The number of ways we can paint is g(nk)=1/n ∑d | n ϕ(d) ((k−1)^n/d +(−1)^n/d (k−1))
Given,
Whether your circle has named sectors (i.e., is fixed) or lacks labels will determine this (i.e. is free).
In the first scenario, inclusion-exclusion can be used to create sets Ai,j of colorings with adjacent sectors I and j having the same color. Next, generally
|Ai1,j1∩⋯∩Air,jr|={(k^n − r r<n) ( k r=n)
And inclusion-exclusion yields f(n, k), the number of sectors that are colored with k colors that are not related to any of Ai, j (i.e., do not have similar adjacent colors):
f(n, k) = ∑r = 0 n−1 (−1)^r (n, r) k^n - r + (−1)^n (n, n)k
And the result of adding and subtracting (1) is:
⟹f(n, k) = ∑r = 0 n−1 (−1)^r (n, r) k^n−r + (−1)^n (n, n)k = (k−1)^n + (−1)^n (k−1)
That is your response to the fixed circle.
Burnside's Lemma, which generates the cycle index of a combinatorial necklace, must be applied if you want the solution for a free circle (assuming the symmetries involved are merely rotations):
Z(Cn) = 1n∑d∣nϕ(d)an/dd
Then, n/d cycles with dN sectors in each cycle, an/dd permutations representing rotations of sectors, and (d) is the Euler Totient Function[4] are used.
Since each cycle must contain a single color from the n available options, we must swap out an/dd with f(n/d, k), resulting in a total of g(n, k) free colorings for n>1*:
g(n, k)=1/n ∑d∣n ϕ(d) ((k−1)^n/d +(−1)^n/d (k−1))
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a newsletter publisher believes that more than 52% of their readers own a personal computer. is there sufficient evidence at the 0.02 level to substantiate the publisher's claim? state the null and alternative hypotheses for the above scenario.
The null hypothesis states that the probability of reader has personal computer is 0.52 whereas alternative hypothesis states opposite
Its given that
The probability that readers has a personal computer = 0.52
The null hypotheses is that the proportion of readers who own a personal computer is equal to 0.53
Null hypotheses = H₀: p = 0.55
The alternate hypotheses is that the proportion of readers who own a personal computer is not equal to 0.55
Alternate hypotheses = H₁: p ≠ 0.55
Determine the type of test:
Since the alternate hypothesis states that the proportion of readers who own a personal computer is different, therefore it is a two-tailed test.
To determine the z-score,
Given level of significance : ∝ = 0.05
So, the z-score at 0.05
Z-score = 1.960 (two tailed)
We Reject H₀ if Z > 1.960
And we accept H₀ if Z < 1.960
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10. Kenji calculated that he needed to
eat about 2000 calories per day
based on his weight, age, and
activity level. For lunch, he ate a
hamburger that had 538 calories.
What percent of Kenji's daily
calorie needs does this hamburger
represent? Show your thinking.
Answer:
26.9%
Step-by-step explanation:
538/2000 = 0.269
Multiply this by 100 to get the percentage
= 26.9%
Can someone help me
Answer: no i need this too :(
Step-by-step explanation:
Answer:
The rule of the translation is (x,y) ------> (x-1,y-5)
B'(-2,1)
C'(3,2)
Step-by-step explanation:
What is the equation in standard form of the line y = | x + 5?
Answer: This is what I came up with after a few tries! 1/9x
Answer:
x+y=5
Step-by-step explanation:
Formula= Ax+By=C
change the equation up a little and get
x+y=5
mia has a certain amount of money. if she buys $4$ pens and $1$ pencil, she will have $\$5$ left over. if she buys $2$ pens and $2$ pencils, she will have $\$3$ left over. if edward arrives with the same amount of money as mia, together they can buy $7$ pens and $4$ pencils and spend all their money. if $a$ is the cost of one pen and $b$ is the cost of one pencil, compute the ordered pair $(a,b)$.
If 2 is the cost of one pen and 6 is the cost of one pencil, compute the ordered pair (2,6)
When Mia buys 4 pens and 1 pencil, she has $5 left; the number of dollars she starts with is 4a+b+5.
When she buys 2 pens and 2 pencils, she has $3 left; the number of dollars she starts with is 2a+2b+3.
Since those two expressions represent the same number, set them equal to each other and simplify to get an equation in a and b.
4a+b+5=2a+2b+3
2a-b=-2 [1]
They can purchase 7 pens and 4 pencils with their entire budget if Edward shows up with the same amount of money that Mia did.
The two of them have twice as much money as Mia did in the beginning, and they can buy 7 pens and 4 pencils with the money they have left over. To get a second equation in a and b, write an equation that says that and simplify it.
7a+4b = 8a+2b+10
a-2b=-10 [2]
solving both the equations 1 and 2:
2a-b = -2 - [1]
a-2b = -10 -[2]
a = 2 , b= 6
if 2 is the cost of one pen and 6 is the cost of one pencil, compute the ordered pair (2,6)
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A bicycle is traveling at a constant speed of 15 miles per hour. The total distance the bicycle travels can be found using the equation: d=15h
The time that it takes for a ride of 24 miles is given as follows:
1.6 hours.
How to obtain the numeric value of a function or of an expression?To obtain the numeric value of a function or of an expression, we replace each instance of the variable in the function or in the expression by the value at which we want to find the desired numeric value.
The distance in this problem is given as the multiplication of the velocity of 15 miles per hour and the time in hours, as follows:
d = 15h.
The variable h can be isolated, thus giving the time in hours for a distance of d miles, as follows:
h = d/15.
The time for a distance of 24 miles is obtained replacing the lone instance of d by 24, as follows:
h = 22
d = 1.6 hours.
Missing InformationThe problem asks for the time for a distance of 24 miles.
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when 500 phone books are recycled, which of the following statements is false? a. conserves around 9 cubic yards in landfill space b. conserves around 17-31 trees c. conserves around 4,077 kilowatt hours of energy d. conserves around 463 gallons of oil please select the best answer from the choices provided
The false statement out of given four option is (a)conserves around 9 cubic yards in landfill space.
What is area ?Area is characterized as the complete space taken up by a level (2-D) surface or state of an item. Take a pencil and draw a square on a piece of paper. It is a 2-D figure. The space the shape takes up on the paper is called its Region. Presently, envision your square is comprised of more modest unit squares
According to question:
That's what first explanation expresses "conserves around 9 cubic yards in landfill space "
Yet, here unit of landfill space is off-base. Since landfill space is an amount that in every case express in region. Unit of region in the proclamation articulation ought to be square yards not cubic yards
The excess amounts units are reliable with what they address.
Subsequently, When 500 telephone directories are reused, then, at that point, false statement is option (a) Monitors around 9 cubic yards in landfill space.
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how many pounds does a 1.98 liter bottle of water weigh on earth? (ignore the weight of the empty plastic bottle, and assume 3 significant digits).
The amount of 198 liters of water weights 4.45 Pound force on the earth.
The density of the water is 1 kg/L.
It means that 1 L of water has 1 kg of water.
So, we can write,
1 liter water = 1 kg water
1.98 liters water = 1.98 kg water.
So, the mass of the water is 1.98 kg.
The weight of a body is given as,
W = Mg
Where,
M is mass of the body and g is the gravitational acceleation,
putting values to find the weight of 1.98 L of water,
W = 1.98 x 10
W = 19.8N.
Converting it into Pounds,
W = 4.45 Pounds force.
Hence, the weight of 1.98 liters of water on earth surface is 4.45 Pound force.
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a fair coin is flipped repeatedly until 50 heads are observed. using the central limit theorem, calculate an approximate value for the probability that at least 80 flips are necessary.
The approximate value for the probability that at least 80 flips are necessary is 0.3897.
Given:
a fair coin is flipped repeatedly until 50 heads are observed
using the central limit theorem, calculate an approximate value for the probability that at least 80 flips are necessary.
