The most appropriate representation to show the relationship between the number of chapters and the total pages of a book would be a scatter plot titled "School Library".
with the x-axis labeled "Number of Chapters" ranging from 0 to 20 and the y-axis labeled "Total Pages" ranging from 0 to 275 with points at (3, 18), (4, 38), (5, 45), (8, 85), (10, 76), (12, 145), (13, 138), (14, 160), (16, 180), and (20, 220).
A scatter plot is a graph used to display the relationship between two variables. In this case, the two variables are the number of chapters and the total number of pages in a book. The plot consists of dots, each representing a single data point. The x-axis represents the independent variable, which in this case is the number of chapters. The y-axis represents the dependent variable, which is the total number of pages. By plotting each data point on the graph, it is easier to visualize the relationship between the two variables.
A line graph is not appropriate for this situation because it suggests a continuous relationship between the two variables, which is not the case here. The number of chapters and total pages are discrete variables, and there is no natural order to the data points that would justify connecting them with a line.
The first scatter plot option is not appropriate because it shows the y-axis ranging up to 450, which is much higher than the maximum value of 275 for the total pages in this data set. This exaggerates the differences between the data points and can be misleading.
The chosen scatter plot is appropriate because it clearly shows the relationship between the number of chapters and the total pages of a book. It is easy to see that as the number of chapters increases, the total pages also tend to increase. The scatter plot also helps to identify any outliers or patterns in the data that may not be apparent from just looking at the numbers. It is a visual tool that helps to quickly understand the data and draw conclusions from it.
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a cannon ball is launched straight up into the air from a height of 8 feet above the ground and with a velocity of 420 feet per second
Write an equation to model the distance d, in feet the cannon ball is above the ground t, seconds after it was fired.
In ΔLMN, the measure of ∠N=90°, NM = 9, ML = 41, and LN = 40. What is the value of the cosine of ∠L to the nearest hundredth?
The value of the cosine of ∠L in triangle LMN is approximately 0.98 using Pythagorean Theorem.
To find the cosine of ∠L in triangle LMN, we first need to use the Pythagorean theorem to find the length of side LM, since only have the lengths of NM and LN:
[tex]LM^2 = LN^2 - NM^2\\LM^2 = 40^2 - 9^2\\LM^2 = 1521[/tex]
[tex]LM = \sqrt{1521}[/tex]
LM = 39
Now that we know the length of all three sides of the triangle, we can use the cosine rule to find the cosine of ∠L:
cos(L) = [tex](LM^2 + LN^2 - NM^2)[/tex] / (2 x LM x LN)
cos(L) = [tex](39^2 + 40^2 - 9^2)[/tex] / (2 x 39 x 40)
cos(L) = 0.975
Rounding to nearest hundredth:
cos(L) = 0.98
Therefore, the value of cosine of ∠L in triangle LMN is approximately 0.98.
The ratio of the neighbouring side to the hypotenuse is known as the cosine of an angle in a right triangle. As L is not a straight angle in this situation, its value must be determined using the cosine method. Whether a triangle is a right triangle or not, the cosine rule can be used to relate the lengths of its sides and angles.
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A diameter of a circle has its endpoints at (-2,-1) & (4,7). What is the equation of the circle.
Check the picture below.
so the center of the circle is the midpoint of that diameter, and its radius is half its length.
