The area within the floor plan that Mutt can roam is determined as 37.7 m².
What is the area that Mutt can roam?
The total possible area that Mutt can roam is calculated as follows;
A = πr²
where;
r is the radius if the circle = length of Mutt's leash = 6 mA = π (6 m)²
A = 113.1 m²
The area outside the 120⁰ is calculated as follows;
θ = 360 - 120
θ = 240⁰
A = 240⁰/360 x 113.1 m²
A = 75.4 m²
The area that Mutt can roam is calculated as follows;
A = 113.1 m² - 75.4 m²
A = 37.7 m²
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please help someone..50 points
Answer:
We can find the sum of the interior angles of any polygon using the formula
[tex]S_{n}=180(n-2)[/tex], where n is the number of sides.
Because each of these polygons have four sides, we can use one formula where our n is 4 to find the sum of the interior angles:
[tex]S_{4}=180(4-2)\\ S_{4}=180*2\\ S_{4}=360[/tex]
Thus, for all four problems, we can set the four angles equal in the four polygons equal to 360 and solve for the variables
(15) *Note the right angle symbol in this problem which always equals 90°
[tex]84+90+(2x+118)+(2x+68)=360\\174+2x+118+2x+68=360\\360+4x=360\\4x=0\\x=0[/tex]
Now, to find the measure of <Y, we simply plug in 0 for x in its equation
m<Y = 2(0) + 118 = 118°
(16):
[tex]82+105+(8x+11)+10x=360\\187+8x+11+10x=360\\198+18x=360\\18x=162\\x=9[/tex]
To find the measure of <F, we plug in 9 for x in its equation
m<F = 10(9) = 90°
(17):
[tex]95+95+(10x-5)+(8x+13)=360\\190+10x-5+8x+13=360\\198+18x=360\\18x=162\\x=9[/tex]
To find the measure of <M, we plug in 9 for x in its equation
m<M = 10(9) - 5 = 85°
(18):
[tex](14x-7)+(11x-2)+93+76=360\\14x-7+11x-2+169=360\\25x+160=360\\25x=200\\x=8[/tex]
To find the measure of <M, we plug in 8 for x in its equation
m<M = 11(8) - 2 = 86°
in a binomial experiment, the . a. probability of success does not change from trial to trial b. probability of success does change from trial to trial c. probability of success could change from trial to trial, depending on the situation under consideration d. probability of success is always the same as the probability of failure
In a binomial experiment, the option (a) probability of success does not change from trial to trial
In a binomial experiment, each trial is independent of the previous trials, and the probability of success remains constant throughout the experiment. Therefore, option (a) is correct.
Option (b) is incorrect because the probability of success does not change from trial to trial.
Option (c) is partially correct because the probability of success could change from trial to trial in certain situations, but this would not be considered a binomial experiment.
Option (d) is incorrect because the probability of success and failure must add up to 1 in a binomial experiment, but they are not necessarily equal to each other.
Therefore, the correct option is (a) probability of success does not change from trial to trial
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If triangle PQR is has a right angle at Q and m<R is 45°, what is the length of PR is PQ is 3?
1. 3
2. 2
3. 2√3
4. 3√2
The length of PR is 3√2
Define triangleA triangle is a polygon with three sides and three angles. It is a two-dimensional figure with three straight sides that connect three non-collinear points. The sum of the angles in a triangle always adds up to 180 degrees.
Since triangle PQR is a right triangle,
Given PQ=3
m<R =45°
m<P =45°(sum of angles of triangle is 180°)
So, RQ=3
Using pythagoras theorem;
PR²=PQ+RQ²
PR=√3²+3²
PR=3√2
So the answer is option 4. 3√2
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the head of the psychology department in a university is interested in finding the attitudes of her students toward implementing an internship as a requirement for completion of the degree. she obtains a list of all students who are psychology majors, randomly selects 100 students from the list, and surveys those who are selected. what type of sampling technique has she employed?
The head of the psychology department has employed a sampling technique called simple random sampling.
This technique involves selecting a sample from the population in such a way that every member of the population has an equal chance of being included in the sample.
In this case, the population of interest is all the psychology major students in the university.
The department head wants to understand their attitudes toward implementing an internship as a requirement for completing their degree.
To obtain a representative sample, she first compiles a list of all psychology majors.
Then, she randomly selects 100 students from this list to participate in her survey.
Simple random sampling is an effective method to ensure that the sample is unbiased and representative of the entire population.
It minimizes selection bias, as each student has an equal chance of being selected.
This allows the department head to generalize her findings and make valid inferences about the attitudes of all psychology students in the university.
To summarize, the department head employed a simple random sampling technique to gather information about students' attitudes towards implementing an internship as a requirement for completing their psychology degree.
This approach helps ensure the sample is representative and unbiased, allowing for accurate and generalizable conclusions.
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pamela registered her new phone number on the do not call registry. how long will her number remain on the list?
If Pamela has registered for the first time, it will remain on the Do Not Call list permanently. If she has re-registered, it will remain on the list for an additional five years from the date of re-registration.
How long do phone numbers remain on the Do Not Call Registry?The length of time that Pamela's phone number will remain on the National Do Not Call Registry depends on whether she registered her number on the Do Not Call Registry for the first time or if she has re-registered her number after it has already been on the list for a while.
If Pamela registered her phone number for the first time, it will be added to the Do Not Call Registry within 31 days of her registration date. Her phone number will remain on the list permanently, unless she requests to remove it or the number is disconnected.
If Pamela has re-registered her phone number after it has already been on the list for a while, her number's registration will be extended for another five years from the date she re-registered it.
Therefore, if Pamela registered her phone number for the first time, it will remain on the list permanently. If she has re-registered her number, it will remain on the list for an additional five years from the date of re-registration.
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all probabilities can be expressed as decimal values ranging from 0.00 to 1.00.
The answer to the given question after considering the two options is true under the condition all probabilities can be expressed as decimal values ranging from 0.00 to 1.00.
Probability is also known as the estimation of possible changes of a particular event taking place. Furthermore, it is important while dealing with calculations in the branch of science and mathematics. It is useful in eliminating the total changes of systematic errors, which are hampering the research population.
Some examples of probability
The probability on the event of rolling a 4 with a die is 1/6.
The probability of getting a tails while tossing a coin is 1/2.
The probability of getting one joker from a deck of cards is 1/51.
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The complete question is
All probabilities can be expressed as decimal values ranging from 0.00 to 1.00. True or False
Yes, it is true that all probabilities can be expressed as decimal values ranging from 0.00 to 1.00.
This is because probabilities represent the likelihood of an event occurring, and the probability of an event can range from impossible (0.00) to certain (1.00). Therefore, probabilities are expressed as decimal values between these two extremes.
Hi! Yes, all probabilities can be expressed as decimal values ranging from 0.00 to 1.00. A probability of 0.00 represents an impossible event, while a probability of 1.00 represents a certain event. Values between these two extremes indicate varying levels of likelihood for the event to occur.
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The table shows the results of a recent survey of sixth grade students at Potter Middle School about their favorite sports.
What fraction of the students chose football or soccer? Express your answer in simplest form.
20% of the students surveyed did not choose soccer, football, or basketball as their favorite sport.
To find the percentage of students who did not choose soccer, football, or basketball as their favorite sport, we need to first find the total number of students who did not choose any of these sports.
Total number of students who chose soccer, football or basketball = 54 + 42 + 24 = 120
Number of students who did not choose any of these sports = 150 - 120 = 30
Therefore, the percentage of students who did not choose soccer, football or basketball as their favorite sport is:
(30/150) x 100% = 20%
So, 20% of the students surveyed did not choose soccer, football, or basketball as their favorite sport.
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--The complete Question is, Out of the 150 students surveyed, 54 chose soccer, 42 chose football, and 24 chose basketball. What percentage of the students surveyed did not choose soccer, football or basketball as their favorite sport? --
Please help this is homework the answers currently in it are wrong it’s also wrong if you round them to the tenth place
Check the picture below.
answer these questions
Answer:
a) model a: 50/hr
model b: 40/hr
b) model a
Step-by-step explanation:
b) since the money raised started at 0, the rate of change can be found by calculating 400/8
The interval within which 95 percent of all possible sample estimates will fall by chance is defined as ______________.A. Lower confidence boundaryB. Upper confidence boundaryC. The sample mean +/- 1.96 standard errorsD. The Central Limit Theorem
The interval within which 95 percent of all possible sample estimates will fall by chance is defined as the sample mean +/- 1.96 standard errors.
C. The sample mean +/- 1.96 standard errors.
This is known as the confidence interval, and it is calculated by taking the sample mean and adding and subtracting 1.96 times the standard error of the sample.
This range provides a level of confidence that the true population parameter falls within this range, based on the sample data.
The Central Limit Theorem is a statistical concept that explains how sample means tend to follow a normal distribution, but it is not directly related to the calculation of confidence intervals.
The lower and upper confidence boundaries refer to the endpoints of the confidence interval.
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The interval within which 95 percent of all possible sample estimates will fall by chance. The correct answer is: C. The sample mean +/- 1.96 standard errors
The interval within which 95 percent of all possible sample estimates will fall by chance is defined as the "Upper and Lower Confidence Boundaries" or "Confidence Interval." This interval is calculated based on the sample mean and standard error, with the common formula being the sample mean +/- 1.96 standard errors for a 95% confidence interval.
This interval is often referred to as the 95% confidence interval. It is calculated by taking the sample mean and adding/subtracting 1.96 times the standard error. This range represents the boundary within which 95 percent of all possible sample estimates are expected to fall by chance.
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help please this is due tonight and im struggling
Thus, the value of x for the given angle of cyclic quadrilateral is found as the x = 50.
Explain about the cyclic quadrilateral:When you hear the word "cyclic," think of the two round wheels on you bicycle. A quadrilateral is a figure with four sides. The result is a cyclic quadrilateral, which is defined as any four-sided shape (quadrilateral) its four vertices (corners) are located on a circle.
A cyclic quadrilateral's opposite angles add up to 180 degrees, making them supplementary to one another.
Given data:
∠T = x + 60°∠R = x + 20°Using the property of cyclic quadrilateral: sum of opposite angle are 180 degrees.
∠T + ∠R = 180
x + 60 + x + 20 = 180
2x + 80 = 180
2x = 180 - 80
2x = 100
x = 50
Thus, the value of x for the given angle of cyclic quadrilateral is found as the x = 50.
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Simplify. 4/5 -1/3
Need answer asap!
Answer:
4/5-1/3=
12/15-5/15=7/5
Step-by-step explanation:
7/5
Hope this helps! =D
6) What is the measure of angle bpc?
a customer spends 21.50 on cupcakes and muffins. the numbet of muffins purchased is 1 few than number of cupcakes. each cupcake costs $2, and each muffin cost $1.25 create a system of equations
Answer: Let's use the following variables to represent the unknown quantities in the problem:
x: the number of cupcakes purchased
y: the number of muffins purchased
From the problem statement, we can write two equations:
The total amount spent on cupcakes and muffins is $21.50:
2x + 1.25y = 21.50
The number of muffins purchased is one fewer than the number of cupcakes:
y = x - 1
These two equations form a system of equations that can be solved simultaneously to find the values of x and y.
Substituting equation 2 into equation 1, we get:
2x + 1.25(x - 1) = 21.50
Simplifying and solving for x:
2x + 1.25x - 1.25 = 21.50
3.25x = 22.75
x = 7
Now that we know x, we can use equation 2 to find y:
y = x - 1 = 7 - 1 = 6
Therefore, the customer purchased 7 cupcakes and 6 muffins, spending a total of $21.50.
Step-by-step explanation:
Decibel Project Management Services, C/O Spr School, Nethaji Nagar,Ramagiri, Nalgonda, Telangana, India, 508001 is the center for jee mains if anybody same centre please let me know
Project management services refer to the professional assistance and support provided to organizations to plan, execute, and manage projects effectively. These services may include a range of activities, such as project planning, scheduling, budgeting, risk management, stakeholder management, quality assurance, and project reporting.
What is project management?Project management services can be provided by both internal and external professionals. Internal project managers are employees of the organization who are responsible for managing projects within the company.
External project management services can be hired from consulting firms, specialized project management companies, or freelance professionals who work independently.
Project management services can help ensure that projects are delivered on time, within budget, and to the required quality standards.
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Explain project Management Services
1. In Design 2, what is the radius of the larger
grassy area?
Answer: 5 m
Step-by-step explanation:
A radius is half of the diameter which is the black line. Hope this helps!
Answer:
The radius of the larger grass area is 5m
Step-by-step explanation:
d=2r
r=d/2
r=10/2
r=5m
I NEED HELP, LIKE NOW!\
What is -27 radical 72
Step-by-step explanation:
-27 [tex]\sqrt{72}[/tex] = -27 [tex]\sqrt{36*2}[/tex] = -27 (6) [tex]\sqrt{2}[/tex] = - 162 [tex]\sqrt{2}[/tex] = - 229.1
At Robinson’s Steakhouse, you can choose from 2 steaks cooked to your liking and have the choice of 2 different sides. What is the probability that a customer will choose a Ribeye, well done or medium with corn?
A- 1/3
B- 1/12
C- 2/7
D- 1/6
the probability of a customer choosing a Ribeye, well done or medium with corn is [tex]1[/tex] out of [tex]12[/tex], which is answer B [tex]- 1/12[/tex] Thus, option B is correct.
What is the probability?There are two possible steaks that a customer can choose from, and for each steak, there are three possible ways to cook it: rare, medium, or well-done. Additionally, there are two possible sides to choose from: corn or some other option.
Thus, there are a total of [tex]2 \times 3 \times 2 = 12[/tex] possible meal combinations that a customer can choose from.
Out of these 12 possibilities, there is only one way to get a Ribeye cooked well-done or medium with corn, since there is only one Ribeye option on the menu.
Therefore, the probability of a customer choosing a Ribeye, well done or medium with corn is 1 out of 12, which is answer B- 1/12
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Si un editor pone un precio de $16 a un libro, se venderán 10,000 copias. Por cada dólar que aumente al precio se dejarán de vender 300 libros. ¿Cuál debe ser el precio al que se debe vender cada libro para generar un ingreso total por las ventas de $124,875?
The price of each book must be either $38.53 or $10.8 to generate a total sales revenue of $1,24,875.
If the prices of a book is $16 then 10000 copies will be sold.
For every dollar that increase in price, 300 books will not be sold.
So if the price of a book increases $x then the total price of sold books is given by,
y = (16 + x)*(10000-300x)
Now total sales revenue of the books is $124875, that is, y = 124875.
So, (16+x)*(10000-300x) = 124875
160000 + 10000x - 4800x - 300x² = 124875
35125 + 5200x - 300x² = 0
25 (1405 + 208x - 12x²) = 0
12x² - 208x - 1405 = 0
Solving the above quadratic equation we get,
x = 22.53 or x = -5.20 (Rounding to two decimal places)
So the amount will be either (16+22.53) = $38.53 or (16-5.20) = $ 10.8.
Hence the price must be either $38.53 or $10.8.
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The translation of the question is -
"If a publisher prices a book at $16, 10,000 copies will be sold. For every dollar that increases in price, 300 books will not be sold. What must be the price each book must sell for to generate a total sales revenue of $124,875?"
2. when conducting a hypothesis test, the hypothesis that illustrates what we really think is going on in the population is called the hypothesis. an. analytical b. hypothetical c. null d. theoretical e. alternative
shawna is going out of town for the day, so she asks a friend to watch her 3 dogs. she wants to leave 12 of a pound of food for each dog. if a can of dog food has 0.75 pounds of food, how many cans should shawna leave?write your answer as a whole number, decimal, fraction, or mixed number. simplify any fractions.
Shawna wants to make sure her three dogs are fed and cared for when she leaves town for the day. She intends to give each of her dogs 12 ounces of food to achieve this. She must therefore leave a total of 36 ounces of food (3 dogs x 12 ounces of food per dog). 36 ounces are equivalent to 2.25 pounds of food because 16 ounces make up one pound.
There are 0.75 pounds of food in each can of dog food. We must divide 2.25 by 0.75 to find the quantity of dog food Shawna should leave for her companion. 3 dog food cans are the end outcome.Shawna ought to give her buddy three cans of dog food so that she can feed her dogs.
Shawna may make sure her dogs have enough food and are well cared for while she is away by leaving adequate food for them. Shawna may put any fears or concerns about her pets' welfare to rest by leaving ample food and clear directions.
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Simplify. 11 3/4-8 1/2
Therefore, 11 3/4 - 8 1/2 = 13/4, or 3 1/4 as a mixed number.
What is mixed number?A mixed number is a type of number that represents a whole number and a fraction together. It is written in the form of a whole number followed by a fraction, such as 3 1/2. The whole number represents the number of whole units, while the fraction represents the part of a unit.
For example, the mixed number 3 1/2 can be interpreted as three whole units and one half of a unit. Another example of a mixed number is 2 3/4, which represents two whole units and three-quarters of a unit. Mixed numbers are commonly used in everyday life, such as in cooking and measuring, and in mathematical calculations involving fractions.
To subtract mixed numbers like these, we need to convert them to improper fractions first:
[tex]11 3/4 = (4 * 11 + 3)/4 = 47/4[/tex]
[tex]8 1/2 = (2 * 8 + 1)/2 = 17/2[/tex]
Now, we can subtract the fractions:
[tex]47/4 - 17/2[/tex]
To subtract these fractions, we need to find a common denominator. The least common multiple of 4 and 2 is 4 × 2 = 8. We can convert both fractions to have a denominator of 8:
[tex]47/4 = (47/4) * (2/2) = 94/8[/tex]
[tex]17/2 = (17/2) * (4/4) = 68/8[/tex]
Now, we can subtract the numerators:
[tex]94/8 - 68/8 = 26/8[/tex]
Finally, we can simplify the result by dividing both numerator and denominator by their greatest common factor, which is 2:
[tex]26/8 = (2 * 13)/(2 * 4) = 13/4[/tex]
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the dimensions of noah’s ark were reported as 3.0 × 102 cubits by 5.0 × 101 cubits. express this size in units of feet (1 cubit = 1.5 ft)
The dimensions of Noah's Ark in feet are 450 feet by 75 feet if the dimensions of Noah's Ark is 3.0 × 102 cubits by 5.0 × 101 cubits.
Noah's Ark is said to have dimensions of 3.0 × 10^2 cubits by 5.0 × 10^1 cubits. To convert these measurements to feet, we can use the conversion factor of 1 cubit = 1.5 feet.
First, we need to convert the length of the ark from cubits to feet. To do this, we multiply the length of the ark in cubits (3.0 × 10^2) by the conversion factor of 1.5 feet/cubit. This gives us a length of
3.0 × 10^2 cubits x 1.5 feet/cubit = 450 feet
Similarly, we can convert the width of the ark from cubits to feet by multiplying the width in cubits (5.0 × 10^1) by the conversion factor of 1.5 feet/cubit. This gives us a width of:
5.0 × 10^1 cubits x 1.5 feet/cubit = 75 feet
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Sally invested some money into a savings account that earns 7.2%
annual simple interest. At the end of 9 years, she earned $745.20 in
interest. How much money did she put into the account initially?
Round to the nearest dollar.
Sally would have invested $1150 initially in the savings account to satisfy the conditions in the question.
What is a savings account?A savings account is a type of bank account that helps people save money over time. It offers a safe and secure way to store money while earning interest on the balance. Unlike checking accounts, savings accounts are intended for long-term storage of funds, with a higher interest rate and regular compounding to help the balance grow. Savings accounts offer flexibility in terms of access to funds and usually allow withdrawals at any time with limits on the number of withdrawals without incurring a fee.
To determine how much money Sally initially invested in a savings account that earns 7.2% annual simple interest, we can use the formula for simple interest: I = Prt. Here, I represents the interest earned, P is the initial principal, r is the annual interest rate as a decimal, and t is the time in years.
Given that Sally earned $745.20 in interest over a period of 9 years with an annual interest rate of 7.2%, we can substitute the values into the formula and solve for P:
I = $745.20
r = 7.2% = 0.072 (decimal)
t = 9 years
Now, P = I / (rt)
P = 745.20 / (0.072 * 9)
P = $1150
Therefore, Sally initially invested $1150 in the savings account.
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what is the degree of the polynomial 8 x to the power of 5 plus 4 x cubed minus 5 x squared minus 9 ?
Out of these powers, the highest is 5.
Therefore, the degree of the polynomial is 5.
The degree of a polynomial is the highest power of the variable in the polynomial. In the given polynomial, the highest power of x is 5,
so the degree of the polynomial is 5.
The degree of a polynomial is the highest power of the variable (x) in the expression.
In the polynomial you provided:
[tex]8x^5 + 4x^3 - 5x^2 - 9[/tex]
Let's identify the terms and their respective powers of x:
[tex]8x^5[/tex]has a power of 5.
[tex]4x^3[/tex]has a power of 3.
[tex]-5x^2[/tex] has a power of 2.
-9 is a constant term, so there is no power of x.
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Aidan wants to find the mass of a
bowling ball.Which unit should he use
Answer:
Aiden should use the Standard unit of Mass
Kilogram.
Step-by-step explanation:
He can use other unit also like gram, pound, ounce, tone etc
Identify the graph of g(x)=3x^2-24x+45
The graph of an equation can be identified by looking at the characteristics of the equation, such as the order.
Quadratics
The equation given is quadratic because the highest exponent is 2; this means the equation has an order of 2. All equations with an order of 2 are quadratic equations. Quadratic equations form parabolas, which look like a U. Additionally, the leading coefficient is positive. This means that the parabola will open upwards, with the vertex being the minimum of the graph.
Other Characteristics
We can find more information from the equation to help us find the graph. Specifically, we can find the y-intercept. To find the y-intercept, simply plug 0 in for x and solve.
g(0) = 3(0)² - 24(0) + 45g(0) = 45This means that the y-intercept is 45.
Additionally, to find the x-coordinate of the vertex, we can use the equation -b/(2a).
[tex]\frac{-b}{2a}[/tex] = [tex]\frac{24}{6}[/tex] = 4The x-value of the vertex is 4. With all of this information, we can identify what the graph will look like. However, if you need to find the full graph, you can plug x-values into the equation, solve for y, and then plot the coordinate pairs. Below is a picture of the graph.
assume that arrivals occur according to a poisson process with an average of seven per hour. what is the probability that exactly two customers arrive in the two-hour period of time between a 2:00 p.m. and 4:00 p.m. (one continuous two-hour period)? b 1:00 p.m. and 2:00 p.m. or between 3:00 p.m. and 4:00 p.m. (two separate one-hour periods that total two hours)?
a) The probability that exactly two customers arrive between 2:00 p.m. and 4:00 p.m. is 0.0915 (or approximately 9.15%).
b) The probability of at least one customer arriving between 1:00 p.m. and 2:00 p.m. or between 3:00 p.m. and 4:00 p.m. is approximately 0.99999917.
For a Poisson process, the number of arrivals in a fixed time interval follows a Poisson distribution.
Let's denote the number of arrivals in a two-hour period as X.
Since the average number of arrivals per hour is 7, the average number of arrivals in a two-hour period is 14.
Therefore, we have λ = 14.
a) Probability of exactly 2 customers arriving between 2:00 p.m. and 4:00 p.m.:
Using the Poisson distribution formula, the probability of X arrivals in a two-hour period is:
[tex]P(X = x) = (e^{-\lambda} * \lambda^x) / x![/tex]
So, for X = 2, we have:
[tex]P(X = 2) = (e^{-14} * 14^2) / 2! = 0.0915[/tex] (rounded to four decimal places)
Therefore, the probability that exactly two customers arrive between 2:00 p.m. and 4:00 p.m. is 0.0915 (or approximately 9.15%).
b) Probability of at least one customer arriving between 1:00 p.m. and 2:00 p.m. or between 3:00 p.m. and 4:00 p.m.:
We can approach this problem by using the complementary probability. The complementary probability of at least one customer arriving in a two-hour period is the probability of no customers arriving in that period. Since the arrival rate is the same for each hour, we can divide the two-hour period into two one-hour periods and use the Poisson distribution formula for each period separately.
The probability of no customers arriving in a one-hour period with λ = 7 is:
[tex]P(X = 0) = (e^{-7}* 7^0) / 0! = 0.000911[/tex]
The probability of no customers arriving in a two-hour period is the product of the probabilities for each one-hour period:
P(no customers in two-hour period) = P(X = 0) * P(X = 0) = 0.000911 * 0.000911 = 8.30e-7
The complementary probability of at least one customer arriving in a two-hour period is:
P(at least one customer in two-hour period) = 1 - P(no customers in two-hour period) = 1 - 8.30e-7 = 0.99999917 (rounded to eight decimal places).
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minimum of [tex]\frac{a}{b+c} + \frac{b}{c+a} + \sqrt{} \frac{2c}{a+b}[/tex]
The minimum of the given expression can be found to be 3 x ∛(√2).
How to find the minimum ?Use these inequalities to find the minimum of the given expression:
(a / (b + c)) + (b / (c + a)) + √(2c / (a + b)) ≥ (a / (√(bc))) + (b / (√(ac))) + √(2c / (√(ab)))
Now, simplify the expression:
(a / (√(bc))) + (b / (√(ac))) + √(2c / (√(ab))) = (√(a²/bc)) + (√(b²/ac)) + (√(2c²/ab))
Apply AM-GM inequality to the terms (√(a²/bc)), (√(b²/ac)), and (√(2c²/ab)):
AM = [(√(a²/bc)) + (√(b²/ac)) + (√(2c²/ab))] / 3 ≥ GM = ∛[(√(a²/bc)) * (√(b²/ac)) * (√(2c²/ab))]
The geometric mean (GM) is:
GM = ∛[(√(a²/bc)) x (√(b²/ac)) x (√(2c²/ab))]
GM = ∛(√(2a²b²c² / a²b²c²))
GM = ∛(√2)
Thus, the minimum of the given expression is:
= 3 x ∛(√2)
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1. The temperature during a blizzard is -12°F.
Which scenario would combine to make zero?
A) The weather drops another 12°F
The weather rises 12°F
The weather drops another -12°F
The weather rises another -12°F
B)
C)
()
Answer:
The answer is Rises 12F
Step-by-step explanation:
-12 degrees is 12 below zero. To reach zero, you have to go up an equal amount. -12 + 12 = 0