The maximum number of edges in a simple undirected disconnected graph of n vertices can be any value that is less than or equal to n(n-1)/2.
What is the graph?The graph is a demonstration of curves that gives the relationship between the x and y-axis.
The maximum number of edges in a simple undirected disconnected graph of n vertices can be found using the formula for the maximum number of edges in an undirected graph,
E = n(n-1)/2.
However, for a disconnected graph, this formula only applies to each connected component of the graph separately. Therefore, the maximum number of edges in a simple undirected disconnected graph of n vertices is n(n-1)/2 for each connected component, so the total maximum number of edges is n₁(n₁-1)/2 + n₂(n₂-1)/2 + ... + nₐ(nₐ-1)/2, where n₁, n₂, nₐ are the number of vertices in each connected component.
So, in general, the maximum number of edges in a simple undirected disconnected graph of n vertices can be any value that is less than or equal to n(n-1)/2.
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Which of the following tables represents a linear relationship that is also proportional? x −1 0 1 y −4 −2 0 x −1 0 1 y −2 0 2 x −1 0 1 y 0 1 2 x −1 0 1 y 1 3 5
The table that represents a linear relationship that is also proportional is; Table B
What is a proportional relationship?In Mathematics, a proportional relationship can be defined as a type of relationship that generates equivalent ratios and as such it can be modeled or represented by the following mathematical expression:
y = kx
Where:
x and y represents the variables.
k represents the constant of proportionality.
For us to have a proportional relationship and equivalent ratios, the variables x and y must have the same constant of proportionality.
Next, we would determine the constant of proportionality (k) using table B as follows:
Constant of proportionality (k) = y/x
Constant of proportionality (k) = -2/-1 = 2 or 2/1 = 2
Constant of proportionality (k) = 2
Thus, table B is correct.
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Answer:
the second one....
x −1 0 1
y −2 −1 0
Step-by-step explanation:
Write an equation of the line in slope-intercept
form.
-2
Ay
-2
N
-2
(2, 2)
2
(0, -2)
4 x
16. diagonal the perimeter of a rectangle is 32 feet. the length is three times as long as the width. find the length of the diagonal. round to the nearest tenth.
The length of the diagonal is 12.6 feet.
"Information available from the question"
The perimeter of a rectangle is 32 feet.
The length is three times as long as the width.
We have to find the length of the diagonal.
Let w = width
then
3w = length.
Because we know the perimeter:
Perimeter of the rectangle is : 2(l + w)
32 = 2(w + 3w)
32 = 2(4w)
16 = 4w
4 feet = w (width)
Length:
3w = 3(4) = 12 feet
Diagonal, we use the Pythagorean theorem:
Let d = diagonal
then,
[tex]d^2 = 4^2 + 12^2[/tex]
[tex]d^2[/tex] = 16 + 144
[tex]d^2[/tex] = 160
d = 12.6 feet
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Help me please . Question in photo below
The inequality that represents the graph is y ≤ -x - 2.
What is inequality in Math?In mathematics, inequality is a declaration of an order connection between two numbers or algebraic expressions (greater than, greater than or equal to, less than, or less than or equal to).
In the graph, we have
1. the line is going down (negative slope) so that's why u have the negative
2. it translated 2 units Downwards on the y-axis so that's why there is - 2
3. the line is Solid so it's going to have the equal sign under it, if the line was dashed it would just be a regular sign fr example (<)
4. the shading is below the line so that means it's going to be Less than or Equal to.
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At the market Ms Winn bought 3/5 lb of grapes And 5/8 lb of cherries. How many ounces of cherries did Ms Winn buy?
12 ounces of cherries did Ms Winn buy.
What is Unit conversion?The same attribute is expressed using a unit conversion, but in a different unit of measurement.
For instance, time can be expressed in minutes rather than hours, and distance can be expressed in kilometres, feet, or any other measurement unit instead of miles.
Given:
Ms. Winn bought = 3/5 lb of grapes
Ms Winn bought = 5/8 lb of cherries.
As, there are 16 ounces in a pound then
= 3 pounds/4 x 16 ounces/pound
= 3 x 4
= 12 ounces
Hence, She buy 12 ounce of cherries.
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Order the simplification steps of the expression below using the properties of rational exponents.
875x³y
·2³. (7.2³)
5xy³ √7x²
(5³) ³. 7. 2(¹+3).
(125) (7) (+) ³
¹2. y
5.
5.7.
.
5xy³ (72²) ³
.
(125-7). 2. y
..