P (h>25)=p(h>=26)= 1-p(h<=26)
Assume the situation is approximately normal
u= np =50(1/2)=25 , s=√(npq) = √( 50)(.5)(.5) =√12.5
z=(x-u)/s = ( 26–25)/√12.5 = 0.283
P(z=0.283) =0.1103
Edit p(z>0.283)=0.1103
P(h <= 80)= 0.5+ 0.1103= 0.6103
P(h>=80) 1 - 0.6103 = 0.3897
Hence we get the required answer.
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calories in school lunches: a university of florida economist conducted a study of virginia elementary school lunch menus. during the state-mandated testing period, school lunches averaged 863 calories. (national bureau of economic research, november 2002.) the economist claimed that after the testing period end, the average caloric content of virginia school lunches dropped significantly.. Set up the null and alternative hypothesis to test the economist's claim
The null and alternative hypothesis test the economist's claim is-
H₀: u = 863 ,H₁: u < 863
What is hypothesis test?
A applied math hypothesis test may be a technique of applied math abstract thought accustomed decide whether or not the info at hand sufficiently support a selected hypothesis. Hypothesis testing permits us to create probabilistic statements regarding population parameters.
Main body:
Let ц =average calories of virginia school lunches
The average calories in the school lunch is 863
Here the economists claims that after the testing period ends, the average caloric content in the lunches were dropped
The null hypothesis is H₀ц = 863
Means H₀ ;The average caloric content in the school lunch is 863
The alternative hypothesis is H₁ц <863
Hence , H₁; the average caloric content in the lunches was dropped.
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A rancher is filling a trough for her horses. The trough already contains 25 gallons of water, and the rancher is adding 11 gallons per minute. How long will it take for the trough to have 80 gallons of water?
Write and solve an equation to find the answer. How many minutes.
Answer: 5 minutes
Step-by-step explanation: The total change in the amount of water in the trough is the difference between the final amount and the initial amount, which is 80 gallons - 25 gallons = 55 gallons.
Since the rancher is adding 11 gallons of water per minute, the time it will take for the trough to have 80 gallons of water is the total change in the amount of water divided by the rate at which the water is being added, which is 55 gallons / 11 gallons/minute = 5 minutes.
Therefore, it will take the rancher 5 minutes to fill the trough with 80 gallons of water.
A coin is flipped 8 times. find the probability of the event: exactly 6 heads a. 0.4375 b. 0.75 c. 0.0039 d. 0.109
The correct option d. 0.109, for the probability of the event: exactly 6 heads out of 8.
Describe the term binomial distribution?The possibility that a value would take one of 2 independent values given a particular combination of factors or assumptions is captured by the statistical distribution known as the binomial distribution.P(X = x) = ⁿCₓ . pˣ . qⁿ⁻ˣ
The probability of getting one head = 1/2.
p = 0.5.
Thus, the probability of getting one tail = 1/2
q = 0.5
Thus, for exactly 6 heads
P(X = 6) = ⁸C₆. (0.5)⁶ (0.5)²
P(X = 6) = 0.109
Thus, the probability of the event: exactly 6 heads on flipping coin 8 times is 0.109.
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If you have 20$ and each cup on lemonade that your selling is $0.75 and you already made $20 how many cups to make $100
Given: -7x < -21. Choose the solution set. {x | x < 3} {x | x > 3} {x | x < -3} {x | x > -3}.
The solution set of the given inequality -7x < -21 is {x | x > 3}.
Define the term inequality?In mathematics, "inequality" refers to a relationship involving two variables or values that aren't even equal to one another.Mathematical expressions with inequalities are those in which the two sides are not equal. Contrary to equations, we compare different values in inequality. Less than (and less than and equal to), greater than (and greater or equal to), or just not equal to signs are used in place of the equal sign.For the stated question-
The given inequality is-
-7x < -21
Dividing both side by -1 will change the direction of the sign.
7x > 21
Now, divide both side by 7
7x/7 > 21/7
x > 3 (solution set)
Thus, the solution set of the given inequality -7x < -21 is {x | x > 3}.
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Answer is actually 1420
Answer:
1420
Step-by-step explanation:
its in the question
Solve the equation
4 2/5 + k = -3 2/11
K=?
In fractional form, the answer is 397/55 and in decimal form it is 7.2181.
The equation can be written as 22/5+k= -31/11
transferring 22/5 to the R.H.S., the sign will turn negative.
thus, k=-31/11-22/5
Further solving the equation by taking L.C.M. of 11 and 5 which comes to 55,
k=(155+242)/55
we get the value of k= 397/55
If we convert the given value of k into decimal, it can also be written as, 7.2181.
Thus, the value of k can b expressed in both numerical and fractional forms.
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What is the equation of a line perpendicular to 3x+ 4y =12and passes thru the point (3,2)? Write the equation in slope-intercept form (y=mx+b)
Answer: 3y= 4x-6
Step-by-step explanation:
given line = 4y= -3x+12
slope= -3/4
so the perpendicular lines slope will be 4/3
new line = y = (4/3)x+c
==> 2 = (4/3)3+c
==> 2 = 4+c
==> c= -2
3y= 4x-6
Answer:
y=4/3X -2Step-by-step explanation:
4y=12-3X
divide both sides by4
y=-3x/4 +3
m1×m2= -1
m1= -3/4
-3/4× m2=-1
m2=4/3
Gradient is now=4/3
m= y -y1/x-x1
4/3= y-2/x-3
3y - 6= 4x - 12
3y= 4x - 12 +6
3y= 4x -6
divide both sides by 3
y =4/3x - 2
Help me please
answers:
1
0
-1
Answer:
Step-by-step explanation:
Using ( 0,0) and (1,1 ). the slope is 1 and the y intercept is 0 because the line cuts the y axis at the origin. The equation of the line is y=1x
mr. and mrs. smith plan to roof the cabin on 2 consecutive days. asusming that the chance of rain is independent of the day, what is the progbability it will rain both days
By using the concept of probability, it can be calculated that
Probability that it will rain on both the days = 0.04
What is probability?
Probability gives us the information about how likely an event is going to occur
Probability is calculated by Number of favourable outcomes divided by the total number of outcomes.
Probability of any event is greater than or equal to zero and less than or equal to 1.
Probability of sure event is 1 and probability of unsure event is 0.
Probability of rain on the first day = 0.2
Probability of rain on the second day = 0.2
Assuming that the chance of rain is independent of the day
Probability that it will rain on both the days = 0.2 [tex]\times[/tex] 0.2 = 0.04
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Complete Question
The Smith family is planning to build a 3-room cabin which consists of 2 bedrooms (BR) and 1 living room (LR). Shown below are the rectangular floor plan (left figure) and a side view of the cabin (right figure). In the side view, the roof forms an isosceles triangle (ABC), the walls are perpendicular to the level floor (ED), AC || ED, F is the midpoint of AC, and BF ⊥ AC.
During the week the Smiths plan to roof the cabin, there is a 20% chance of rain each day.
Mr. and Mrs. Smith plan to roof the cabin on 2 consecutive days. Assuming that the chance of rain is independent of the day, what is the probability that it will rain both days?
given vector u equals open angled bracket negative 11 comma negative 5 close angled bracket and vector v equals open angled bracket 4 comma 8 close angled bracket comma what is projvu?
The required projection of u onto v is the vector (-23/20)i - (23/10)j, or approximately <-1.5, -2.13>.
To calculate the projection of vector v onto vector u (proj_vu), we can use the formula:
[tex]proj_{vu} =\dfrac {(v \times u)}{||u||^2} *v[/tex]
Here, u is the vector -11i - 5j and v is the vector 4i + 8j.
Compute the dot product of u and v.
u · v = (-11)(4) + (-5)(8)
= -92
Compute the magnitude of v.
