A track-and-field coach recorded the length of each student's standing long jump. The data is summarized in the box plot.
Standing Long Jumps
0
+
2
4
+
Feet
6
8
10
Choose all of the statements that can be concluded from this data.
A. The median jump length is 5 feet, which is the average length of a standing long jump for the students represented in the box plot.
B. The median jump length is 5 feet, which is the length of the middle student's long jump if the students were ordered by the length of
their long jump.
C. The interquartile range of the long jumps is 4 feet, which means that about half of the students' long jumps are within 4 feet of the
median.
D. The interquartile range of the long jumps is 4 feet, which means that about half of the students' long jumps are within 2 feet of the
median.
A
Answer:
A because of the average length showed
what is the volume of the prism
Answer:
8/15 cm
Step-by-step explanation:
Volume = length x width x height
Volume = 4/5 cm x 1/5 cm x 10/3 cm
Volume = 4/25 cm x 10/3 cm
Volume = 40/75 cm = 8/15 cm
Brainliest, please :)
Answer:
[tex]\frac{8}{15}[/tex]
Step-by-step explanation:
Volume of prism = [tex]l[/tex] · [tex]w[/tex] · [tex]h[/tex]
which means
[tex]\frac{10}{3} *\frac{4}{5} *\frac{1}{5}[/tex]
which is [tex]\frac{8}{15}[/tex] by using cross simplify
Hope this helps ;D
Need help on the Sin(4x) part of the question please!!
a. The equivalent expression for cos(4x) in terms of just x is 8cos⁴x - 8cos²x + 1
b. The equivalent expression for sin(4x) in terms of just x is 4sinxcos³x - 2sinxcosx
a. The equivalent trigonometric expression for cos(4x)To find the trigonometric expression for cos(4x)
cos(4x) = cos[2(2x)]
Now from trigonometric identities
cos2Ф = 2cos²Ф - 1
Let 2x = Ф.
So, cos(4x) = 2cos²2x - 1
Also, cos2x = 2cos²x - 1
So, substituting cos2x into cos4x, we have
cos(4x) = 2cos²2x - 1
cos(4x) = 2[2cos²x - 1]² - 1
cos(4x) = 2[4cos⁴x - 4cos²x + 1] - 1
cos(4x) = 8cos⁴x - 8cos²x + 2 - 1
cos(4x) = 8cos⁴x - 8cos²x + 1
So, the equivalent expression for cos(4x) in terms of just x is 8cos⁴x - 8cos²x + 1
b. The equivalent trigonometric expression for sin(4x)To find the expression for sin(4x)
sin(4x) = sin2(2x)
From trigonometric identities sin2Ф = 2sinФcosФ
Let 2x = Ф
So, sin(4x) = sin2(2x)
= 2sin2xcos2x
Since
sin2x = 2sinxcosx and cos2x = 2cos²x - 1Substituting these into the equation, we have
sin(4x) = 2sin2xcos2x
sin(4x) = (2sinxcosx)(2cos²x - 1)
sin(4x) = 4sinxcos³x - 2sinxcosx
So, the equivalent expression for sin(4x) in terms of just x is 4sinxcos³x - 2sinxcosx
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Find two consecutive numbers such that sum of four times the first and triple the second is 157. (Linear Function)
Step-by-step explanation:
Set up a system of equations,
Consective numbers appear before and after so we need two number such that
[tex]x + 1 = y[/tex]
or
[tex]x - y = - 1[/tex]
Likewise, we also know that
[tex]4x + 3y = 157[/tex]
Let multiply the top equation by 3.
We get
[tex]3x - 3y = - 3[/tex]
Then we add the bottom equation to that
[tex]4x + 3y = 157[/tex]
[tex]7x = 154[/tex]
[tex]x = 22[/tex]
Then we plug in x for the original equation,
[tex]22 + 1 = 23[/tex]
So the two numbers are 22,23.
Find and compare the growth rates in the weekly number of specialty items produced at each factory.
Show your work.
0.129 is the change in the growth rate of company.
