"Although part of your question is missing, you might be referring to this full question: Work out the sum of the interior angles of a pentagon".
A pentagon is a polygon with five sides. We can use a formula to get the pentagon's interior angle total. According to the formula, (n-2) x 180 degrees can be used to calculate the total of any polygon's internal angles. This formula can be changed to n=5 for a pentagon, giving us (5-2) x 180 degrees = 540 degrees. Consequently, a pentagon's internal angles add up to 540 degrees.
The sum of the interior angles of a pentagon can also be computed by dividing it by the number of sides, and the result can then be subtracted from 180 degrees to determine each inner angle. So, a pentagon's internal angles are each (540/5)-180 degrees, or 108 degrees.
In conclusion, a pentagon's interior angles add up to 540 degrees, and each interior angle is 108 degrees. In order to solve mathematical problems involving polygons, it can be helpful to comprehend the formulas used to calculate these numbers.
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I will give brainliest and ratings if you get this correct
Answer:
This is the equation we have to use in order to find the eigenvalues and eigenvectors of matrix A:
det(A - λI) = 0
where λ is the eigenvalue and I is the identity matrix.
So we have:
A - λI = [ -5-λ 1 2 ]
[ 0 -2-λ 0 ]
[ 4 2 -3-λ ]
And the determinant is:
det(A - λI) = (-5-λ)(-2-λ)(-3-λ) - 8(2+λ) = -λ^3 + 4λ^2 + 23λ - 40
We can factor this to get:
det(A - λI) = -(λ - 5)(λ - 2)(λ + 4)
So the eigenvalues are λ1 = 5, λ2 = 2, and λ3 = -4.
To find the eigenvectors for each eigenvalue, we need to solve the system of linear equations:
(A - λI)x = 0
For λ1 = 5, we have:
[ -5-5 1 2 ] [ x1 ] [ 0 ]
[ 0 -2-5 0 ] [ x2 ] = [ 0 ]
[ 4 2 -3-5] [ x3 ] [ 0 ]
which simplifies to:
[ -10 1 2 ] [ x1 ] [ 0 ]
[ 0 -7 0 ] [ x2 ] = [ 0 ]
[ 4 2 -8 ] [ x3 ] [ 0 ]
We can solve this system to get:
x1 = -1/2 x2
x3 = -1/2 x2
So the eigenvector for λ1 = 5 is:
v1 = [ x1, x2, x3 ] = [ -1/2, 1, -1/2 ]
For λ2 = 2, we have:
[ -5-2 1 2 ] [ x1 ] [ 0 ]
[ 0 -2-2 0 ] [ x2 ] = [ 0 ]
[ 4 2 -3-2] [ x3 ] [ 0 ]
which simplifies to:
[ -7 1 2 ] [ x1 ] [ 0 ]
[ 0 -4 0 ] [ x2 ] = [ 0 ]
[ 4 2 -5 ] [ x3 ] [ 0 ]
We can solve this system to get:
x1 = -2/3 x2
x3 = -4/3 x2
So the eigenvector for λ2 = 2 is:
v2 = [ x1, x2, x3 ] = [ -2/3, 1, -4/3 ]
For λ3 = -4, we have:
[ -5+4 1 2 ] [ x1 ] [ 0 ]
[ 0 -2+4 0 ] [ x2 ] = [ 0 ]
[ 4 2 -3+4] [ x3 ] [ 0 ]
which simplifies to:
[ -1 1 2 ] [ x1 ] [ 0 ]
[ 0 2 0 ] [ x2 ] = [ 0 ]
[ 4 2 1 ] [ x3 ] [ 0 ]
We can solve this system to get:
x1 = -2/5 x2
x3 = 1/2 x2
So the eigenvector for λ3 = -4 is:
v3 = [ x1, x2, x3 ] = [ -2/5, 0, 1/2 ]
To determine matrix A's sign definiteness, we must compute the determinant of all of A's primary submatrices. A square submatrix generated by eliminating the equal amount of rows and columns from the top left corner of A is known as a primary submatrix.