[tex]||v|| = \sqrt{(4^2 + 8^2)} \\= \sqrt{80}\\ = 4\sqrt{5[/tex]
Compute [tex]proj_{vu}[/tex]using the formula.
[tex]proj_{vu} = \dfrac{u \times v} {||v||^2} * v\\ proj_{vu} = (-92 / (80)) * (i + 2j)\\proj_{vu} = (-23/20)i - (23/10)j[/tex]
Therefore, the projection of u onto v is the vector (-23/20)i - (23/10)j, or approximately <-1.5, -2.13>.
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The question is incomplete, the complete question is given below:
Find the projection of vector v onto vector u or what is proj_vu?
Where.
Vector u = <-11, -5>
Vector v = <4, 8>
which is a characteristic of any function created by the product of two linear factors?
The characteristic of any function created by the product of two linear factors has two x-intercepts.
According to the question;
We are required to determine which is a characteristic of any function created by the product of two linear factors.
The product of two linear factors results in a quadratic function.
Since a quadratic function is a polynomial of degree two, 2.
In essence, the resulting function created by the product of two linear factors has two x-intercepts.
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A town has a population of 15000 and grows at 4. 5% every year. To the nearest tenth of a year, how long will it be until the population will reach 20700?.
At a 4.5% annual growth rate, it will take 8.4 years to double the population from 15,000 to 20700.
What is percent?In essence, percentages are fractions with a 100 as the denominator. We place the percent symbol (%) next to the number to indicate that the number is a percentage. For instance, you would have received a 75% grade if you answered 75 out of 100 questions correctly on a test (75/100). A value or ratio that may be stated as a fraction of 100 is referred to as a percentage in mathematics. If we need to calculate a percentage of a number, we should divide it by its entirety and then multiply it by 100. Hence, the percentage means, a part per hundred. The word per cent means per 100. It is represented by the symbol “%”.
Here,
The initial population=15000
Growth rate=4.5%
Final population=20700
Population growth=15000*4.5%
=675
Let n be the number of years.
Final population=initial population + Population growth*number of years
20700=(15000+675n)
675n=20700-15000
675n=5700
n=5700/675
n=8.4 years
It will take 8.4 years to grow the population from 15000 to 20700 at the growth rate of 4.5% per year.
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If I drive at ......... miles per hour, my journey will take ......... hours.
How long will my journey take if I drive at ......... miles per hour?
Answer:
Step-by-step explanation: 70 2.5 60
A statistics class designed a survey to learn the favorite season of the freshmen class.
Let A be the event that the name of the favorite season starts with the letter S.
Let B be the event that the name of the favorite season does not start with the letter S.
There are l__l outcomes in the sample space.
There are l__l outcomes in event A.
There are l__l outcomes in event B.
There are 4 outcomes in the sample space.
There are 2 outcomes in event A.
There are 2 outcomes in event B.
Sample Space:
A sample space is a set of potential results from a random experiment. The letter "S" is used to denote the sample space. Events are the subset of possible experiment results. Depending on the experiment, a sample area could contain a variety of results. Discrete or finite sample spaces are those that have a finite number of outcomes. The random experiment's sample spaces are written in curly brackets, " ".
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There are 4 outcomes in the sample space.
There are 2 outcomes in event A.
There are 2 outcomes in event B.
Sample Space:
Several possible outcomes from a random experiment make up a sample space. The sample space is designated with the letter "S".
Events are a subset of potential experiment outcomes.
A sample region could have a range of outcomes, depending on the experiment.
Any sample space with a finite number of outcomes is said to be discrete or finite. Sample spaces for the random experiment are denoted by " " curly brackets.
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If r=[2,1] and s=[-3,2] calculate 2r-3s
Answer: -5,4
Step-by-step explanation:
2,1 x 2 = 4,2
-3,2 x 3 = -9,6
-9,6
- 4,2 = -5,4
consider a function z(x, y) and its partial derivative (∂z/∂y)x. can this partial derivative still be a function of x?
A function z(x, y) and its partial derivative (∂z/∂y)x is aslo a function.
