Answer:
18gall
Step-by-step explanation:
In a word processing document or on a separate piece of paper, use the guide to construct a two column proof proving AC > EF, given BC = EF. Upload the entire proof below.
Given:
BC = EF
Prove:
AC > EF
STATMENT REASON
1. 1.
2. 2. Betweenness
3. AC > BC 3.
4. 4.
The given information and the transitive property of inequalities, we can prove that [tex]AC[/tex] is greater than [tex]EF[/tex] .
What is the transitive property of inequalities?Statement Reason
[tex]BC = EF[/tex] Given
Betweenness Given
[tex]AC > BC[/tex] Given
[tex]AC > EF[/tex] Transitive property [tex](3, 1)[/tex]
Explanation:
[tex]BC = EF[/tex] Given: Given statement that BC is equal to EF.
Betweenness Given: Given statement that states the concept of betweenness, where BC is between AC and EF.
AC > BC Given: Given statement that [tex]AC[/tex] is greater than BC.
[tex]AC > EF[/tex] Transitive property: Using the transitive property, we can conclude that [tex]AC[/tex] is greater than EF (based on statement 3 and 1).
Therefore, using the given information and the transitive property of inequalities, we can prove that AC is greater than [tex]EF[/tex] .
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PLEASE HELP FAST 35 POINTS
calculate (p o q) (0)
0 is the value of (p o q) (0) in function .
What are functions in mathematics?
Function, in mathematics, a formula, rule, or law that defines the relationship between one variable (the independent variable) and another (the dependent variable).
Functions are ubiquitous in mathematics and essential in the natural sciences for formulating physical relationships. A function is a relationship between inputs, with each input associated with exactly one output. Each function has a domain and a codomain or scope.
P(0) = 0
Q(0) = - 1
(P o q)(0) = P(0) * Q(0)
= 0 * - 1
= 0
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Find a formula for the exponential function passing through the points
(-3, 5/8 ) and (3, 40).
The exponential function is y=5.[tex]2^x[/tex].
What is exponential function?
A mathematical function called an exponential function is employed frequently in everyday life. It is mostly used to compute investments, model populations, determine exponential decline or exponential growth, and so forth.
Here the exponential function is [tex]y=ab^x[/tex]
Since (-3,5/8) is on the graph, -[tex]\frac{5}{8}[/tex]=[tex]ab^{-3}[/tex] -----> 1
Since (3, 40) is on the graph, 40=[tex]ab^3[/tex] ------> 2
So, [tex]\frac{ab^3}{ab^{-3}}=\frac{40}{\frac{-5}{8}}[/tex]
=> [tex]b^{3+3}=8\times8[/tex]
=> [tex]b^6=2^6[/tex]
=> b = 2
put b=2 into 2 then,
=> 40= [tex]a\times2^3[/tex]
=> 8a=40
=> a =5
Then the exponential function is y=5.[tex]2^x[/tex].
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The area of a rectangle gets reduced by 9 square units if its length is reduced by 5 units and the breadth is increased by 3 units. If we increase the length by 3 units and breadth by 2 units, th
e area is increased by 67 square units. Find the length and breadth of the rectangle.
Answer:
length = 17; breadth = 9
Step-by-step explanation:
Let x = area of rectangle; a = length; b = breadth.
+) a × b = x (1)
+) (a - 5) × (b + 3) = x - 9 => x = ab + 3a - 5b - 15 + 9 (2)
+) (a + 3) × (b + 2) = x + 67 => x = ab + 2a + 3b + 6 - 67 (3)
Replace (1) into (2) & (3):
[tex]\left \{ {{3a - 5b=6} \atop {2a+3b=61}} \right. = > \left \{ {{a=17} \atop {b=9}} \right.[/tex]
A fruit basket contains 12 apples and 7 pears. How many pears do you need to add to the basket to make the ratio of apples to pears as 2:3?
Answer:
35 pears
Step-by-step explanation:
To make the ratio of apples to pears in the fruit basket 2:3, we need to find out how many pears we need to add.
The current ratio of apples to pears is 12:7. To make it 2:3, we need to multiply both sides of the ratio by a common factor that will transform 12 into 2 and 7 into 3.
Let's find that common factor:
12 : 2 = 6
7 : 3 = 2.333...
Since 12 can be transformed into 2 by dividing by 6, and 7 can be transformed into 3 by multiplying by 2, the common factor is 6.
Now, let's multiply both sides of the original ratio by 6:
12 * 6 : 7 * 6 = 72 : 42
So, the ratio of apples to pears after adding the appropriate number of pears to the basket to make it 2:3 would be 72:42.
To find out how many pears we need to add, we can subtract the current number of pears (7) from the desired number of pears (42):
42 - 7 = 35
Therefore, we need to add 35 pears to the basket to make the ratio of apples to pears 2:3.
I need this by today at 11:59 PM please help.
From given sample space, No. of toothpicks each student will get is 51.
What exactly is a sample space?
In mathematics, a sample space is the set of all possible outcomes of an experiment or a random phenomenon. It is denoted by the symbol "S" and is a fundamental concept used in calculating probabilities. For example, when flipping a coin, the sample space is {heads, tails}. When rolling a fair six-sided die, the sample space is {1, 2, 3, 4, 5, 6}. The sample space for a more complex event may involve multiple variables and outcomes.
Now,
Total Toothpicks = 918
Total students = 18
then
Toothpicks per student = 918/18=51
Hence,
No. of toothpicks each student will get is 51.
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[4x2+(5+1)]÷2 can I please get help :)
6. center (-2, 8), tangent to y = -4
The radius of the circle is 12, and the equation of the circle is:
(x + 2)² + (y - 8)² = 144
What is a circle?
It is the center of an equidistant point drawn from the center. The radius of a circle is the distance between the center and the circumference.
To find the equation of a circle that is tangent to a horizontal line at a given point, we can use the standard form of the equation of a circle:
(x - h)² + (y - k)² = r²
where (h, k) is the center of the circle and r is the radius.
In this case, the center of the circle is (-2, 8), which gives us:
(x + 2)² + (y - 8)² = r²
To find the radius, we need to know where the circle intersects the y = -4 line. Since the circle is tangent to the line, the distance from the center of the circle to the line is equal to the radius.
The distance between a point (x, y) and a horizontal line y = k is given by |y - k|.
In this case, the distance between the center (-2, 8) and the line y = -4 is |8 - (-4)| = 12.
Therefore, the radius of the circle is 12, and the equation of the circle is:
(x + 2)² + (y - 8)² = 144
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Complete question:
What is the center at (-2, 8), tangent to the line y = -4?
What was the mean number of goals scored?
Answer:
2.5 goals/game
Step-by-step explanation:
In order to find the mean we need to find the total of numbers and then divide them by the amount we have.
0,0,1,1,3,3,3,4,5,5
If you add these numbers together you get 25, if you divide 25 by ten then you end up with 2.5
A satellite calculates the distances and angle shown in the figure below (not to scale).Find the distance between the two cities. Round to the nearest tenth.
The distance between city A and city B is approximately 442.3 km.
What is the law of cosine?
The Law of Cosines, also known as the Cosine Rule, is a mathematical formula that relates the lengths of the sides of a triangle to the cosine of one of its angles. Specifically, it states that:
c² = a² + b² - 2ab cos(C).
We can use the Law of Cosines to find the distance between City A and City B. Let's call this distance d.
From the information given, we know that:
The distance between the satellite and city A is 450 km.
The distance between the satellite and city B is 340 km.
The angle between city A, the satellite, and city B is 1.5 degrees.
Using the Law of Cosines, we have:
d² = 450² + 340² - 2(450)(340)cos(1.5)
d² = 202500 + 115600 - 2(450)(340)cos(1.5)
d² = 318100 - 122328.8
d² = 195771.2
d = √195771.2
d ≈ 442.3
Therefore, the distance between city A and city B is approximately 442.3 km (rounded to the nearest tenth).
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We have 2 squares. One square is shaded 2/12 and the other shaded square in the diagram is 2/15 shaded. How much of the total diagram is shaded?
A.0.148
B.0.148 repeated
C. 0.3
D.0.3 repeated
The correct answer is C. 0.3, which is equivalent to 3/10.
What are fractions?
A fraction is a mathematical representation of a quantity that expresses a part of a whole or a ratio between two quantities.
To find the total fraction of the diagram that is shaded, we need to add the fractions representing the shaded areas of the two squares.
Given that one square is shaded 2/12 and the other shaded square is 2/15, we can add these fractions:
2/12 + 2/15
To add fractions, we need to find a common denominator. The least common multiple (LCM) of 12 and 15 is 60, so we can use 60 as the common denominator for both fractions:
(2/12) + (2/15) = (2/12) * (5/5) + (2/15) * (4/4)
= 10/60 + 8/60
Now we can add the numerators:
= (10 + 8)/60
= 18/60
= 3/10
So, the total fraction of the diagram that is shaded is 3/10.
Hence, the correct answer is C. 0.3, which is equivalent to 3/10.
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Briana helps her mother make a quilt The quilt is 6 feet wide and 12 feet long
Briana and her mother will need to measure and cut the fabric for the quilt. They will need to decide on a pattern and color scheme for the quilt. They will need to sew the pieces of fabric together to create the quilt top. They will need to layer the quilt top with batting and backing fabric and then quilt the layers together. Finally, they will need to bind the edges of the quilt.
Please help I’m confused
The intersection points in the function is (-4, 61)
What is the points of intersection to the functionTo find the intersection points of two functions, we can set them equal to each other and solve for x. Substituting x = -4, we have:
4(-4)² + 3(-4) + 3 = (-4)³ + 7(-4)² - 3(-4) + d
Simplifying, we get:
64 - 12 + 3 = -64 + 112 + 12 + d
d = -77
So the two functions intersect at x = -4 and y = 61. Therefore, the only intersection point is (-4, 61).
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Use custom relationships to create a graph, showing the solution region of the system of inequalities, representing the constraints of the situation. Did Mark and label it point represents a viable combination of guest School district is planning a banquet to honor his teacher of the year and raise money for the scholarship foundation. The budget to hold the banquet in a hotel room and miles is $3375 the venue can hold no more than 125 guest the cost is $45 per adult but only $15 per student because caterer offers a student discount discount
We can label the point (75, 50) as the optimal solution for the banquet, as it represents the maximum number of guests that can be invited while staying within the constraints.
What is banquet?
A banquet is a large formal meal that usually involves multiple courses and is served to a group of people on special occasions such as weddings, awards ceremonies, or fundraising events. Banquets often include speeches, presentations, and entertainment, and are typically held in a large venue such as a hotel ballroom, banquet hall, or conference center. Banquets can be hosted for a variety of purposes, such as to honor a special guest, celebrate an achievement, or raise money for a charitable cause.
To create a graph showing the solution region of the system of inequalities representing the constraints of the situation, we can use custom relationships to define the variables and constraints.
Let's define the variables:
Let x be the number of adult guests.
Let y be the number of student guests.
Now, let's write the system of inequalities representing the constraints of the situation:
The total number of guests cannot exceed 125: x + y ≤ 125
The cost of hosting the banquet cannot exceed $3375: 45x + 15y ≤ 3375
To graph this system of inequalities, we can plot the boundary lines of each inequality and shade the region that satisfies all the constraints.
The boundary lines of each inequality are:
x + y = 125 (the line that connects the points (0, 125) and (125, 0))
45x + 15y = 3375 (the line that connects the points (0, 225) and (75, 0))
To find the viable combinations of guests that satisfy all the constraints, we need to shade the region that is below the line x + y = 125 and to the left of the line 45x + 15y = 3375.
The resulting graph should look like this:
The point where the two lines intersect, (75, 50), represents the maximum number of adult guests (75) and the maximum number of student guests (50) that can be invited to the banquet while staying within the budget and venue capacity. Any point within the shaded region represents a viable combination of guests.
We can label the point (75, 50) as the optimal solution for the banquet, as it represents the maximum number of guests that can be invited while staying within the constraints.
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the difference of 25 and a number?
Answer: 30 and 5
Step-by-step explanation:
if h(x) =x+2/x-2, then dy/dx= ?
Answer: To find the derivative of the function h(x), we can use the quotient rule, which states that if f(x) = u(x) / v(x), then f'(x) = [v(x)u'(x) - u(x)v'(x)] / [v(x)]^2.
Using this rule, we can find the derivative of h(x) as follows:
h(x) = (x + 2) / (x - 2)
h'(x) = [(x - 2)(1) - (x + 2)(1)] / (x - 2)^2 // apply the quotient rule and differentiate numerator and denominator
h'(x) = (-2 - 2x) / (x - 2)^2
Therefore, the derivative of h(x) is h'(x) = (-2 - 2x) / (x - 2)^2.
Step-by-step explanation:
A four-sided shape with the top side labeled as 10.2 cm. The height is labeled 5 cm. A portion of the base from the perpendicular to a vertex is labeled 4 cm. The portion of the base from the perpendicular to the right vertex is 6.2 cm.
What is the area of the figure?
25.5 cm2
45.5 cm2
51 cm2
56.1 cm2
The area of the figure is 51 cm², which is option C.
What is area?In mathematics, area refers to the measure of the size of a two-dimensional surface or shape. It is typically expressed in square units, such as square meters (m²) or square centimeters (cm²), and can be calculated for a variety of geometric shapes, including squares, rectangles, triangles, circles, and more complex shapes such as trapezoids or polygons.
To find the area of the figure, we need to identify the shape of the figure. From the given information, we know that the figure has a top side, a height, and a base. We are also told that the base is divided into two parts by a perpendicular, and one of the parts is labeled as 4 cm, while the other part from the perpendicular to the right vertex is 6.2 cm.
Based on this information, we can draw the figure as a trapezoid, where the top side is the shorter base, the height is the vertical distance between the two bases, and the longer base is the sum of the two parts of the base.
Using the given information, we can calculate the longer base:
longer base = 4 cm + 6.2 cm = 10.2 cm
Now we can use the formula for the area of a trapezoid to find the area of the figure:
A = (1/2)h(b₁ + b₂)
where h is the height, b₁ is the shorter base, and b₂ is the longer base.
Plugging in the given values, we get:
A = (1/2)(5 cm)(10.2 cm + 10.2 cm) = 51 cm²
Therefore, the area of the figure is 51 cm² , which is option C.
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Complete Question:
A four-sided figure has one side labeled 10.2 cm, a height of 5 cm, and a portion of the base from the perpendicular to a vertex labeled 4 cm. The portion of the base from the perpendicular to the right vertex is labeled 6.2 cm. What is the area of the figure?
If PQRS is a rectangle, PR = 9x + 1, and QS = 13x - 11, find TR. (TR is half of the PR bisecter)
Answer: the length of TR is 24.5.
Step-by-step explanation: 9x + 1 = 13x - 11
22 = 4x
x = 5.5
Presently that we know x, ready to discover the values of PR and QS:
PR = 9x + 1 = 9(5.5) + 1 = 49
QS = 13x - 11 = 13(5.5) - 11 = 56
Since TR is half of the PR bisector, ready to discover it by separating PR by 2:
TR = PR/2 = 49/2 = 24.5
A piano has a ratio of 6 black keys for every 15 white keys. Write a ratio to represent the ratio of white keys to black keys.
15 to 6
six over fifteen
6:15
15:21
Answer:
The answer is 15:6 or 15 to 6
Step-by-step explanation:
white=15
black=6
white ratio black
15:6
Which expression represents the phrase The product of a number and ten decreased by eight.
A. n -8 x 10
B. 8n -10
C. 10xn8
D. 10n - 8
The statement "The product of a number and ten decreased by eight" is represented by the correct equation D. 10n - 8.
What is a number's product?A number's product is the outcome of multiplying it by another number.
What additional mathematical expressions are there?Addition, subtraction, multiplication, division, exponents, and square roots are some other examples of mathematical expressions.
What is an exponent?A mathematical action known as an exponent symbolizes the repeated multiplication of the same integer. It is represented by a tiny number above and to the right of a base number.
For instance, 23 signifies that the number 2 has been multiplied three times, for a result of 8.
The sentence "The product of a number and ten decreased by eight" is correctly expressed as D. 10n - 8.
With this formula, a number is multiplied by 10 first, and the result is then reduced by 8.
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14 points!! PLEASE HELP MARKING BRAINLIST
Answer:
x = 58.03°
Step-by-step explanation:
Given:
17 cm is the length of the hypotenuse9 cm is the length of the adjacent sideSolve for x:
cos x = adjacent / hypotenusex = [tex]cos^{-1}(\frac{adjacent}{hypotenuse})[/tex]1. [tex]x=cos^{-1}(\frac{9}{17})=58.03[/tex]
Answer:
So, the measure of angle x is equal to 58.03.
A savings account starts with $312.50. After 9 years of continuous compounding at an interest rate, r, the account has $1250.
What is the interest rate percentage?
Round the answer to the nearest hundredth.
someone said it was 10.98% but i submitted that and it said it was wrong so i do not know
Okay, let's walk through this step-by-step:
The initial balance of the savings account: $312.50
The final balance after 9 years: $1250
Let's call the interest rate r.
We know the final balance is the initial balance times (1 + r)^9
(because of continuous compounding over 9 years)
So:
312.50 = (1 + r)^9
312.50 / (1 + r)^9 = 1250
Solving for r:
(312.50 / 1250)^(1/9) = 1 + r
0.2504 = 1 + r
0.7596 = r
Converting to a percentage:
0.7596 * 100% = 75.96%
Rounding to the nearest whole percent: 76%
So the interest rate is 76%.
Does this make sense? Let me know if you have any other questions!
PLEASE HELP!!!! Luke is training for a long-distance bike race. On Tuesday, after riding for 1 hour, he has travelled 5 miles along a straight highway. After 3 hours, he has travelled 17 miles. Write the equation of the line that models Luke’s bike ride. What does the x represent? What does the y represent?
Answer: y=6x-1
Step-by-step explanation:
y=6x-1
x represents the time luke has been riding(hours) and the y represents the distance he has travelled (miles)
You survey students in your class about the number of movies they watched last month. The results are shown in the table.
Required frequency table is
Movie Number of students
1) Action 6
2) Comedy 4
3) Horror 7
4) Drama 5
5) Romance 8
What is frequency table?
A frequency table is a statistical tool used to organize data by counting the number of occurrences of each unique item or value in a dataset. It is a way to summarize and present data in a concise and structured manner, making it easier to understand and analyze.
For example, if you have a dataset of students' grades, you can create a frequency table by listing all the possible grades (e.g., A, B, C, D, F) and counting how many times each grade appears in the dataset. The resulting table will show the frequency or number of times each grade was earned by the students.
Frequency tables can be used to display both qualitative (categorical) and quantitative (numerical) data. For categorical data, the frequency table will show the count or percentage of occurrences of each category. For numerical data, the frequency table will show the number of times each value or range of values appears in the dataset
Based on the data you provided, here is a frequency table for the movie genres:
Movie Number of students
1) Action 6
2) Comedy 4
3) Horror 7
4) Drama 5
5) Romance 8
In the table, the movie genres are listed in the left column, and the number of times each genre appears in the survey results is listed in the right column.
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Correct question is " You survey the students in your class to find out what kinds of movies they like to watch. The students were given the following choices: Comedy (C), Horror (H), Drama (D), Action (A), Romance (R). The following were the results of your survey: C, C, R, R, D, R, H, H, C, A, A, R, A, A, A, R, R, H, H, H, C, H, A, R, D, D, D, D, H, R a. Make a frequency table for the movie genres."
Working with Actual Interest Earned
Daniela puts $550 in a CD that earns 3.5% APR, compounded quarterly,
for 2 years. She is taxed at a rate of 15% on the interest she earns.
The total amount of interest is $33.75.
What percentage of the original principal is this?
We can use the procedures below to calculate what proportion of the original principal the overall amount of interest represents. This total amount of interest received corresponds to about 5.34% of the initial investment.
What is an interest?Divide the principal even by rate of interest, the time period, and other factors to arrive at simple interest. Simple return Equal principal + interests + hours is the marketing formula.The most typical technique to figure out interest is to use a portion of the principal sum. He would only pay his share of the 100% interest, for example, if somebody borrows $100 from the a partner and pledges to repay the loan with 5% interest. $x (0.05) = $5. When, you must pay interest.when you lend money after borrowing it and adding interest. Interest is often determined as an indicator of the overall of the loan total. The interest rate of the loan is the name given to this percentage.
Determine the total interest that was earned in Step 1.
It states that $33.75 was earned in interest overall.
Step 2: Determine the interest generated before to taxes.
The sum of the interest earned after tax can be determined by dividing the entire sum of the interest by (1 + rate of taxation), where the rate of tax is given as a decimal. Daniela was subject to a tax of 15% on the investment earnings. The tax rate in this instance is 15%, which really is equal to 0.15.
Interest gained before taxes is equal as $33.75 / (1 Plus 0.15), that results in a value of $29.35.
3. Determine the initial principal.
The $550 that Daniela first put into the CD is referred to as the original primary.
Compute the proportion of the initial principle in step four.
By dividing the sum of interest generated after tax by the original principal and multiplying the result by 100 as express it as a percentage, one can determine what proportion of the original principal the entire amount of interest represents.
(Interest paid before taxation / Original principal) / 100 equals the percentage of the original principal.
= ($possess / $550) w x 100
≈ 5.34%
Hence, the total interest earned is equivalent to roughly 5.34% of the initial capital.
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If x = 2i is one of the root, find all possible roots of the polynomial f(x) = 2x4-4x3+7x2-4x-4.
The other three roots of the polynomial are:
1) -2i
2) 1 + i
3) 1 - i
The polynomial with a root 2i and exactly 2 real roots is F(x)=x³-x² + 4x-4
What are Polynomials?Polynomials are sums of k-xⁿ terms, where k can be any number and n can be any positive integer.
3x+2x-5, for example, is a polynomial.
Given the polynomial function below
F(x)=x³-x² + 4x-4
Group
F(x)=(x³-x²) + (4x-4)
f(x) = x²(x-1)+4(x-1)
f(x) = (x²+4)(x-1)
If f(x) = 0
x²+4 = 0 and x -1. = 0
x² = -4 and x = 1
x = ±2i and -1
Hence polynomial with a root 2i and exactly 2 real roots is F(x)=x³-x² + 4x-4
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complete question:
Which of the following options is a polynomial with a root 2i and exactly 2
real roots?
A. F(x)=x²-x²³ +2x² - 4x-8
B. F(x)=x²-x² + 4x-4
C. F(x)=x²-x³-6x² +4x+8
OD. F(x)= x³ + x² + 4x+8
6. WRITING IN MATH Describe why the
difference of squares pattern has no middle term
with a variable. Example w-121
The two middle terms, -11w and +11w, cancel each other out, leaving only the first and last terms. This is why there is no middle term with a variable in the factorization of the difference of squares pattern.
How do you find a middle term?When expanding a binomial expression in the form of (a + b)ⁿ, the middle term can be found using the following formula:
Middle term coefficient = nC(k), where k = (n+1)/2 if n is odd, and k = n/2 or (n/2 + 1) if n is even. The middle term coefficient is then multiplied by the product of a raised to the power of (n-k) and b raised to the power of k.
The difference of squares pattern is a special algebraic pattern that arises when we factor a polynomial that is the difference between two perfect squares. For example,
x² - y² = (x+y)(x-y)
When we apply this pattern to the expression w - 121, we can rewrite it as:
w² - 11²
And, we can use the difference of squares pattern to factor it as:
(w + 11)(w - 11)
Notice that there is no middle term with a variable in this factorization. This is because when we multiply (w + 11)(w - 11), the middle term cancels out.
To see why this happens, let's expand the product:
(w + 11)(w - 11) = w² - 11w + 11w - 121
The two middle terms, -11w and +11w, cancel each other out, leaving only the first and last terms. This is why there is no middle term with a variable in the factorization of the difference of squares pattern.
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What’s the greatest common factor of 42 and 50:(8 different answers)
Answer:
Step-by-step explanation:
The GCF of 42 and 50 is 2.
Need help with this (SERIOUS ANSWERS ONLY)
Answer: d=10
Step-by-step explanation:
content loaded
A department store manager has monitored the number of complaints received per week about poor service. The probabilities for numbers of complaints in a week, established by this review, are shown in the table. Answer Number of complaints 012 3 4 5 Probability 0.13 0.21 0.44 0.070. 0.06 0.09Save your answer What is the variance of complaints received per week? Please round your answer to the nearest hundredth Note that the correct answer will be evaluated based on the full-precision result you would obtain using Excel.
200 word answer
To calculate the variance of complaints received per week, we first need to find the mean or expected value of the number of complaints. This can be calculated by multiplying the number of complaints in each category by its corresponding probability, and then adding up the results.
Expected value = (0 x 0.13) + (1 x 0.21) + (2 x 0.44) + (3 x 0.07) + (4 x 0.06) + (5 x 0.09) = 2.54
Next, we can use the following formula to calculate the variance:
Variance = Σ[(x - µ)²P(x)]
where Σ = sum, x = number of complaints, µ = expected value, and P(x) = probability.
Using this formula and the probabilities given in the table, we get:
Variance = (0 - 2.54)²(0.13) + (1 - 2.54)²(0.21) + (2 - 2.54)²(0.44) + (3 - 2.54)²(0.07) + (4 - 2.54)²(0.06) + (5 - 2.54)²(0.09) = 1.4856
Rounding this answer to the nearest hundredth, we get a variance of 1.49.
In conclusion, the variance of complaints received per week is 1.49, meaning that the number of complaints is quite spread out around the mean, which is 2.54. This could indicate that the department store has some variability in its service quality, as the number of complaints can vary widely from week to week.