The principal submatrices of A are:
A1 = [-5]
A2 = [ -5 1 ]
[ 0 -2 ]
A3 = [ -5 1 2 ]
[ 0 -2 0 ]
[ 4 2 -3 ]
The determinants of these matrices are:
det(A1) = -5
det(A2) = (-5)(-2) - (0)(1) = 10
det(A3) = (-5)(-2)(-3) + 2(0)(4) + (1)(0)(2) - (-3)(1)(4) - 2(0)(-5) - (-2)(2)(-5) = -92
Because A1's determinant is negative, A is not positive definite. A is not negative definite since the determinants of A1 and A2 have different signs. As a result, A is infinite.
suppose you want to double the area of the patio shown at the right. find the increase x of both the length and width of the patio
The New Area based on the information will be 168ft
How to calculate the areaExpanding the above equation, we get:
120ft² + 22x + x² = 240ft²
Rearranging and simplifying, we get:
x² + 22x - 120 = 0
Since the increase cannot be negative, we take the positive value of x:
x = 2
Therefore, the increase in both the length and width of the patio should be 2ft to double its area.
New Length = 10ft + 2ft = 12ft
New Width = 12ft + 2ft = 14ft
New Area = 12ft x 14ft = 168ft²
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A pool measuring 18 meters by 30 meters is surrounded by a path of uniform width, as shown in the
figure. If the area of the pool and the path combined is 1900 square meters, what is the width of
the path?
Answer: 3 meters
Step-by-step explanation:
The area of the rectangular region is given by:
(18 + 2x) * (30 + 2x) = 18*30 + 36x + 60x + 4x^2
Simplifying this expression, we get:
4x^2 + 96x - 1300 = 0
Dividing both sides by 4, we get:
x^2 + 24x - 325 = 0
Now we can solve for x using the quadratic formula:
x = (-b ± sqrt(b^2 - 4ac)) / 2a
where a = 1, b = 24, and c = -325.
Plugging in these values, we get:
x = (-24 ± sqrt(24^2 - 4(1)(-325))) / 2(1)
x = (-24 ± sqrt(936)) / 2
x = (-24 ± 30) / 2
x = 3 or -27
Since the width of the path cannot be negative, the only possible solution is x = 3 meters. Therefore, the width of the path surrounding the pool is 3 meters.
Determine the volume of the "leaning" regular hexagonal prism.
It has a base perimeter of 36 inches, a slanted height of 11 inches, and is leaning at
70°. The base is a regular hexagon with a perimeter of 36 inches.
6.70%
11"
The volume of the leaning regular hexagonal prism, can be found to be 351. 89 inch ³.
How to find the volume ?A right triangle can be constructed in a regular hexagon by linking the midpoint of one side and a vertex to the center. This specially-crafted triangle comprises two legs, one of which is half the size of the primary side (acting as the hypotenuse) while the remaining leg lies parallel to the hexagon's apothem (height).
The height of the prism can be found with cosine to be:
h = slanted height x Cos (angle )
h = 11 x Cos ( 70 degrees )
h = 3. 762 inches
We can then find the volume of the leaning hexagonal prism to be:
= Area x Height
= 93. 528 x 3. 762
= 351. 89 inch ³
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a rectangle has a perimeter of 48 in. the length and width are scaled by a factor of 2.5. what is the perimeter of the resulting rectangle?
The calculated value of the perimeter of the scaled rectangle is 120 inches
Calculating the perimeter of the scaled rectangleFrom the question, we have the following parameters that can be used in our computation:
Perimeter = 48 in
Scale factor = 2.5
Using the above as a guide, we have the following:
Perimeter of the scaled rectangle = Perimeter * Scale factor
Substitute the known values in the above equation
Perimeter of the scaled rectangle = 48 * 2.5
Evaluate
Perimeter of the scaled rectangle = 120
Hence, the perimeter of the scaled rectangle is 120
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URGENT HELP PLEASE PLEASE CAN YOU HELP
Answer:
1/2
Step-by-step explanation:
Let's check if this is a positive of negative slope. Remember that when checking slope, you need to read the graph from left to right.
So let's see: When we look at the graph from left to right, is it moving up or down?
It is moving up, correct!
Therfore, this must be a positive slope.
Ok, now we need to pick 2 points.
I will choose: ( 6 , 0 ) & ( 2 , -2 )
To move between those pouints, we need to move up 2 and 4 units to the right.
Slope is defined as:
Change is y over change in x
Change in y is positive 2
Change in x is positive 2
Therfore, slope is [tex]\frac{2}{4}[/tex]
or, 1/2
8) Elana's Math Class has 24 students. She miscounted the class total and
recorded it as 21 students. What is her percent error?
what us the rate of change in the value of one share of company’s stock, in dollars per day, from Day 0 to Day 15
Check the picture below.
the slope goes by several names
• average rate of change
• rate of change
• deltaY over deltaX
• Δy over Δx
• rise over run
• gradient
• constant of proportionality
however, is the same cat wearing different costumes.
[tex]\begin{array}{llll} f(x)~from\\\\ x_1 ~~ to ~~ x_2 \end{array}~\hfill slope = m \implies \cfrac{ \stackrel{rise}{f(x_2) - f(x_1)}}{ \underset{run}{x_2 - x_1}}\impliedby \begin{array}{llll} average~rate\\ of~change \end{array} \\\\[-0.35em] ~\dotfill\\\\ \begin{cases} x_1=0\\ x_2=15 \end{cases}\implies \cfrac{f(15)-f(0)}{15 - 0}\implies \cfrac{11-5}{15}\implies \cfrac{6}{15}\implies \cfrac{2}{5}[/tex]
Convert 8 5/8 to a decimal. Show your work.
Answer: 8.625
Step-by-step explanation:The eight stays an 8 snd 5:8 is .625. Add these together and you get 8.625.
The table shown represents a proportional realshipbship between a and b. Form an equation that represents the relationship between a and b and identify the constant of proportionality. Write your answer in the space provided
Answer:
y=3x
Step-by-step explanation:
y=kx
21/7=3
15/5=3
6/2=3
Each relationship in the table has a constant of proportionality of 3.
Find the surface area of a cube with edges 6.44 cm long.
Answer:
Step-by-step explanation:
The surface area of a cube is given by the formula:
SA = 6s^2
where s is the length of an edge.
Substituting s = 6.44 cm into the formula, we get:
SA = 6(6.44 cm)^2
SA = 6(41.4736 cm^2)
SA = 248.8416 cm^2
Therefore, the surface area of the cube is 248.8416 cm^2.
|y-x| if y>x Write each of the following expressions without using the absolute value
The solution of the expression is; |y-x| = y - x without using absolute value.
What is mean by expression?Numerical articulation is characterized as the assortment of the numbers factors and works by utilizing tasks like expansion, deduction, increase, and division.
Given that;
from the question the expression is;
⇒ |y−x| , if y > x
⇒ If y > x,
⇒ y - x > 0
then |y-x| is equal to (y-x),
since (y-x) is always positive in this case.
Therefore, The solution of the expression is; |y-x| = y - x
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Danielle likes to purchase items at estate sales, clean them up, then resale them online for a profit. She recently purchased an antique dresser with a mirror at an estate sale, cleaned it up, and advertised it for 250% of her purchase price. Danielle sold the dresser for $255, which was 15% less than the advertised price.
To the nearest whole dollar, how much did Danielle purchase the antique dresser for and what was her initial advertised price?
A. purchase price: $120, advertised price: $300
B. purchase price: $108, advertised price: $270
C. purchase price: $130, advertised price: $325
D. purchase price: $117, advertised price: $293
Answer:
The correct answer is D. purchase price: $117, advertised price: $293.
Step-by-step explanation:
Writing a function rule given a table of ordered pairs. A table of values of a linear function is shown below. Find the output when the input is n. Type your answer in the space provided.
The output for an input of n is given as follows:
f(n) = -4 - 2n.
How to define a linear function?The slope-intercept representation of a linear function is given by the equation presented as follows:
y = mx + b
The coefficients of the function and their meaning are described as follows:
m is the slope of the function, representing the change in the output variable y when the input variable x is increased by one.b is the y-intercept of the function, which is the initial value of the function, i.e., the numeric value of the function when the input variable x assumes a value of 0. On a graph, it is the value of y when the graph of the function crosses the y-axis.For this problem, we have that when x increases by one, y decays by two, hence the slope m is given as follows:
m = -2.