[tex]~~~~~~~~~~~~\textit{middle point of 2 points } \\\\ (\stackrel{x_1}{-2}~,~\stackrel{y_1}{-1})\qquad (\stackrel{x_2}{4}~,~\stackrel{y_2}{7}) \qquad \left(\cfrac{ x_2 + x_1}{2}~~~ ,~~~ \cfrac{ y_2 + y_1}{2} \right) \\\\\\ \left(\cfrac{ 4 -2}{2}~~~ ,~~~ \cfrac{ 7 -1}{2} \right) \implies \left(\cfrac{ 2 }{2}~~~ ,~~~ \cfrac{ 6 }{2} \right)\implies \stackrel{ center }{(1~~,~~3)} \\\\[-0.35em] ~\dotfill[/tex]
[tex]~~~~~~~~~~~~\textit{distance between 2 points} \\\\ r(\stackrel{x_1}{-2}~,~\stackrel{y_1}{-1})\qquad (\stackrel{x_2}{4}~,~\stackrel{y_2}{7})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ \stackrel{ radius }{r}=\sqrt{(~~4 - (-2)~~)^2 + (~~7 - (-1)~~)^2} \implies r=\sqrt{(4 +2)^2 + (7 +1)^2} \\\\\\ r=\sqrt{( 6 )^2 + ( 8 )^2} \implies r=\sqrt{ 36 + 64 } \implies r=\sqrt{ 100 }\implies r=10 \\\\[-0.35em] ~\dotfill[/tex]
[tex]\textit{equation of a circle}\\\\ (x- h)^2+(y- k)^2= r^2 \hspace{5em}\stackrel{center}{(\underset{1}{h}~~,~~\underset{3}{k})}\qquad \stackrel{radius}{\underset{10}{r}} \\\\[-0.35em] ~\dotfill\\\\ ( ~~ x - 1 ~~ )^2 ~~ + ~~ ( ~~ y-3 ~~ )^2~~ = ~~10^2\implies {\large \begin{array}{llll} (x-1)^2+(y-3)=100 \end{array}}[/tex]
Someone please help me I need help with this homework assignment
Answer:
A
Step-by-step explanation:
A has a positive slope
Yolanda and her friends were asked to paint a mural on a wall at the park. Yolanda is making a scale drawing of the mural. If every 2 inches of her drawing represents 3 feet of the actual wall, what is the area in square feet of the actual mural?
If every 2 inches of Yolanda's drawing represents 3 feet of the actual wall, we can use the scale factor to convert the dimensions of the drawing to the dimensions of the actual wall.
Since we are dealing with area, we need to square the scale factor.
2 inches : 3 feet
(2 inches / 3 feet)^2 = (2/36)² = 1/324
This means that every square inch of Yolanda's drawing represents 1/324 square feet of the actual wall.
If the area of the mural in Yolanda's drawing is A square inches, then the area of the actual mural is:
A (square inches) x (1/324) (square feet per square inch) = A/324 square feet
Therefore, to find the area of the actual mural in square feet, we need to first find the area of the mural in Yolanda's drawing and then divide by 324.
If the area of the mural in Yolanda's drawing is, for example, 500 square inches, then the area of the actual mural is:
500 (square inches) / 324 = 1.54 square feet (rounded to two decimal places)
Therefore, the area of the actual mural is 1.54 square feet.
[tex] \: \: [/tex]
if it cost $15 to fill a gas tank in 1995, how much would it have cost to fill the same tank in 2015?
If the cost to fill a gas tank in 1995 is $15 then the cost to fill a gas tank in 2015 is equals to the $31.25.
Price Index is a effective method of comparing relative change in the price of a quantity with respect to its price in a reference year. This year which we use as a reference is called the base year and price index is ratio of the price of a product in a year to its price in the base year ( expressed in percentage ).
The cost to fill a gas tank in 1995 = $15
Price index in 1995 = 100.8%
price index in 2015 = 210.0%
In this case we want to determine the cost to fill a gas tank in 2015. Let the required cost value be x dolars. Using the formula, price index in 1995/price index in 2015 = reference value/ value in 2015
=> 100.8% /210% = 15/x
=> 2015 cost value, x =( 15 × 210 )/100.8
=> x = 3150/100.8
=> x = 31.25
Hence, required value is $31.25.
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Complete question:
If it cost $15 to fill a gas tank in 1995, how much would it cost to fill the same tank in 2015. 1995 index is 100.8%
2015 index is 210.0% round your answer nearest cent.
a manufacturer of a certain type of large ma- chine wishes to buy rivets from one of two manufac- turers. it is important that the breaking strength of each rivet exceed 10,000 psi. two manufacturers (a and b) offer this type of rivet and both have rivets whose breaking strength is normally distributed. the mean breaking strengths for manufacturers a and b are 14,000 psi and 13,000 psi, respectively. the stan- dard deviations are 2000 psi and 1000 psi, respectively. which manufacturer will produce, on the average, the fewest number of defective rivets?