According to statement
we have to find and compare the growth rate of the company weekly.
we use the growth rate formula is
GROWTH RATE = present - past / present
Substitute the values in this formula
1st week = 220-190 / 220
1st week = 0.136
2nd week = 252-220 / 252
2nd week = 32 / 252
2nd week = 0.126
3rd week = 290-252 / 290
3rd week = 0.131
4th week = 337 - 290 / 337
4th week = 0.139
5th week = 380 - 337 / 380
5th week = 0.113
6th week = 440 - 380 / 440
6th week = 0.136
7th week = 505 - 440 / 505
7th week = 0.128
Now we find the average value of growth rate
Average = 0.136 + 0.126+0.131+0.139+0.113+0.136+0.128 /7
Average = 0.909/7
Average = 0.129
So, 0.129 is the change in the growth rate of company.
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What is the square root of pi?
Pi is a Greek number that plagues mathematics, physics, and circles to the point where pi-fatigue is actually a thing. Pi is an infinite number, however it will henceforth only be written as 3.14159.
I have two solutions to your problem.
The first, and probably less appealing answer, but most used everywhere, would be to use a calculator.
But if you find yourself without a calculator at the ready, I hope you’re prepared to math quite dubiously.
Finding the square power, inverse of a radical, or whatever is multiplied by itself to equal 3.14159, is the second step. We must start someplace to start our attempt, and that place is 3.14159. Since 1 squared equals 1 and 2 squared equals 4, our result, expressed in decimal form, is larger than 1 but less than 2. After that, we just start divising and multiplying the decimals again until we have calculated the square root of pi.
TL;DR
1.7724531 is the approximate square root of pi.
Answer:
1.77245385091
Step-by-step explanation:
What is the tax due for a single taxpayer reporting a taxable income of $65,725?
The tax due for the single taxpayer whose income is as described is; $14,459.5.
What is the tax due for the single taxpayer?It follows from the task content that the tax due for a single taxpayer whose taxable income is; $65,725 is to be determined.
Since, the taxable income falls between the range; $40,526 to $86,375, 22% of the income is the tax due and hence, the tax due can be evaluated as follows;
= (22/100) × $65,725
= 14,459.5
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What is another way to name angle 3?
O Angle MVK
O Angle LVM
O Angle LVK
O Angle KVM
Answer:
intimately there are three types of angles a cute angle and angle between zero and 90° right angle and angle 90 degree angle of two angle and angle between 90 and 180 degree
A mass weighing 16 pounds is attached to a spring whose spring constant is 36 lb/ft. what is the period of simple harmonic motion?
The period of simple harmonic motion is T = 4.19 seconds:
For given question,
A mass weighing 16 pounds is attached to a spring whose spring constant is 36 lb/ft.
So, we have mass (m) = 16 pounds
spring constant (k) = 36 lb/ft.
Let T be the period of simple harmonic motion.
Using the formula for the period of simple harmonic motion,
⇒ T = 2π√(m/k)
⇒ T = 2 × π × √(16/36)
⇒ T = 2 × π × √(0.444)
⇒ T = 2 × π × 0.666
⇒ T = 1.333 × π
⇒ T = 4.19 seconds
Therefore, the period of simple harmonic motion is T = 4.19 seconds
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Patient a weighs 135.8 pounds.patient b weighs 135 2/5 ibs. which patient has the greater weight or if their weights are equal
Answer:
patient A has the greater weight
please help! this is the last one i need and i forgot how to do it!
Based on the information, Christian would have $5525.5 of annuity.
How to calculate the annuity?According to given information, the number of coffees per week is 3 then, per month is 3x4 = 12
For each coffee is $4.5. Then monthly expenditure for coffees is 12 x 4.5 = $54
Rate of interest r = 1.6% = 1.6/100 = 0.016 and for monthly compounding r = 0.016/12 = 0.00133
n = number of payments = 8 x 12 = 96
We can use the formula for finding the future value as below
FV = C x [ ( 1 + r )n-1 ] / ( r )
FV = 54 x [ ( 1 + 0.00133 )96 – 1 ] / (0.00133)
= 54 x [ (1.13609 - 1)] / (0.00133)
= 54 x 0.13609 / (0.00133)
= 54 x 102.3233
= 5525.5
Therefore Christian would have $5525.5 of annuity.
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Which expression is equivalent to -7(y - 2)
The expression equivalent to -7(y - 2) is -7y + 14
Which expression is equivalent to -7(y - 2)?
Given the expression; -7(y - 2)
We expand the expression by multiplying each element inside the parentheses the element out i.e -7
-7(y - 2)
[ -7 × y and -7 × -2 ]
-7y + 14
Therefore, the expression equivalent to -7(y - 2) is -7y + 14.
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Please give the answer
Answer: See the attached image below for the filled in table.
=========================================================
Explanation:
The domain is the set of all allowed x inputs of a function.
The term "radicand" refers to the stuff under the square root.
We cannot have a negative number under the square root. Therefore, the radicand must be 0 or larger.
The first function must have [tex]4x+6 \ge 0[/tex] which becomes [tex]4x \ge -6[/tex] and leads to [tex]x \ge -\frac{6}{4}[/tex] aka [tex]x \ge -\frac{3}{2}[/tex]
So x = -3/2 is the smallest input allowed. Which is where the interval notation of [tex]\left[-\frac{3}{2}, \infty)[/tex] comes from. It's the interval spanning from -3/2 (inclusive) to infinity. This represents the set of all possible x inputs of the first function.
--------
Follow this same idea for problem 2. The steps would be something like this:
[tex]-20x - 6 \ge 0\\\\-20x \ge 6\\\\x \le \frac{6}{-20}\\\\x \le -\frac{3}{10}\\\\[/tex]
The inequality sign flips because we divided both sides by a negative number. That then leads to the interval notation of [tex](-\infty, -\frac{3}{10}\big][/tex]
The interval spans from negative infinity (exclusive) to -3/10 (inclusive).
--------
Problem 3 would have these steps
[tex]5x-16 \ge 0\\\\5x\ge 16\\\\x\ge \frac{16}{5}\\\\\big[\frac{16}{5}, \infty)\\\\[/tex]
No sign flip happens since we divided both sides by a positive number.
--------
Lastly, here are the steps for problem 4
[tex]20+6x \ge 0\\\\6x \ge -20\\\\x \ge -\frac{20}{6}\\\\x \ge -\frac{10}{3}\\\\\big[-\frac{10}{3}, \infty)[/tex]
Don't forget to use the square bracket to include the endpoints mentioned. We always use curved parenthesis for either infinity because we can't ever reach infinity. In a sense, we "approach" infinity.
Once again, all of this is summarized in the filled out table shown below (attached image). Feel free to ask any questions if they come to mind.
Which of the following systems of linear inequalities is represented by the
solution graphed below?
O A. y>2 and ys x
O B. y22 and rex
O C. x> 2 and y2 x
O D. x22 and y > x
The solution graphed below represents the y>2 and [tex]y\leq x[/tex] system of linear inequalities.
When a polynomial of degree 1 is compared to another algebraic expression of degree less than or equal to 1, this is an example of a linear inequality, which is an inequality involving at least one linear algebraic expression.
Expressions that compare two linear expressions using inequality symbols are referred to as linear inequalities.
Addition, subtraction, multiplication, and division are the four types of operations that can be performed on linear inequalities.
Equivalent inequality refers to linear inequalities with the same solution.
From the given graph, it can be seen that the line parallel to the x-axis represents y>2 and the other inclined line represents [tex]y\leq x[/tex] .
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Find the height of the triangle by applying formulas for the area of a triangle and your knowledge about triangles.
The correct answer is 8.5 in.