Hence:
f(n) = -2n + b.
When n = 1, f(n) = -6, hence the intercept b is obtained as follows:
-6 = -2 + b
b = -4.
Hence the equation is:
f(n) = -2n - 4.
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In a particular class of 29 students, 11 are men. What fraction of the students in the class are women?
Answer:
Step-by-step explanation:
Q:
In a particular class of 29 students, 11 are men. What fraction of the students in the class are women?
A:
29-11=18
18/29 are women
A(n) __________ is an amount returned after purchase or deducted from the purchase price.
Step-by-step explanation:
A(n) discount is an amount returned after purchase or deducted from the purchase price.
adam bought a skateboard that is on sale for 35% off. the original cost is $150. what is the sale price? show your work
Answer:
$97.50
Step-by-step explanation:
Purchase Price:
$150
Discount:
(150 x 35)/100 = $52.50
Final Price:
150 - 52.50 = $97.50
Determine whether the equation has no solution, one solution, or infinitely many solutions. -2 ( 11 - 12x )= -4 ( 1 - 6x) Explain your conclusion. Enter your answer, your work, and your explanation in the box provided.
Answer:
No solution
Step-by-step explanation:
-2(11-12x) = -4(1-6x)
Distribute the -2 and -4:
-22 + 24x = -4 + 24x
Subtract 24x from both sides:
-22 = -4
Since this is a contradiction, there is no solution. The equation is inconsistent.
Answer:
No Solution.
Explanation:
When solving for x, the two values do not equate to each other.
Hailey goes to a store an buys an item that costs a dollars. She has a coupon for 35%
off, and then a 8% tax is added to the discounted price. Write an expression in terms
of a that represents the total amount that Hailey paid at the register.
Hailey goes to a store an buys an item that price of a dollars, so the expression that represents the total amount that Hailey paid at the register in terms of a is 0.702a.
The amount of discount that Hailey receives is 35% of the original price, which is 0.35a. Therefore, the discounted price she pays is a - 0.35a = 0.65a.
The amount of tax that is added to the discounted price is 8% of the discounted price, which is 0.08(0.65a) = 0.052a.
So the total amount that Hailey paid at the register is the discounted price plus the tax:
total amount = discounted price + tax
total amount = 0.65a + 0.052a
Simplifying this expression, we get:
total amount = 0.702a
Therefore, the expression that represents the total amount that Hailey paid at the register in terms of a is 0.702a.
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Need help please !!
Geometry
Answer:
complementary since the angles sum up to 90
You have a choice of receiving a wage of $34,000 per year, $2840 per month, $650 per week, or $18 per hour. Which pay choice would you take? Assume a 40-hour work week with 52 weeks per year.
Based on calculation, the highest hourly wage is $2,840 per month which gives us $17.75 per hour.
Which pay choice is the best choice take?For purpose of making a comparison, we can calculate the hourly wage for each option.
Hourly wage for $34,000 per year:
= $34,000 / (40 hours per week * 52 weeks per year)
= 16.3461538
= $16.35 per hour.
Hourly wage for $2,840 per month:
= $2,840 / (4 weeks per month * 40 hours per week)
= $17.75 per hour
Hourly wage for $650 per week:
= $650 / 40 hours per week
= $16.25 per hour
Hourly wage for $18 per hour.
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Calculator The diameter of a ball is 9 in. What is the volume of the ball? Use 3.14 for pi. Enter your answer as a decimal in the box. Round only your final answer to the nearest hundredth. in³
To find the volume of a ball, we use the formula V = (4/3)πr³, where r is the radius of the ball. We are given the diameter of the ball, which is 9 inches.
The radius of the ball is half of the diameter, so
r = 9/2 = 4.5 inches.
Substituting this value of r in the formula, we get:
V = (4/3)π(4.5)³V = (4/3)π(91.125)V = 4.1888 × 91.125V ≈ 381.71
Therefore, the volume of the ball is approximately 381.71 cubic inches.
When rounded to the nearest hundredth, the answer is 381.71.
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What is the end behavior of the function f of x equals negative 2 times the cube root of x?
What is the end behavior of the function f of x equals negative 2 times the cube root of x?
As x → –∞, f(x) → 0, and as x → ∞, f(x) → 0.
As x → 0, f(x) → –∞, and as x → ∞, f(x) → 0.
As x → ∞, f(x) → ∞, and as x → –∞, f(x) → –∞.
As x → –∞, f(x) → ∞, and as x → ∞, f(x) → –∞.
The end behavior of the given function is As x → –∞, f(x) → –∞, and as x → ∞, f(x) → –∞.
What is end behavior of function?The term "end behavior" describes the behaviour or trend of a function's graph as its x-values go closer to positive or negative infinity. It explains how the function "ends" or acts when x is extremely large (positive infinity) or extremely small (negative infinity). The degree and leading coefficient of the polynomial formulation of the function can be used to predict the final behaviour. For instance, the left and right ends of the graph will both point upward for a function with an odd-degree polynomial and a positive leading coefficient (towards positive infinity).
For the function f(x) = -2∛x as x approaches negative infinity because the function has a negative coefficient in front of the cube root, which means that as x decreases significantly, the absolute value of the cube root increases. The function also approaches negative infinity as x approaches very big (positive) values and the cube root approaches very small absolute values. As a result, the function's final behaviour is that it approaches negative infinity as x gets closer to both negative and positive infinity.
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The end behavior of the given function is As x → –∞, f(x) → –∞, and as x → ∞, f(x) → –∞.
What is end behavior of function?The term "end behavior" describes the behaviour or trend of a function's graph as its x-values go closer to positive or negative infinity. It explains how the function "ends" or acts when x is extremely large (positive infinity) or extremely small (negative infinity). The degree and leading coefficient of the polynomial formulation of the function can be used to predict the final behaviour. For instance, the left and right ends of the graph will both point upward for a function with an odd-degree polynomial and a positive leading coefficient (towards positive infinity).
For the function f(x) = -2∛x as x approaches negative infinity because the function has a negative coefficient in front of the cube root, which means that as x decreases significantly, the absolute value of the cube root increases. The function also approaches negative infinity as x approaches very big (positive) values and the cube root approaches very small absolute values. As a result, the function's final behaviour is that it approaches negative infinity as x gets closer to both negative and positive infinity.
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Answer:
The function f(x) = -2∛x represents a cube root function that is multiplied by -2.
As x approaches negative infinity, the cube root of x becomes more negative, and when it is multiplied by -2, it becomes more positive. Therefore, as x → –∞, f(x) → ∞.
As x approaches positive infinity, the cube root of x becomes more positive, and when it is multiplied by -2, it becomes more negative. Therefore, as x → ∞, f(x) → –∞.
Therefore, the correct answer is: As x → –∞, f(x) → ∞, and as x → ∞, f(x) → –∞. D.
Answer:
The function f(x) = -2∛x represents a cube root function that is multiplied by -2.
As x approaches negative infinity, the cube root of x becomes more negative, and when it is multiplied by -2, it becomes more positive. Therefore, as x → –∞, f(x) → ∞.
As x approaches positive infinity, the cube root of x becomes more positive, and when it is multiplied by -2, it becomes more negative. Therefore, as x → ∞, f(x) → –∞.
Therefore, the correct answer is: As x → –∞, f(x) → ∞, and as x → ∞, f(x) → –∞. D.
Quadrilateral CDEF is inscribed in circle A.
If m∠CFE = (2x + 6)° and m∠CDE = (2x − 2)°, what is the value of x?
22
44
46
89
The quadrilateral is inscribed inside the circle and x = 44
Given data ,
Let the quadrilateral be inscribed inside the circle as shown in the figure
Now , the measure of angles are
m∠CFE = (2x + 6)°
m∠CDE = (2x − 2)°
And , opposite sides of the angles of quadrilateral are supplementary
So , m∠CFE + m∠CDE = 180°
On simplifying , we get
2x + 6 + 2x - 2 = 180
4x + 4 = 180
4x = 176
x = 44
Hence , the angle is solved and x = 44
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The complete question is attached below :
Quadrilateral CDEF is inscribed in circle A.
If m∠CFE = (2x + 6)° and m∠CDE = (2x − 2)°, what is the value of x?
A) 22
B) 44
C) 46
D) 89
Answer: 44
Step-by-step explanation:
i took the test
Indirect measurement, pls help, I am stuck on this question.
The building is, 246 feet tall.
Since, We know that;
Two or more triangles will always be referred to as similar if on comparing their corresponding properties, some common relations holds. Some of the relations are relations between their length of sides, relations among their internal angles etc.
To determine the height of the building, we have;
height of pole = 7 ft
total length of the building's shadow = 167 ft
the length of the shadow of the pole = 4.75 ft
Let the height of the building be represented by h. On comparison, we have;
4.75/ 167 = 7/h
4.75h = 167 x 7
= 1169
h = 1169/ 4.75
h = 246.11
Hence, The building is 246 ft. tall.
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In triangle ABC, a=6, b=7, and cos C=1/4 A.) Find the exact area of the triangle. B.) Find C C.) Find sin A in simplest radical form.
A.) Area = (1/2) × 7 × 6 × √(15)/4 = 21√(15)/4
B.) Angle C is 75 degrees.
C.) Sin(A) is 3√(255)/85 in simplest radical form.
What is trigonometry?Trigonometry is a branch of mathematics that examines triangle-related relationships and calculations, particularly the measurement of triangle sides and angles.
A.) We can apply the following formula to determine the triangle's area:
Area = (1/2) × b × a × sin(C)
Since we know b=7 and a=6, we have:
Area = (1/2) × 7 × 6 × sin(C)
To find sin(C), we can use the fact that cos(C) = 1/4 and the Pythagorean identity:
sin²(C) + cos²(C) = 1
sin(C) = √(1 - cos²(C)) = √(1 - 1/16) = √(15/16) = √(15)/4
B.) To find C, we can use the Law of Cosines:
c² = a² + b² - 2ab×cos(C)
c² = 6² + 7² - 2(6)(7)(1/4) = 85/2
c = √(85)/2
Now we can use the Law of Cosines again to find angle C:
cos(C) = (a² + b² - c²)/(2ab)
cos(C) = (6² + 7² - (√(85)/2)²)/(267) = 1/4
C.) To find sin(A), we can use the Law of Sines:
sin(A)/a = sin(C)/c
sin(A) = asin(C)/c = 6(√(15)/4)/(√(85)/2) = 3×√(15)/√(85) = √(255)/85
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A data set of the least purchased menu items at a bakery is best shown as a _____
Answer:
A data set of the least purchased menu items at a bakery is best shown as a (Report)
Step-by-step explanation:
Have A Good Day :)
LMNP is rotated 180° clockwise about the origin.
L 0.1
m 3,4
N 5.4
P 9.0
What are the coordinates of N.
Consider the quadratic equation x2 + 9x + 10 = 0. Which of the following is the correct form after substituting a, b, and c into the
Quadratic Formula?
a) Find the mean and median of the following gasoline prices per gallon in California:
regular:
$
3.14
$3.14, mid-grade:
$
3.21
$3.21, premium:
$
3.28
$3.28, diesel:
$
3.53
$3.53. Round to the nearest cent.
The calculated median and the mean gasoline prices per gallon in California are 3.25 and 4.49, respectively
Finding the median and the mean gasoline prices per gallon in California:From the question, we have the following parameters that can be used in our computation:
Prices = 3.14, 3.21, 3.28, 3.53
Start by sorting the number of prices in ascending order
So, we have
3.14, 3.21, 3.28, 3.53
As a general rule.
The median is the middle number
Using the above as a guide, we have the following:
Median = middle number = 1/2 *(3.21 + 3.28)
Evaluate
Median = middle number = 3.25
For the mean, we have
Mean = (3.14 + 3.21 + 3.28 + 3.53)/3
Evaluate
Mean = 4.49
Hence, the value of the median is 3.25
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