The manufacturer B is calculated to produce, on the average, the fewest number of defective rivets amongst all the manufacturers.
To determine which manufacturer will produce, on average, the fewest number of defective rivets, we need to calculate the proportion of defective rivets for each manufacturer.
Let X be the breaking strength of a rivet from manufacturer A, and let Y be the breaking strength of a rivet from manufacturer B. Then:
P(X < 10000) = P((X - μ_A) / σ_A < (10000 - μ_A) / σ_A) = P(Z_A < -2.5) ≈ 0.0062
where Z_A is a standard normal random variable, and we use the given values μ_A = 14000 psi and σ_A = 2000 psi.
Similarly:
P(Y < 10000) = P(Z_B < -3) ≈ 0.0013
where Z_B is a standard normal random variable, and we use the given values μ_B = 13000 psi and σ_B = 1000 psi.
Therefore, the proportion of defective rivets for manufacturer A is approximately 0.0062, and the proportion of defective rivets for manufacturer B is approximately 0.0013.
Since manufacturer B has a lower proportion of defective rivets, on average, it will produce fewer defective rivets than manufacturer A. So the manufacturer that will produce, on average, the fewest number of defective rivets is manufacturer B.
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a classroom recorded all the heights, in inches, of their students and calculated the mean, median and mode. the heights are listed below: 38,38,39,39,40,40,40,40,40,40,40,41,42,42,43 after this project, a new student joined the class and wanted to be included in the data. the new student is much taller than the rest of the class at a height of 51 inches. what impact will this have on the statistics that were calculated?
The impact on the mode will be insignificant.
When a new student joined the classroom with a height of 51 inches, the statistics that were calculated will be
impacted in the following ways:
Mean: The mean is calculated by adding up all the heights and then dividing the total by the number of heights. Since
the new student is much taller than the rest of the class, the addition of 51 to the data set will increase the sum of the
data set by a significant amount. This will cause the mean to increase.
Median: The median is the middle number when the data set is ordered from lowest to highest. Since the data set has
an odd number of values, the median is 40. When a new student joins the class with a height of 51 inches, this will
cause the median to increase to 40.5.
Mode: The mode is the number that appears most often in the data set. Since the mode of the given data is 40, adding
a new student with a height of 51 will not change the mode. Therefore, the impact on the mode will be insignificant.
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Jake has 32 quarters on his desk and molly has q quarter in her purse
which algebraic expression represents the total number of quarters that Jake and molly have
According to given information, the algebraic expression that represents the total number of quarters that Jake and Molly have is: 32 + q.
What is algebraic expression?
An algebraic expression is a mathematical phrase that contains numbers, variables, and arithmetic operations, such as addition, subtraction, multiplication, and division. It can also include exponents, roots, and other mathematical symbols.
The algebraic expression that represents the total number of quarters that Jake and Molly have is:
32 + q
where 32 represents the number of quarters that Jake has on his desk and q represents the number of quarters that Molly has in her purse.
Adding these two quantities together gives the total number of quarters that Jake and Molly have.
Therefore, the algebraic expression that represents the total number of quarters that Jake and Molly have is:
32 + q
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PLEASE ANSWER SOON AS POSIBLE...GOD BLESS AMERICA
4÷2=
12÷2=
6÷3=
45÷9 =
Answer:
4÷2=2
12÷2=6
6÷3=3
45÷9 =5
Step-by-step explanation:
Jeremy rides his bike at a rate of 12 miles per hour. The table below
represents the number of hours and miles Kevin rides. Assume both bikers
ride at a constant rate.
Answer:
A) Jeremy has the greater speed.
B) y = 23x
C) See graph
D) The slope is 23. This means that Lauren can travel 23 miles in 1 hour.
Step-by-step explanation:
Part A:
Kevin's rate is 11.5 miles per hour.
Take two points, I used (2,23) and (4,46) to find the rate for Kevin.
Find the change in y over the change in x. The y values are 46 and 23. The x values are 4 and 2. You find the change by subtracting
[tex]\frac{46-23}{4-2}[/tex] = [tex]\frac{23}{2}[/tex] = 11.5
Part B:
If Kevin's rate is 11.5, then Lauren's rate is 23
Part C:
See graph
Part D :
The slope for C is 23. This means that Lauren can ride 23 miles in one hour.
Helping in the name of Jesus.
1. Browse laptops from three retailers to get a rough idea of what laptops are being sold.
You can get a sense of what laptops are available, which brands are well-liked, and what specifications are shared by various models by looking through these three stores.
What is the browse laptops?Amazon:
Go to Amazon's homepage and hover over the “Electronics” category in the top menu bar.
Click on “Computers & Accessories” in the dropdown menu.
Under “Laptops,” you can browse through the different categories such as “
2-in-1 Laptops," "Traditional Laptops," and "Gaming Laptops."
You can also use the filtering options on the left-hand side of the page to narrow down your search by brand, price, screen size, and more.
Best Buy:
Go to Best Buy's homepage and click on "Laptops & Computers" in the top menu bar.
You can browse through the different categories such as "Laptops," "Gaming PCs," and “Chromebooks.”
You can also use the filtering options on the left-hand side of the page to narrow down your search by brand, price, screen size, and more.
Dell:
Go to Dell's homepage and click on “Laptops & 2-in-1 PCs" in the top menu bar.
You can browse through the different categories such as "Consumer Laptops," "Gaming Laptops," and "Mobile Workstations.”
You can also use the filtering options on the left-hand side of the page to narrow down your search by brand, price, screen size, and more.
Therefore, By browsing through these three retailers, you can get an idea of what laptops are available, what brands are popular, and what features and specs are common across different models.
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Over a period of one week, the Dow Jones Industrial Average (DJIA) did the following: On Monday the DJIA went down by 3.2%, on Tuesday it went up by 11.2%, on Wednesday it went up by 0.7%, on Thursday it went down by 4.8%, and on Friday it went down by 9.4%. Find the percentage increase/decrease of the DJIA over the week. Round your answer to the nearest hundredth of a percentage.
The percentage increase/decrease of the DJIA over the week is a decrease of 6.53%.
What is percentage?Percentage is a way of expressing a number as a fraction of 100. It is denoted by the symbol "%".
A decreased percentage refers to the amount or rate by which a quantity or value has decreased from its original or initial value, expressed as a percentage of the original value.
According to given information:
To find the percentage increase/decrease of the DJIA over the week, we need to calculate the overall change in the index and express it as a percentage of the initial value.
Let's assume that the DJIA started the week at a value of 100. Then, the following changes would occur:
On Monday, it went down by 3.2%, so its value decreased to 96.8.
On Tuesday, it went up by 11.2%, so its value increased by 11.2% of 96.8, or 10.82, to reach 107.62.
On Wednesday, it went up by 0.7%, so its value increased by 0.7% of 107.62, or 0.75, to reach 108.37.
On Thursday, it went down by 4.8%, so its value decreased by 4.8% of 108.37, or 5.20, to reach 103.17.
On Friday, it went down by 9.4%, so its value decreased by 9.4% of 103.17, or 9.70, to reach 93.47.
Therefore, over the week, the DJIA decreased by 6.53% (from 100 to 93.47).
Rounding this to the nearest hundredth of a percentage, we get a decrease of 6.53%.
So, the percentage increase/decrease of the DJIA over the week is a decrease of 6.53%.
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Diagonals of a parallelogram bisect each other true or false
Please help me out!
A telephone poll asked people whether they like playing golf. 3,360 people said they like playing golf and 3,640 people said they do not like playing golf. What percentage of the people polled like playing golf?
Write your answer using a percent sign.
48% of the people polled like playing golf.
What is Algebraic expression ?
An algebraic expression is a mathematical phrase that can contain variables, constants, and mathematical operations such as addition, subtraction, multiplication, division, and exponentiation. Algebraic expressions are used to represent and solve problems in many areas of mathematics, science, engineering, and finance.
The percentage of people polled who like playing golf can be calculated by dividing the number of people who like golf (3,360) by the total number of people polled (3,360 + 3,640 = 7,000) and then multiplying by 100 to express the answer as a percentage:
(3360 ÷ 7000) x 100% = 48%
Therefore, 48% of the people polled like playing golf.
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The measure of angle w is 100°, and the measure of angle z is 68°. a triangle has angles x, y, z. the exterior angle to angle x is w. what is the measure of angle y? 12° 32° 80° 168°
The measure of angle y is 32°.
To find the measure of angle y, follow these steps:
1. Since the exterior angle to angle x is w, and w measures 100°, we can use the fact that the sum of an interior angle and its corresponding exterior angle is 180°.
So, angle x = 180° - 100° = 80°.
2. Now we know that a triangle has angles x, y, and z.
The sum of angles in a triangle is always 180°.
We have x = 80° and z = 68°,
so we can find angle y as follows:
y = 180° - (80° + 68°)
= 180° - 148°
= 32°.
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Can someone solve this please
The association on the line is a negative linear assosciation and other solutions are shown below
Calculating the slopeTo find the slope of the line passing through the given points, we use the slope formula
slope = (change in y) / (change in x)
Let's use the points (0, 90) and (8, 40) to find the slope:
slope = (40 - 90) / (8 - 0) = -50 / 8 = -6.25
Calculating the y-interceptThe y-intercept is 90 i,e, when x = 0
Calculating the equation of a lineThe equation is represented as
y = mx + c
Where
m = slope and c = y when x = 0
So, we have
y = -6.25x + 90
The association on the line is a negative linear assosciation
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Krystal is catering a dinner for an organization. Dessert will be homemade ple and 1 cup of either chocolate or vanilla ice cream. The chocolate ice cream costs
$8 per gallon and the vanilla ice cream costs $6 for a 5-quart container. There are 4 cups in 1 quart and 4 quarts in 1 gallon; therefore, each container of
chocolate ice cream contains 16 servings and each container of vanilla ice cream contains 20 servings. Based on the budget, Krystal wants to spend no more
than $70 on ice cream, and she needs at least 150 servings of ice cream.
Let c represent the number of gallons of chocolate ice cream and v represent the number of 5-quart containers of vanilla ice cream.
Which system of inequalities can be used to determine the number of gallons of chocolate ice cream and the number of 5-quart containers of vanilla ice cream
that Krystal can buy for this dinner?
A
B
C
D
6c+8v ≤ 70
16c+20v > 150
8c + 6v 2 70
16c+20v ≤ 150
8c + 6v < 70
16c+20v < 150
8c + 6v ≤ 70
16c+20v2 150
Option A is the answer. The system of inequalities that can be used to determine the number of gallons of chocolate ice cream and the number of 5-quart containers of vanilla ice cream that Krystal can buy for this dinner is:
8c + 6v ≤ 70
8c + 6v ≤ 7016c + 20v ≥ 150
Step by step explanation of the inequalityThe cost of c gallons of chocolate ice cream is $8c, and the cost of v containers of vanilla ice cream is $6v. Krystal wants to spend no more than $70 on ice cream, so the inequality for the total cost of ice cream is:
8c + 6v ≤ 70
Krystal needs at least 150 servings of ice cream, and each gallon of chocolate ice cream provides 16 servings, while each container of vanilla ice cream provides 20 servings. The inequality for the total number of servings of ice cream is:
16c + 20v ≥ 150
Therefore, the system of inequalities that can be used to determine the number of gallons of chocolate ice cream and the number of 5-quart containers of vanilla ice cream that Krystal can buy for this dinner is:
8c + 6v ≤ 70
16c + 20v ≥ 150
Option A is the correct answer.
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What is the radius of a sphere with a volume of 12,348π cubic feet?
Answer:Radius = 21
Step-by-step explanation:
Volume of a sphere = 4/3 * pie * radius^3
12,348 pie = 4/3 * pie radius ^3
12,348 = 4/3 * radius^3
(12,348 * 3)/ 4 = radius^3
9261 = radius^3
radius = 21
an urn contains 12 balls, five of which are red. the selection of a red ball is desired and is therefore considered to be a success. if a person draws three balls from the urn, what is the probability of three successes?
The probability of selecting three red balls or having three successes when drawing balls from the urn is 0.045, which is equivalent to 4.5%.
The probability of three successes can be calculated using the binomial probability distribution formula. Since there are only two outcomes for each ball drawn (success or failure), and the trials are independent, the binomial distribution applies.
The probability of drawing a red ball on the first attempt is 5/12. Since the ball is not replaced, the probability of drawing a red ball on the second attempt is 4/11. Similarly, the probability of drawing a red ball on the third attempt is 3/10.
To obtain the probability of three successes, we need to multiply these probabilities together:
P(three successes) = (5/12) x (4/11) x (3/10)
P(three successes) = 0.04545 or approximately 0.045
Therefore, the probability of drawing three red balls or three successes from the urn is 0.045 or 4.5%. This means that out of every 100 sets of three balls drawn, we can expect to get three red balls in approximately 4-5 sets.
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ow must the units be set up in order to get from the number of eggs used to make a certain number of cookies to the number of eggs needed to make some other number of cookies?
To get from the number of eggs used to make a certain number of cookies to the number of eggs needed to make some other number of cookies, you would use a proportional relationship.
Let's say x represents the number of eggs used to make a certain number of cookies, y represents the number of cookies made, and z represents the number of eggs needed to make some other number of cookies.
Then, we can set up the proportion:
x eggs / y cookies = z eggs / (some other number of cookies)
We can then solve for z by cross-multiplying:
z eggs = x eggs * (some other number of cookies) / y cookies
This formula tells us how many eggs are needed to make the specified number of cookies, based on the number of eggs used and the number of cookies originally made.
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Adults leaving a library were surveyed about the possibility of an annual fee of $100
to support the library. Of those surveyed, 80% said they were in favor of the fee.
The survey takers concluded incorrectly that 80% of the adult residents of the city
are in favor of the fee.
What would be a better survey? What might be a more believable value for the
percent of adult residents of the city who are in favor of the fee?
The better survey would be when the possibility of adults in favour of fee and not in favour of fee is same that is 50% each.
Explain about the unbiased survey:Everything in surveys revolves around asking the appropriate questions in the right ways since they are meant to elicit feedback. Many polls purposefully and unintentionally ask one-sided questions.
An objective question attempts to avoid using leading language and is fact-based rather than judgmental.
Biased questionnaire items use word choice and sentence structure in a way that affects how respondents react. This is sometimes done on purpose. This usually happens as a result of inadequate survey planning and assessment.
Here are a few advices.
Check your questions to make sure they won't lead to bias in the responses.Make sure all potential responses are included in the answer choices.Ask as few and straightforward inquiries as you can.Don't ask participants to think more than is necessary.Given query:
When adults left a library, they were asked if they would be open to paying a $100 yearly fee to support it. 80% of those polled indicated their support for the fee.The survey respondents came to the false conclusion that the fee is supported by 80% of the city's adult residents.Thus, the better survey would be when the possibility of adults in favour of fee and not in favour of fee is same that is 50% each.
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Please help me will give brainliest
One real-world situation that could be modeled by the arithmetic sequence f(n) = 100 + 25n, for n ≥ 1, is the cost of a monthly subscription service for an online course.
What is Arithmetic Sequence?An arithmetic sequence is a sequence of numbers where each term is found by adding or subtracting a constant value from the previous term. The constant value is called the common difference and determines the rate at which the sequence increases or decreases.
One real-world situation that could be modeled by the arithmetic sequence f(n) = 100 + 25n, for n ≥ 1, is the cost of a monthly subscription service for an online course.
Assuming that the initial cost of the service is $100 and the subscription fee increases by $25 every month, then the formula
=> f(n) = 100 + 25n
It can be used to calculate the cost of the subscription for any given month n.
For example, the cost of the subscription for the 5th month would be
f(5) = 100 + 25(5) = $225.
Similarly, the cost of the subscription for the 10th month would be
f(10) = 100 + 25(10) = $350.
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Determine the number of 5 MB documents that could fit on a 16 GB flash drive.
Answer:
3200
Step-by-step explanation:
If we know the fact that :
1GB = 1000MB
We can form an equation to show that 16000MB divided by 5MB should give you your answer.
The answer you get is 3200.
This means that you can fit 3200 5 MB files into a 16GB flash drive.
Hoped this helped,
thank you
please please please please please please please please please please please help me out
Find the surface area of the sphere
The calculated value of the surface area of the sphere is 676π
Finding the surface area of the sphereGiven that
Radius, r = 13 inches
The formula for the surface area of a sphere is:
Surface area = 4πr^2
where r is the radius of the sphere
Substituting the given value of radius r = 13 inches, we get:
Surface area = 4π * 13^2
So, we have
Surface area = 676π
Hence, the surface area is 676π
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write in fully simplified slope intercept form please
Answer:
Step-by-step explanation:
O is the center of the regular nonagon below. Find its perimeter. Round to the
nearest tenth if necessary.
Thus, the perimeter of the regular nonagon with centre O is found as: 78.57 units.
Explain about the perimeter of regular polygon:A closed, 2D structure with a finite number of line segments is referred to as a polygon. A polygon's number of vertices and its number of line segments are always identical. The perimeter of a closed figure is the sum of the lengths of its outermost sides. It is the sum of the lengths of a polygon's sides.
P = (Side length) x n
The apothem of each of the 9 isosceles triangles that make up the regular nonagon is 12 cm.
The angle at the circle's centre is 360/9 = 40º.
Hence, the sides of the regular nonagon, if the apothem of a isosceles triangles is 12 cm.
2*12 tan (40/2) = 8.73 cm
Then the perimeter:
P = 9 x 8.73
P = 78.57 units
Thus, the perimeter of the regular nonagon with centre O is found as: 78.57 units.
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amy, beth, and jo listen to four different songs and discuss which ones they like. no song is liked by all three. furthermore, for each of the three pairs of the girls, there is at least one song liked by those two girls but disliked by the third. in how many different ways is this possible? (2012amc10b problem 24 or 2012amc12b problem 16) (a) 108 (b) 132 (c) 671 (d) 846 (e) 1105
The number of different ways in which no song is liked by all three and there is at least one song liked by those two girls but disliked by the third is (b) 132 ways.
Let the song that is liked by Amy and Beth (but not Jo), Beth and Jo (but not Amy), and Amy and Jo (but not Beth), be denoted as : AB, BJ, and AJ.
Similarly, let the letters "A, B, J, and N" denote the song that is liked by only Amy, only Beth, only Jo, and none of them, respectively.
We know that there is at least 1 AB, BJ, and AJ, there must be 3 songs out of 4 songs which Amy, Beth, and Jo listened to.
The fourth song can be of any type : N, A, B, J, AB, BJ, and AJ (there is no ABJ because "no-song" is liked by all three),
So, we must find the number of ways to rearrange AB, BJ, AJ and a song from the set {N, A, B, J, AB, BJ, AJ}.
⇒ Case 1: Fourth song choices = N, A, B, J
All the four of choices for fourth song are different from the first 3 songs.
⇒ Number of ways to rearrange = 4! × 4 choices = 96.
⇒ Case 2: Fourth song choices = AB, BJ, AJ
All 3 of choices for fourth song repeat in the first three songs.
So, Number of ways to rearrange = (4!/2!) × 3 = 36,
So, total number of ways = 96 + 36 = 132.
Therefore, the required number of ways of arrangement is 132 ways, the correct option is (b).
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The given question is incomplete, the complete question is
Amy, Beth, and Jo listen to four different songs and discuss which ones they like. no song is liked by all three. furthermore, for each of the three pairs of the girls, there is at least one song liked by those two girls but disliked by the third. in how many different ways is this possible?
(a) 108
(b) 132
(c) 671
(d) 846
(e) 1105