On dividing 28.5 by 10 we get 2.85.
What is Equation Modelling?Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem.
Given is 28.5 divided by 10.
Assume that on dividing 28.5 by 10, we get [x]. Then -
10x = 28.5
x = 28.5/10
x = 2.85
Therefore, on dividing 28.5 by 10 we get 2.85.
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Find the volume of the cylinder. Use 3.14 for pi. *
5
13
Answer:
1021.02
Step-by-step explanation:
hope this helped!
Hi can someone help me to solve this? I would be so appreciated if you willing to help me
Nora and Farhan were asked to simplify (2x²/y)³
Nora wrote this : (2x²/y)³ = 2x⁶/y³
Farhan wrote this : (2x²/y)³ = 8x⁵/y
Both Nora and Farhan obtained the wrong solutions.
(i) Highlight the possible misconceptions that Nora and Farhan might have.
Nora's misconceptions:
Farhan's misconceptions:
(ii) provide the correct solution :
Answer:
HOPE ITS HELPFUL TO yours
Normalmente, el concepto griego "logos" se entiende como la máxima expresión de la cultura racionalista occidental, fundada por las primeras escuelas de filosofía clásica. De hecho, el nombre de las disciplinas científicas provienen de él: biología, filología, psicología, tecnología, etc. No obstante, el concepto "logos" no tiene un significado tan abstracto, puesto que involucra tanto el pensamiento como la acción, tanto lo interno como lo externo, tanto la idea mental como el decir la palabra. Tema:_________________________________________________________ Idea Principal: ___________________________________________________
Concept: "Logos" has had a significant impact on Western thought. Importance: its recognition of the interplay between rational thought and empirical observation Acknowledgement: role of language and discourse in shaping our understanding of the world.
Topic: The concept of "Logos" in Greek philosophy and its significance in modern scientific fields.
The concept of "Logos" is central to Greek philosophy and has been interpreted in various ways throughout history. In its most basic sense, "Logos" refers to rational thought, speech, and language. It is often associated with the divine or the cosmic principle that governs the universe, as well as human reasoning and discourse.
The significance of "Logos" can be seen in its influence on modern scientific fields, including biology, psychology, and technology, among others. The term "biology," for example, comes from the Greek words "bios" (life) and "logos" (word or reason), reflecting the idea that the study of life requires both empirical observation and rational analysis.
Similarly, the field of psychology, which deals with the workings of the human mind and behavior, derives its name from the Greek word "psyche," meaning "soul," and "logos," meaning "reason." This reflects the idea that the study of the mind and behavior requires both empirical research and theoretical analysis.
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Translation: The Greek word "logos" is typically interpreted as the pinnacle of Western rationalist civilization, having been established by the first schools of classical philosophy. In reality, he is responsible for the names of many scientific fields, including biology, philology, psychology, technology, and others. Since it requires both mind and action, internal and external, the mental notion and pronouncing the word, the concept of "logos" does not have such an abstract meaning. Topic:____________________________________________________ Principal Concept:
can you find the answer for m
Answer:
m∠LMK = 50°
Step-by-step explanation:
This is an isosceles triangle. Isosceles triangles have two sides of equal length and two equal angles. This means ∠K and ∠M will have the same degrees.
The sum of the angles of a triangle is 180°. The following equation can be arranged and solved for the missing angles:
\(x+x+80=180\\2x+80=180\\2x=100\\x=50\)
Therefore, m∠LMK = 50°.
Jose's ball is stuck on the roof of his home, which is 8 feet high. He wants to use a ladder to climb up and get his ball. If he sets the base of the ladder 6 feet away from his home, what is the minimum length that the ladder can be? Explain how you solved this question using context and at least three sentences. Hint: Draw your the scenario and label given values.
Answer:
10 feet
Step-by-step explanation:
It becomes a right-angled triangle with height of 8feet and base of 6feet.
Using Pythagoras theorem:
a² = b² + c²
a² = 8² + 6²
a² = 64 + 36
a² = 100
a = √100
a = 10
Help please! (15 points)
Evan spent 20 hours doing homework last week. This week he spent 25 hours doing homework. He says that he spent 125% more time doing homework this week. Is he correct? Show your work to justify your decision.
Answer:
Yes, he is correct.
Step-by-step explanation:
5 is 25% of 20
We know he spends 25 hours.
