative critical value, reject the null hypothesis in favor of the alternative hypothesis. If not, fail to reject the null hypothesis.
Based on the results, you can determine if there is sufficient evidence to refute the publisher's claim at the 0.02 significance level. However, just based on the given information, there is not enough information to determine if there is sufficient evidence at the 0.02 level to refute the publisher's claim. We need the sample size.
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Find the coordinate of the midpoint segment for(7, 0), (3, 4)
a.2,5
b.5,2
c.7,4
d.2, 5
Hello please help I’m having trouble answering this question
radius = 14m, angle of sector=ø area of sector = 462m². Find ø
Answer:
HERE'S YOUR ANSWERStep-by-step explanation:
HOPE IT WILL HELP YOU!!(✿^‿^)(✿^‿^)Answer:
Step-by-step explanation:
what is the unit rate if the car traveled 300 km within 2.5 hrs
The unit rate of the given expression through which the relation is satisfied is 300km / 2.5 hrs = 120 km / hr
What about unit rate?
In mathematics, a unit rate is a ratio between two quantities in which one quantity is expressed in terms of one unit of measure. It is commonly used to compare the cost or value of two or more items. For example, if a store charges $4 for 2 pounds of bananas, then the unit rate is $2 per pound of bananas.
The general formula for calculating unit rate is:
Unit rate = Quantity of one item ÷ Cost or value of that item
This formula can be used to find the unit rate of any item or quantity, as long as the quantity and cost or value are known. Unit rate is a useful tool in mathematics, as it allows for easy comparison of different quantities or values, and helps to make complex calculations more straightforward.
According to the given information:
The unit rate = [tex]\frac{Distance}{Time}[/tex]
i.e , unit rate = 300/2.5 = 120
⇒ 120km/hr.
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Jabari is walking to the park from school. The school is located on the map shown. He walks 2 units west and 4 units south to stop at a store to buy a snack. He then walks 6 units west and 4 units south to get to the park. If Jabari were to walk in a straight path from the school to the park, what would be the distance?
Answer: = 11.3 units
Step-by-step explanation: Work is attached below <3
The amount of money in a bank account can be expressed by the exponential equation
A = 500 (1.04) ¹2t, How many years will it take for the amount in the account to be
more than $5000?
It will take approximately 58.71 years for the amount in the account to be more than $5000.
We can solve for the number of years it will take for the amount in the account to be more than $5000 by setting the given equation equal to 5000 and solving for t:
5000 = 500 (1.04)^t
Dividing both sides by 500, we get:
10 = (1.04)^t
To solve for t, we can take the logarithm of both sides.
1 = t * log(1.04)
Simplifying, we get:
t = 1/log(1.04)
Evaluate
t ≈ 58.71
Therefore, it will take approximately 58.71 years for the amount in the account to be more than $5000.
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Please solve 2x-y greater than or equal to 3
This is the inequality in slope-intercept form, where the slope is 2 and the y-intercept is -3. the solution to the inequality[tex]2x - y \geq 3[/tex] is represented by the shaded region above the line. [tex]y=2x-3[/tex].
What is inequality?In mathematics, an inequality is a statement that compares two values or expressions using a relational operator, such as less than (<), greater than (>), less than or equal to (≤), greater than or equal to (≥), or not equal to (≠). Thet learn more about degree being compared can be numbers, variables, or expressions.
An inequality expresses that one value is smaller or larger than another, or that they are not equal. For example, x > 5 is an inequality that says x is greater than 5, while y ≤ 10 is an inequality that says y is less than or equal to 10.
by the question.
To solve 2x - y ≥ 3, we need to isolate y on one side of the inequality.
First, we can add y to both sides to get:
[tex]2x \geq y + 3[/tex]
Next, we can subtract 3 from both sides to get:
[tex]2x - 3\geq y[/tex]
Alternatively, we can switch the inequality sign and write:
[tex]y \geq 2x - 3[/tex]
So, the solution is:
[tex]y \leq 2x - 3[/tex]
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pls answer!!!
worth 60 points <33
Answer:
a. 4
b. -2
c. 0,5
Step-by-step explanation:
1. 4
2.2
3.0,5
IT IS SAYING TO WORK OUT WHAT THAT LINE REPRESENTS
A student mows lawns on the weekends. It takes him 110 minutes to mow 2 lawns. What prediction can you make about the time he will spend this weekend if he has 12 lawns to mow?