(875x³y)
The simplification steps are as follows:
(2³)(7.2³) = 2³+3 = 128
(5³)³ = 125
(1 + 3) = 4
72² = 5184
125 - 7 = 118
So, the simplified expression is:
118 (5xy³) (5184³) 2y
What is properties of rational exponents?Properties of rational exponents are rules that dictate how to simplify expressions with fractional exponents. Some of the key properties are:
Product of Powers: (a^m)(a^n) = a^(m+n)Quotient of Powers: (a^m)/(a^n) = a^(m-n)Power of a Power: (a^m)^n = a^(mn)Power of a Product: (ab)^m = a^m b^mPower of a Quotient: (a/b)^m = a^m / b^mZero and Negative Exponent: a^0 = 1, a^(-n) = 1/a^nFractional Exponent: a^(m/n) = (a^m)^(1/n)
These properties are used to simplify expressions with rational exponents, which are exponents that are in the form of a fraction.
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60 suitcase marked down 20%
1.20×60=12001200/100=12
12suitcase
What quantity of 68% hydrochloric acid solution must be mixed with a 16% hydrochloric acid solution to produce 1629.33 mL of 19% solution?
The quantity of 68% hydrochloric acid solution must be mixed are;
94 ml of 68% Acid type I
1,535.33 ml 16.00% acid type II
How to solve algebraic word problems?The quantities and percentages given are;
Acid type I 68% ---------------- x liters
Acid type II 16% ------ 1629.33 - x liters
Mixture 19% ---------------- 1629.33
Thus, by combination of the values given we have;
68% x + 16%(1629.33 - x ) = 19% * 1629.33
Multiply through by 100 to get;
68x + 16(1629.33 - x ) = 30957.27
68x + 26069.28 - 16x = 30957.27
68x - 16 x = 30957.27 - 26069.28
52x = 4,887.99
x = 4,887.99/52
x = 94 ml of 68% Acid type I
Acid type II 16% ------ 1629.33 - 94
= 1,535.33 ml 16.00% acid type II
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x2+6x-40 factored form
Answer:
(x + 10)(x - 4)
Step-by-step explanation:
x² + 6x - 40
consider the factors of the constant term (- 40) which sum to give the coefficient of the x- term.
the factors are + 10 and - 4 , since
10 × - 4 = - 40 and 10 - 4 = + 6 , then
x² + 6x - 40 = (x + 10)(x - 4) ← in factored form
Which one is the correct answer?
Answer:
Last option: Stocks which drop from 5.25 by 1.35
Step-by-step explanation:
5.25 + (- 1.35) = 5.25 - 1.35
This represents a decrease in value of stock which starts at 5.25 and drops by 1.35.
The stock value at end of day = 5.25 - 1.35 = $3,9
here is a scatterplot of the data for 13 colonies of sparrowhawksthe value for the data set is 0.5602. what is the correlation? use 4 decimal places.
The correlation between the two variables in the data set for 13 colonies of sparrowhawks is 0.5602.
This means that there is a moderate positive correlation between the two variables, indicating that when one variable increases, the other variable is likely to increase as well.
To calculate the correlation coefficient, we can use Pearson’s correlation coefficient equation:
r = (n * Σxiyi - Σxi * Σyi) / √[(n * Σxi2 - (Σxi)2) * (n * Σyi2 - (Σyi)2)]
Where: n = the number of observations Σxi = the sum of all x-values Σyi = the sum of all y-values Σxiyi = the sum of the products of each x-value and y-value Σxi2 = the sum of the squares of each x-value Σyi2 = the sum of the squares of each y-value
Plugging in the values for our data set, we get:
r = (13 * 0.5602 - (13 * 0.5602)) / √[(13 * 0.2532 - (13)2) * (13 * 0.2532 - (13)2)]
r = 0.5602
This means that there is a moderate positive correlation between the two variables in the data set, indicating that when one variable increases, the other variable is likely to increase as well.
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Jordan compared 10 books at the school library. The following table shows the number of chapters and the total number of pages for each book.
Number of Chapters 3 4 5 8 10 12 13 14 16 20
Total Pages 18 38 45 85 76 145 138 160 180 220
Which of the following representations is most appropriate to show the relationship between the number of chapters and the total pages of a book?
Answer:
B.
Step-by-step explanation:
i think 99.9% sure!
Answer:
he representation that is most appropriate to show the relationship between the number of chapters and the total pages of a book is given by:
Graph 3
How to choose the correct graph?
Before choosing the correct graph, we must classify the function as discrete or continuous, as follows:
Discrete function: the input values of the function are only certain values on an interval.
Continuous function: the input values of the function are all the real values in the interval.
Then the graph of each type of function is given as follows:
Discrete function: dots.
Continuous function: solid line.
The input and output variables in this problem are given as follows:
Input variable: number of chapters.
Output variable: number of pages.
The number of chapters assumes only integer values, hence the function has a discrete domain, meaning that the graph is composed by dots.
However, the first graph is correct, as the third graph has a range of input and output values that is not present on the table, while the range in the first graph is according to the table.
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Step-by-step explanation:
Find the measure of the exterior angle.
The value of exterior angle is 108°.
What are exterior angles ?
An exterior angle is an angle which is formed by one of the sides of any closed shape structure such as polygon and the extension of its adjacent side.
Given:
Interior angles : (a+10)° and 44°
Thus , we know that
Exterior angle = sum of interior opposite angles
Therefore , Exterior angle = (a+10)° + 44°
or
2a° = (a+10)° + 44°
or
a = 54°
Therefore , exterior angle = 2a = 2*54° = 108°
Thus , the value of exterior angle is 108°.
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Simplify each expression and eliminate negative exponents
x^5 multiply x^8
(2x^3)^2
x^-3 • x ^5
Y^6 • y^9
(3x)^3
Y^7• y^-3
Z^-8 • z ^3
x^-2 x ^-6 x^4
X^15 by x^10
Here are the simplified expressions for each equation:
(x⁵) * (x⁸) * (2x³)² * (x⁻³) * (x⁵) = (x⁵) * (x⁸) * (2x⁶) * (x⁻³) * (x⁵) =
2x⁽⁵⁺⁸⁺⁶⁻³⁺⁵⁾ = 2x²¹
(y⁶) * (y⁹) = y⁽⁶⁺⁹⁾ = y¹⁵
(3x)³ = 27x³
(y⁷) * (y⁻³) = y⁽⁷⁻³⁾= y⁴
(z⁻⁸) * (z³) = z⁽⁻⁸⁺³⁾ = z⁻⁵
(x⁻²) * (x^⁻⁶) * (x⁴) = x⁽⁻²⁻⁶⁺⁴⁾ = x⁻⁴
(x¹⁵) * (x¹⁰) = x⁽¹⁵⁺¹⁰⁾ = x²⁵
What is expression?An expression or mathematical expression is a finite collection of symbols that is well-formed according to context-dependent norms. In mathematics, an expression is a phrase that has at least two numbers or variables and at least one arithmetic operation. Addition, subtraction, multiplication, or division are all examples of math operations. Term is defined as a constant, a single variable, or a combination of a variable and a constant multiplied or divided. An expression in mathematics is a collection of numbers, variables, and functions (such as addition, subtraction, multiplication or division etc.)
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the simplified expressions for each equation is:
a) 2x²¹ b) y¹⁵
c) 27x³ d) y⁴
e) z⁻⁵ f) x⁻⁴
g) x²⁵
What is expression?An expression or mathematical expression is a finite collection of symbols that is well-formed according to context-dependent norms. In mathematics, an expression is a phrase that has at least two numbers or variables and at least one arithmetic operation.
Addition, subtraction, multiplication, or division are all examples of math operations. Term is defined as a constant, a single variable, or a combination of a variable and a constant multiplied or divided.
An expression in mathematics is a collection of numbers, variables, and functions (such as addition, subtraction, multiplication or division etc.)
Here are the simplified expressions for each equation:
(x⁵) * (x⁸) * (2x³)² * (x⁻³) * (x⁵) = (x⁵) * (x⁸) * (2x⁶) * (x⁻³) * (x⁵) =
2x⁽⁵⁺⁸⁺⁶⁻³⁺⁵⁾ = 2x²¹
(y⁶) * (y⁹) = y⁽⁶⁺⁹⁾ = y¹⁵
(3x)³ = 27x³
(y⁷) * (y⁻³) = y⁽⁷⁻³⁾= y⁴
(z⁻⁸) * (z³) = z⁽⁻⁸⁺³⁾ = z⁻⁵
(x⁻²) * (x^⁻⁶) * (x⁴) = x⁽⁻²⁻⁶⁺⁴⁾ = x⁻⁴
(x¹⁵) * (x¹⁰) = x⁽¹⁵⁺¹⁰⁾ = x²⁵
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your grade in a class is determined by the average of three test scores. you scored 70 and 88 on the first two tests. to earn at least 76 for this course, how much do you have to score on the third test? let x be the score you will earn on the third test.
In order to score at least 76 for the full course, you have to score a total of 70 marks on the third test.
Average is calculated by first adding all the values of the total number of terms in a problem by the total number of terms.
Suppose there are five terms in a given problem, the formula will stand as:
Average of five terms = (n1 + n2 + n3 + n4 + n5)/5.
In this problem, the score of the first two tests are provided and the average of the three final tests is provided.
Marks scored in 1st test = 70
Marks scored in 2nd test = 88
Average marks = 76
Let the score of the third test be [tex]x[/tex]
Therefore, (70 + 88 + [tex]x[/tex])/3 = 76
(158 + [tex]x[/tex])/3 = 76
158 + [tex]x[/tex]= 228
[tex]x[/tex]= 228-158 = 70
Hence, the test score of the third test has to be 70 in order to get an average of 76 in the final marks.
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during a lab activity, a 14-year-old student took his resting pulse rate. he counted 20 beats in 20 seconds. he calculated his pulse rate for a minute and compared the result to the data shown in the table below. is his pulse rate in the normal range for children?
Yes, his pulse rate is in the normal range for children. His pulse rate was calculated to be 120 beats per minute, which falls within the range of 60-100 beats per minute.
The student took his resting pulse rate by counting the number of beats in 20 seconds. He then multiplied his result by three to calculate his pulse rate for a minute. To determine if his pulse rate was within the normal range for children, he compared his result to the data shown in the table. His pulse rate of 120 beats per minute was within the range of 60-100 beats per minute, so it was considered to be normal for children. To ensure accuracy, the student could have taken his pulse rate for a longer period of time, such as 30 or 60 seconds, before calculating his pulse rate for a minute. This would have given him a more accurate result.
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What is the lateral surface area of the triangular prism below? PLEASE HELP ASAP
Answer:
96
Step-by-step explanation:
large rectangle area = 7* (4+3+5) =7*12 =84
top & bottom 2 little triangles:
look at the bottom one:
triangle area formula = 1/2 base * height
so it's a right angle triangle, so the height is 4, base is 3
so area = 1/2 * 3* 4 =6
you have another one on the top
so 12
total = 84+12 =96
MULTIPLE CHOICE GIVING BRAINLIEST AND 100 POINTS
please please please thank youuu
Answer:
6.00
Step-by-step explanation:
4r + g = 24
4r + 2g = 30 Subtract equation 2 from equation 1
-g = -6
so g = cost of gravity = 6 dollars
I need answer ASAP the question is in the picture
Answer:
assuming that it can be solved, then yes
Step-by-step explanation:
A circular skating rink has a radius of 40 feet. Which expression can be used to find the circumference of the skating rink, in feet?
2.40.π is the expression can be used to find the circumference of the skating rink.
What is Circle?A circle is a shape consisting of all points in a plane that are at a given distance from a given point, the centre.
Given that a circular skating rink has a radius of 40 feet.
Radius = 40 ft.
We need to find the expression can be used to find the circumference of the skating rink.
The formula for circumference of circle is 2πr.
Circumference=2.40.π.
Hence, 2.40.π is the expression which can be used to find the circumference of the skating rink.
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Answer: 2 x 40 x pie
Step-by-step explanation:
Using the formula 1/a+1/b=1/c, express the variable b in terms of the variables a and c. Find b.
b =
The variable b in terms of the variables a and c is b = ac/(a - c)
How to express variable b in terms of variable a and cFrom the given formula expressed as
1/a + 1/b = 1/c
We want to express variable b in terms of the variables a and c. We would make variable b the subject of the formula.
Subtracting 1/a from the left hand side of the equation and the right hand side of the equation, it becomes
1/a - 1/a + 1/b = 1/c - 1/a
1/b = 1/c - 1/a
1/b = (a - c)/ac
Taking the reciprocal of the left hand side of the equation and the right hand side of the equation, it becomes
b = ac/(a - c)
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find median in the following distribution
Answer:
A=2
B=2+3÷2=2.5
C=10+15÷2=12.5
D=20
Directions: Based on the information given in the following problem, compute the gross pay.
Regular salary: $984 per month
Overtime rate: $10.39 per hour (14 hours overtime to be paid)
Round your answers to two decimal places.
gross pay: $
The gross pay of the worker when using the given parameters is; $1,129.46
How to calculate the Gross Pay?Gross pay is defined as the total amount of money you get before taxes or any other deductions are subtracted from your salary.
Net pay is defined as the amount of pay remaining for issuance to an employee after deductions have been taken from individual's gross pay.
Thus;
Gross pay = Net pay + deductions
Net pay = Gross pay - deductions
The parameters are;
Regular salary: $984 per month
Overtime rate: $10.39 per hour (14 hours overtime to be paid)
Gross Pay = 984 + 14(10.39)
Gross Pay = $1,129.46
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observations are drawn from a bell-shaped distribution with a mean of 130 and a standard deviation of 5. there are 1,500 observations in the data set. a. approximately what percentage of the observations are less than 140?
