When we do a confidence interval for the mean, we use T-distribution to determine the number of standard deviations needed for our confidence
The T-distribution is a way to describe a collection of observations in which the majority of the observations are close to the mean and the remaining observations are the tails on either side. It is a type of normal distribution that is utilized for data with unknown variance and smaller sample sizes.
We use the T-distribution to obtain the required critical value, which is nothing more than the number of standard deviations from the center taken to obtain the confidence interval, despite the fact that there is no population standard deviation and only sample metrics—the sample mean and standard deviation—are used. As a result, the solution to this problem is T-distribution.
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Solve for b in A = a + b
——-
3
Help ASAP!!
Answer: The correct answer is b=2a
Step-by-step explanation:
Solve for b
A = (a + b)/3
Flip the equation
1/3a + 1/3b = a
Add (-1)/3a to both sides.
1/3a + 1/3b + −1/3a = a + −1/3a
1/3b = 2/3a
Divide both sides by 1/3
(1/3b)/(1/3) = (2/3a)/(1/3)
b=2a
Answer:
[tex]b = 3A - a[/tex] (if A and a are two different variables).
[tex]b = 2a[/tex] (If the A and a denote the same variable.
Step-by-step explanation:
[tex]A = \frac{(a + b)}{3}[/tex]
Isolate the variable, b. Note the equal sign, what you do to the one side, you do to the other.
Do the opposite of PEMDAS. PEMDAS is the order of operations, and stands for:
Parenthesis
Exponents (& Roots)
Multiplication
Division
Addition
Subtraction
~
First, multiply 3 to both sides of the equation:
[tex]A (*3) = \frac{(a + b)}{3} (* 3)\\A * 3 = (a + b)[/tex]
Next, subtract a from both sides of the equation:
[tex]A * 3 = a + b\\3A = a + b\\3A (-a) = a (-a) + b\\b = 3A - a[/tex]
[tex]b = 3A - a[/tex] is your answer.
IF, however, you meant to put both lower case variable a (or vice versa), then you can further simplify:
[tex]b = 3a - a\\b = 2a[/tex]
[tex]b = 2a[/tex] is your answer if the a are supposed to be the same variable.
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Please help! Question below
The system of equation that is used to determine the number of cans of soup purchased and the number of frozen dinners purchased is 300x+450(x+5)=6000mg.
What is meant by linear equation?A linear equation can be generated by equating a linear polynomial over some field with zero coefficients. The values that, when substituted for the unknowns, make the equality true are the solutions of such an equation. The phrase linear equation is frequently used to refer to this specific scenario, in which the variable is appropriately referred to as the unknown.
Each solution in the case of two variables can be regarded as the Cartesian coordinates of a point on the Euclidean plane. A linear equation's solutions form a line in the Euclidean plane, and every line can be seen as a set.
Sodium contains in a can of soup is 300mg
Sodium contains in a can of frozen dinners is 450mg
Let the number of cans of soup purchased be x
Then, the number of frozen dinners purchased=x+5
Total sodium purchased=6000mg
So, 300x+450(x+5)=6000mg
Therefore, the system is 300x+450(x+5)=6000mg
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the difference of two numbers is 6 . two times the smaller is 3 more than the larger. find the two numbers.
The larger number is 15 and the smaller number is 9.
What is substitution method?
In order to solve a system of equations, the substitution method is typically used in mathematics. This approach involves first solving the equation for one variable, then changing the value of the variable in the second equation.
Suppose
'a' be the larger number and 'b' be the smaller number.
As the difference of two numbers is 6.
⇒ a - b = 6 ..(1)
As two times the smaller is 3 more than the larger.
⇒ 2b = 3 + a ..(2)
From equation (2),
a = 2b - 3
Substitute the value of 'a' in equation (1)
2b - 3 - b = 6
b - 3 = 6
b = 6 + 3
b = 9
Substitute b = 9 in equation (1),
a - 9 = 6
a = 6 + 9
a = 15
Hence, the larger number is 15 and the smaller number is 9.