20 hours are 100%, and 5 hours is 25%.
If we add them, we get 125%.
Multiply the starting price by the right term that uses the compound average to show that the arithmetic mean does not recover the final price while the geometric and continuous means do. Convert the percent averages to fractions.
$53. 07 x (1 + arith mean) 3 = 53.07 x (1 + #21 %) 3 = #22
$53. 07 x (1 + geom mean) 3 = 53.07 x (1 + #23 %) 3 = $ #24
$53. 07 x e cont mean x 3 = 53.07 x e #25 % x 3 = $ #26
I need help filling out numbers #21 through #26
The values for numbers #21 through #26 are as follows:
#21: 2.33% or 0.0233. #22: $56.4842. #23: 1.85% or 0.0185. #24: $56.4148. #25: 3.64% or 0.0364. #26: $57.4397
#21: 2.33% (arithmetic mean as a fraction: 0.0233)
#22: $56.4842 (result of the calculation)
#23: 1.85% (geometric mean as a fraction: 0.0185)
#24: $56.4148 (result of the calculation)
#25: 3.64% (continuous mean as a fraction: 0.0364)
#26: $57.4397 (result of the calculation)
To fill out numbers #21 through #26, we need to calculate the values for each term using the given information and convert the percentages to fractions.
#21: The arithmetic mean is given as a percentage. Convert it to a fraction by dividing by 100. Therefore, #21 = 2.33% = 0.0233.
#22: Multiply the starting price ($53.07) by the compound factor (1 + arithmetic mean)^3. Substitute the value of #21 into the calculation. Therefore, #22 = $53.07 x (1 + 0.0233)^3 = $56.4842.
#23: The geometric mean is given as a percentage. Convert it to a fraction by dividing by 100. Therefore, #23 = 1.85% = 0.0185.
#24: Multiply the starting price ($53.07) by the compound factor (1 + geometric mean)^3. Substitute the value of #23 into the calculation. Therefore, #24 = $53.07 x (1 + 0.0185)^3 = $56.4148.
#25: The continuous mean is given as a percentage. Convert it to a fraction by dividing by 100. Therefore, #25 = 3.64% = 0.0364.
#26: Multiply the starting price ($53.07) by the continuous factor e^(continuous mean x 3). Substitute the value of #25 into the calculation. Therefore, #26 = $53.07 x e^(0.0364 x 3) = $57.4397.
Hence, the values for numbers #21 through #26 are as calculated above.
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Katrina is going to order sweatshirts for her girls mentoring group. The sweatshirts will have the group logo printed on the front. Katrina asks two local companies to give her a price.
MH Designs will charge $21. 50 for each of the sweatshirts.
Print Rich will charge $18 for each sweatshirt plus a one-time setup cost of $70.
Justify how to determine the number of sweatshirts Katrina would need to order from each company for the costs to be the same.
Use a visual representation to explain when the total cost from MH Designs would be less than the total cost from Print Rich
If Katrina orders 62.5 sweatshirts or fewer, the total cost from MH Designs would be less than the total cost from Print Rich.
To determine the number of sweatshirts that Katrina would need to order from each company for the costs to be the same, you would need to set up and solve an equation. The equation would represent the total cost of the sweatshirts from each company.
From MH Designs, the total cost would be $21.50 per sweatshirt * the number of sweatshirts ordered.
From Print Rich, the total cost would be $18 per sweatshirt * the number of sweatshirts ordered + $70 for the one-time setup cost.
You can set up the equation like this:
$21.50/sweatshirt * x sweatshirts = $18/sweatshirt * x sweatshirts + $70
Where x represents the number of sweatshirts being ordered.
Solving for x, you get x = 62.5 sweatshirts.
So, if Katrina orders 62.5 sweatshirts or fewer, the total cost from MH Designs would be less than the total cost from Print Rich.
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3 · (7 – 2) – 23 – (10 – 4) : 9
Answer:
-14:9
Step-by-step explanation:
Given :
3 · (7 – 2) – 23 – (10 – 4) : 9
Now,
3 · (7 – 2) – 23 – (10 – 4) : 9
21-6-23-6:9
21-35:9
-14:9
Answer will be -14:9
Evaluate the integral: S1 0 (-x³ - 2x² - x + 3)dx
The integral: S1 0 (-x³ - 2x² - x + 3)dx is -1/12
An integral is a mathematical operation that calculates the area under a curve or the value of a function at a specific point. It is denoted by the symbol ∫ and is used in calculus to find the total amount of change over an interval.