So, approximately 2.28% of the observations are less than 140.
To find the percentage of observations that are less than 140, we need to find the standard score (z-score) that corresponds to 140, and then use a standard normal table to find the proportion of data that is less than that z-score.
The standard score is calculated as follows:
z = (140 - 130) / 5 = 2
Using a standard normal table, we can find the proportion of data that is less than 2 standard deviations from the mean. This proportion is approximately 0.0228 or 2.28%.
Mean is nothing but the average of data.
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Which ordered pair makes both inequalities true? y≤ -x + 1 y > x
(-3,5)
(-2, 2)
(-1, -3)
(0, -1)
NEED ASAP!!!!
Answer:
(-2,2)
Step-by-step explanation:
First, let's look at the 2 inequalities:
y ≤ -x + 1
y > x
Just by looking at the second inequality, we can remove any ordered pairs where x is greater than or equal to y. This eliminated the ordered pairs (-1,-3) and (0,-1). Now, the answer has to be (-3,5) or (-2,2). Knowing this, we can plug x and y into the equation and see if either of the answers are true.
(-3,5):
x = -3
y = 5
y ≤ -x + 1
5 ≤ -(-3) + 1
5 ≤ 3 + 1
5 ≤ 4
NOT TRUE
(-2,2)
x = -2
y = 2
2 ≤ -(-2) + 1
2 ≤ 2 + 1
2 ≤ 3
TRUE
So, since plugging in the ordered pair (-2,2) into the inequality gives us a true answer while (-3,5) doesn't, the order pair (-2,2) must be out answer.
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a man has a garden measuring 84 m by 56 m. he wants to divide them equally into the minimum number of square plots. what is the length of each square plot?
If a man has a garden and he divide them equally into minimum number of square plots , then length of each square plot is 28m .
the length of the garden is = 84m ;
the width of garden is = 56m ;
the man is dividing the garden into equally minimum number of square plots ,
then , Factors of Width = 2×2×2×2×7 = 2×28 ;
the Factors of Length is = 2×2×2×3×7 = 3×28 ;
So , we will notice with a side of 28 m each , we can make 2 squares along the width of the garden ;
Similarly , with the side = 28m each, we can make 3 squares along the length of the garden ;
That means , we can make 6 squares of 28m side.
Therefore , the minimum length of each square plot = 28 m.
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To ride go carts at Rick's Play Zone, it costs $4 per ride plus $3 to rent a helmet. The total cost, y, in dollars, depends on x, the number of times you ride the go carts. Write an equation to represent this situation.
The linear equation that represents this situation will be y = 4x + 3.
What is a linear equation?A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.
The linear equation is given as,
y = mx + c
Where m is the slope of the line and c is the y-intercept of the line.
To ride go-carts at Rick's Play Zone costs $4 per ride plus $3 to rent a helmet.
Let 'y' be the total cost in dollars and 'x' be the number of times you ride the go-carts. Then the equation is given as,
y = 4x + 3
The equation that represents this situation will be y = 4x + 3.
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Simplify the expression (6^4)2.
what decimal number corresponds to the binary number 11111111?
The decimal number that corresponds to the binary number 11111111 is 255.
What is decimal number?The decimal numeral system is the most widely used system for representing both integer and non-integer values. It is the Hindu-Arabic numeral system's expansion to non-integer numbers. Decimal notation is the method of representing numbers in the decimal system. A decimal number is made up of two parts: a whole number and a fractional component separated by a decimal point. The decimal point is the dot between the whole number and the fractions. 25.5, for example, is a decimal number.
Here,
In binary, each digit represents a power of 2, starting with the rightmost digit. The rightmost digit in 11111111 represents 2^0, the second digit from the right represents 2^1, and so on. To convert a binary number to decimal, you add up the value of each digit times the corresponding power of 2.
For 11111111, the calculation would be:
=1 * 2^7 + 1 * 2^6 + 1 * 2^5 + 1 * 2^4 + 1 * 2^3 + 1 * 2^2 + 1 * 2^1 + 1 * 2^0 = 128 + 64 + 32 + 16 + 8 + 4 + 2 + 1
=255
The decimal equivalent of the binary number 11111111 is 255.
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the distance between points (3,5) and (-2,1)=
Answer:
Slope: y= 4/5x+21/8
The distance is 4 units up and 5 units to the right.
Step-by-step explanation: