The figure below is a map showing 12 cities and 17 roads connecting certain pairs of cities. Paula wishes to travel along exactly 13 of those roads, starting at city A and ending at city L, without traveling along any portion of a road more than once. (Paula is allowed to visit a city more than once.)
A (0)
B (1)
C (2)
D (3)
E (4)
Answers
The number of routes that Paula can take using graph theory is; E: 4
How to find the number of possible routes?We will observe that out of the 12 cities, 6 of them possess 3 edges going in/out of them.
The 6 cities are such that there are 2 at the top, 2 at the bottom, and 1 on each side.
In graph theory terms, we can say that they are of degree 3.
Thus, at least 1 edge connecting to each of these cities cannot therefore be used. Furthermore, the same concept applies to the start and end points, due to the fact that we don't want to return to them.
There are 6 + 2 = 8 vertices that we can tell have 1 unused edge, and then we have 17 - 13 = 4 unused edges to work with due to the fact that we have 17 edges in total, and as such must use exactly 13 of them).
Finally, we notice that at each of the 2 cities marked with an O on a path in the image attached, that there are 2 possibilities such that it's either we continue straight and cross back over that same path later, or we will make a left turn, and then turn rightward when we approach the junction again.
This gives us a total of;
2 * 2 = 4 possible different routes
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Related Questions
what does "and" mean in maths?
Answers
Answer:
and mean another questions
Answer:
add
Step-by-step explanation:
for example two and two makes
Which equation is in standard form?
a. X +3= -5y
b. 5-y=x
c. y =3x + 6
d. -8x+ 3y = 12
Answers
选项 (d)
option (d)
!!!!!!!!!
Write the following ratios in their simplest form.
27:30
Answers
Answer:
9/10
Step-by-step explanation:
Answer:
9:10
Step-by-step explanation:
27:30 = 9:10
BRAINLIEST PLEASE
What is the number that comes in 21,7,15,11 times table
Answers
Answer:
i think it is 105
but 105 divide by 11 is 9.54
Bc I just think it is
please help me i need it
Answers
Answer:
75 degrees
Step-by-step explanation:
Since angle ABD = angle ABC + angle CBD, and we know each of those, we can add them to get the answer.
30+45=75 degrees.
Which of the following would be proportional to 3/5? 3/10 12/15 12/20. 18/20
Answers
Answer:
15/20
Step-by-step explanation:
It is the only one that can be simplified into 3/5
Answer:
12/20
Step-by-step explanation:
Mofor has homework assignments in five subjects. He only has time to do two of
them.
Answers
The decision of which two homework assignments to complete depends on Mofor's individual circumstances and priorities.
If Mofor only has time to do two homework assignments out of the five subjects, he will need to choose which subjects to prioritize. The specific subjects he chooses to work on will depend on various factors such as his strengths, weaknesses, upcoming deadlines, and personal preferences. Here are a few strategies he could consider:
1. Prioritize based on importance: Mofor can prioritize the homework assignments that carry more weight in terms of grades or have upcoming deadlines. This way, he ensures that he completes the assignments that have a higher impact on his overall academic performance.
2. Focus on challenging subjects: If Mofor finds certain subjects more difficult or time-consuming, he can prioritize those assignments to allocate more time and effort to them. This approach allows him to concentrate on improving his understanding and performance in subjects that require extra attention.
3. Balance workload: Mofor can choose to distribute his efforts evenly across subjects, selecting two assignments from different subjects. This strategy ensures that he maintains a balanced workload and avoids neglecting any particular subject.
The decision of which two homework assignments to complete depends on Mofor's individual circumstances and priorities. It is essential for him to consider his academic goals, time constraints, and personal strengths to make an informed decision.
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you can open PDF
\( \frac{4}{5} + \frac{2}{3} \)
![you can open PDF[tex] \frac{4}{5} + \frac{2}{3} [/tex]](https://i5t5.c14.e2-1.dev/h-images-qa/contents/attachments/zAmv40qeo8eLlWaQnGPKp2IJcS9F4QtN.jpeg)
Answers
\( \frac{4}{5} + \frac{2}{3} \\ \frac{4 \times 3}{5 \times 3} + \frac{2 \times 5}{3 \times 5} \\ \frac{12}{15} + \frac{10}{15} \\ = \frac{22}{15} \: or \: 1 \frac{7}{15} \)
Evaluate the expression below when n = 9. If needed, answer as a fraction or a decimal.
n² + 6n ÷ 3
Answers
Answer:
Below
Step-by-step explanation:
Put '9' where 'n' is and compute
(9)^2 + 6(9) ÷ 3 =
81 + 54 ÷3 =
81 + 18 = 99
A one-way trolley ticket to Old Town costs 3.50. How much will it cost for Ahyeon and three friends to ride to Old Town and home again?
Answers
Answer:
$28
Step-by-step explanation:
Each round trip will be double the price of a one-way trip, so will be ...
2 × $3.50 = $7.00
Diego and his 3 friends will require a total of 4 round-trip tickets for a cost of ...
4 × $7.00 = $28.00
What rigid motion maps the solid-line figure onto the dotted-line figure?
A reflection
B. rotation
C. translation
Answers
Answer:
A. Reflection
Step-by-step explanation:
I believe the answer would be reflection
0,2,4,6,8 write a function f(n) that represents the nth term of the sequence, where f(1)=0
Answers
The function f(n) = 2n – 2 represents the nth term of the sequence 0, 2, 4, 6, 8.
What is sequence?
In mathematics, a sequence is an ordered list of numbers, usually written in a specific pattern. Each number in the sequence is called a term, and the position of a term in the sequence is called its index or subscript.
A function f(n) that represents the nth term of the sequence given above can be written as follows:
f(n) = 2n – 2
This function can be explained as follows:
The function f(n) represents the nth term of the given sequence. The first term of the sequence is 0, which is equal to f(1). The second term of the sequence is 2, which is equal to f(2). This pattern can be seen throughout the sequence, as each subsequent term is two more than the preceding one. Thus, the general form of the function can be written as f(n) = 2n – 2, where n represents the nth term of the sequence.
For example, when n = 5, the function f(n) = 2n – 2 = 10. This is equal to the fifth term of the sequence, 8.
Therefore, the function f(n) = 2n – 2 represents the nth term of the sequence 0, 2, 4, 6, 8.
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I
3. (5 points) Herman and Rosie need to wash the walls on the side of the school. Herman
has a power washer, which could complete the job in 10 hours. Rosie has a manual
scrubber, which could complete the job in 15 hours. in
they work together, how many hours
will it take them to clean the wall?
Answers
Answer:
It would take them 6 hours. Six hours is 3/5 of Herman’s required time. 6 hours is 2/3 of Rosie’s, so 3/5 +2/5= the project being complete.
Fine the end behavior and x-value of holeEquation is to the right
Answers
Given the function:
\(\: f\mleft(x\mright)=\frac{x+1}{\left(x-3\right)\left(x^2-1\right)}\)The end behaviour of the function f(x) describes the behaviour of the function as x approaches +∞ and -∞.
When x approaches +∞,
\(\lim _{x\rightarrow\infty}f(x)=\text{ }\lim _{x\rightarrow\infty}\frac{x+1}{(x-3)(x^2-1)}=0\)Thus, as x approaches +∞, the function f(x) approaches zero.
When x approaches -∞,
\(\lim _{x\rightarrow-\infty}f(x)=\text{ }\lim _{x\rightarrow-\infty}\frac{x+1}{(x-3)(x^2-1)}=0\)Thus, as x approaches -∞, the function f(x) approaches zero.
x-value of the hole:
For a rational function f(x) given as
\(f(x)=\frac{p(x)}{q(x)}\)Provided that p(x) and q(x) have a common factor (x-a), the function f(x) will have a hole at x=a.
Thus, from the function f(x)
\(f(x)=\frac{x+1}{(x-3)(x^2-1)}\)by expansion, we have
\(f(x)=\frac{x+1}{(x-3)(x^{}-1)(x+1)}\)The expression (x-1) is a common factor of the numerator and the denominator.
Thus,
\(\begin{gathered} x-1=0 \\ \Rightarrow x=1 \end{gathered}\)Hence, the x-value of the hole is 1.
Find what minimum population size you need to have if you have a 99% confidence, 100 standard deviation and want a size 3 margin of error
Answers
A minimum population size of approximately 7373 to achieve a 99% confidence interval with a margin of error of 3 and a known standard deviation of 100.
How to calculate the minimum population size?To calculate the minimum population size required to achieve a 99% confidence interval with a margin of error of 3 and a known standard deviation of 100, we can use the following formula:
n = [(z-value × SD) / ME]²
Where:
n = the minimum sample size required
z-value = the critical value for the desired confidence level (99% in this case)
SD = the known standard deviation (100 in this case)
ME = the desired margin of error (3 in this case)
First, we need to determine the z-value for a 99% confidence level. Using a standard normal distribution table, we find that the z-value for a 99% confidence level is approximately 2.576.
Substituting the values into the formula, we get:
n = [(2.576 × 100) / 3]²
Simplifying this expression, we get:
n = 7373.08
Therefore, we would need a minimum population size of approximately 7373.
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Solve this system by substitution. y = 3x - 12 6x + y = 6 *Remember to write your answer as a coordinate voint (x, y).
Answers
6x+3x-12=6
9x-12=6
+12= 18/9 x=2
Y=6-12
Y=-6 (2,-6
The opposite of 1.5 is ? So the opposite 1.5 ? Which is equal to the opposite of ? Which is ? The second statement is ?
Answers
The equation ^2 −4+^2 +2=−4
a. Is a parabola
b. Is an ellipse
c. Is a hyperbola
d. Is a circle
e. None of the above
Answers
Answer:
Step-by-step explanation:
None. Your notation is unclear.
Eli works in an electronic repair shop.he earns $9.00 an hour plus a bonus for each item he repairs. Write a formula that will help Eli determine how much money he earn in one week. Let’s let a=total amount earned h=hours worked in one week n= number of items repaired b=bonus amount for each item
Answers
Answer:
a = 9h + nb
Step-by-step explanation:
1) Variables:
a=total amount earned
h=hours worked in one week
n=number of items repaired
b=bonus amount for each item
2) He earns $9.00 an hour plus a bonus for each item repaired.
=> he earns 9 times the number of hours plus value of the bonus times the number of items repaired
=> a = 9h + nb
Select all the correct answers.
Third
B.
90 feet
A. 16, 200 feet
√180 feet
C. √16, 200 feet
180 feet
D.
The area of a baseball field bounded by home plate, first base, second base, and third base is a square. If a player at first base throws the ball to a
player at third base, what is the distance the player has to throw?
First
90 feet
Home
Reset
Next
Answers
The diagonal distance from home plate to third base is approximately √16,200 feet.
The correct answers are:
B. 90 feet
C. √16,200 feet
D. 180 feet.
In baseball, the bases are arranged in a square shape.
The distance between each base is 90 feet.
Therefore, the correct answer for the distance a player at first base has to throw to a player at third base is 90 feet (option B).
To find the diagonal distance from home plate to third base, we can use the Pythagorean theorem.
Since the area of the baseball field is a square, the diagonal distance represents the hypotenuse of a right triangles.
The two legs of the right triangle are the sides of the square, which are 90 feet each.
Using the Pythagorean theorem \((a^2 + b^2 = c^2),\) we can calculate the diagonal distance:
a = b = 90 feet
\(c^2 = 90^2 + 90^2\)
\(c^2 = 8,100 + 8,100\)
\(c^2 = 16,200\)
c = √16,200 feet (option C)
Therefore, the diagonal distance from home plate to third base is approximately √16,200 feet.
The options A, √180 feet, and 180 feet are incorrect because they do not represent the correct distances in the given scenario.
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A drama teacher has a budget of $120 to spend on materials to create costumes for a play. She can buy 1 square yard of white material for $8, while 1 square yard of blue material costs $10. Let x represent the number of square yards of white fabric purchased and y be the number of square yards of blue fabric. Then the inequality 8x+10y≤120 graphed below determines how many square yards of each type of fabric can be bought without exceeding the budget. If the teacher wants to buy 10 square yards of white fabric, what is the greatest whole number of square yards of blue fabric that she can buy without exceeding the budget?
Answers
Inequalities are used to relate unequal expressions
The greatest whole number of square yards the teacher can buy is 4
The inequality is given as:
\(8x + 10y \le 120\)
When the number of square yards of the white fabrics is 10.
It means that: x = 10
So, we have:
\(8 \times 10 + 10y \le 120\)
\(80 + 10y \le 120\)
Collect like terms
\(10y \le 120 - 80\)
\(10y \le 40\)
Divide both sides by 10
\(y \le 4\)
The above inequality means that:
The greatest whole number of square yards the teacher can buy is 4
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Using the region names in the image below, select all regions that represent:
A ∩ B' ∩ C
3 group Venn Diagram with Roman numeral labeled regions
A intersection not B intersection C. Region I: Items only in group A, not in B or C. Region II: Items in A and B, but not C. Region III: Items only in B, not in A or C. Region IV: Items in A and C, but not B. Region V: Items in A, B, and C. Region VI: Items in B and C, but not A. Region VII: Items only in C, not in A or B. Region VIII: Items not in any of the groups.
Answers
Items in A and C, but not B is the required region.
What is set?Sets are groups of well-defined objects or components in mathematics. A set is denoted by a capital letter, and the cardinal number of a set is enclosed in a curly bracket to indicate how many members there are in a finite set.
Given:
A ∩ B' ∩ C
That means,
A intersection not B intersection C.
B' is the complement of set B.
So, the region is,
Items in A and C, but not B.
Therefore, the items in A and C but not in B.
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600(2)/94(0.6(2)+169
Answers
Answer:
2172.7
Step-by-step explanation:
Answer:
the full answer would be 2172.76595745
Paula designed a garden bed in a shape of an irregular prism. it took 5 cubic feet of dirt to cover the bed a depth of 6 inches. how much area does her garden bed cover in square feet?
Answers
Answer:
10 ft^2.
Step-by-step explanation:
6 inches = 0.5 feet.
As the depth is a uniform 0.5 feet:
Area = volume / depth
= 5 / 0.5
= 10 ft^2.
The area that the garden bed cover is 10 ft², at a depth of 6 in (0.5 ft.)
What is an equation?
An equation is an expression that shows the relationship between two or more variables and numbers.
12 in = 1 ft, hence 6 in = 0.5 ft.
The volume of the dirt = Area of the bed * Depth of the bed
Hence:
5 ft³ = Area * 0.5 ft.
Area = 10 ft²
The area that the garden bed cover is 10 ft², at a depth of 6 in (0.5 ft.)
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Maine has a cold climate in the winter. What is the probability of the temperature falling below 32 Fahrenheit in Maine during the month of January.
Answers
The probability is closer to one than zero.
Probability theory is used to analyze and predict the likelihood of events happening in various fields such as statistics, gambling, physics, finance, and more. It allows us to make informed decisions based on the likelihood of different outcomes. In probability theory, the total number of possible outcomes is important to determine the probability of a single event occurring. By comparing the favorable outcomes to the total outcomes, we can calculate the probability of an event happening.
Probability is a measure of the likelihood of an event to occur. Many events cannot be predicted with total certainty. We can predict only the chance of an event to occur i.e., how likely they are going to happen, using it. Probability can range from 0 to 1, where 0 means the event to be an impossible one and 1 indicates a certain event. Probability for Class 10 is an important topic for the students which explains all the basic concepts of this topic. The probability of all the events in a sample space adds up to 1.For example, when we toss a coin, either we get Head OR Tail, only two possible outcomes are possible (H, T). But when two coins are tossed then there will be four possible outcomes, i.e {(H, H), (H, T), (T, H), (T, T)}.
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which of the following would be an acceptable first step in simplifying the expression?
Answers
Solution:
Given:
\(\frac{cos\text{ }x}{1-sin\text{ }x}\)The only acceptable first step in simplifying the expression from the options that would not change or alter the values of the expression is by multiplying (1 + sin x) to both the numerator and the denominator.
Therefore, the correct answer is OPTION B.
On the past two quizzes, a student scored a 75 and 83. Write and solve a compound inequality to find the possible values for the 3rd quiz score that would give her an average between 85 and 90, inclusive.
Answers
The possible values for a third quiz score that would give her an average between 85 and 90, inclusive is: 97 ≤ x ≤ 112.
How to determine the average?In Mathematics, the average of these quiz scores can be calculated by using the following formula:
Average = Sum of quiz score/Number of quiz scores
Note: Let the variable q represent the student's score on the third (3rd) quiz.
Substituting the given parameters into the formula, we have the following;
Average = (75 + 83 + q)/3
Average = (158 + q)/3
This ultimately implies that, an average between 85 and 90, inclusive is given by this compound inequality:
85 ≤ (158 + q)/3 ≤ 90
Multiplying all through by 3, we have the following:
255 ≤ (158 + q) ≤ 270
Subtracting 158 from both sides of the inequality, we have the following:
97 ≤ x ≤ 112
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Felicity needs to buy 3 dozen cookies for a party. The first 16 cookies cost $0.28 each. The rest cost $0.19.
What is Felicity's total cost?
Answers
Answer: $8.28
Step-by-step explanation: 3 dozens are 36 cookies. The first 16, $0.28 each will be $4.48. The rest will cost $0.19 each so $0.19 x 20 = $3.80
$4.48 + $3.80 =
Answer:$8.28
Step-by-step explanation
Multiply 16x0.28 you will get $4.48 then
you Multiply 20x0.19 you get 3.8 also known as 3.80 you add
3.80+4.48+$8.28
The following angles are supplementary to each other.
m∠C = (x + 19)° and m∠D = (3x − 19)°
Determine x.
60
45
38
19
Answers
Answer:
45
Step-by-step explanation:it gives you the answer chiices if you plug each number into x and then do the equation you will get 180
Answer: 45
Step-by-step explanation:
Did the test.
What is the degree of this monomial? 20x
Answers
Answer:
1
Step-by-step explanation: