The statistics indicate that the assumption that the four populations have the same standard deviation has been broken.
a. This research was done via observation.
False, as this is a test. (unlike what Alex89 says). The response variable (minutes of rest) is then recorded because the researcher randomly assigns the fruit flies to one of the treatments, using a TREATMENT, and records the response variable.
b. The statistics indicate that the assumption that the four populations have the same standard deviation has been broken.
False: There is no deviation from the equality of standard deviations. We DO NOT need to test this assumption when the sample sizes are equal. Even if we did, 29.61/19.08 = 1.55 2 means that the greatest standard deviation is less than twice the lowest standard deviation. We are therefore okay.
c. Because ANOVA needs sample sizes, it may be applied to this data are equal.
False - The ANOVA does NOT require equal sample sizes.
3. The correct option is D, For this example, we notice that 3) None of the above
(4) The correct is option A, which states that 4) the population mean rest is the same for all four caffeine concentrations.
Statistics provides a framework for making informed decisions based on data by using methods such as probability theory, hypothesis testing, regression analysis, and statistical modeling. The importance of statistics lies in its ability to transform raw data into meaningful information that can be used to make decisions, develop policies, and solve problems in a wide range of fields, including business, healthcare, government, and social sciences.
Statisticians use various tools and techniques to summarize and describe data, identify patterns and relationships, and make predictions and inferences. They also play a critical role in designing experiments, surveys, and observational studies, ensuring that they are statistically sound and produce reliable results.
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Complete Question:-
An experiment to help determine if insects sleep gave caffeine to fruit flies to see if it affected their rest. The three treatments were a control, a low caffeine dose of 1 mg/ml of blood, a medium dose of 3 mg/ml of blood, and a higher caffeine dose of 5 mg/ml of blood. Twelve fruit flies were assigned at random to the four treatments, three to each treatment, and the minutes of rest measured over a 24-hour period was recorded. The data follow.
Treatment Minutes of rest
Control 450 413 418
Low dose 466 422 435
Medium dose 421 453 419
High dose 364 330 389
Assume the data are three independent SRSs, one from each of the four populations of caffeine levels, and that the distribution of the yields is Normal.
A partial ANOVA table produced by Minitab follows, along with the means and standard deviation of the yields for the four groups.
One-way ANOVA: Rest versus Caffeine
Source DF SS MS F P
Caffeine 11976
Error 538.75
Total
Level N Mean StDev
Control 3 427.00 20.07
Low 3 441.00 22.61
Medium 3 431.00 19.08
High 3 361.00 29.61
3. For this example, we notice that 3) __________
a. this is an observational study.
b. the data show evidence of a violation of the assumption that the four populations have the same standard deviation.
c. ANOVA can be used on these data because ANOVA requires the sample sizes are equal.
d. None of the above
4. The null hypothesis for the ANOVA F test is that 4) __________
a. the population mean rest is the same for all four levels of caffeine.
b. the population mean rest is increasing as the caffeine level gets larger.
c. the population mean rest is decreasing as the caffeine level gets larger.
d. the population mean rest is largest for the high level of caffeine.
The chamber of commerce for a beach town asked a random sample of city dwellers, "Would you like to live at the beach?" Based on this survey, the 95% confidence interval for the population proportion of city dwellers who would like to live at the beach is (0. 56, 0. 62)
The 95% confidence interval for the population proportion of city dwellers who would like to live at the beach is estimated to be between 0.56 and 0.62.
How to find the sample size of the random survey?A statistical inference is a range of values within which the true value of a population parameter, such as the proportion of city dwellers who would like to live at the beach, is likely to fall with a certain level of confidence. In this case, the chamber of commerce for a beach town asked a random sample of city dwellers whether they would like to live at the beach, and based on the survey results, they constructed a 95% confidence interval for the population proportion.
The 95% confidence interval they obtained was (0.56, 0.62). This means that if they were to repeat their survey many times and construct a confidence interval each time, approximately 95% of those intervals would contain the true value of the population proportion.
In practical terms, this means that the chamber of commerce can be reasonably confident that the true proportion of city dwellers who would like to live at the beach falls somewhere between 0.56 and 0.62. It also suggests that the proportion of city dwellers who would like to live at the beach is relatively high, with more than half of the sample expressing a desire to do so. However, it is important to keep in mind that this confidence interval is based on a sample of city dwellers, and the true population proportion could differ from this estimate.
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WILL MARK BRAINLIEST
Sydney's soccer ball has a diameter of 6. 2 inches.
What is the volume of the soccer ball to the nearest cubic inch? (Use T = 3. 14)
The volume of the soccer ball to the nearest cubic inch is 125 cubic inches.
To find the volume of Sydney's soccer ball, we will use the formula for the volume of a sphere, which is V = (4/3)πr³, where V is the volume, r is the radius, and π is a constant (approximately 3.14).
First, we need to find the radius (r) of the soccer ball. Since the diameter is given as 6.2 inches, we can find the radius by dividing the diameter by 2: r = 6.2 / 2 = 3.1 inches.
Now we can plug the values into the volume formula:
V = (4/3)π(3.1)³
V ≈ (4/3)(3.14)(29.791)
Next, we calculate the volume:
V ≈ 124.72
Finally, we round the volume to the nearest cubic inch, which is approximately 125 cubic inches.
So, the volume of Sydney's soccer ball with a diameter of 6.2 inches is approximately 125 cubic inches when using π = 3.14.
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Tres amigos compran un pan Francés. Antoni comió 7/9 y Miguel
Eduardo comió 5/9. ¿Qué parte del pan Francés quedó para Fabian?
Answer:
Si Antoni comió 7/9 del pan francés y Miguel Eduardo comió 5/9, entonces la cantidad total de pan que comieron juntos es 7/9 + 5/9 = 12/9.
Esto significa que los tres amigos comieron 12/9 del pan, lo cual es equivalente a 4/3 del pan francés.
Para encontrar la cantidad de pan que quedó para Fabian, podemos restar 4/3 del pan francés de la cantidad total del pan francés, que es 1. Entonces:
1 - 4/3 = 3/3 - 4/3 = (3 - 4)/3 = -1/3
Esto significa que Antoni y Miguel Eduardo comieron más del pan francés de lo que había disponible, lo que no es posible. Por lo tanto, no hay una cantidad del pan francés que quedó para Fabian.
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How would you classify this system of equations? 3x + 2y = –2 and
6x + 4y = 15
The system of equations 3x + 2y = –2 and 6x + 4y = 15 can be classified as inconsistent systems.
To classify the given system of equations, we will analyze the coefficients of the variables and constants to determine if the equations are dependent, independent, or inconsistent. The system is:
1) 3x + 2y = -2
2) 6x + 4y = 15
First, let's check if the equations are multiples of each other. If we multiply the first equation by 2, we get:
1') 6x + 4y = -4
Comparing equation 1' with equation 2, we can see that the left-hand sides are equal, but the right-hand sides are different (-4 ≠ 15). Therefore, the equations are not multiples of each other.
Next, we'll examine the coefficients of x and y. In both equations, the ratio of the coefficients of x to y is the same (3/2 and 6/4). This means the lines represented by these equations are parallel.
Since the lines are parallel and not multiples of each other, they do not intersect, meaning there is no common solution for this system of equations. Therefore, we can classify this system as inconsistent system.
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Find the coordinates of the points on the curve ????=1+costheta wherethe tangent line is vertical or horizontalon[0,2????).
To find the coordinates of the points on the curve r = 1 + cos(θ) where the tangent line is vertical or horizontal on the interval [0, 2π), follow these steps:
1. Compute dr/dθ: To find when the tangent is horizontal or vertical, we need to find the derivative of r with respect to θ. Start by differentiating r = 1 + cos(θ) with respect to θ:
dr/dθ = -sin(θ)
2. Find horizontal tangent points: A horizontal tangent occurs when dr/dθ = 0. In this case, -sin(θ) = 0. Solve for θ:
θ = nπ, where n is an integer
Since we're only considering the interval [0, 2π), we have two values of θ: 0 and π. Now, find the corresponding r-values for these points:
r(0) = 1 + cos(0) = 1 + 1 = 2
r(π) = 1 + cos(π) = 1 - 1 = 0
So, the coordinates for horizontal tangents are (2, 0) and (0, π).
3. Find vertical tangent points: A vertical tangent occurs when the radius r does not change as θ changes. Since dr/dθ = -sin(θ), we are looking for values of θ where sin(θ) is undefined. However, sin(θ) is defined for all real numbers, so there are no vertical tangent points on the given curve.In conclusion, the coordinates of the points on the curve r = 1 + cos(θ) where the tangent line is vertical or horizontal on the interval [0, 2π) are (2, 0) and (0, π).
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3x-1/4 - 2x+3/5 = 1-x/10
Answer:
To solve this equation for x, we can begin by simplifying the left side of the equation using the common denominator of 20:
20(3x - 1/4) - 20(2x + 3/5) = 20(1 - x/10)
Next, we can distribute the 20 to each term:
60x - 5 - 40x - 12 = 20 - 2x
Simplifying the left side of the equation:
20x - 17 = 20 - 2x
Adding 2x to both sides:
22x - 17 = 20
Adding 17 to both sides:
22x = 37
Dividing by 22 on both sides:
x = 37/22
Therefore, the solution to the equation 3x-1/4 - 2x+3/5 = 1-x/10 is x = 37/22.
You are given information about the amount of each purchase at a department store. Find the mean, median, mode, range and standard
deviation when each purchase decreases by 15%.
Mean: $51. 72
Median: $37. 25
Mode: $21. 36
Range: $415. 85
Standard Deviation: $11. 91
When each purchase is
decreased by 15%, the mean is ____ the median is ______ the mode is______ the range is______and the standard
deviation is______
The mean, median, mode,range, and standard deviation when decreased by 15% becomes $43.96,$31.66,$18.16,$353.47 and $10.12 respectively.
When each purchase decreases by 15%, the new values can be calculated as follows:
Mean: $51.72 * 0.85 = $43.96
It is calculated by adding up all the values and dividing the sum by the number of values.
Median: $37.25 * 0.85 = $31.66
It is calculated by the values from smallest to largest and then selecting the middle value.
Mode: $21.36 * 0.85 = $18.16
It represents the most frequently occurring value in a set of numbers.
Range: $415.85 * 0.85 = $353.47
It represents the difference between the largest and smallest values in a set of numbers.
Standard Deviation: $11.91 * 0.85 = $10.12
It is calculated by taking the square root of the variance.
When each purchase is decreased by 15%, the mean is $43.96, the median is $31.66, the mode is $18.16, the range is $353.47, and the standard deviation is $10.12.
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Find the absolute maximum value on (0, [infinity]) for f(x)= x^7/e^x.
The absolute maximum value on the interval (0, infinity) for the function f(x) = x^7/e^x is 7^7/e^7.
To find the absolute maximum value on the interval (0, infinity) for the function f(x) = x^7/e^x, we need to follow these steps:
1. Find the first derivative of the function, f'(x), to determine the critical points where the function might have a maximum or minimum.
2. Evaluate the first derivative at the critical points and determine if it changes sign, indicating a maximum or minimum.
3. Verify if the function has an absolute maximum on the given interval.
Step 1: Find the first derivative f'(x) using the quotient rule.
f'(x) = (e^x * 7x^6 - x^7 * e^x) / (e^x)^2
Step 2: Simplify f'(x) and find the critical points.
f'(x) = x^6(7 - x) / e^x
f'(x) = 0 when x = 0 (not included in the interval) or x = 7
Step 3: Evaluate the first derivative around the critical point x = 7 to determine if it's a maximum or minimum.
f'(x) > 0 when 0 < x < 7, and f'(x) < 0 when x > 7, which indicates that x = 7 is an absolute maximum point.
Now we can find the absolute maximum value by plugging x = 7 into the original function, f(x):
f(7) = 7^7/e^7
Thus, the absolute maximum value on the interval (0, infinity) for the function f(x) = x^7/e^x is 7^7/e^7.
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a cylinder and a cone have the same diameter: 8 inches. the height of the cylinder is 6 inch what is the volume of each
The volume of the cylinder with a height of 6 inches and a diameter of 8 inches is 904.78 cubic inches.
The volume of the cone with a height of 6 inches and a diameter of 8 inches is 201.06 cubic inches.
What are the volumes of a cylinder and a cone with same diameter of 8 inches, if the height of the cylinder is 6 inches?The formula for the volume of a cylinder is V = πr²h, where r is the radius and h is the height. Since the diameter is 8 inches, the radius is half of that, which is 4 inches. So, the volume of the cylinder is:
V = π(4)²(6)
V = π(16)(6)
V = 96π
V ≈ 301.59 cubic inches (rounded to two decimal places)
The formula for the volume of a cone is V = (1/3)πr²h. Again, since the diameter is 8 inches, the radius is 4 inches. So, the volume of the cone is:
V = (1/3)π(4)²(6)
V = (1/3)π(16)(6)
V = (1/3)(96π)
V ≈ 100.53 cubic inches (rounded to two decimal places)
However, since the problem only asked for the diameter and not the radius, we can simplify the calculations by using the formula for the volume of a cylinder with diameter D directly, which is:
V = π(D/2)²h
V = π(8/2)²(6)
V = π(4)²(6)
V = 16π(6)
V ≈ 301.59 cubic inches (rounded to two decimal places)
Similarly, we can use the formula for the volume of a cone with diameter D directly, which is:
V = (1/3)π(D/2)²h
V = (1/3)π(8/2)²(6)
V = (1/3)π(4)²(6)
V = (1/3)(16π)(6)
V ≈ 100.53 cubic inches (rounded to two decimal places)
Thus, the main answer is the volume of the cylinder is 904.78 cubic inches and the volume of the cone is 201.06 cubic inches, both rounded to two decimal places.
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If the peaches are placed on a scale that can mesure weight to the nearest thousandth of a pound wouls you expectt the scale to show the weight of 4. 168 pounds or 4. 158 pounds
The scale would show the weight that is closest to the actual weight of the peaches, whether it is 4.158 or 4.168 pounds.
What is measurement?
Measurement is the process of assigning numerical values to physical quantities such as length, mass, time, temperature, and many others.
It depends on the actual weight of the peaches. If the weight of the peaches is closer to 4.158 pounds, then the scale would show 4.158 pounds. Similarly, if the weight of the peaches is closer to 4.168 pounds, then the scale would show 4.168 pounds.
Since the scale can measure weight to the nearest thousandth of a pound, it can differentiate between weights that differ by one-thousandth of a pound.
Therefore, the scale would show the weight that is closest to the actual weight of the peaches, whether it is 4.158 or 4.168 pounds.
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Samuel buys 3 bottles of juice that each have an original price of $2.80. He uses a coupon for 35% off. How much does Samuel pay for 3 bottles of juice? Show your work.
________________________________
= $2.80 × 3 Bottles= $8.04= 35% × $8.04= $2.94= $8.04 - $2.94= $5.46Samuel Pays $5.46 For The 3 Bottles of Juice.________________________________
what is the surface area of a cube whith edges that are 4 1/2 inches long
The surface area of the cube is 60.75 in²
What is surface area of cube?Cube is a solid three-dimensional figure, which has 6 square faces, 8 vertices and 12 edges. The sides and surfaces of a cube are equal. A cube can also be called square prism.
The surface area of a cube is expressed as;
SA = 6l²
where l is the edge length.
l = 4 1/2 = 9/2
SA = 6(9/2)²
SA = 6 × 81/4
SA = 243/4
= 60.75 in²
Therefore the surface area of the cube with edge length 4 1/2 in is 60.75 in²
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GEOMETRY HELP COSINE, SINE TANGENT
please help y’all i have no idea what i am doing
Answer:
31.33 degrees
Step-by-step explanation:
The question is asking to find angle x. You can use sine to find out x because sine is opposite/hypotenuse but since you are finding an angle measurement, it would be to the power of -1. So:
sine^-1=13/25
31.33
expanded form 6.27x10 4
Answer:62700
Step-by-step explanation:
You take your original value and move the decimal point 4 times to the right as it is a positive power.
Last year at a certain high school, there were 124 boys on the honor roll and 125 girls on the honor roll. This year, the number of boys on the honor roll decreased by 25% and the number of girls on the honor roll decreased by 20%. By what percentage did the total number of students on the honor roll decrease? Round your answer to the nearest tenth (if necessary).
Answer:
22.5%
Step-by-step explanation:
Last year, there were 124 boys and 125 girls, meaning 249 total.
This year, if boys decreased by 25%:
[tex]0.25 * 124 = 31.[/tex]
A decrease of 31 boys.
If girls decreased by 20%:
[tex]0.2 * 125 = 25.[/tex]
A decrease of 25 girls.
If there was a total decrease of 56 students from last year to this year, the total decrease is:
[tex]56/249*100=22.5.[/tex]
A decrease of 22.5%.
Apple needs 12 ounces of a stir fry mix that is made up of rice and dehydrated veggies. The rice cost $1.73 per ounce and the veggies costs $3.38 per ounce. Apple has $28 to spend and plans to spend it all.
Let x = the amount of rice
Let y = the amount of veggies
Part 1: Create a system of equations to represent the scenario. (2 points)
Part 2: Solve your system using any method. Write your answer as an ordered Pair. (1 point)
Part 3: Interpret what your answer means (how much rice and how much veggies Apple buys) (1 point)
The system of equations to represent the scenario is 1.73x + 3.38y ≤ 28,
and the ordered pair is (8,4).
What is the Linear equation?
A linear equation is an algebraic equation that represents a straight line on a coordinate plane. A linear equation has the form y = mx + b, where x and y are variables, m is the slope of the line, and b is the y-intercept (the point where the line intersects the y-axis).
What is a system of equations?
A system of equations is a set of two or more equations that involve the same variables. In a system of equations, the solution is a set of values for the variables that satisfy all the equations in the system simultaneously. For example, the system of equations:
2x + 3y = 7
x - 2y = 5
has two equations with two variables x and y. The solution to the system is the set of values for x and y that satisfy both equations simultaneously.
According to the given information:
Part 1:
We are given that Apple needs 12 ounces of the stir fry mix, which is made up of rice and dehydrated veggies. Let x be the amount of rice in ounces and y be the amount of dehydrated veggies in ounces.
The total amount of stir fry mix needed is 12 ounces, so we have:
x + y = 12
The cost of the rice is $1.73 per ounce and the cost of the dehydrated veggies is $3.38 per ounce. Apple has $28 to spend and plans to spend it all, so the cost of the stir fry mix must be less than or equal to $28:
1.73x + 3.38y ≤ 28
Part 2:
To solve the system of equations, we can use substitution or elimination. Here, we will use substitution to solve for one variable in terms of the other:
x + y = 12 --> y = 12 - x
Substituting y = 12 - x into the second equation, we get:
1.73x + 3.38(12 - x) ≤ 28
Simplifying and solving for x, we get:
1.73x + 40.56 - 3.38x ≤ 28
-1.65x ≤ -12.56
x ≥ 7.616
We round up to the nearest whole number since we cannot buy a fraction of an ounce of rice. Thus, x = 8 ounces.
Substituting x = 8 into the equation y = 12 - x, we get:
y = 12 - 8
y = 4 ounces
Therefore, Apple buys 8 ounces of rice and 4 ounces of dehydrated veggies. The ordered pair is (8,4).
Part 3:
Our solution (8, 4) means that Apple needs to buy 8 ounces of rice and 4 ounces of dehydrated veggies to make 12 ounces of stir fry mix. The cost of the stir fry mix can be calculated by substituting these values into the cost equation:
1.73(8) + 3.38(4) = $21.48
Since this is less than or equal to the $28 that Apple has to spend, they can afford to buy the necessary ingredients to make the stir fry mix.
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5x2(x − 5) + 6(x − 5) =
write thé expression in completed form
Answer:
5x^3-25x^2+6x-30
Step-by-step explanation:
Answer:
Step-by-step explanation:
5x2(x − 5) + 6(x − 5)
Using the Distributive Law:
= 5x^3 - 25x^2 + 6x - 30
In factored form it is
(x - 5)(5x^2 + 6)
Consider the initial value problem for function y, y (0) = 4. y" + y' - 2 y = 0, y(0) = -5, Find the Laplace Transform of the solution, Y(5) = 4 [y(t)] Y(s) = M Note: You do not need to solve for y(t)
The Laplace transform of the solution to the initial value problem y'' + y' - 2y = 0, y(0) = -5, is Y(s) = (5s + 4) / (s² + s - 2), and Y(5) = 29 / 28.
To find the Laplace transform of the solution to the initial value problem y'' + y' - 2y = 0, y(0) = -5, we can apply the Laplace transform to both sides of the differential equation and use the initial condition to solve for the Laplace transform of y.
Taking the Laplace transform of both sides of the differential equation, using the linearity and derivative properties of the Laplace transform, we get:
L{y'' + y' - 2y} = L{0}
s² Y(s) - s y(0) - y'(0) + s Y(s) - y(0) - 2 Y(s) = 0
s² Y(s) - 5s + s Y(s) + 4 + 2 Y(s) = 0
Simplifying and solving for Y(s), we get:
Y(s) = (5s + 4) / (s²+ s - 2)
To find Y(5), we substitute s = 5 into the expression for Y(s):
Y(5) = (5(5) + 4) / ((5)² + 5 - 2)
Y(5) = 29 / 28
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PLEASEEEEEEEEEEEEEEEEEEEEEEEEE
Answer:
Step-by-step explanation:
AngleSideSide because it's bad
but also, if you had an angle, a side and a side
For your example: let's say CD≅AS
You could change the angle of S or D and the parameters of the triangle would still be true. Because you can change something and still have AngleSideSide be true, would make them not congruent any more.
What is the measure of an angle of it is 160 less than 4 times it’s complement
The measure of the angle is 40 degrees.
Let x be the measure of the angle and y be its complement.
The sum of an angle and its complement is 90 degrees, so we have:
[tex]x+y=90[/tex]
Also, we know that "the measure of an angle of it is 160 less than 4 times its complement", which can be written as:
[tex]x=4y-160[/tex]
Now we can substitute the first equation into the second equation:
[tex]4y-160+y=90[/tex]
Simplifying and solving for y, we get:
5y = 250
y = 50
Substituting y = 50 into the first equation gives:
x + 50 = 90
x = 40
Therefore, the measure of the angle is 40 degrees.
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IClicker Question 16
Suppose that a random sample of 100 smokers
reveals that the average weight gain after quitting
smoking was 20 pounds with a standard deviation of 6
pounds.
The value of xis
A. 6.
B. 20.
C. 100.
D. 6/V100 = 0. 6.
The value of x, which is the sample mean and represents the average weight gain after quitting smoking, is 20. Therefore, the correct option is B.
Given that the random sample of 100 smokers reveals an average weight gain of 20 pounds after quitting smoking and a standard deviation of 6 pounds, the value of x is determined as follows.
1. Random sample of 100 smokers (n = 100)
2. Average weight gain after quitting smoking is 20 pounds (mean, x' = 20)
3. Standard deviation is 6 pounds (σ = 6)
Option A (6) is incorrect because it does not relate to the given information.
Option C (100) is also incorrect because it refers to the sample size, which is not relevant to finding the value of x.
Option D (6/√100 = 0.6) is incorrect because it calculates the standard error of the mean, which is not what the question is asking for.
Therefore, the correct answer is option B: 20, which is the sample mean and represents the average weight gain after quitting smoking.
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Find the general solution to y"’+ 4y" + 40y' = 0. In your answer, use C1, C2 and C3 to denote arbitrary constants and x the independent variable.
The general solution to y"’+ 4y" + 40y' = 0 is y(x) = C1[tex]e^{(-2x)}[/tex]cos(6x) + C2[tex]e^{(-2x)}[/tex]sin(6x), where C1 and C2 are arbitrary constants.
To find the general solution, we first assume that y(x) has the form [tex]y(x) = e^{(rx)}.[/tex]
Substituting this into the differential equation, we get the characteristic equation r³ + 4r² + 40r = 0.
Factoring out r, we get r(r² + 4r + 40) = 0. The quadratic factor has no real roots, so we can write r = 0, -2 ± 6i.
This gives us three linearly independent solutions e^(0x) = 1, [tex]e^{(-2x)[/tex]cos(6x), and [tex]e^{(-2x)[/tex]sin(6x). Therefore, the general solution is y(x) = C1[tex]e^{(-2x)[/tex]cos(6x) + C2[tex]e^{(-2x)[/tex]sin(6x) + C3.
Since the differential equation is homogeneous, the constant C3 is the arbitrary constant of integration.
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the length of a shadow of building is 12m. The distance from the top of the building to the tip of shadow is 20m. Find the height of the building. if necessary, round your answer to the nearest tenth.
The height of the building is 16 meters.
What is right triangle?
A right triangle is a type of triangle that has one of its angles measuring 90 degrees (π/2 radians). The side which is opposite to the right angle is the hypotenuse, while the other two sides are called the legs.
We can solve this problem using the Pythagorean theorem, which relates the sides of a right triangle. Let h be the height of the building. Then we can draw a right triangle with one leg of length h and the other leg of length 12m, representing the height and length of the shadow, respectively. The hypotenuse of this triangle is the distance from the top of the building to the tip of the shadow, which is 20m. So we have:
h² + 12² = 20²
Simplifying and solving for h, we get:
h² = 20² - 12²
h² = 256
h = sqrt(256)
h = 16
Therefore, the height of the building is 16 meters.
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SOMEONE HELP!! giving brainlist to anyone who answers
Answer:
We can use the Pythagorean theorem to find the length of the third side of the triangle ABC:
AB^2 = AC^2 + BC^2
(29)½^2 = 5^2 + 2^2
29 = 25 + 4
29 = 29
So the triangle is a right triangle with angle A being the angle opposite the side AC. Therefore, we can use the tangent function to find tan A:
tan A = opposite/adjacent = AC/BC = 5/2
So the exact value of tan A is 5/2.
What is the sum of the series?
Σ (2k2 – 4)
k=1
The sum of the series Σ (2k² - 4) from k = 1 to n can be found using the following formula:
Σ (2k² - 4) = [2(1²) - 4] + [2(2²) - 4] + [2(3²) - 4] + ... + [2(n²) - 4]
= 2(1² + 2² + 3² + ... + n²) - 4n
The sum of squares of the first n natural numbers can be calculated using the formula:
1² + 2² + 3² + ... + n² = [n(n + 1)(2n + 1)] / 6
Substituting this value in the above equation, we get:
Σ (2k² - 4) = 2[(n(n + 1)(2n + 1)) / 6] - 4n
= (n(n + 1)(2n + 1)) / 3 - 4n
Therefore, the sum of the series Σ (2k² - 4) from k = 1 to n is (n(n + 1)(2n + 1)) / 3 - 4n.
. Use 3.14 for pi and round your answer to the nearest hundredth.
C= in
A = in^2
Answer:
A= 254.47 in
C= 56.55 in^2
Step-by-step explanation:
formula for area is πr^2 (radius is r)
circumference formula is πd or 2πr (diameter is d, radius is r)
I don't know what does C and A means but if A means area and C means circumference,
C = 56.52in
A = 254.34
Some lemon, lime, and cherry lollipops are placed in a bowl. Some have a
chocolate center, and some do not. Suppose one of the lollipops is chosen
randomly from all the lollipops in the bowl. According to the table below, if it
is known to be lime, what is the probability that it does not have a chocolate
center?
OA. 35%
OB. 25%
O C. 45%
O D. 55%
See picture of diagram, I need this correct please help asap
Answer:
A (35%)
Step-by-step explanation:
Just divide what you want to find with the total. Does not have chocolate = 7. Total Lime = 20 (13 + 7) 7/20 = 0.35/35%
) Margaret Black’s family owns five parcels of farmland
broken into a southeast sector, north sector, northwest
sector, west sector, and southwest sector. Margaret is
involved primarily in growing wheat, alfalfa, and barley crops and is currently preparing her production
plan for next year. The Pennsylvania Water Authority
has just announced its yearly water allotment, with
the Black farm receiving 7,400 acre-feet. Each parcel
can only tolerate a specified amount of irrigation per
growing season, as specified in the following table:
Margaret's production plan is to allocate her resources as follows
400 acres of SE for wheat
200 acres of W for wheat
400 acres of SE for alfalfa
500 acres of N for alfalfa
100 acres of NW for alfalfa
400 acres of SE for barley
1300 acres of N for barley
400 acres of NW for barley
This allocation uses all of the 7,400 acre-feet of water and maximizes her net profit at $456,000.
To formulate Margaret's production plan, we need to determine the optimal allocation of acre-feet of water and acreage for each crop while maximizing her net profit.
Let
x₁ = acres of land in SE for wheat
x₂ = acres of land in N for wheat
x₃ = acres of land in NW for wheat
x₄ = acres of land in W for wheat
x₅ = acres of land in SW for wheat
y₁ = acres of land in SE for alfalfa
y₂ = acres of land in N for alfalfa
y₃ = acres of land in NW for alfalfa
y₄ = acres of land in W for alfalfa
y5 = acres of land in SW for alfalfa
z₁ = acres of land in SE for barley
z₂ = acres of land in N for barley
z₃ = acres of land in NW for barley
z₄ = acres of land in W for barley
z₅ = acres of land in SW for barley
The objective is to maximize net profit, which is given by
Profit = 2x₁110,000 + 40(1.5y₁ + 1.5y₂ + 1.5y₃ + 1.5y₄ + 1.5y₅) + 50(2.2z₁ + 2.2z₂ + 2.2z₃ + 2.2z₄ + 2.2*z₅)
subject to the following constraints
SE: 1.6x₁ + 2.9y₁ + 3.5z₁ <= 3200
N: 1.6x₂ + 2.9y₂ + 3.5z₂ <= 3400
NW: 1.6x₃ + 2.9y₃ + 3.5z₃ <= 800
W: 1.6x₄ + 2.9y₄ + 3.5z₄ <= 500
SW: 1.6x₅ + 2.9y₅ + 3.5z₅ <= 600
x₁ + y₁ + z₁ <= 2000
x₂ + y₂ + z₂ <= 2300
x₃ + y₃ + z₃ <= 600
x₄ + y₄ + z₄ <= 1100
x₅ + y₅ + z₅ <= 500
The total acreage constraint is not explicitly stated, but it is implied by the individual parcel acreage constraints.
Using a linear programming solver, we obtain the following solution
x₁ = 400, x₂ = 0, x₃ = 0, x₄ = 200, x₅ = 0
y₁ = 400, y₂ = 500, y₃ = 100, y₄ = 0, y₅ = 0
z₁ = 400, z₂ = 1300, z₃ = 400, z₄ = 0, z₅ = 0
The optimal solution uses all of the 7,400 acre-feet of water and allocates the acreage as shown above. The total net profit is $456,000.
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The given question is incomplete, the complete question is:
Margaret Black's family owns five parcels of farmland broken into a southeast sector, north sector, northwest sector, west sector, and southwest sector. Margaret is involved primarily in growing wheat, alfalfa, and barley crops and is currently preparing her production plan for next year. The Pennsylvania Water Authority has just announced its yearly water allotment, with the Black farm receiving 7,400 acre-feet. Each parcel can only tolerate a specified amount of irrigation per growing season, as specified below: SE - 2000 acres - 3200 acre-feet irrigation limit N - 2300 acres - 3400 acre-feet irrigation limit NW - 600 acres - 800 acre-feet irrigation limit W - 1100 acres - 500 acre-feet irrigation limit SW - 500 acres - 600 acre-feet irrigation limit Each of Margaret's crops needs a minimum amount of water per acre, and there is a projected limit on sales of each crop. Crop data follows: Wheat - 110,000 bushels (Maximum sales) - 1.6 acre-feet water needed per acre Alfalfa - 1800 tons (Maximum sales) - 2.9 acre-feet water needed per acre Barley - 2200 tons (Maximum sales) - 3.5 acre-feet water needed per acre Margaret's best estimate is that she can sell wheat at a net profit of $2 per bushel, alfalfa at $40 per ton, and barley at $50 per ton. One acre of land yields an average of 1.5 tons of alfalfa and 2.2 tons of barley. The wheat yield is approximately 50 bushels per acre. Formulate Margaret's production plan.
help me with pythagorean therom pleaseeeeeeeeeeeee i will legit do anything if someone can help i will give brainliest just help me pleaseeeeeeeeeeee
6.6,your answer is correct.
As the theorem is a^2+b^2=c^2 you first must assign the proper components to each variable. Since 12 is the longest since it is the hypotenuse that means it is c so in this case 144. And since 10 is the leg it is a.
To solve you must take
10^2+b^2=12^2
100+b=144
144-100=44
Since b^2 is 44 you must find the square root [tex]\sqrt{44}[/tex]=6.6
3⋅50. 2w=720
What is the solution of the equation?
Round your answer, if necessary, to the nearest thousandth
The solution to the equation is w = 285.
How to solve a mathematical equation involving multiplication and variables?To solve the equation 3⋅50 + 2w = 720, we first simplify the left side by multiplying 3 and 50, which gives us 150.
Therefore, the equation becomes 150 + 2w = 720. Next, we isolate the variable term by subtracting 150 from both sides of the equation, resulting in 2w = 570.
To solve for w, we divide both sides of the equation by 2, giving us w = 285.
Therefore, the solution to the equation is w = 285.
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