Function:
In set math, function refers an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable)
Given,
Consider a function z(x, y) and its partial derivative (∂z/∂y)x.
Here we need to identify that the partial derivative still be a function of x.
In order to find the solution for this function, we must know the definition of partial derivative,
The definition of partial derivative is, "partial derivative of any function having several variables is its derivative with respect to one of those variables where the others are held constant."
Here the partial derivative of a function f with respect to the differently x is variously denoted by f’x, fx, ∂xf or ∂f/∂x.
The symbol ∂ is partial derivative.
So, as per the definition of the partial derivative, the given partial derivative (∂z/∂y)x is also a function.
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on the 6th grade arithmetic test, the average score was 94! which of these interpretations is the most likely to be correct?
More students received a 94 than any other score on the test. So, option B is the correct answer.
The mode of any given data set is the value that occurs in the given data set the most. This is that one value that occurs more than any other value in any given data set. From the given problem, we can easily understand that 94 is the mode of the set since it is the average score. This means that more students received a 94 than any other score on the test.
The first option is not the correct answer because we have not been told that 99 was the highest score on the test. We have also not been told no student scored below 50 or that a score of 91 was slightly below average.
This means option B is the correct answer.
The question you might be looking for is -
The mode score on the 6th-grade math test was 94! Which of these interpretations must be correct?
a. 99 was the highest score on the test.
b. More students received a 94 than any other score
c. No student scored below a 50
d. A score of 91 was slightly below average.
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if the null hypothesis is true, what value is expected on average for the repeated-measures t statistic?
A repeated-measures test's null hypothesis is that the population as a whole will have a mean difference of μD = 0.
What is Null Hypothesis?
In probability and statistics, the null hypothesis is a comprehensive statement or default status that there is zero happening or nothing happening.
The t statistic is calculated from the difference between the sample parameter in question and the value of the corresponding population parameter assumed under the null hypothesis. If the hypothesis is true, the difference between the values (and the corresponding t statistic) is expected to be zero.
A repeated-measures test's null hypothesis is that the population as a whole will have a mean difference of μD = 0.
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hurry, please!
A rectangle is shown on a coordinate plane with vertices A(Negative 4, 8), B(1, 8), C(1, Negative 1), and D(Negative 4, Negative 1).
On a coordinate plane, a rectangle has 4 points. Point A is (negative 4, 8), point B is (1, 8), point C is (1, negative 1), point D is (negative 4, negative 1).
What are the dimensions of the rectangle?
The base is 4 units and the height is 9 units.
The base is 5 units and the height is 7 units.
The base is 5 units and the height is 9 units.
The base is 9 units and the height is 3 units..
Answer: The base is 4 units and the height is 9 units.
Step-by-step explanation: To find the dimensions of the rectangle, we can use the coordinates of the points A, B, C, and D. The base of the rectangle is the distance between the points A and B, or the distance between the points C and D. We can find this distance by subtracting the x-coordinates of the points: 1 - (-4) = 5. Therefore, the base of the rectangle is 5 units.
Next, we can find the height of the rectangle by subtracting the y-coordinates of the points A and C, or the points B and D. We can do this by subtracting the y-coordinates of the points: 8 - (-1) = 9. Therefore, the height of the rectangle is 9 units.
Therefore, the dimensions of the rectangle are a base of 5 units and a height of 9 units, so the correct answer is A; The base is 4 units and the height is 9 units.
the number line shows point m at 15,490 rounded to the nearest thousand?
Answer:
I can't see the number line, but I'll say 15,000
The solution is, 15000 when 15,490 rounded to the nearest thousand.
What is round off?Rounding off means a number is made simpler by keeping its value intact but closer to the next number. It is done for whole numbers, and for decimals at various places of hundreds, tens, tenths, etc.
here, we have,
given that, 15,490
now, we have to rounded to the nearest thousand.
we get, 490 < 500
so, it is 15000
Hence, The solution is, 15000 when 15,490 rounded to the nearest thousand.
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