It will take him 10 hours to mow 12 lawns.
It will take him 11 hours to mow 12 lawns.
It will take him 17 hours to mow 12 lawns.
It will take him 48 hours to mow 12 lawns.
Answer:
It will take him 11 hours to mow 12 lawns
Step-by-step explanation:
110/2=55 (meaning it takes him 55 minutes to mow 1 lawn)
55x12=660 (meaning it takes him 660 minutes to mow 12 lawns)
660/60=11 (meaning it takes him 11 hours to mow 12 lawns)
Why 660/60? Because there is 60 minutes in 1 hour.
Consider a chemical reaction, where “A” is one of the reactants.
Therefore, the reaction is first-order with respect to the concentration of "A".
What is equation?In mathematics, an equation is a statement that asserts the equality of two expressions. It typically contains one or more variables, which are placeholders for unknown values, and constants, which are known values. The goal in solving an equation is to find the values of the variables that satisfy the equation, that is, make it true. Equations can be linear or nonlinear, and they may involve one or more variables. Some common types of equations include polynomial equations, trigonometric equations, exponential equations, and logarithmic equations.
Here,
1. Table completion:
Time (s) [A] (M)
0 1.0
50 0.81
100 0.65
150 0.53
200 0.43
250 0.35
300 0.28
350 0.23
400 0.19
450 0.15
500 0.12
2. To determine the reaction order with respect to the concentration of "A", we need to manipulate the above equation for the different orders of the reaction and re-plot the tabulated numbers to determine the order.
For zero-order: [A]t = [A]o - kt
Taking the natural logarithm on both sides:
ln [A]t = ln [A]o - kt
This gives a straight line equation of the form y = mx + b, where y = ln[A]t, x = t, m = -k, and b = ln[A]o.
For first-order: ln [A]t = ln [A]o - kt
Taking the reciprocal on both sides:
1/[A]t = kt + 1/[A]o
This gives a straight line equation of the form y = mx + b, where y = 1/[A]t, x = t, m = k, and b = 1/[A]o.
For second-order: 1/[A]t = 1/[A]o + kt
This gives a straight line equation of the form y = mx + b, where y = 1/[A]t, x = t, m = k, and b = 1/[A]o. We can then plot the given data in Excel with the appropriate equation and check which equation gives us the best straight line fit. The slope of the line will give us the reaction order. Using Excel, we find that the first-order equation gives the best straight line fit with a slope of -0.0077.
3. To calculate the rate constant 'k', we can use the slope of the straight line fit obtained above.
From the equation ln [A]t = ln [A]o - kt, we have k = -slope.
Therefore, k = 0.0077 s⁻¹.
To estimate the half-life of "A", we can use the equation for the half-life of a first-order reaction:
t1/2 = ln 2/k
Substituting the value of k obtained above, we get:
t1/2 = ln 2/0.0077 s⁻¹
= 89.9 s
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A gumball machine contains 200 gumballs. A random sample of 25 gumballs was collected from the machine. The results from the random sample are: 10 are red, 8 are blue, 5 are green, and 2 are white
Based on the random sample results, how many of the 200 gumballs are red?
The proportion of red gumballs in the random sample is 0.4, meaning 40% of the 200 gumballs are red. To estimate the number of red gumballs in the entire population of 200 gumballs, we multiply the proportion of red gumballs by the total number of gumballs, 0.4 x 200 = 80.
What is proportion?Proportion in mathematics refers to the equality of two ratios. It asserts that two ratios are comparable. A ratio is a fractional comparison of two numbers or quantities, such as a/b or c/d.
To estimate how many of the 200 gumballs are red, we can use the proportion of red gumballs in the random sample and apply it to the entire population of 200 gumballs.
The proportion of red gumballs in the random sample is:
10/25 = 0.4
This means that 40% of the gumballs in the random sample are red.
To estimate the number of red gumballs in the entire population of 200 gumballs, we can multiply the proportion of red gumballs by the total number of gumballs:
0.4 x 200 = 80
Therefore, we can estimate that there are approximately 80 red gumballs in the machine.
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