What is Heron's formula in math?Heron's formula, formula credited to Heron of Alexandria for finding the area of a triangle in terms of the lengths of its sides. In symbols, if a, b, and c are the lengths of the sides: Area = Square root of√s(s - a)(s - b)(s - c) where s is half the perimeter, or (a + b + c)/2.we know that
The formula of area of triangle is equal to
[tex]A = \frac{1}{2} (b) (h)[/tex]
We have
b = BC = 6 in
h = AD = x in
substitute
[tex]A = \frac{1}{2} (6) (x)[/tex]
[tex]A = 3x^{2} in^{2} ..................(1)[/tex]
Heron's Formula is a method for calculating the area of a triangle when you know the lengths of all three sides.
Let a,b,c be the lengths of the sides of a triangle.
The area is given by:-
[tex]A = \sqrt{p(p-a) (p-b) (p-c)}[/tex] where p is half the perimeter
[tex]p = \frac{a +b+ c}{2}[/tex]
a = 9 in , b= 9 in, c = 6 in
[tex]p = \frac{9 + 9 + 6}{2} = 12 in[/tex]
Find the area
[tex]A = \sqrt{12( 12 - 9) (12-9) (12 - 6)}[/tex]
[tex]A = \sqrt{12 (3)(3)(6)}[/tex]
[tex]A = \sqrt{648}[/tex]
[tex]A = 25.46 in^{2}[/tex]
Substitute the value of the area in the equation 1 and solve for x
[tex]A = 3x in^{2}[/tex]
25.46 = 3x
x = 25.46/3
x = 8.5 in
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The complete question is -
HELP PLEASE! Find the height of the triangle by applying formulas for the area of a triangle and your knowledge about triangles.
A. 8 in.
B. 11.3 in.
C. 8.5 in.
D. 6.2 in.
Use properties to rewrite the given equation. Which equations have the same solution as 2.3p – 10.1 = 6.5p – 4 – 0.01p? Select two options. 2.3p – 10.1 = 6.4p – 4 2.3p – 10.1 = 6.49p – 4 230p – 1010 = 650p – 400 – p 23p – 101 = 65p – 40 – p 2.3p – 14.1 = 6.4p – 4
The equations have the same solution are 2.3p – 6.5p + 0.01p =– 4 + 10.1 and -4.19p = 6.1
linear equationThis are equations that has a leading degree of 1. GIven the expression as shown below
2.3p – 10.1 = 6.5p – 4 – 0.01p
Collect the like terms
2.3p – 6.5p + 0.01p =– 4 + 10.1
Simplify
-4.19p = 6.1
Hence the equations have the same solution are 2.3p – 6.5p + 0.01p =– 4 + 10.1 and -4.19p = 6.1
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A _____ is an interval estimate of an individual y value, given values of the independent variables. Group of answer choices prediction interval confidence interval interval estimation regression
A confidence interval is an interval estimate of an individual y value, given values of the independent variables.
According to statement
we have to find a interval which give an estimate of an individual y value, given values of the independent variables.
Confidence interval tells that more than just the possible range around the estimate. It also tells about how stable the estimate is. A stable estimate is one that would be close to the same value if the survey were repeated.
So, A confidence interval is an interval estimate of an individual y value, given values of the independent variables.
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Irene knows her blood type is A, but William does not know his blood type. However, William knows that his mother and father both had blood type B. Irene and William's first child is a boy with type O blood. Based on this information, William's blood type could be
Based on this information, William's blood type could be either B or O.
What is Segregation of alleles?
Allele pairs (several features of the same gene) are segregated during meiosis so that they can be transferred selectively to different gametes.During meiosis, maternal and paternal alleles separate.What is genotype vs phenotype ?
Genotype: An organism's genetic makeup. Phenotype. physical characteristic that arises within an organism as a result of its genotype. Probability law.Genotype - the set of alleles that make up an organism.How does genotype influence phenotype ?
The alleles you have for a specific gene or collection of genes are referred to as your genotype. The physical attribute itself, or phenotype, can be affected by both genotype and environmental variables.Learn more about Genotype
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volume of cylinder 8cm and 12 cm
[tex]v=\pi(8)(12)[/tex]
The volume of the cylinder is 301.593 cubic centimeter.
What is the volume of the given cylinder ?Volume exists as a scalar quantity representing the amount of three-dimensional space enclosed by a sealed surface. For example, the space that a substance or 3D shape inhabits or contains. The volume stands often quantified numerically utilizing the SI-derived unit, the cubic meter.
A cylinder contains traditionally been a three-dimensional solid, one of the most essential curvilinear geometric shapes. Geometrically, it has been regarded as a prism with a circle as its base.
The dimensions of the cylinder is given as - 8 cm and 12 cm .
The formula of the volume of the cylinder is given as -
V = π * (8) * (12)
Thus the volume is = 96π ≈ 301.593 cubic centimeter.
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Which number line represents the solution set for the inequality 3(8 – 4x) < 6(x – 5)?
A number line from negative 5 to 5 in increments of 1. An open circle is at 3 and a bold line starts at 3 and is pointing to the left.
A number line from negative 5 to 5 in increments of 1. An open circle is at 3 and a bold line starts at 3 and is pointing to the right.
A number line from negative 5 to 5 in increments of 1. An open circle is at negative 3 and a bold line starts at negative 3 and is pointing to the left.
A number line from negative 5 to 5 in increments of 1. An open circle is at negative 3 and a bold line starts at negative 3 and is pointing to the right.
The solution to the inequality is x > 3
The number line that represent the solution set will be:
A number line from negative 5 to 5 in increments of 1. An open circle is at 3 and a bold line starts at 3 and is pointing to the right. The correct option is the second option
Linear InequalitiesFrom the question, we are to determine the number line that represents the solution set for the given inequality
The given inequality is
3(8 – 4x) < 6(x – 5)
First, we will solve the inequality
3(8 – 4x) < 6(x – 5)
Clear the brackets
24 - 12x < 6x - 30
Collect like terms
24 + 30 < 6x + 12x
54 < 18x
Divide both sides by 18
3 < x
∴ x > 3
Hence, the number line that represent the solution set will be:
A number line from negative 5 to 5 in increments of 1. An open circle is at 3 and a bold line starts at 3 and is pointing to the right. The correct option is the second option
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Other than translation, what transformation is used to create this frieze pattern?
180° rotation
vertical reflection
horizontal reflection
translation
Other than translation, the transformation that is used to create this frieze pattern is; B: Vertical Reflection
How to Identify the Transformation?Now, we see all the Frieze Patterns on top are being transformed using Translation as it is the exact same pattern throughout the top.
Now, for the bottom we see that is is simply a reflection of the one on top and so it is a vertical reflection because it is reflected across the x-axis.
A vertical reflection reflects a graph vertically across the x-axis, while a horizontal reflection reflects a graph horizontally across the y-axis.
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The table represents a function.
X f(x)
-4 -2
-1 5
3 4
5 -8
What is f(5)?
-8
-1
1
8
Answer: -8
Step-by-step explanation:
When x = 5, f(x) = -8.
The value of the function f(5) = -8.
We have,
The concept used to find the value of f(5) is function evaluation.
In this case, we are given a function represented by a table with x and f(x) values.
To evaluate the function at a specific value, such as f(5), we look for the corresponding x-value in the table and determine the corresponding f(x) value.
In this example, we found that when x = 5, f(x) is -8 by looking at the table provided.
To find the value of f(5), we need to look at the table and find the corresponding value of the function when x = 5.
From the given table, when x = 5, f(x) is -8.
Therefore,
The value of the function f(5) = -8.
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please help thank you! will give brainliest!
A'(-6, -10), B'(-3, -13) and C'(-5, -1) are the vertices of the ΔA'B'C' given that the vertices of the ΔABC are A(-6, -7), B(-3, -10) and C(-5, 2) and translation rule (x, y) → (x, y-3) is applied. This can be obtained by putting coordinate values of vertices in the translation rule and then vertices of ΔA'B'C' are found.
Find the vertices of ΔA'B'C' :Given that,
In ΔABC, the vertices are A(-6, -7), B(-3, -10) and C(-5, 2)
The translation rule that must be applied is ⇒ (x, y) → (x, y-3)
By applying the translation rule to each of the vertices of ΔABC we get,
A(-6, -7) → A'(-6, -7-3) = A'(-6, -10)B(-3, -10) → B'(-3, -10-3) = B'(-3, -13)C(-5, 2) → C'(-5, 2-3) = C'(-5, -1)That is,
(-6, -7) → (-6, -10)(-3, -10) → (-3, -13)(-5, 2) → (-5, -1)These new coordinates are the vertices of ΔA'B'C'.
Hence A'(-6, -10), B'(-3, -13) and C'(-5, -1) are the vertices of the ΔA'B'C'.
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WILL MAKE BRAINLIEST!!
Solve for x.
Answer:
8
Step-by-step explanation:
51 + 4x + 7 = 90 - combine like terms
58 + 4x = 90 - subtract 58 from each side
4x = 32 - divide both sides by 4
x = 8
Answer:
x = 8
Step-by-step explanation:
The red square indicates that there is a right triangle. All right triangles have angles equal to 90°. Therefore, we can find the value of "x" by setting the sum of both the interior angles to 90°.
(4x + 7) + 51° = 90° <----- Sum of both angles is 90°
4x + 58 = 90° <----- Combine 58 and 7
4x = 32 <----- Subtract 58 from both sides
x = 8 <----- Divide both sides by 4
Lola wins $240
She spends $48 on a dress.
What percentage of the $240 has she spent?
Answer:
Step-by-step explanation:
$240 = 100
$48 = X
100 * 48 = 240X
4800 / 240 = 240X / 240
X = 20
She spent 20% on the dress
Your family is going on vacation for two nights. You don't want to spend more than $135 on a hotel room for your vacation. Write an inequality to represent how much you can spend each night on your hotel room.
Answer:
Step-by-step explanation:
$135 is less than or equal to 2 nights at the hotel (h)
135</=2h
PLS HELP AND EXPLAIN . math related
Answer:
(0,0)
Step-by-step explanation:
The y-intercept (where the graph of the equation crosses the y-axis) occurs where x = 0. If you substitute 0 for x in the equation, y = 0. So the y-intercept is at (0,0).
2. 2x+6y=6
-x-3y = -3
Solution(s):
PLEASE HELP SOLVE FOR X AND Y
Answer:
x = 0, y = 1
Step-by-step explanation:
2x + 6y = 6 → (1)
x - 3y = - 3 ( add 3y to both sides )
x = 3y - 3 → (2)
substitute x = 3y - 3 into (1)
2(3y - 3) + 6y = 6 ← distribute parenthesis and simplify left side
6y - 6 + 6y = 6
12y - 6 = 6 ( add 6 to both sides )
12y = 12 ( divide both sides by 12 )
y = 1
substitute y = 1 into (2)
x = 3(1) - 3 = 3 - 3 = 0
solution is x = 0 , y = 1
Consider an unstructured overlay network in which each node randomly chooses c neighbors. If P and Q are both neighbors of R, what is the probability that they are also neighbors of each other
The probability value become is 2c/(N-1).
According to the statement
we have given that If P and Q are both neighbors of R, and by considering unstructured network in which each node randomly chooses c neighbors.
we have to find that the probability of neighbors that they are also neighbors of each other.
So, For this purpose to find the probability is
Consider a network of N nodes unstructured and let
If each node chooses c neighbors at random,
then the probability that P will become by choose Q, or Q chooses P is roughly 2c/(N-1).
And the probability outcomes value become is 2c/(N-1).
So, The probability value become is 2c/(N-1).
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Latoya, Kevin, and Milan have a total of $117 in their wallets. Milan has 4 times what Latoya has. Latoya has $9 less than Kevin. How much do they have in
their wallets?
Answer:
Step-by-step explanation:
Let Kevin have x dollars. Then Latoya has x - 9 dollars and Milan has 4(x - 9) dollars.
x + (x-9) + 4(x-9) = 177
7x - 40 = 177
7x = 217
x = 31
Kevin has $31
Latoya has 31 - 9= $22
Milan has 4*24 = $96