To evaluate the integral:
\($ \int_0^1 (-x^3 - 2x^2 - x + 3)dx $\)
We can integrate each term of the polynomial separately using the power rule of integration, which states that:
\($ \int x^n dx = \frac{x^{n+1}}{n+1} + C $\)
where C is the constant of integration.
So, we have:
\($ \int_0^1 (-x^3 - 2x^2 - x + 3)dx = \left[-\frac{x^4}{4} - \frac{2x^3}{3} - \frac{x^2}{2} + 3x\right]_0^1 $\)
Now we can substitute the upper limit of integration (1) into the expression, and then subtract the result of substituting the lower limit of integration (0):
\($ \left[-\frac{1^4}{4} - \frac{2(1^3)}{3} - \frac{1^2}{2} + 3(1)\right] - \left[-\frac{0^4}{4} - \frac{2(0^3)}{3} - \frac{0^2}{2} + 3(0)\right] $\)
Simplifying:
\($ = \left[-\frac{1}{4} - \frac{2}{3} - \frac{1}{2} + 3\right] - \left[0\right] $\)
\($ = -\frac{1}{12} $\)
Therefore,
\($ \int_0^1 (-x^3 - 2x^2 - x + 3)dx = -\frac{1}{12} $\)
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A survey was given to a random sample of 1350 residents of a town to determine whether they support a new plan to raise taxes in order to increase education spending. Of those surveyed, 64% of the people said they were in favor of the plan. At the 95% confidence level, what is the margin of error for this survey expressed as a percentage to the nearest tenth?
The margin of error for the survey, rounded to the nearest tenth, is approximately 4.0% when expressed as a percentage.
To determine the margin of error for a survey at the 95% confidence level, we need to calculate the standard error. The margin of error represents the range within which the true population proportion is likely to fall.
The formula for calculating the standard error is:
Standard Error = sqrt((p * (1 - p)) / n)
where p is the sample proportion and n is the sample size.
In this case, the sample proportion is 64% (or 0.64) since 64% of the 1350 surveyed residents support the plan.
Plugging in the values:
Standard Error = \(\sqrt{(0.64 * (1 - 0.64)) / 1350)}\)
\(= \sqrt{(0.2304 / 1350)} \\= \sqrt{(0.0001707)}\)
≈ 0.0131
Now, to find the margin of error, we multiply the standard error by the appropriate critical value for a 95% confidence level. The critical value corresponds to the z-score, which is approximately 1.96 for a 95% confidence level.
Margin of Error = z * Standard Error
= 1.96 * 0.0131
≈ 0.0257
Finally, to express the margin of error as a percentage, we divide it by the sample proportion and multiply by 100:
Margin of Error as Percentage = (Margin of Error / Sample Proportion) * 100
= (0.0257 / 0.64) * 100
≈ 4.0%
Therefore, the margin of error for this survey, expressed as a percentage to the nearest tenth, is approximately 4.0%.
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2) lame furniture company makes two products for its adoring public: chairs (c) and tables (t). each chair requires 5 hours of labor (l) and 12 linear feet of rich mahogany (m), and each table requires 9 hours of labor and 24 linear feet of rich mahogany. the company has 300 labor hours available this week, and the warehouse has 800 linear feet of rich mahogany available. profit for each chair is $900 and for each table is $1300. in order to maximize profit, how many tables and how many chairs should be produced? (use excel) a) t
The mentioned company should do production of atleast 50 chairs and 0 tables in order to maximize its profit.
Let's represent the number of chairs and tables produced by the company as "x" and "y" respectively.
The constraints of the problem can be summarized as follows:
5x + 9y ≤ 300 (labor constraint)
12x + 24y ≤ 800 (mahogany constraint)
x, y ≥ 0 (non-negativity constraint)
The objective is to maximize the profit, which can be represented as:
Profit = 900x + 1300y
We can use linear programming to solve this problem. First, we can graph the constraints on a coordinate plane and shade the feasible region (the region that satisfies all the constraints)
We can evaluate the objective function from the graph at each corner point to determine the maximum profit,
(0, 0): Profit = 0
(0, 33.33): Profit = 43,333.33
(20, 10): Profit = 29,000
(50, 0): Profit = 45,000
Therefore, the company should produce 50 chairs and 0 tables to maximize its profit.
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What is the IQR for the following set of data
17, 11, 12, 18, 12, 16, 15, 14, 13
Answer:
First, we have to set it from least to greatest 11, 12, 12, 13, 14, 15, 16, 17, 18
The interqurtile range is q3 - q1
Q3 is 16.5 and the q1 is 12
16.5 - 12 = 4.5
Step-by-step explanation:
Answer is 4.5
Interquartile range (IQR) :
The interquartile range shows the range in values of the central 50% of the data. To find the interquartile range, subtract the value of the lower quartile ( or 25%) from the value of the upper quartile ( or 75%).
=> IQR = Q3 – Q1
Here,
First Arrange the data in ascending order.
11, 12, 12, 13, 14, 15, 16, 17, 18
Median = 14.
Q1 = 12 and Q3 = 16.5
IQR = Q3 - Q1 => 16.5 - 12 = 4.5
Answer is 4.5
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help me with this answer please
Answer:
(0,3)
Step-by-step explanation:
on the y-axis, the point is 3 points above 0 so its (0,3)
Answer:
(0,3)
Step-by-step explanation:
y - intercept is where the line intersects the y-axis and that is at the point (0,3)
Please answer if you actually know.
Answer:
A is correct bro because W(work done)=F(force)*S(distance)
Step-by-step explanation:
Answer:
A
Step-by-step explanation:
carney needs $60 to buy her mother a gift. She has saved 25% of that amount so far. Bow much has she saved so far
Answer:
$15.00
Step-by-step explanation:
25% of anything means a quarter of that thing. (ie.1/4 of $60 which is $15).
OR
(25/100)*$60
0.25*60=$15
Economic growth typically results in rising standards of living and prosperity. However, it also invites negative externalities such as environmental degradation due to over- exploiting of natural resources. As such, the world is confronted with the dilemma of growth versus environmental sustainability. Developing a model explaining the disparity of economic development concentrating on drivers such as tourism sustainability, technological innovation and the quality of leadership would be important not only to facilitate future economic growth in developing countries, but also to the environmental and sociocultural sustainability which ultimately lead to global sustainable development. The present research objective is to develop and test framework of sustainable development by considering the elements of tourism, technological innovation, and national leadership. This further would facilitate growth, environmental and socio-cultural sustainability. Understanding the integration of these dimensions would enable the building of a Sustainable Development Framework (SDF) that would provide better insight in promoting the SDGS agenda. Ultimately, growth and environmental sustainability can be achieved which will benefit the society, the economy, and nations and of course for future sustainable policy recommendation. Based on the issue above, you are required to propose relevant econometric approaches with the aims to test sustainable development by considering the elements of tourism, technological innovation, and national leadership. Question 1 [10 marks] [CLO2] Based on the scenario above, a. Propose an appropriate model specification based on the scenario above. [4 marks] used in the [4 marks] [2 marks] b. Justify the selection of the dependent and independent variables model. c. Justify the selection of the sample period.
According to the given information, the sample period should be from 2010-2020.
a) Model specification
The model specification based on the scenario above is as follows:
SDF= f(T, TI, NL)
Where: SDF= Sustainable Development Framework
T= Tourism
TI= Technological innovation
NL= National leadership
b) Justification for the selection of the dependent and independent variables model:
Dependent variable: The dependent variable in this model is Sustainable Development Framework (SDF). The model seeks to develop a framework for sustainable development that would facilitate growth, environmental and socio-cultural sustainability.
Independent variables:
The independent variables are tourism sustainability, technological innovation, and quality of leadership. These variables drive economic development. The inclusion of tourism sustainability reflects its importance in the global economy and its potential to drive growth.
The inclusion of technological innovation reflects its potential to enhance productivity and create new industries. The inclusion of national leadership reflects the role of governance in promoting sustainable development and managing negative externalities.
c) Justification for the selection of the sample period:
The sample period should be selected based on the availability of data for the variables of interest. Ideally, the period should be long enough to capture trends and patterns in the data. However, it should not be too long that the data becomes obsolete or no longer relevant.
Additionally, the period should also reflect the context and relevance of the research question. Therefore, the sample period for this study should cover the last decade to capture the trends and patterns in the data and reflect the relevance of the research question.
The sample period should be from 2010-2020.
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Convert to a mixed number and simplify: 83 over 6
Answer:
\(13\frac{5}{6}\)
Step-by-step explanation:
\(\frac{60}{6}=10\) (low estimate to make later estimates easier)
\(10+\frac{24}{6} =14\) (high estimate, must make lower)
\(14*6\neq 83\) (incorrect estimate)
\(84-83=1\) (correcting estimate)
\(14-\frac{1}{6} =13\frac{5}{6}\) (corrected estimate)
The graph below shows segment FG and point P what is the first coordinate of point M
Note that the first coordinate of M is -1. (Option D)
Why is this so?
Given :- coordinates of F = (-4,-2) = (x1,y1)
coordinates of G = (2,-2) = (x2,y2)
coordinates of P = (2,-8) = (x3,y3)
and distance between point M and P is half of the distance between FG
To find :- first coordinate of point M
solution :- let the coordinate of M be (x4,y4)
as we know that distance between of the opposite point of parallel line segments are equal
so, second coordinate of M = -8
now by distance formula
FG = √(x2-x1)² + (y2-y1²)
= √[2-(-4)]² + [-2-(-2)]²
= √(2+4)² + (2-2)²
= √(6)² + (0)²
=√36
F G = 6
so, distance between point M and P = 1/2 × F G
= 1/2 × 6
= 3units
again, by distance formula
MP = √(x3-x⁴)² + (y3-y4)²
3 = √(2-x⁴)² + [-8-(-8)]²
squaring on both side
(3)² = (√(2-x⁴)² + [-8-(-8)]²)²
9 = (2-x⁴)² + [-8-(-8)]²
9 = (2-x⁴)²+(0)²
9 = (2-x⁴)²
√9 = 2-x⁴
3 = 2-x⁴
x⁴ = 2-3
x⁴ = -1
Hence the first coordinate of M is -1
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Full Question:
Although part of your question is missing, you might be referring to this full question:
Point M is located in the third quadrant.
The distance between point M and point P is half the distance between point F and point G.
• Segment MP is parallel to segment FG. What is the first coordinate of point M?
by how much does -12 exceed -15
Answer:
By 3.
Step-by-step explanation:
-12-3=-15
Hope this helps!
Answer:
-12 exceeds -15 by 3
Step-by-step explanation:
To find out by how much a exceeds b, subtract a - b.
For example, by how much does 8 exceed 6?
Here, a = 8 and b = 6.
a - b = 8 - 6 = 2
2 is correct since we know that 8 is 2 greater than 6.
Now we do this problem.
By how much does -12 exceed -15?
a = -12; b = -15
a - b = -12 - (-15) = -12 + 15 = 3
Answer: -12 exceeds -15 by 3
A sociologist finds that for a certain segment of the population, the number of years of formal education have a mean of 13.2 years and a standard deviation of 2.96 years.if 35 people are randomly selected from this group, find the probability that their mean years of education is at least 12 years.
To find the probability that the mean years of education for a sample of 35 people is at least 12 years, we need to use the Central Limit Theorem (CLT) and the properties of the normal distribution.
Given:
- Mean (μ) of the population = 13.2 years
- Standard deviation (σ) of the population = 2.96 years
- Sample size (n) = 35
Using the CLT, we know that for a sufficiently large sample size (n ≥ 30), the sampling distribution of the sample mean approaches a normal distribution, regardless of the shape of the population distribution.
To calculate the probability, we need to standardize the sample mean using the z-score formula and then find the corresponding area under the standard normal curve.
Step 1: Calculate the standard error of the mean (SE):
SE = σ / √n
SE = 2.96 / √35
SE ≈ 0.5013
Step 2: Calculate the z-score for the given mean of 12 years:
z = (x - μ) / SE
z = (12 - 13.2) / 0.5013
z ≈ -2.395
Step 3: Find the area under the standard normal curve for z ≥ -2.395:
P(z ≥ -2.395) can be obtained using a standard normal distribution table or a calculator. The corresponding area is approximately 0.9911.
Therefore, the probability that the mean years of education for a sample of 35 people is at least 12 years is approximately 0.9911, or 99.11%.
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Two APs have same common difference. If the first term is -1 and that of the other is -8. then the difference between their 4th term is?
Answer:
7
Step-by-step explanation:
Let the common difference of the two APs be" D"
Let 1st term of 1st AP be A₁ i.e = -1
And the first term of the second AP b₁ i.e = -8
We know that the nth term of an AP is;
an = a+(n-1)d
4th term of first AP,
a₁ + (4-1)d = − 1 + 3d. --Eqn. 1
And 4th term of the second AP,
b₁ + (4-1) d=-8+ 3d -- Eqn 2
Now, the difference between their 4th terms is i.e.
= (- 1+ 3d ) - (-8 + 3d )
= -1 + 3d + 8 - 3d = 7
So, the answer is 7.
pls do 1 throw 7 ill name you brainleiss and give you all my points
Answer:
the first one is correct
2) 0.805
3)0.25675
4)234.5
5)190.5
6)1.884666667
7)59.375
Step-by-step explanation:
Answer:
2) 0.805
3)0.25675
4)234.5
5)190.5
6)1.884666667
7)59.375
Step-by-step explanation:
Blas y Raul se han colocado en línea recta en lados opuestos de un generador eólico para medir su altura el terreno es llano y los dos amigos están separados por 41 m cada uno desde su posición mide el ángulo con el que se ve el generador desde el suelo qué altura tiene el generador
Answer:
La pregunta esta incompletea porque no incluye el angulo de Raul y el angulo de Blas. Busque un ejemplo similar y encontre que el angulo de Blas es 60° y el de Raul es 45°. Suponiendo que ambos midieron el angulo desde el suelo:
tangente 60° = altura / (41 - d)
tangente 45° = altura / d
altura = (41 - d) · tangente 60° = (41 - d) · 1.73205
altura = d · tangente 45° = d · 1
d = 71.01408 - 1.73205d
2.73205d = 71.01408
d = 71.01408 / 2.73205 = 25.993 ≈ 26 metros
sustituimos:
altura = d · tangente 45° = 26 · 1 = 26 metros
La altura del generador es de 26 metros
What is the probability of a magnitude 7.0-7.9 earthquake in the Los Angles area in the next 30 years if the recurrece interval of such an earthquake is 95 years
The probability of a magnitude 7.0-7.9 earthquake occurring in the Los Angeles area in the next 30 years is approximately 0.283, or about 28.3%.
To estimate the probability of a magnitude 7.0-7.9 earthquake in the Los Angeles area in the next 30 years, given a recurrence interval of 95 years, we can use the Poisson distribution. The Poisson distribution is often used to model the occurrence of rare events, such as earthquakes.
Let λ be the average number of earthquakes of magnitude 7.0-7.9 that occur in the Los Angeles area per unit time, which is given by:
λ = 30 years / 95 years = 0.3158 earthquakes per year
Now, let X be the number of earthquakes of magnitude 7.0-7.9 that occur in the Los Angeles area in the next 30 years. X follows a Poisson distribution with mean λ, which can be expressed as:
P(X = k) = (e^(-λ) * λ^k) / k!
where e is the base of the natural logarithm, and k is the number of earthquakes.
To find the probability of at least one earthquake occurring in the next 30 years, we can sum the probabilities of X = 1, 2, 3, ... up to infinity:
P(X ≥ 1) = 1 - P(X = 0) = 1 - e^(-λ) = 1 - e^(-0.3158) ≈ 0.283
Therefore, the probability of earthquake in next 30 years is approximately 0.283, or about 28.3%.
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find the value of x
Answer:
x = 12
Step-by-step explanation:
In a pair of intersecting lines the vertically opposite angles are equal.
\( \longrightarrow \) (6x + 7)° = (8x - 17)°
\( \longrightarrow \) 6x + 7 = 8x - 17
Subtract 8x + 7 from both sides:
\( \longrightarrow \) 6x + 7 - (8x + 7) = 8x - 17 - (8x + 7)
\( \longrightarrow \) (6x - 8x) + (7 - 7) = (8x - 8x) + (-17 - 7)
6x - 8x = -2x:
\( \longrightarrow \) -2x + (7 - 7) = (8x - 8x) + (-17 - 7)
7 - 7 = 0:
\( \longrightarrow \) -2x = (8x - 8x) + (-17 - 7)
8x - 8x = 0:
\( \longrightarrow \) -2x = -17 - 7
-17 - 7 = -24:
\( \longrightarrow \) -2x = -24
Divide both sides by -2:
\( \longrightarrow \) \( \sf \dfrac{-2x}{-2} = \dfrac{-24}{-2} \)
\( \sf \dfrac{-2}{-2} = 1 \)
\( \longrightarrow \) \( \sf x = \dfrac{-24}{-2} \)
\( \sf \dfrac{-24}{-2} = 12 \)
\( \longrightarrow \) x = 12
Partial fraction decomposition
20x+9/25x^2+20x+4
Step-by-step explanation:
We have
\( \frac{20x + 9}{25 {x}^{2} + 20x + 4 } \)
Let's factor the denomiator first,
the denomaitor is a perfect square so we get
\( \frac{20x + 9}{(5x + 2) {}^{2} } \)
Now, we must think of two fractions that
\( \frac{a}{(5x + 2) {}^{2} } + \frac{b}{5x + 2} \)
We use a perfect square term for one fraction, then a linear one for the next, because if we set both of the denomiator to the same factor, we would get a inconsistent system.
So right now, we have
\( \frac{a}{(5x + 2) { }^{2} } + \frac{b}{5x + 2} = \frac{20x +9 }{25 {x}^{2} + 20x + 4 } \)
\(a + (5x + 2)b = 20x + 9\)
\(5b (x)= 20\)
\(a + 2b = 9\)
\(b = 4\)
so that means that a is
\(a + (2)(4) = 9\)
\(a + 8 = 9\)
\(a = 1\)
So our equation is
\( \frac{1}{(5x + 2) {}^{2} } + \frac{4}{5x + 2} \)
An elevator starts on the ground floor. It goes up 7 floors. Down 3 floors then up 4 floors. What floor is the elevator on now?
I’ll love your comment and give it 5 stars!
Answer: Floor 8
Step-by-step explanation:
Starting on from the ground floor, the elevator goes up 7 floors. We are now on floor 7.
Then it goes down 3 floors, so 7 - 3 = 4, we are now on floor 4.
Finally, the elevator goes up 4 floors, 4 + 4 = 8, we are now on floor 8
Answer:
It is on the 8th floor.
Step-by-step explanation:
0 + 7 = 7
7 - 3 = 4
4 + 4 = 8
Show that cos^2α+cos^2β+cos^2γ=1
We can use the Pythagorean identity one more time to get:
cos^2(a)t + cos^2(B) + cos^2(y) = 1
What is Trigonometry ?
Trigonometry is the branch of mathematics that studies the relationships between the sides and angles of triangles. Trigonometry is found throughout geometry because every shape with equal sides can be broken down into a collection of triangles.
The identity you want to prove is:
cos^2(a)t cos^2(B) + cos^2(y) = 1
We can start by using the Pythagorean identity for sine and cosine:
sin^2(x) + cos^2(x) = 1
cos^2(x) = 1 - sin^2(x)
We can use this identity to substitute for cos^2(a)t and cos^2(B):
cos^2(a)t cos^2(B) = (1 - sin^2(a)t)(1 - sin^2(B))
Expanding this expression, we get:
cos^2(a)t cos^2(B) = 1 - sin^2(a)t - sin^2(B) + sin^2(a)t sin^2(B)
Now we can substitute this expression back into the original identity:
cos^2(a)t cos^2(B) + cos^2(y) = 1
(1 - sin^2(a)t)(1 - sin^2(B)) + cos^2(y) = 1
Expanding the left side and simplifying, we get:
1 - sin^2(a)t - sin^2(B) + sin^2(a)t sin^2(B) + cos^2(y) = 1
sin^2(a)t sin^2(B) + cos^2(y) = sin^2(a)t + sin^2(B)
Now we can use the Pythagorean identity again:
sin^2(a)t + sin^2(B) = 1 - cos^2(a)t - cos^2(B)
Substituting this expression, we get:
sin^2(a)t sin^2(B) + cos^2(y) = 1 - cos^2(a)t - cos^2(B)
Finally, we can use the Pythagorean identity one more time to get:
cos^2(a)t + cos^2(B) + cos^2(y) = 1
which is the identity we wanted to prove.
To learn more about Trigonometry from the given link
https://brainly.in/question/1131710
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3. Sally invested $5,000.00 in a savings account earning 3.49% simple interest. At the same time
Jon invested $3,000.00 in a money market account at a simple interest rate of 7.5%. How many
years will it take for the two to have the same amount of money in their accounts? How much
money do they have after that time period?
Answer:
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