Whether a disconnected graph is problematic depends on its application. In network theory, it might represent critical separations, but in connected systems like transportation, it signifies issues. The context, such as economic, ecological, or psychological networks, determines its value.
Explanation:A disconnected graph is not inherently a bad thing; its value depends on the context in which it is used. For example, in network theory, a disconnected graph might accurately represent separate clusters within a network, indicating areas that do not communicate or interact with each other. This could be critical for understanding the structure of social networks, the Internet, or ecological systems. On the other hand, in applications where connectivity is essential, such as in the design of transportation or communication networks, a disconnected graph could signify a problem that needs addressing. Thus, it's crucial to consider the specific needs of the application or system being analyzed.
Economists use graphs to depict connections and costs, highlighting the importance of understanding the underlying story a graph tells. The fact that all graphs have a genealogy and a narrative is essential in interpreting them correctly. For instance, a graph showing disconnected components in an economic network could indicate areas of inefficient resource allocation or potential opportunities for improvement.
Ultimately, whether a disconnected graph is seen as a disadvantage depends on the goals of the analysis. In ecological studies, reconnecting fragmented landscapes is often beneficial, although careful planning is needed to avoid drawbacks. Similarly, in the context of relational connectivity theory (RCT), connectivity and the loss thereof have profound implications on wellbeing, demonstrating that the concept of dis/connection transcends mathematical graphs and touches on broader socio-psychological themes.
If 10% of 60 is 6, what is 5% of 60?
Explain how you found your answer
Answer:
3
Step-by-step explanation:
If we already know that 10% of 60 is 6 and that 5% is one half of 10%, we can just divide the 10% value by two to find the 5% of 60.
Can someone help me with the question in the image below
Answer:
x=8
Step-by-step explanation:
we know that
The diagonals of a parallelogram bisect each other. That means, each diagonal cuts the other into two equal parts.
so
[tex]5x=6x-8[/tex]
Solve for x
[tex]6x-5x=8\\x=8[/tex]
Which system of equations has no solutions...please help quick
For a system to have no solutions the lines must be parallel (they cannot intersect).
So the answer is the graph on the top right.
Answer: top right and bottom right
Step-by-step explanation:
For there to be a solution the lines have to cross at one time so when they are not touching there is no solution
the base of parellogram is twice its height . if the area is 648msq find its base and height
Answer:
h=18m, b=2m
Step-by-step explanation:
Let the base be b and height be h
Condition 1:
b=2h ----(1)
Condition 2:
Area=b*h
b*h=648 -----(2)
Putting (1) into (2)
2h*h=648
2h^2=648
Dividing both sides by 2
h^2=324
Taking sq root on both sides
h=18 m
Now
Putting value of h in eq (1)
b=2(18)
b=36 m
Steve had s songs on his music player.
He bought n new songs. What is the
dependent variable? Explain.
Answer: n since that number depends on s, the songs he already had.
Final answer:
The dependent variable in Steve's music player scenario is the total number of songs after buying new songs, represented by T = s + n. As the number of new songs purchased (n) changes, the total (T) changes, demonstrating a linear relationship between n and T.
Explanation:
In the scenario where Steve had s songs on his music player and he bought n new songs, the dependent variable is the total number of songs Steve has after the purchase. To define this in terms of a mathematical relationship, we can express the total number of songs (T) as an equation:
T = s + n
Here, s is the original number of songs, and n is the number of new songs purchased. The dependent variable is T (the total number of songs), which depends on the value of n (the number of songs bought). If we change the independent variable n, the total number of songs T will also change.
To illustrate this with a dataset, suppose Steve originally had 5 songs (s = 5). If he buys:
1 new song (n = 1), then T = 5 + 1 = 6 songs in total.3 new songs (n = 3), then T = 5 + 3 = 8 songs in total.5 new songs (n = 5), then T = 5 + 5 = 10 songs in total.The relationship between the number of new songs purchased (n) and the total number of songs (T) is linear, as T increases by the same amount that n does.
Mitchel owns a livestock trailer that can hold a maximum of 5,000 pounds. The average weight of each goat is 90 pounds, and the average weight of each calf is 360 pounds. Mitchel would like to know how many goats and calves he can transport in a single trip.
Mitchel can transport a 1:1 ratio of goats to calves in his livestock trailer, equating to 11 goats and 11 calves per trip, given their respective average weights of 90 and 360 pounds and the trailer's weight limit of 5000 pounds.
Explanation:Mitchel has a livestock trailer with a weight limit of 5,000 pounds. Given that each goat weights about 90 pounds and each calf about 360 pounds, we need to calculate how many of each animal the trailer can accommodate within its weight limit, while taking into account their average weights.
Let's look at one possible solution, using goats and calves in a 1:1 ratio. This would be 90 + 360 = 450 pounds per set of goat and calf. To fit within the trailer's weight limit, we then divide the total weight capacity by the weight of one set of animals: 5,000 / 450 = 11.11, which we round down to 11. This tells us that Mitchel can transport 11 goats and 11 calves in his trailer for each trip.
It's important to mention that this distribution can be adjusted according to need, as long as the total weight of the animals is kept below the trailer's weight limit.
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Use row operations to solve the system
x + y – z = -2
4x – y + z = 7
X – 3y + 2z =-5
Answer:
(x, y, z) = (1, 12, 15)
Step-by-step explanation:
As with any set of linear equations, there are many possible routes to a solution. We might simplify the notation a bit by writing the coefficients in an augmented matrix. The columns, left to right, represent the coefficients of x, y, and z, in order, and the constant term.
The row operations we'll use are multiplying a row by a value and adding that result to another row, replacing the other row by the sum.
We can make things a little simpler by writing the second equation first. Then the augmented matrix we're starting with is ...
[tex]\left[\begin{array}{ccc|c}4&-1&1&7\\1&1&-1&-2\\1&-3&2&-5\end{array}\right][/tex]
Adding the second row to the first, we get ...
[tex]\left[\begin{array}{ccc|c}5&0&0&5\\1&1&-1&-2\\1&-3&2&-5\end{array}\right][/tex]
Dividing the first row by 5 gives ...
[tex]\left[\begin{array}{ccc|c}1&0&0&1\\1&1&-1&-2\\1&-3&2&-5\end{array}\right][/tex]
Subtracting this from the second row, and again from the third row, we are left with ...
[tex]\left[\begin{array}{ccc|c}1&0&0&1\\0&1&-1&-3\\0&-3&2&-6\end{array}\right][/tex]
Multiplying the second row by 3 and adding that to the third row, we get ...
[tex]\left[\begin{array}{ccc|c}1&0&0&1\\0&1&-1&-3\\0&0&-1&-15\end{array}\right][/tex]
Subtracting the third row from the second gives ...
[tex]\left[\begin{array}{ccc|c}1&0&0&1\\0&1&0&12\\0&0&-1&-15\end{array}\right][/tex]
Finally, multiplying the last row by -1, we have the solution:
[tex]\left[\begin{array}{ccc|c}1&0&0&1\\0&1&0&12\\0&0&1&15\end{array}\right][/tex]
This matrix corresponds to the equations ...
x = 1y = 12z = 15_____
The purpose of our choice of row operations is to make the diagonal elements 1 and the off-diagonal elements 0. That is how we end up with the final equations shown.
As we said, there are many ways to go about this. In general, one can ...
if necessary, swap rows until the diagonal term of interest is non-zero. If you are doing this using a computer program, generally you want the diagonal term to have the coefficient with the largest magnitude. When doing this by hand, you may want to arrange the rows to avoid fractions when you do the normalizing.divide the row by the coefficient of the diagonal element to "normalize" the diagonal element to a value of 1zero the other elements in that column by multiplying the row just normalized by the element in another row, then subtracting the product. (The 4th matrix shown above shows this for the first column.)proceed to the next diagonal element and repeat the process until all diagonal elements are 1. If you cannot make all diagonal elements 1, then the system of equations does not have a unique solution. If any row becomes all zeros, the system is "dependent" and has infinite solutions. If a row is zeros except for the rightmost column, the system is "inconsistent" and has no solutions.A car was purchased for $39150.00 and is expected to be worth $10800.00 in 9 years. Determine the rate at which the van depreciates in value.
Answer:
The annual rate of depreciation of the car is 8.05% or 72.41/9
Step-by-step explanation:
1. Let's review the information given to us to answer the question correctly:
Price of the purchase of the car = $ 39,150
Price after 9 years = $ 10,800
2. Determine the rate at which the van depreciates in value.
Let's calculate what is the percentage of depreciation after 9 years, this way:
Percentage of depreciation after 9 years = [1 - (Price after 9 years/Price of the purchase of the car)] * 100
Replacing with the values we know:
Percentage of depreciation after 9 years = [1 - (10,800/39,150)] * 100
Percentage of depreciation after 9 years = [1 - 0.2759] * 100
Percentage of depreciation after 9 years = 72.41%
Annual rate of depreciation = 72.41/9 = 8.05%
Graph f(x)=3sin(12x)−5 . Use 3.14 for π .
Answer:
see attached
Step-by-step explanation:
The given function is a vertical expansion of the sine function by a factor of 3 and a translation downward by 5 units.
It will oscillate between -8 and -2, with a midline at y = -5. The multiplier 12 indicates the period of the function will be 2π/12 = π/6 ≈ 0.5233... for the given value of π.
A graphing calculator is a useful tool for creating the graph.
Answer:
Step-by-step explanation:
took the test
which of the following is the graph of (g - f)(x)
Answer:
It's the third one
Guaranteed!!
Hence, the graph second is correct.
What is the simplification?
Simplification is reducing the expression/fraction/problem in a simpler form. It makes the problem easy with calculations and solving.
Here,
[tex]f(x)=-x\\g(x)=2x[/tex]
So,
[tex]g(x)-f(x)=2x-(-x)\\\\(g-f)(x)=2x+x\\\\(g-f)(x)=3x[/tex]
Draw the graph:-
Hence, the graph second is correct.
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Find the volume of each figure
Which expression can be used to approximate the expression below, for all positive numbers a, b, and x, where a. 1 and b.
1?
log,
logo
logna
logna
logo
log,
log,b
logo
logo
Save and
Next
Submit
Step-by-step explanation:
We have,
[tex]\log _{a}x[/tex]
To find, the value of [tex]\log _{a}x[/tex] = ?
∴ [tex]\log _{a}x[/tex] , where a, b and x are positive
a ≠ 1 and b ≠ 1
We know that,
The logarithm identity,
[tex]\log_{p}m=\dfrac{\log_{y}m}{\log_{y}p}[/tex]
∴ [tex]\log _{a}x[/tex] = [tex]\dfrac{\log_{b}x}{\log_{b}a}[/tex]
Where, b is the common base of logarithm
∴ The value of [tex]\log _{a}x[/tex] = [tex]\dfrac{\log_{b}x}{\log_{b}a}[/tex]
Thus, the required option A) [tex]\dfrac{\log_{b}x}{\log_{b}a}[/tex] is correct.
-37=x-9.9 , what’s the value of x ?
Answer:
x= 3.73737373737......
Step-by-step explanation:
To find x, divide -9.9 to both sides.
-37 = x-9.9
-9.9 -9.9
3.73737373737...= x
This is a repeating decimal.
can you give a description of the relationship between the years since the tree was transplanted and its height in inches? if so what is it?
Answer:
The height of the tree is 18 inches plus 8 inches for each year since the tree was transplanted.Explanation:
Please, find attached an image with the table that accompanies this question.
1. Pattern
The table is:
Years: 2 4 5 8 9
Height (in.): 34 50 58 82 90
The most simple pattern is a linear pattern. A linear pattern has a constante rate of change.
The rate of change between two points is:
rate of change = change in the output / changee in the inputFind the rate of change for the data:
(50 - 34) in / (4 - 2) year = 16in / 2year = 8in/year(58 - 50) in / (5 - 4) year = 8in/1year = 8 in/year(82 - 58) in / (8 - 5) year = 24in / 3year = 8 in/year(90 - 82) in / (9 - 8) year = 8in / 1 year = 8 in/yearHence, the heigth and the years since the tree was transplantated show a linear relationship: every year the tree grew 8 inches.
2. Intial height:
You can find the initial height of the tree by using the rate of change of the height.
At year 2: height = 34 inchesAt year 1: height = 34 inches - 8 inches = 26 inchesAt year 0: height = 26 inches - 8 inches = 18 inches3. Relationship
You can describe the relationship in terms of the initial height and the numbers of years since the tree was transplantated.
Then, the height of the tree is 18 inches plus 8 inches for each year since the tree was transplanted.
You can even write an equation (function):
name H the height of the tree in inchesname y the number of years since the tree was transplantatedthe equation is: H = 18 + yWhat is an equation of the line that passes through the point (3,6) and is parallel to the line 2x+3y=21
Answer: y= -2/3+8
Step-by-step explanation:
a parking lot has total of 60 cars and trucks. the ratio of cars to trucks is 7:3 how many cars are in the parking lot. How many trucks are in the parking lot justify your anwsers
A store offers a discount of 30 % on all refrence of books. If a dictionary cost $12 before the discount what is the dollar amount of the discount.
Answer:
3.6
Step-by-step explanation:
30%×12= 3.6
30%=0.3
Between the hours of 10PM and 6AM, the
temperature decreases an average of ¾ of a degree
per hour. How many minutes will it take for the
temperature to decrease by 5°F?
Final answer:
It will take 400 minutes for the temperature to decrease by 5°F, calculated by dividing 5°F by the rate of ¾°F/h, resulting in 6.6667 hours, which is then converted into minutes (6.6667 hours × 60 minutes/hour = 400 minutes).
Explanation:
To calculate the time it will take for the temperature to decrease by 5°F, knowing that the temperature decreases at a rate of ¾ of a degree per hour, we can use the following steps:
Divide the total desired temperature decrease (5°F) by the rate of temperature decrease per hour (¾°F/h).
Calculate the total hours required for a 5°F decrease.
Since we want to find the time in minutes, we multiply the hours by 60 (as there are 60 minutes in an hour).
Step 1: 5°F divided by ¾°F/h = 5 ÷ 0.75 = 6.6667 hours
Step 2: 6.6667 hours are needed.
Step 3: 6.6667 hours × 60 minutes/hour = 400 minutes
Therefore, it will take 400 minutes for the temperature to decrease by 5°F.
evaluate 15/k when k=3 ?
15/k
15/3
5
Hope this helps! ;)
Answer:
5
Step-by-step explanation:
Since k=3 you would put 3 under 15. Now the equation would look like this: 15/3 instead of 15/k. Then you would divide 15 by 3 which is 5.
(PLEASE HELP THIS IS DUE IS 20 MINUTES, THERES ALSO TWO QUESTIONS)
1.) Micah has a garden. He constructs a scale model of the garden using the scale 1 inch: 2 feet. The garden has a length of 6 feet. What is the length of the garden in Micah’s model? (1 point show your work, 1 point correct answer)
2.)The figure on the left represents a scale drawing of the figure on the right. What is the scale? (2 pts. 1pt show work, 1 pt correct answer)
THE PICTURE IS FOR THE SECOND QUESTION
Answer:1. 3 inches
Step-by-step explanation:1 inch =2ft 2x3=6
To find the length of the garden in Micah's model, we need to set up a proportion using the given scale. The scale for the figure on the left to the figure on the right can be determined by comparing corresponding lengths.
Explanation:1.) To find the length of the garden in Micah's model, we need to use the scale 1 inch: 2 feet. Since the garden has a length of 6 feet, we can set up a proportion:
1 inch / 2 feet = x inches / 6 feet
Cross-multiplying, we get 2 feet * x inches = 1 inch * 6 feet
Simplifying, we have 2x inches = 6 inches, so x = 3 inches.
Therefore, the length of the garden in Micah's model is 3 inches.
2.) The scale of the figure on the left to the figure on the right can be determined by comparing the corresponding lengths. If we measure the lengths of a certain side of the left figure and the right figure, we can find the scale. For example, if the length of a side of the left figure is 2 cm, and the corresponding side on the right figure is 4 cm, the scale is 1 cm: 2 cm.
Therefore, the scale is 1 cm: 2 cm.
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Based on the given triangle, the cosine of the 30 degree angle is:
P.S.
It is not 1/3 (third option)
Answer:
[tex]\frac{\sqrt{3} }{2}[/tex]
Step-by-step explanation:
Remember SOHCAHTOA
The cosine of an angle in a right triangle is the adjacent sides length divided by the hypotenuses length
In this case, for the angle 30 degrees, the adjacent length is [tex]\sqrt{3}[/tex] and the hypotenuse's length is 2
So, the cosine of the 30 degree angle is the first option:
[tex]\frac{\sqrt{3} }{2}[/tex]
1/2 (5n-6) = -6(-2n-5)
An architect plans to buy 5 stone spheres and 3 stone cylinders. For the same amount, she can buy 2 stone spheres and 6 stone cylinders. If one stone cylinder costs $36.81, how much does each stone sphere cost?
The cost of each stone sphere is $ 36.81
Solution:
Given that,
An architect plans to buy 5 stone spheres and 3 stone cylinders
For the same amount, she can buy 2 stone spheres and 6 stone cylinders
Let "x" be that same amount
Let "a" be the cost of each stone sphere
Cost of each stone cylinder = $ 36.81
Therefore,
x = 5 stone spheres and 3 stone cylinders
x = 5a + 3(36.81)
Similarly,
x = 2 stone spheres and 6 stone cylinders
x = 2a + 6(36.81)
Equate both,
[tex]5a + 3(36.81) = 2a + 6(36.81)\\\\5a + 110.43 = 2a + 220.86\\\\5a - 2a = 220.86 - 110.43\\\\3a = 110.43\\\\a = 36.81[/tex]
Thus cost of each stone sphere is $ 36.81
By setting up and solving equations based on the given scenarios, we find that the cost of each stone sphere is also $36.81, the same as one stone cylinder.
Explanation:Let's denote the cost of one stone sphere as S and the cost of one stone cylinder as C. We know one stone cylinder costs $36.81. We are given two scenarios involving the purchase of stone spheres and cylinders with equal total cost. In the first scenario, 5 stone spheres and 3 stone cylinders are bought, and in the second, 2 stone spheres and 6 stone cylinders are purchased.
Formulating these scenarios into equations gives us:
5S + 3C = 2S + 6CConsidering C = $36.81Substituting the value of C into the equation simplifies it to:
5S + 3(36.81) = 2S + 6(36.81)
Simplifying further:
5S + 110.43 = 2S + 220.86
Subtracting 2S and 110.43 from both sides results in:
3S = 110.43
Dividing both sides by 3 gives:
S = $36.81
Therefore, each stone sphere also costs $36.81.
The farmer looks out in the barnyard and Cesar pigs and the chickens. He says to his daughter, “ I count 40 heads in 100 feet. How many pigs and how many chickens are out there?”
Answer:
There are 10 pigs and 30 chickens
Step-by-step explanation:
Let the number of pigs be x
let the number of chickens be y
Then there are 40 heads . So the total number of pigs and chickens is 40
x + y = 40-----------------------(1)
We know that pigs have 4 legs and chickens have 2 legs
4x + 2y = 100----------------------(2)
Solving (1) and (2)
multiply (1) by 2
2x + 2y = 80-------------------------(3)
subtract (3) from (2)
4x + 2y = 100
2x + 2y = 80
----------------------------
2x = 20
----------------------------
[tex]x = \frac{20}{2}[/tex]
x = 10
Now Substituting x in (1), we get
10 + y = 40
y = 40 - 10
y = 30
What is the missing denominator in
the expression below?
Answer:
The denominator should be 3. Hope this helps.
7/10×1/2 please help me
Answer:
7/20
Step-by-step explanation:
7/10 * 1/2
By multiplying
7/20
0.35
Answer: 7/20 or .35
Step-by-step explanation: .7 times .5 is .35
Solve the equation 11x + 7 = 73?
Answer:
6
Step-by-step explanation:
11x + 7 = 73
- 7 - 7
11x = 66
divide 66 by 11 and you get 6
Answer:
x = 6
Step-by-step explanation:
Step 1: Subtract 7 from both sides
11x + 7 - 7 = 73 - 7
11x = 66
Step 2: Divide both sides by 11
11x = 66
11x / 11 = 66 / 11
x = 6
Answer: x = 6
A circle has a diameter of 7.6 feet. Which measurement is closest to the circumference of the circle in feet?
The circumference of the circle is 23.89 ft
The circumference of a circle is the distance around it and it can be calculated by the formula:
Circumference = π x diameter
The circumference is therefore:
= 22/7 x 7.6
= 167.2 / 7
= 23.89 feet
The option given that is closest to 23.89 ft is the right answer.
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1.125 divided by (3/4) (3/4) +6(14/3)
When the turnpike littered the toll, traffic increased from 1,500 cars per day to 2,700
What was the percentage of the increase in traffic volume?
Answer:
80%
Step-by-step explanation:
The percentage change between two numbers can be calculated as ...
percentage change = ((new value)/(old value) -1) × 100%
= (2700/1500 -1) × 100% = (1.80 -1) × 100% = 80%
Traffic volume increased 80%.