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Solve -6 = a/-4 the a/-4 is in fraction form by the way
Answer:
a = 24
Step-by-step explanation:
1. Multiply all terms by the same value to eliminate fraction denominators
-6 = [tex]\frac{a}{-4}[/tex]
-4(-6) = -4 · [tex]\frac{a}{-4}[/tex]
2. Cancel multiplied terms that are in the denominator
-4(-6) = -4 · [tex]\frac{a}{-4}[/tex]
-4(-6) = a
3. Multiply the numbers
-4(-6) = a
24 = a
4. Move the variable to the left
24 = a
a = 24
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Lin runs 5 laps around a track in 6 minutes
a. How many minutes per lap is that
Answer: 0.83 laps per minute.
Step-by-step explanation:
Answer:
Step-by-step explanation:
0.83 is the answer
there are 3 seniors and 15 juniors in mrs. gillis’s math class. three students are chosen at random from the class. a. what is the probability that the group consists of a senior and two juniors? b. if the group consists of a senior and two juniors, what is the probability that stephanie, a senior, and jan, a junior, are chosen?
The answer of a) Probability = 0.386 and of b) Probability = 0.017
Explain probability.
Estimating the likelihood that experiments will succeed or fail is one use of probability theory. The likelihood of flipping a coin and getting heads or tails, for example, or the likelihood of making a research error, can all be calculated using probabilities. In order to fully appreciate this area of mathematics, it is crucial to comprehend the formula for computing probabilities in equiprobable sample spaces, as well as the probabilities of the complementary event, etc., as well as the likelihood of two occurrences joining together.
no of seniors = 3
no of juniors = 15
a) probability that a group consist of a senior and two juniors =
[tex]\frac{^{3}C_{1} * ^{15}C_{2}}{^{18}C_{3}} \\= \frac{3*105}{316}=0.386\\[/tex]
b) if the name of a student given then there is only one way to select it
For example = we have to select 1 senior which name is already given means there is only one way to select it, and 2 junior in which one name is given then it can only selected by one way, but still one junior student has to be selected out of remaining 14 student which can be selected by ([tex]^{14}C_{1}=14[/tex]) different ways.
probability = [tex]\frac{1*1*^{14}C_{1} }{^{18}C_{3} }=\frac{14}{316}=0.017[/tex]
Hence the answer of a) is 0.386 and of b) is 0.017
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Alina invests $1300 in one account and $1200 in an account paying 2 % higher interest. At the end of one year she had earned $99 in interest. At what rates did she invest?
Answer:
3%
Step-by-step explanation:
Apply distributive property as shown on all products-
All equations need to be distributed equally
x=3%
As shown, this should be what you do...
It's fine if you don't, but a little birdie said you should, just sayin'...
1300x+1200(x+0.02)=99
Rearrange
2500x+24=99
2500=75
[tex]75/100\\Properties[/tex]
[tex]3/100\\Prioritized(mathematically)[/tex]
1.numbers going up in value descending order 2.the number being divided dividend 3.numbers going down in value estimation 4.an approximate value close to the actual value divisor 5.the number divided by ascending order
1. Numbers going up in value - Ascending order
2. The number being divided - Dividend
3. Numbers going down in value - Descending order
4. An approximate value close to the actual value - Estimation
5. The number divided by - Divisor
When the value of numbers is increasing then it's said to be in ascending order. Similarly, when the value of numbers is decreasing then it's said to be in descending order.
The number which is getting divided is called a dividend and the number through which we divide the dividend is called the divisor.
Estimation is said to be the approximate value or the value which is close to the actual value.
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The complete question is -
Match the following-
1. numbers going up in value
2. the number being divided
3. numbers going down in value
4. an approximate value close to the actual value
5. the number divided by
Options - descending order, dividend, estimation, divisor, ascending order.
Suppose one balloon costs $3. Complete the table to find the cost of different numbers of balloons that Lucy might buy. Using the rate of the table what would be the cost of 23 balloons?
The linear function y = 3x is used to calculate the cost of 23 balloons as $69
Linear FunctionA linear function is a function that represents a straight line on the coordinate plane. For example, y = 3x - 2 represents a straight line on a coordinate plane and hence it represents a linear function. Since y can be replaced with f(x), this function can be written as f(x) = 3x - 2.
A linear function is of the form f(x) = mx + b where 'm' and 'b' are real numbers. Isn't it looking like the slope-intercept form of a line which is expressed as y = mx + b? Yes, this is because a linear function represents a line, i.e., its graph is a line. Here,
'm' is the slope of the line'b' is the y-intercept of the line'x' is the independent variable'y' (or f(x)) is the dependent variabley = 3x
x = number of balloons
The cost of 1 balloon = $3
the cost of 23 balloon = x
x = 23 * 3
x = 69
The cost of 23 balloon is $69
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HELPPPPPPPPPP MEEE YALL ARE SLAY
Answer:
B) Corresponding angles are congruent, therefore 2x + 42 = 76.
Step-by-step explanation:
Yes, corresponding angles are congruent, however, the given angles do not fit the definition of a corresponding angle.
Instead, they form a straight line, which is 180° in total. If you were to solve using option B), the answer would look instead as:
(2x + 42)° + (76)° = 180°
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A pilot was scheduled to depart at 4:00 pm, but due to air traffic, her departure has been delayed by 16 minutes. Air traffic control approved a new flight plan that will allow her to arrive four times faster than she calculated in her original flight plan. Let x represent the time, in minutes, of her original flight. Create an equation that can be used to predict the number of minutes after 4:00 pm she will arrive at her destination.
Using the equation y=x/4+16, it is possible to estimate how many minutes will pass after 4:00 pm when she reaches her destination.
What is equation?The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two expressions 3x + 5 and 14, which are separated by the 'equal' sign.
Here,
Let x be the time of original flight before delay.
Let y be the new time of flight after delay.
She will to arrive 4 times faster that in original flight time,
y=x/4
The flight is delayed by 16 minutes,
y=x/4+16
The equation that can be used to predict the number of minutes after 4:00 pm she will arrive at her destination will be y=x/4+16.
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Answer:b
Step-by-step explanation: did the test
the mean and standard deviation of the heights of american women are 63.8 inches and 4 inches, respectively. find an approximate probability that the mean height of a randomly selected 100 american women is between 63 and 64 inches (round off to second decimal place).
The probability that the mean height of the American women is between 63 and 64 is 0.6687
The probability of an event occurring is defined by probability. There are numerous instances in real life where we may need to make predictions about how something will turn out. The outcome of an event may be known to us or unknown to us. When this happens, we say that there is a chance that the event will happen or not.
Mean = 63.8
S = 4
n = 100
P(63 <=X-bar<=64) = P(63.638/4/[tex]\sqrt{100}[/tex] < z < 64.638/4/[tex]\sqrt{100}[/tex])
=P(0.2 < z < 0.5)
=P(z<0.5) - P(z<-2)
0.6915 - 0.0228
0.6687
So, the probability is 0.6687
p-values from the z table
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What is the average rate of change of the function on the interval from x = 2 to x = 4? f(x)=10(2)x
Answer:
B because (16-4)/2=6
Step-by-step explanation:
1. From the window of one building, the angle of elevation to the top of a second building
is 41° and the angle of depression to the bottom is 54°. The buildings are 56 m apart.
a. How tall is the second building?
b. How high up is the window?
Answer:
a) the second building is 118.69 m tall
b) the height of the window from the ground is 70.077 m
Step-by-step explanation:
Attached is a sketch of the building. Look over the sketch before reading the explanation.
Use SOH CAH TOA.
Let [tex]O_{1}[/tex] be the height of the window from the ground.
Therefore we can say that [tex]O_{1}+O_{2}[/tex] is the height of the second building.
We can say that
[tex]O_{1}=tan(x_{1} )*A_{1}[/tex]
Therefore
[tex]O_{1}=tan(54)*56[/tex]
[tex]O_{1}=70.077[/tex]
[tex]O_{2}=tan(x_{2} )*A_{2}[/tex]
[tex]O_{2}=tan(41)*56[/tex]
[tex]O_{2} =48.68[/tex]
[tex]70.007+48.68=118.69[/tex]
254.4 / 0.001 what is the solution?
Answer: 254400
Step-by-step explanation:
We notice that dividing by 0.001 is the same as multiplying by 1000.
So we take 254.4 timed 1000= 254400
Answer:
254,400
Step-by-step explanation:
1. Count how many zeros are in 0.001
0.001 = 3 zeros
2. Move the decimal point according to the zeros
(There are 3 zeros, so move the decimal point to the right 3 times):
254.4
2,544.
25,440.
254,400
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Which equations represent circles that have a diameter of 12 units and a center that lies on the y-axis? select two options. x2 (y – 3)2 = 36 x2 (y – 5)2 = 6 (x – 4)² y² = 36 (x 6)² y² = 144 x2 (y 8)2 = 36
The equation of the circle on the y-axis is x² +(y-3)² = 36.
Here we have to find the equation of the circle
Data provided:
diameter(d) = 12 units
so radius(r) = 6 units
The center lies on the y-axis
The general equation of the circle:
(x-x1)² + (y - y1)² = r²
where (x1, y1) is the point on the circle.
So by putting x1 = 0 and y1 = 3 and r = 6 as the center lies of y-axis
x² + ( y - 3)² = 6²
x² + (y-3)² = 36
Therefore we get the equation as x² + (y-3)² = 36
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at a sale, a sofa is being sold for of the regular price 33% the sale price is 184.80 what is the regular price?
The regular price is 275.82, according to given question.
What do you mean by regular price?
Regular price is the cost at which a provider continuously and actively sells goods or services to the general public over an extended period of time.
According to data in the given question,
We have the given information:
Sale discount 33% and the sale price 184.80.
Now, we will calculate the regular price:
Let Regular Price = x
33% Discount of x = 33/100 * x
33% Discount of x = 33x/100
Regular price - 33% Discount = Sale price
x-33x/100=184.80
(100x-33x)/100=184.80
67x/100=184.80
67x=18480
x=18480/67
x=275.82
Therefore, the regular price is 275.82.
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By using compatible numbers, the estimate is
Use a calculator to multiply 92 × 12. What do you get?
Circle whether the estimates were all less than or greater than
the actual product.
Answer:
92*12=1104
Step-by-step explanation:
There are 60 seconds in a minute and 60 minutes in an hour. How many seconds are in one hour?
Answer:
3600
Step-by-step explanation:
we just have to multiply 60 by 60.
A triangle has 2 angles that measure 60 degrees, what is the measurement of the opposite exterior angle?
Answer:
Step-by-step explanation:
The function g(x)=2^x-1 models the number of bacteria after x days. In how many days
will there be 256 bacteria?
day weight (ounces) monday 23 22 23 24 tuesday 23 21 19 21 wednesday 20 19 20 21 thursday 18 19 20 19 friday 18 20 22 20 what is the mean of the sampling distribution of sample means when this process is in control?
The value of the required mean of the sampling distribution of sample means is approx. 21 ounces when this process is in control.
Sample mean: The arithmetic mean of the values of the variables in the sample. If the samples are drawn from probability distributions with a common expected value, the sample mean is an estimate of that expected value.
Sample means for all days using formula,
Monday = (23+22+23+24)/4 = 23
Tuesday = (23+21+19+21)/4 = 21
Wednesday = (20+19+20+21)/4 = 20
Thursday = (18+19+20+19)/4 = 19
Friday = (18+20+22+20)/4 = 20
We have to calculate the mean of sampling distribution of sample means.
Mean of the sampling distribution of sample means = Sum of sample means of all days / Number of days
= (23+21+20+19+20)/5
= 20.6 = 21 ounces
Hence, the required mean is approx. 21 ounces.
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35 Points!!!! 7 2/5= 2/3x −4 1/2
Enter your answer as a mixed number in simplest form in the box.
Solving for x in the equation 7 2/5 = 2/3x −4 1/2 gives 17 17/20
How to determine the value of xIn the given equation, we find the value of x by applying the following operations
7 2/5 = 2/3x −4 1/2
7 2/5 = 2x/3 −4 1/2
collecting like terms
7 2/5 + 4 1/2 =
2x/3 = 119/10
multiplying by 3
2x = 119/10 * 3
2x = 357/10
dividing by 2
x = 357 / 10 * 1/2
x = 357/20
x = 17 17/20
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Let A be a complex (or real) n x n matrix, and let x in C^n be an eigenvector corresponding to an eigenvalue (lambda) in C Show that for each nonzero complex scalar (nu) , the vector (nu) x is an eigenvector of A
The vector (nu) x is an eigenvector of A and corresponds to each nonzero complex scalar (nu) (lambda).
Let x in Cn be an eigenvector of A that corresponds to an eigenvalue. Assume that A is a n x n matrix (lambda). Ax = (lambda)x follows.
Let (nu) now be a complex scalar that is nonzero. A((nu)x) = A((nu)x) = A((nu)x) = A((nu)x) = A((nu)x) = A((nu)x)
As a result, (nu)x is an eigenvector of A that corresponds to (nu) (lambda).
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Determine if the subset of R^2 consisting of vectors of the form [a b], where a + b = 1 is a subspace. Select true or false for each statement. This set is closed under scalar multiplications This set is a subspace This set is closed under vector addition The set contains the zero vector
This set is closed under scalar multiplications. Statement 1 is false.
This set is a subspace. This statement is also false because this set does not contain a zero vector so it is not a subspace.
This set is closed under vector addition. This is false. Because let v and w be two vectors such that v=(v1,v2); w=(w1,w2).
The set contains the zero vector. Statement 4 is false because the sum of two zero vectors cannot be equal to 1.
Since v and w are vectors satisfying the condition of space so v1+v2=1;w1+w2=1
Now we check whether v+w also belongs to the same space or not.
v+w=(v1,v2)+(w1,w2)=(v1+w1, v2+w2)
We shall check whether components of v+w also add up to 1.
v1+w1+v2+w2=v1+v2+w1+w2=1+1=2
So it means that this space is not closed under addition too.
Consider a vector v=(v1,v2) from the space.
Obviously v1+v2=1
Now let us take a constant 'c' and consider the behavior of
cv=c(v1,v2)=(cv1,cv2)
Now we check whether components of this vector add up to 1.
cv1+cv2=c(v1+v2)=c\neq 1
which clearly indicates that vectors of this space are not closed under scalar multiplication.
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Ms. Apple bought a new chair that was 25% off and saved $14. What was the sale price of the chair? What was the original price?
Answer:
Original price was $56
Step-by-step explanation:
If $14 is 25% then to find 100% multiply $14 by 4
then you will get $56
Determine whether the given point is on the line. Explain your reasoning. (6, -2); y= 1/2x-5
The point (6, -2) lie on the given line segment y= 1/2x-5.
What is point and line segment?A point denotes exact location on any surface,
and the collection of points in the definite pattern is called line.
So, every line itself have infinite points.
Given point = (6, -2)
Hence, the given line = y= 1/2x-5
So, to find whether any point is on the line or not,
we have to put the point on line.
If it satisfies it will lie on line segment.
If not it will not pass through given line segment.
y= 1/2x-5
Putting x= 6 and y= -2
-2 = 3- 5
Hence, -2 = -2
Hence the (6, -2) lie on the given line segment y= 1/2x-5
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a probability distribution has a mean of 22 and a standard deviation of 2. use chebychev's inequality to estimate the probability that an outcome of the experiment lies between 13 and 31. a) 0.9506 b) 0.9917 c) 0.0494 d) 0.0083 e) 0.2222 f) none of the above
Using Chebychev's inequality the probability shows an outcome of the experiment between 13 and 31 is equal to 0.9506.
As given in the question,
Mean 'μ' = 22
Standard deviation 'σ' = 2
Apply Chebychev's inequality we have,
P ( | X - μ | ≤ kσ ) ≥ 1 - (1/k²)
Where 'k' is the constant value.
Estimation of probability with outcome lies between 13 and 31 using Chebychev's inequality is :
P ( 13 < X < 31 )
= P ( 13 -22 < X - μ < 31 - 22 )
= P ( -9 < X - μ < 9 )
= P ( | X - μ |≤ 9)
= P [ |X - μ | ≤ (9/2) ×2 ]
= P( |X - μ | ≤ Kσ)
≥ 1 - ( 1/k²)
here k = 9/2
= 1 - (1 / (9/2)²)
= 1 - 4/81
= (81 -4) / 81
= 77/ 81
= 0.9506
Therefore, the probability for which outcome lies between 13 and 31 using Chebychev's inequality is equal to 0.9506.
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Given f(x) = |x|, g(x)=|x+4|-2 is what kind of
transformation ?
The transformation of the function g ( x ) = | x + 4 | - 2 is
Horizontal shift : Left by 4 units
Vertical shift : Down by 2 units
How does the transformation of a function happen?
The transformation of a function may involve any change.
Usually, these can be shifted horizontally (by transforming inputs) or vertically (by transforming output), stretched (multiplying outputs or inputs)
If the original function is y = f(x), assuming the horizontal axis is the input axis and the vertical is for outputs, then:
Horizontal shift (also called phase shift):
Left shift by c units: y=f(x+c) (same output, but c units earlier)
Right shift by c units: y=f(x-c)(same output, but c units late)
Vertical shift:
Up by d units: y = f(x) + d
Down by d units: y = f(x) - d
Stretching shift:
Vertical stretch by a factor k: y = k × f(x)
Horizontal stretch by a factor k: y = f(x/k)
Given data ,
Let the parent function be f ( x )
The value of f ( x ) = | x |
Now , the transformation from the first function f ( x ) to g ( x ) is of the form
g ( x ) = | x + 4 | - 2
And , transformation is
y = a | x - h | + k
where the values of y , a , x , h and k are
The value of a = 1
The value of h = -4
The value of k = -2
Now , The Horizontal shift is given by
Left shift by c units: y=f(x+c) (same output, but c units earlier)
Right shift by c units: y=f(x-c)(same output, but c units late)
So , h = -4 means left shift by 4 units
And , The Vertical shift is given by
Up by d units: y = f(x) + d
Down by d units: y = f(x) - d
So , k = -2 means down shift by 2 units
Hence , The transformation of the function g ( x ) = | x + 4 | - 2 is
Horizontal shift : Left by 4 units
Vertical shift : Down by 2 units
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3. coach walker gets a shipment of 153 uniforms. he puts them in boxes of 10. how many boxes can he fill? how many uniforms will be left over? boxes.
By using division, it can be calculated that
Coach Walker needs 15 boxes to fill the uniforms and 3 uniforms will be left over.
What is division?
Division is the process by which value of single unit can be calculated from the value of multiple unit.
The number to be divided is known as dividend, the number by which the dividend is divided is the divisor, the result obtained is the quotient and the remaining part is the remainder.
There is a well known formula for division
Divisor x Quotient + Remainder = Dividend.
This is a problem sum on division
Total number of uniforms = 153
Number of uniforms in one box = 10
Number of boxes he can fill = 153 [tex]\div[/tex] 10
The quotient in this case is 15 and the remainder is 3
Coach Walker needs 15 boxes to fill the uniforms and 3 uniforms will be left over.
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