Kitsap Corporation has provided the following contribution format income statement. Assume that the following information is within the relevant range. Sales (3,000 units) $ 180,000 Variable expenses 108,000 Contribution margin 72,000 Fixed expenses 62,400 Net operating income $ 9,600 The contribution margin ratio is closest to:
The contribution margin ratio can be calculated by dividing the contribution margin by the sales. In this case, the contribution margin ratio for Kitsap Corporation is closest to a certain value.
The contribution margin ratio is calculated by dividing the contribution margin by the sales. In the given information, the contribution margin is stated as $72,000 and the sales as $180,000.
Contribution Margin Ratio = (Contribution Margin / Sales) * 100
Contribution Margin Ratio = ($72,000 / $180,000) * 100
Contribution Margin Ratio = 40%
Therefore, the contribution margin ratio for Kitsap Corporation is 40%. The contribution margin ratio represents the proportion of each dollar of sales that is available to cover fixed expenses and contribute to net operating income. In this case, for every dollar of sales, 40 cents contribute towards covering fixed expenses and generating net operating income. The higher the contribution margin ratio, the greater the portion of sales revenue available to cover fixed costs and generate profit.
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A water tank has a density of 1000 kg/m3 and a mass of 100 kg.Calculate the volume of the water tank.l
[tex]D=m/V[/tex]
D = densitym = massV = volumeSolutionWe're given:
D = 1000 kg/m³m = 100 kgV = ?Plug these values into the equation and solve for V:
[tex]D=m/V\\1000=100/V\\V=100/1000\\V = 0.1[/tex]
The volume of the water tanks is 0.1 m³.
Answer:
0.1
Step-by-step explanation:
To calculate the volume of the tank, we will use the formula D = m ÷ V.
Here: D = density, m = mass, and V is the volume.
The formula rearranged for the volume is V = m ÷ d.
Here are the formulae:
[tex]\boxed{\boxed{\begin{aligned}\sf{d=m\div V}\\\sf{d\times V=m}\\\sf{V=m\div d\end{aligned}}}}[/tex]
Insert the values into the appropriate formula, i.e., V = m ÷ d:
V = 100 ÷ 1000V = 0.1 m³Hence, the volume of the water tank is 0.1 cubic meters
In a Stock Dividend Multiple Choice Assets increase, Liabilities decrease. Assets decrease, Liabilities increase. Assets increase, Liabilities increase. Assets decrease, Liabilities decrease. Assets don't change, Liabilities don't change.
In a Stock Dividend Assets don't change, Liabilities don't change.
In a stock dividend scenario, where a company issues additional shares of its own stock to existing shareholders, the impact on the company's balance sheet is as follows:
Assets don't change, Liabilities don't change.
When a company declares a stock dividend, it is essentially distributing a portion of its retained earnings or accumulated profits to its shareholders in the form of additional shares. This means that the company is not receiving any new assets or incurring any new liabilities in the process.
From an accounting perspective, the value of the stock dividend is reflected in the equity section of the balance sheet. The retained earnings account decreases by the value of the dividend, while the common stock or additional paid-in capital account increases by the same value. This adjustment does not affect the company's assets or liabilities.
Therefore, the correct answer is: Assets don't change, Liabilities don't change.
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A mountaibn has a 21-degree slope. the mountain reaches an altitude of 468 feet. if you hike to the tolp of the mountine starting at sea level, how far will you hike?
Hike will be of approximately 1201.75 feet to reach the top of the mountain starting from sea level.
The distance you will hike to reach the top of the mountain, we can use trigonometry and the given information about the slope and altitude.
The slope of the mountain is given as 21 degrees, and the altitude you reach is 468 feet.
Let's assume that the horizontal distance you hike is represented by "x."
Using trigonometry, we can use the tangent function to relate the angle and the opposite side (altitude) to the adjacent side (distance hiked).
Tangent of the slope angle = Opposite / Adjacent tan(21 degrees)
Tangent of the slope angle = 468 feet / x
To solve for x, we can rearrange the equation
x = 468 feet / tan(21 degrees)
we can find the tangent of 21 degrees, which is approximately 0.3894.
x = 468 feet / 0.3894
x ≈ 1201.75 feet
Therefore, you will hike approximately 1201.75 feet to reach the top of the mountain starting from sea level.
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How did the different levels of society have more or less money in the shang dynasty?
In the Shang Dynasty, the levels of society had varying levels of wealth. The ruling elite, including the royal family and high-ranking nobles, possessed significant wealth and power, while the commoners and lower classes had less access to resources and economic opportunities.
The Shang Dynasty in ancient China had a hierarchical social structure where wealth and resources were concentrated in the hands of the ruling elite. The royal family and high-ranking nobles occupied the top positions in society and enjoyed considerable wealth and privileges. They owned vast lands, controlled resources such as bronze and jade, and had access to luxury goods.
In contrast, the commoners and lower classes had limited economic resources. They mostly engaged in agricultural activities, working as farmers or laborers. They had less access to land, resources, and opportunities for upward mobility. Their wealth was modest, and their standard of living was generally lower compared to the ruling elite.
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At breakfast, lunch, and dinner, Joe randomly chooses with equal probabilities either an apple, an orange, or a banana to eat. On a given day, what is the probability that Joe will eat at least two different kinds of fruit
At breakfast, lunch, and dinner, Joe randomly chooses with equal probabilities either an apple, an orange, or a banana to eat.The probability of eating at least two different kinds of fruit, which is 26/27 .
Joe has three options (apple, orange, banana) with equal probabilities, the probability of choosing one specific fruit is 1/3. Therefore, the probability of eating only one kind of fruit is (1/3) * (1/3) * (1/3) = 1/27.
To find the probability of eating at least two different kinds of fruit, we subtract the probability of eating only one kind from 1. This is because the complementary event of eating at least two different kinds is eating only one kind.
1 - 1/27 = 26/27.
So, the probability that Joe will eat at least two different kinds of fruit on a given day is 26/27 or approximately 0.962.
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Math question the it’s below it contains Data, M.A.D etc please if u can help me help me I’m suffering rn
The mean absolute deviation for the data-set in this problem is given as follows:
C. 3 and 5/9.
How to obtain the mean absolute deviation of the data-set?The dot plot shows the number of times that each observations appears in the data-set.
Considering the dot plot, the mean of the data-set is given as follows:
Mean = (2 x 2 + 1 x 3 + 1 x 5 + 1 x 9 + 3 x 10 + 1 x 12)/(2 + 1 + 1 + 1 + 3 + 1)
Mean = 7.
The sum of the deviations is given as follows:
2 x |2 - 7| = 10.1 x |3 - 7| = 4.1 x |5 - 7| = 2.1 x |9 - 7| = 2.3 x |10 - 7| = 9.1 x |12 - 7| = 5.Hence the mean absolute deviation in this problem is given as follows:
MAD = (10 + 4 + 2 + 2 + 9 + 5)/(2 + 1 + 1 + 1 + 3 + 1)
MAD = 3.55.
Hence option C is the correct option for this problem.
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Abigail, ben , carmela, and david are standing in line, in that order, with carmela halfway between abigail and david. if the distance between abigail and ben 3 feet, and the distance between carmela and david is twice the distance between carmela and ben, which equation can be used to find the distance, x, feet , between abigail and david?
The algebraic equation that can be used to find the distance, x, between Abigail and David is x = 3 + 2b.
Let's break down the given information and determine the equation to find the distance, x, between Abigail and David.
Carmela is halfway between Abigail and David: This means that the distance between Abigail and Carmela is equal to the distance between Carmela and David. Let's denote this distance as d.
The distance between Abigail and Ben is 3 feet: Let's denote this distance as 3.
The distance between Carmela and David is twice the distance between Carmela and Ben: Let's denote the distance between Carmela and Ben as b. Therefore, the distance between Carmela and David is 2b.
Based on the given information, we can construct the equation:
Distance between Abigail and David = Distance between Abigail and Carmela + Distance between Carmela and David
x = d + 2b
Now, let's substitute the given information into the equation:
x = d + 2b
x = 3 + 2b
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In a gasoline direct-injection system, the location of the ________ varies, depending on the design.
In a gasoline direct-injection system, the location of the fuel injector varies, depending on the design. The correct answer is fuel injector.
The fuel injector is defined as a device that delivers gasoline directly into the combustion chamber of an engine. Its location within the system can affect the efficiency and performance of the engine, as well as the emissions it produces. Therefore, the design of the gasoline direct-injection system is crucial in determining the optimal location of the fuel injector.
Therefore, In a gasoline direct-injection system, the location of the fuel injector varies, depending on the design.
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Ô Exercise 15 1. Find the derivatives ax + b
Answer:
Step-by-step explanation:
Answer is in the pic...
Covalent bonds form between hydrogen and oxygen atoms in a water molecule as a result of thea. polarity of water molecules.b. sharing of electrons between atoms.c. surface tension of water.d. transfer of electrons between atoms.
Covalent bonds form between hydrogen and oxygen atoms in a water molecule as a result of the sharing of electrons between the atoms.
Covalent bonds are formed when atoms share electrons in order to achieve a stable electron configuration. In the case of a water molecule (H2O), each hydrogen atom shares one of its electrons with the oxygen atom. This sharing of electrons allows both atoms to achieve a more stable configuration by filling their outer electron shells.
The oxygen atom has six valence electrons, while each hydrogen atom has one valence electron. In order to achieve a stable configuration, the oxygen atom needs two additional electrons, while each hydrogen atom needs one additional electron. By sharing electrons, each hydrogen atom contributes one electron to the shared pair, while the oxygen atom contributes two electrons. This results in a total of two covalent bonds between the oxygen atom and the two hydrogen atoms in a water molecule.
Therefore, the correct answer is b. sharing of electrons between atoms. Covalent bonds are characterized by the sharing of electrons, and in the case of water, this sharing leads to the formation of the molecule's stable structure.
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If a $500 billion increase in investment spending increases income by $500 billion in the first round of the multiplier process and by $450 in the second round, income will eventually increase by: If a $500 billion increase in investment spending increases income by $500 billion in the first round of the multiplier process and by $450 in the second round, income will eventually increase by: $3,000 billion. $2,500 billion. $4,000 billion. $5,000 billion.
If a $500 billion increase in investment spending increases income by $500 billion in the first round of the multiplier process and by $450 billion in the second round, income will eventually increase by $2,500 billion.
The multiplier effect refers to the cumulative impact of an initial increase in spending on the overall income in an economy. In this case, the initial increase in investment spending is $500 billion, which leads to a direct increase in income by the same amount in the first round of the multiplier process. However, in subsequent rounds, the impact of the initial increase diminishes, resulting in a smaller increase in income.
The multiplier process follows a diminishing marginal propensity to consume (MPC), where individuals tend to save a portion of their additional income. Since the increase in income from the initial round is $500 billion, and in the second round it is $450 billion, we can infer that the MPC is 0.9 ([$450 billion increase]/[$500 billion initial increase]).
To calculate the eventual increase in income, we can use the formula for the multiplier: Multiplier = 1 / (1 - MPC). Plugging in the value of MPC (0.9), we find the multiplier to be 10 (1 / (1 - 0.9)).
Therefore, the eventual increase in income can be calculated as the product of the initial increase in spending and the multiplier: $500 billion * 10 = $5,000 billion. Thus, income will eventually increase by $5,000 billion.
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Analyze: remove all organisms except trees. click advance year a few times and select the data tab. was your prediction correct? explain what you found.
After removing all organisms except trees and advancing the year a few times while selecting the data tab, the accuracy of the prediction depends on the specific simulation or model being used.
The accuracy of the prediction would depend on the sophistication and accuracy of the simulation or model used. While such simulations can provide insights into tree growth patterns and dynamics, they are often simplified representations of complex ecosystems. Real-world ecological systems are influenced by numerous factors, including climate, soil conditions, competition for resources, diseases, pests, and interactions with other organisms. A simulation that only focuses on trees and excludes other organisms would neglect these crucial ecological dynamics.
Furthermore, the long-term behavior of trees is subject to uncertainties and unpredictability. Factors like climate change, natural disasters, and human activities can have significant impacts on tree populations, which may not be accurately captured in the simulation. Therefore, while the simulation may provide some general trends or patterns, its predictions might not align with real-world outcomes.
In conclusion, when removing all organisms except trees and advancing the year in a simulation, the accuracy of the prediction would depend on the specific model used.
However, due to the complexity of ecosystems and the exclusion of important ecological factors, the simulation's prediction may not accurately reflect real-world outcomes.
Understanding and predicting tree growth and behavior require comprehensive consideration of various ecological variables and their interactions.
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In , both feet can be off the ground at once. To avoid full impact on the joints, use . can be a better activity type for overweight individuals. increase(s) the number of calories used in a workout. Running is an example of . Short, high intensity segments included in a workout is/are called .
Introducing short, high-intensity segments in a workout is called interval training. This method can help boost calorie expenditure and improve overall fitness.
When engaging in running, there are moments during the running gait cycle where both feet are off the ground simultaneously. This phenomenon is known as the flight phase. Running is considered a high-impact activity, which means it puts stress on the joints, especially for individuals who are overweight or have joint-related issues. To mitigate this impact, low-impact exercises such as swimming or cycling can be more suitable for overweight individuals as they provide cardiovascular benefits with reduced stress on the joints.
While running may not be the ideal choice for overweight individuals concerned about the joint impact, it can be advantageous for increasing the number of calories burned during a workout. Running is a weight-bearing exercise that engages multiple muscle groups and requires more energy expenditure compared to low-impact exercises. This increased calorie burn can be beneficial for weight loss and improving cardiovascular fitness.
Interval training refers to a workout method that involves alternating periods of high-intensity exercise with periods of low-intensity or rest. This technique can be applied to various exercises, including running. By incorporating short, high-intensity segments, such as sprinting or running at a faster pace, into a workout, individuals can challenge their cardiovascular system, improve endurance, and burn more calories in a shorter amount of time. Interval training is known for its efficiency and effectiveness in boosting overall fitness levels.
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For students who earned a score of 20 or lower on the quiz, the cumulative frequency is __________ and the relative cumulative frequency is __________.
The cumulative frequency of students who earned a score of 20 or lower on the quiz is 34
The relative cumulative frequency of students who earned a score of 20 or lower on the quiz is 0.68
From the given image
The cumulative frequency of students who earned a score of 20 or lower on the quiz is = 4 + 8 + 15 + 7
= 34.
Total frequency is = 4 + 8 + 15 + 7 + 7 + 3 + 4 + 2 = 50.
The relative cumulative frequency is = 34/50 = 0.68 = 68%
Therefore, The cumulative frequency of students who earned a score of 20 or lower on the quiz is 34 and the relative cumulative frequency is 0.68
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Given question is incomplete, the complete question is below
For students who earned a score of 20 or lower on the quiz, the cumulative frequency is __________ and the relative cumulative frequency is __________.
The ratio a: bis 5:7.
The ratio b c is 7: 11.
What is the ratio a: b c in its simplest form?
If ratio a: bis 5:7 and the ratio b:c is 7: 11 then the simplest form of ratio a : b : c is 35 : 49 : 77.
Given that ratio a: b is 5:7.
The ratio b :c is 7: 11.
We have to find the ratio a: b c in its simplest form.
To simplify the ratio a : b : c, we can combine the ratios by multiplying the corresponding terms:
a : b : c = (5×7) : (7 × 7) : (7 × 11)
= 35 : 49 : 77
Therefore, the simplified ratio of a : b : c is 35 : 49 : 77.
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a cashier has a total of 30 bills, made up of ones, fives, and twenties. the number of twenties is 9 more than the number of ones. the total value of the money is $351. how many of each denomination of bills are there? (hint: let x
The problem needs determining the number of ones, fives, and twenties in a cashier's total of 30 bills, with more information regarding the relationship between twenties and ones and total value of the money.
To solve this, let's assign variables to represent the unknown quantities. Let's say the number of ones is x. Therefore, the number of twenties would be x + 9, according to the information given.
To calculate the total value of the money, we need to consider the value of each bill. A one-dollar bill has a value of $1, a five-dollar bill has a value of $5, and a twenty-dollar bill has a value of $20.
Now we can set up an equation to represent the total value:
x(1) + (x + 9)(20) + (30 - x - (x + 9))(5) = 351.
Simplifying the equation, we have:
x + 20x + 180 + 150 - 5x = 351,
36x + 330 = 351,
36x = 21,
x ≈ 0.583.
Since we cannot have a fraction of a bill, we must round the number of ones to the nearest whole number, which gives us 1. Therefore, there is 1 one-dollar bill.
The number of twenties can be found by substituting x into the expression x + 9, giving us 1 + 9 = 10 twenties.
Finally, to determine the number of fives, we subtract the total number of ones and twenties from the total number of bills: 30 - 1 - 10 = 19 fives.
Therefore, there is 1 one-dollar bill, 19 five-dollar bills, and 10 twenty-dollar bills in the cashier's total of 30 bills, amounting to a total value of $351.
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Charles Horton Cooley and George Herbert Mead both have theories on how individuals develop and modify their sense of self. What makes these theories different from one another
Charles Horton Cooley and George Herbert Mead both contributed to the understanding of self-development, but their theories differ in terms of the primary influence on the formation of self.
Cooley's theory emphasizes the role of social interactions and the "looking-glass self," while Mead's theory focuses on the significance of language and symbolic interaction. Charles Horton Cooley's theory of self-development revolves around the concept of the "looking-glass self." Cooley argued that individuals develop their sense of self through social interactions and feedback from others.
According to Cooley, people imagine how they appear to others and interpret their reactions, forming their self-perception based on these social reflections. The looking-glass self emphasizes the influence of social relationships and the perception of others in shaping one's identity.
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Harry paid $11.50 for a pizza and bounced a check. His bank paid the check because he has overdraft protection but charged him a $20 fee. How much did the pizza cost him
3x{x-x-30} explain this expression
Step-by-step explanation:
[tex]3x (x - x - 30) =( 3x \times x) - (3x \times x) -( 3x \times 30) = {3x}^{2} - {3x}^{2} - 90x = - 90x \\ [/tex]
a food truck sells 1200 burgers a week on average. the truck operates 7 days a week. (we will assume no variability from day to day.) the food truck owner of wants to be sure that the ingredients are fresh and that hamburger is not kept in the refrigerator more than 2 days on average. if each burger uses .25 pounds of hamburger, what should the maximum pounds of hamburger in the food truck be?
To ensure that the hamburger is not kept in the refrigerator for more than 2 days on average, the food truck should have a maximum of approximately 42.86 pounds of hamburger.
Given that the food truck sells an average of 1200 burgers per week, and it operates 7 days a week, we can calculate the total burgers sold per day:
Burgers per day = Total burgers per week / Number of days per week
Burgers per day = 1200 burgers / 7 days
Burgers per day ≈ 171.43 burgers
Since each burger uses 0.25 pounds of hamburger, we can calculate the maximum pounds of hamburger needed per day:
Pounds of hamburger per day = Burgers per day * Hamburger per burger
Pounds of hamburger per day = 171.43 burgers * 0.25 pounds/burger
Pounds of hamburger per day ≈ 42.86 pounds
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The maximum pounds of hamburger that should be stored in the food truck to ensure freshness and avoid exceeding 2 days on average is approximately 42.86 pounds.
To ensure that the hamburger is not kept in the refrigerator for more than 2 days on average, we need to calculate the maximum pounds of hamburger that should be stored in the food truck.
Average number of burgers sold per week = 1200
Number of operating days per week = 7
Weight of hamburger per burger = 0.25 pounds
To calculate the maximum pounds of hamburger, we can use the following formula:
Maximum pounds of hamburger = Average burgers sold per day × Number of days
First, we calculate the average number of burgers sold per day:
Average burgers sold per day = Average burgers sold per week / Number of operating days per week
Average burgers sold per day = 1200 / 7
Average burgers sold per day ≈ 171.43 (rounded to two decimal places)
Now, we can calculate the maximum pounds of hamburger:
Maximum pounds of hamburger = Average burgers sold per day × Weight of hamburger per burger
Maximum pounds of hamburger = 171.43 × 0.25
Maximum pounds of hamburger ≈ 42.86 (rounded to two decimal places)
Therefore, the maximum pounds of hamburger that should be stored in the food truck is approximately 42.86 pounds.
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how many independent variables can you test in a single experiment?
The number of independent variables that can be tested in a single experiment depends on various factors, including the research design, resources, and the complexity of the study. In general, it is best to limit the number of independent variables to maintain control over the experiment and facilitate clear interpretation of results.
In simpler experiments, researchers often focus on a single independent variable to study its effect on the dependent variable while controlling for other factors. This allows for a clear cause-and-effect relationship to be established.
However, in more complex experiments, researchers may introduce multiple independent variables to examine their combined effects or interactions. This can provide insights into how different factors influence the outcome simultaneously.
The exact number of independent variables that can be tested in a single experiment varies, but it is generally recommended to keep the number manageable and avoid excessive complexity. This ensures that the experiment remains feasible, interpretable, and effectively addresses the research question or hypothesis.
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What expression represents the value of x?
A: X=square root of w(w+z)
B: X=sqaure root of z(w+z)
C: X=sqaure root of wy
D: X= square root of wz
The expression to find the value of x is x = √(w + z)² - v².
How to find the side of a right triangle?A right angle triangle is a triangle that has one angle as 90 degrees. The
sum of angles in a triangle is 180 degrees.
Therefore, the expression to find x can be done using Pythagoras's theorem as follows:
c²= a² + b²
where
a and b are the other legsc = hypotenuseTherefore, the expression to find x is as follows:
x² = (w + z)² - v²
square root both sides
Therefore,
x = √(w + z)² - v²
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What’s the area of the figure?
Answer:
233 in²
Step-by-step explanation:
You want the area of the composite figure shown.
AreaThe area is the sum of the areas of the parts. The parts include a triangle, and a rectangle with a missing corner.
Triangle areaThe area of the triangle is given by the formula ...
A = 1/2bh
where b is the base and h is the height.
Here, we need to figure the missing dimension contributing to the height. The sum of right-side vertical line segments is 4 + 5 + 17 = 26. The bottom left vertical line segment is 6, so the height of the triangle is 26 -6 = 20.
The area of the triangle is ...
A = 1/2(12 in)(20 in) = 120 in²
Rectangle areaThe overall dimensions of the rectangle at lower right are 17 in wide by (4+5) = 9 in tall. From that, a piece is removed that is 8 in wide by 5 in tall. The remaining area is ...
A = LW
A = (17 in)(9 in) -(8 in)(5 in) = (153 -40) in² = 113 in²
Blue areaThe area shaded blue is the sum of the triangle area and the area of the notched rectangle:
total area = 120 in² +113 in² = 233 in²
The area of the figure is 233 square inches.
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3. Above are pictures of a regular pyramid and prism, both with square bases. One side of the
base of the pyramid has a length of 10 inches, one side of the base of the prism has a length of
10 inches, both solids have a height of 12 inches. The pyramid has a slant height of 13 inches.
Show ALL your work!
a. Which one has the larger surface area and by how much?
b. Which has the larger volume and by how much?
A book on the Nuer, which details their way of life based on firsthand observation is known as a(n) ___________________________________ and is based on fieldwork.
A book on the Nuer that provides a detailed account of their way of life based on firsthand observation is known as an ethnography and is based on fieldwork.
An ethnography is a form of qualitative research that involves firsthand observation and documentation of a particular culture or social group. It is a comprehensive study that aims to provide an in-depth understanding of the group's way of life, customs, beliefs, and practices. In the context of the Nuer, an ethnography would focus specifically on their culture, traditions, social structure, economic activities, religious beliefs, and other aspects that shape their way of life.
To produce an ethnography, the author typically engages in fieldwork, which involves immersing themselves in the culture and community being studied. This often includes living among the Nuer people, participating in their daily activities, conducting interviews, and observing their rituals and interactions. The firsthand experience and direct engagement with the Nuer community allow the author to gather detailed and accurate information to present a comprehensive account of their way of life in the book.
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LCM of x2 - x + 1 amnd x3 + 1 is
The LCM of x² - x + 1 and x³ + 1 is x³ + 1.
To find the LCM of two polynomials, we need to factorize each polynomial completely. In this case, x² - x + 1 is already in its irreducible form, so we cannot further factorize it. On the other hand, x³ + 1 can be factored as (x + 1)(x² - x + 1).
Next, we identify the common factors between the two polynomials, which is x² - x + 1. Since it appears in both polynomials, we include it in the LCM.
Finally, we multiply the common factors and the remaining factors from each polynomial. In this case, the LCM is (x²- x + 1)(x + 1), which simplifies to x³ + 1.
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My friend has $20$ stuffed animals. All of them are either cats or dogs, and all of them either have short or long fur. ${}12$ of them are cats, $15$ of them have long fur, and $4$ of them are short-furred dogs. How many stuffed animals are long-furred cats?
Answer:
11
Step-by-step explanation:
There are 8 dogs total with 4 being short furred, so 4 are long furred. If 15 total stuffed animals have long fur and 4 of them are dogs, 11 of them are cats.
Seven sticks with lengths 2, 3, 5, 7, 11, 13 and 17 inches are placed in a box. Three of the sticks are randomly selected. What is the probability that a triangle can be formed by joining the endpoints of the sticks
The probability to form a triangle using the endpoints of the sticks is 3/35 or approximately 0.0857 (rounded to four decimal places).
Length of the seven sticks in inches = 2, 3, 5, 7, 11, 13, and 17.
Number of sticks selected randomly = 3
To determine the probability of forming a triangle by randomly selecting three sticks from the given set,
Consider the triangle inequality theorem.
According to the theorem, for a triangle to be formed,
The sum of the lengths of any two sides of the triangle must be greater than the length of the third side.
Let us analyze the possibilities,
Selecting sticks with lengths 2, 3, and 5,
In this case, we can form a triangle because 2 + 3 > 5, 3 + 5 > 2, and 5 + 2 > 3.
Selecting sticks with lengths 2, 3, and any other stick greater than 5,
As the longest stick is greater than the sum of the two smaller sticks (2 + 3), we can form a triangle.
Selecting sticks with lengths 2, 3, and the longest stick (17),
In this case, we cannot form a triangle because 2 + 3 is not greater than 17.
In total, there are 3 possible combinations that can form a triangle out of the total 7C3 = 35 combinations selecting 3 sticks out of 7.
Probability
= favourable outcomes / total number of outcomes
= 3/ 35
Therefore, the probability of forming a triangle is 3/35.
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what number is that which if increased by 20 of itself equals 48
Answer:
28
Step-by-step explanation:
let the number be n then increased by 20 = n + 20 and
n + 20 = 48 ( subtract 20 from both sides )
n = 28
