Find the volume generated by rotating the region bounded by y = 6 sin(x), y = 0, x = 27, and r = 37, about the y-axis. Express your answer in terms of . Volume =
Answers
Given the curve, y = 6 sin x, y = 0, x = 27, and r = 37,which bound the region to be rotated about the y-axis.
We have to find the volume generated by rotating the region about the y-axis.
Therefore, the formula for the volume of the solid of revolution is given by:
V = π∫[a, b] f²(y) dy
Here, a = 0 and b = 27, and f (y) is the inverse of the function x = 6 sin x.
So, y = 6 sin x is equivalent to
x = sin⁻¹(y/6),
which is the inverse function of y = 6 sin x.
Therefore, we have:
f(y) = sin⁻¹(y/6)
The radius of revolution is given by the distance between the y-axis and the curve.
Therefore,r = x = sin⁻¹(y/6) + 37
Thus, the formula for the volume is given by:
V = π∫[0, 6] (sin⁻¹(y/6) + 37)² dy
Here, we use u-substitution,
let u = sin⁻¹(y/6) + 37,
therefore du/dy
= 1/√[1 - (y/6)²]6(du)
= (1/√[1 - (y/6)²]) dy
Therefore, the integral becomes:
V = π ∫[37, 37.1] u² sin⁻¹(u - 37)
du = 5.068 π cubic units
The value of V is expressed in terms of π, which is the exact form of the volume generated by rotating the region about the y-axis.
Therefore, the volume of the solid of revolution is 5.068 π cubic units.
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Related Questions
2^8 in standard form
Answers
Answer: 256
Step-by-step explanation:
2^8=2*2*2*2*2*2*2*2=256
Please help! Big grade! Extra points!! Help asap!
Answers
Answer:
5
Step-by-step explanation:
Answer:
y = 3
Step-by-step explanation:
y - 3 = 2(x + 1)
If you simplify the right side of the equal sign, you'll get...
y - 3 = 2x + 2
then you would add 3 to both sides...
y - 3 (+3) = 2x + 2 (+3)
which will make...
y = 2x + 5
and since x = -1, you plug it in..
y = 2(-1) + 5
which will give you..
y = -2 + 5
which will make it..
y = 3
Write a possible equation for a cosine function that has a maximum point at (1, 11) and a minimum point at (8, 3).
Answers
M = A + |B| is the function's highest possible value. When sin or cos x equals 1, this maximum value is reached. m = A |B| is the function's lowest possible value. If either cos x or sin x is equal to 1, this minimum will be reached.
How do you find the maximum and minimum of a cosine function?The sine and cosine functions are graphed; to find the values of the sine and cosine functions for a variety of various degrees of angles, use a calculator, computer, or a collection of trigonometry tables (or radian).Because the sine and cosine functions have periods of 2, the patterns are continually repeated to the left and right.The sine and cosine functions can have a number of additional terms and factors added to them, changing how they look.The graph of the sine functions can be vertically shifted by adding the extra term A to the equation y = A + sin x. The sine function can have different amplitudes because to the additional element B in the equation y = B sin x. The graph's highest and minimum values, or one half of those values, make up the amplitude, or | B |, which is the maximum deviation from the x-axis. Both y = A + B sin x and y = A + B cos x are produced by combining these values. The minimum and maximum values for these two functions are specified by the following formulas. M = A + |B| is the function's highest possible value. When sin or cos x equals 1, this maximum value is reached. m = A |B| is the function's lowest possible value.If either cos x or sin x is equal to 1, this minimum will be reached.Example :
Draw the y = 1 + 2 sin x function on a graph. Which values represent the function's maximum and minimum?1 + 2 = 3 is the highest possible value. 1 + 2 = 1 is the minimum value.To Learn more About sin or cos refer To:
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Expand and simplify
(x + 1)(x + 2)(x + 3)
Answers
Im using my casio calculator :)
The assessment for this lesson is a discussion of a mathematical statement. You have to determine if the statement is true or false. If it is false, you explain your reasoning.
1.) For all real numbers a and b, 2a • b = a2 + b2
Answers
Answer:
It's false.... correct is a2+2ab+b2
Step-by-step explanation:
This cannot be factored anymore although. when we try to substitute a with 5 and b with 2, the answer in the right hand side of the equation is -9. That's why it's false.
suppose there is an integer k such that every man on a desert island is willing to marry exactly k of the women on the island and every woman on the island is willing to marry exactly k of the men. also, suppose that a man is willing to marry a woman if and only if she is willing to marry him. show that it is possible to match the men and women on the island so that everyone is matched with someone that they are willing to marry
Answers
The Hall's Marriage Theorem holds, and there exists a perfect matching of the men and women on the island so that everyone is matched with someone they are willing to marry.
The Hall's Marriage Theorem.
Let there be m men and w women on the island.
It is possible to match them so that everyone is matched with someone they are willing to marry.
First, we need to prove that for any subset S of men on the island, the number of women that they are collectively willing to marry is at least |S|k.
Let S be any subset of men on the island.
Since every man is willing to marry exactly k women, the number of women that any single man is willing to marry is k.
The number of women that S collectively is willing to marry is at least |S|k.
Next, we need to prove that for any subset T of women on the island, the number of men that they are collectively willing to marry is at least |T|k.
Let T be any subset of women on the island.
Since every woman is willing to marry exactly k men, the number of men that any single woman is willing to marry is k.
The number of men that T collectively is willing to marry is at least |T|k.
Now, we need to show that the Hall's Marriage Theorem holds.
That is, we need to show that for any subset S of men on the island, the number of women that they are collectively willing to marry is at least |S|, and for any subset T of women on the island, the number of men that they are collectively willing to marry is at least |T|.
Suppose, for the sake of contradiction, that there exists a subset S of men on the island such that the number of women that they are collectively willing to marry is less than |S|.
Then, by the first proof, the number of women that they are collectively willing to marry is at least |S|k. Since |S|k < |S|, this leads to a contradiction.
Similarly, suppose there exists a subset T of women on the island such that the number of men that they are collectively willing to marry is less than |T|.
Then, by the second proof, the number of men that they are collectively willing to marry is at least |T|k. Since |T|k < |T|, this leads to a contradiction.
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a rectangular storage container with a lid is to have a volume of 16 m3. the length of its base is twice the width. material for the base costs $8 per m2. material for the sides and lid costs $16 per m2. find the dimensions of the container which will minimize cost and the minimum cost.
Answers
The minimum cost of the container is $576, and the dimensions that minimize the cost are a width of 2 meters, length of 4 meters, and height of 2 meters.
To minimize the cost, we need to find the dimensions of the container that minimize the total cost, taking into account the cost of the base, sides, and lid.
Let's start by defining the dimensions of the rectangular container:
Let the width of the base be "w" meters.
The length of the base will be twice the width, so the length is "2w" meters.
The height of the container is "h" meters.
The volume of the container is given as 16 m³, so we can write the equation:
Volume = Length × Width × Height
16 = 2w × w × h
16 = 2w²h
w²h = 8 ----(Equation 1)
Now, let's find the cost of the base, sides, and lid.
Cost of the base:
The base is a rectangle with dimensions of length = 2w and width = w.
Area of the base = length × width
Area of the base = (2w) × w = 2w²
Cost of the base = Area of the base × Cost per m² = 2w² × $8 = 16w²
Cost of the sides and lid:
The container has two sides with dimensions of length = 2w and height = h.
The container has two sides with dimensions of width = w and height = h.
The container has a lid with dimensions of length = 2w and width = w.
Area of each side = length × height = 2w × h = 2wh
Area of each side = width × height = w × h
Area of the lid = length × width = 2w × w = 2w²
Total area of the sides and lid = 2(2wh) + 2(wh) + 2w² = 4wh + 2wh + 2w² = 6wh + 2w²
Cost of the sides and lid = Total area × Cost per m² = (6wh + 2w²) × $16 = 96wh + 32w²
Now, we need to express the cost in terms of one variable, either w or h, so we can find the minimum value. Since Equation 1 relates w, h, and the volume, we can express h in terms of w.
From Equation 1:
w²h = 8
h = 8/w²
Now, substitute h in the cost equation:
Cost = 16w² (cost of the base) + (96wh + 32w²) (cost of the sides and lid)
Cost = 16w² + 96w(8/w²) + 32w²
Cost = 16w² + 768/w + 32w²
Cost = 48w² + 768/w ----(Equation 2)
To find the minimum cost, we differentiate Equation 2 with respect to w and set it equal to zero:
d(Cost)/dw = 96w - 768/w² = 0
96w = 768/w²
w³ = 8
Taking the cube root of both sides:
w = 2
Substituting w = 2 back into Equation 1:
w²h = 8
(2)²h = 8
4h = 8
h = 2
Therefore, the dimensions of the container that minimize the cost are:
Width (w) = 2 meters
Length = 2w = 4 meters
Height (h) = 2 meters
The minimum cost can be found by substituting the values of w and h into Equation 2:
Cost = 48w² + 768/w
Cost = 48(2)² + 768/2
Cost = 48(4) + 384
Cost = 192 + 384
Cost = $576
So, the minimum cost of the container is $576, and the dimensions that minimize the cost are a width of 2 meters, length of 4 meters, and height of 2 meters.
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Find the value of r so that the line through (8,r) and (4,5) has a slope of -4
Answers
Answer:
r = - 11
Step-by-step explanation:
Calculate the slope m using the slope formula and equate to - 4
m = \(\frac{y_{2}-y_{1} }{x_{2}-x_{1} }\)
with (x₁, y₁ ) = (4, 5) and (x₂, y₂ ) = (8, r)
m = \(\frac{r-5}{8-4}\) = \(\frac{r-5}{4}\) = - 4 ( multiply both sides by 4 )
r - 5 = - 16 ( add 5 to both sides )
r = - 11
i roll a die n times, n∈ℕ. find the probability that numbers 1 and 6 are both observed at least once.
Answers
The probability of both 1 and 6 being observed at least once when rolling a die n times is given by P(A ∪ B), which is equal to 1 - (11/6)^n + (2/3)^n.
To find the probability that numbers 1 and 6 are both observed at least once when rolling a die n times, we can use the principle of inclusion-exclusion.
Let A be the event that 1 is not observed in n rolls, and B be the event that 6 is not observed in n rolls.
Then, the probability of A and B not occurring is (5/6)^n and the probability of their union, denoted by A ∪ B, is 1 - (5/6)^n.
However, this includes cases where neither 1 nor 6 are observed at least once. To exclude these cases, we can use the same principle to count the number of ways in which neither 1 nor 6 are observed and subtract it from the total number of possible outcomes, which is \(6^n\).
Let C be the event that neither 1 nor 6 are observed in n rolls. Then, the probability of C occurring is (4/6)^n = (2/3)^n. By inclusion-exclusion, the probability of both 1 and 6 being observed at least once in n rolls is:
P(A ∪ B) = 1 - (5/6)^n - (5/6)^n + (2/3)^n
Simplifying this expression gives:
P(A ∪ B) = 1 - (11/6)^n + (2/3)^n
Therefore, there are 1 - (11/6)^n + (2/3)^n probability that numbers 1 and 6 are both observed at least once.
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if ∫5-1f(x)dx = 12 and ∫5-4f(x)=3.6, find ∫4-1f(x)dx
Answers
The value of ∫4-1f(x)dx is 8.4.
We are given two definite integrals:
∫5-1f(x)dx = 12
∫5-4f(x)dx = 3.6
We want to find the value of ∫4-1f(x)dx.
We can use the property of definite integrals that states:
∫a-bf(x)dx = ∫a-cf(x)dx + ∫c-bf(x)dx
We can split the interval [4, 1] into two intervals: [4, 5] and [5, 1]. Therefore, we have:
∫4-1f(x)dx = ∫4-5f(x)dx + ∫5-1f(x)dx
Since we know that ∫5-1f(x)dx is given as 12, we can substitute this value into the equation:
∫4-1f(x)dx = ∫4-5f(x)dx + 12
Now, let's focus on the integral ∫5-4f(x)dx. It is given as 3.6. Therefore, we can rewrite it as:
∫5-4f(x)dx = ∫5-1f(x)dx - ∫4-5f(x)dx
Plugging in the values we know:
3.6 = 12 - ∫4-5f(x)dx
We can solve for ∫4-5f(x)dx by subtracting 3.6 from 12:
∫4-5f(x)dx = 12 - 3.6 = 8.4
Substituting this back into the equation for ∫4-1f(x)dx:
∫4-1f(x)dx = ∫4-5f(x)dx + 12 = 8.4 + 12 = 20.4
Therefore, the value of ∫4-1f(x)dx is 20.4.
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Help is very appreciated
for a moving object, the force acting on the object varies directly with the object's acceleration. When a force of 15 N acts on a certain object, the acceleration
of the object is 3 m/s^2 of the acceleration of the object becomes 5 m/s^2, what is the force?
Answers
The force acting on the object is 25 N when the acceleration of the object becomes 5 m/s².
According to the problem, the force (F) varies directly with the object's acceleration (a), which can be expressed as F = k × a, where k is the proportionality constant. To find the value of k, we can use the given information that when F = 15 N, a = 3 m/s²:
15 N = k × 3 m/s²
k = 5 Ns²/m
Now, we can use the value of k to find the force (F) when the acceleration (a) becomes 5 m/s²:
F = k × a
F = 5 Ns²/m × 5 m/s²
F = 25 N
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Factorize:
(2a - b)² - (a - 2b)²
Answers
Answer:
3(a - b)(a + b)
Step-by-step explanation:
Factorize: (2a - b)² - (a - 2b)²
Different of Perfect a Square rule: a² - b² = (a + b)(a - b)(2a - b)² - (a - 2b)² = [(2a - b) + (a - 2b)] × [(2a - b) - (a - 2b)]
1. Distribute and Simplify:
Distribute the (+) sign on the first bracket and simplify: [(2a - b) + (a - 2b)] → 2a - b + a - 2b → (3a - 3b)
Distribute the (-) sign on the first bracket and simplify: [(2a - b) - (a - 2b)] → 2a - b – a + 2b → (a + b)
We now have:
(3a - 3b)(a + b)
2. Factor out the Greatest Common Factor (3) from 3a - 3b:
(3a - 3b) → 3(a - b)
3. Add "(a + b)" back into your factored expression:
3(a - b)(a + b)
Hope this helps!
Answer:
3[a + b][a - b]
Step-by-step explanation:
Let us recall a useful formula. This formula can factorize any subtraction between perfect squares. The formula is known as a² - b² = (a - b)(a + b).
Let's apply the formula in the given expression as we can see that two perfect squares are being subtracted from each other. Then, we get:
\(\implies (2a - b)^{2} - (a - 2b)^{2}\)
\(\implies [(2a - b) - (a - 2b)][(2a - b) + (a - 2b)]\)
Since the expression(s) inside the parentheses ( ) cannot be simplified further, we can open the parentheses ( ). Then, we get:
\(\implies [(2a - b) - (a - 2b)][(2a - b) + (a - 2b)]\)
\(\implies [2a - b - a + 2b][2a - b + a - 2b]\)
Now, we can combine like terms and simplify:
\(\implies [2a - b - a + 2b][2a - b + a - 2b]\)
\(\implies [a + b][3a - 3b]\)
Three is common in 3a - 3b. Thus, we can factor 3 out of the expression:
\(\implies [a + b][3a - 3b]\)
\(\implies [a + b] \times [3a - 3b]\)
\(\implies [a + b] \times 3[a - b]\)
\(\implies \boxed{3[a + b][a - b]}\)
Therefore, 3[a + b][a - b] is the factorized expression of (2a - b)² - (a - 2b)².
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Can someone help me pls
Answers
Answer:
63 in²
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightGeometry
Area of a Triangle: A = 1/2bhStep-by-step explanation:
Step 1: Define Variables
Base b = 14 in
Height h = 9 in
Step 2: Find Area A
Substitute [Area]: A = 1/2(14 in)(9 in)Multiply: A = (7 in)(9 in)Multiply: A = 63 in²write 1875/100 in its lowest terms
Answers
Answer:
hii
Step-by-step explanation:
18.75 answer
is
correct
what are the domain and range of the following quadratic
Answers
Answer:
ranalllldooo
Step-by-step explanation:
suiiiiiii
Fill in the blanks below with the correct units. (a) A large horse weighs about 1 . (b) A bucket holds about 4 of water. (c) A piece of paper is about 8 wide.
Answers
Each sentence should be completed with the correct unit as follows:
A large horse weighs about 1 pound. A bucket holds about 4 liter of water. A piece of paper is about 8 inches wide.What is measurement?Measurement can be defined as an act or process through which the size, weight, magnitude, quantity, volume (capacity), dimensions, or distance traveled by a physical object or body is taken, especially for the purpose of an experiment.
In Mathematics, the correct unit of measurement for the weight of a physical body such as a large horse is either pound, grams, or kilograms. Additionally, the correct unit of measurement for the volume (capacity) of a physical object such as a bucket is either liter, gallon, cubic centimeter, or cubic meter.
Lastly, the correct unit of measurement for the size (width) of a physical object such as a piece of paper is either inches, feet, centimeter, or meter.
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angela rolls a standard, fair six-sided die until she rolls in that order on three consecutive rolls. what is the probability that she will roll the die an odd number of times?
Answers
The probability that Angela will roll the die an odd number of times to get three consecutive rolls in order can be calculated by considering the possible outcomes and their probabilities.
To start, let's look at the possible outcomes for Angela to roll the die an odd number of times. For her to achieve three consecutive rolls in order, she needs to roll the die either 1, 3, 5, 7, or any other odd number of times.
Next, let's consider the probability of each of these outcomes:
1. If Angela rolls the die once, she has a 1/6 probability of getting the desired sequence in one roll.
2. If Angela rolls the die three times, she needs to calculate the probability of getting the desired sequence on the third roll. The first two rolls can be any number, but on the third roll, she needs to roll the specific sequence. The probability of getting the desired sequence on the third roll is 1/6.
3. If Angela rolls the die five times, the first four rolls can be any numbers, but on the fifth roll, she needs to roll the specific sequence. The probability of getting the desired sequence on the fifth roll is 1/6.
We can see a pattern here: for Angela to roll the die an odd number of times and achieve the desired sequence, the last roll must be the specific sequence. Therefore, the probability for each odd number of rolls will always be 1/6.
Now, let's calculate the overall probability:
Since Angela can roll the die 1, 3, 5, 7, or any other odd number of times, we need to add up the probabilities for each of these cases. The probability of rolling the die an odd number of times is equal for each case, which is 1/6. Since there are infinitely many possible odd numbers of rolls, we can represent this as the sum of an infinite geometric series.
The probability of rolling the die an odd number of times to get three consecutive rolls in order is therefore:
1/6 + 1/6 + 1/6 + ... (infinitely many terms)
To find the sum of this infinite geometric series, we can use the formula for the sum of an infinite geometric series:
Sum = a / (1 - r)
In this case, a = 1/6 (the first term) and r = 1/6 (the common ratio).
Sum = (1/6) / (1 - 1/6)
Sum = (1/6) / (5/6)
Sum = 1/5
So, the probability that Angela will roll the die an odd number of times and get three consecutive rolls in order is 1/5.
In summary, the probability of rolling the die an odd number of times and achieving three consecutive rolls in order is 1/5.
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Sam is eating a Big Hamburger. The first bite was 20% of the Hamburger, the second bite was 20% of what is left and so every next bite is 20% of what is left. is it possible for sam to eat the entrie burger if contunies to eat 20% of what is remaing each bite
Answers
No,Sam will not be able to finish the large hamburger if he only bites 20 percent of what is left.
Given that Sam can bite 20% of a hamburger.
We are required to find whether Sam will be able to eat the large hamburger.
Suppose the size of the hamburger be 100 units.
Here the first bite was 20% of the hamburger.
So the remaining portion of the hamburger is 100-(100(20/100))=80 units.
The second bite was 20% of 80%. Again the remaining portion is 80-(80*20/100)=80-16=64 units.
After the third bite the remainig portion is 64-(64*20/100)=64-12.8=51.2 units.
After the fourth bite the remaining portion is 51.2-(51.2*20/100)=51.2-10.24=40.96 units.
Since the criterion is that Sam will bite 20% of what is left , this remaining portion will never be zero.It will always be a fraction like 0.000000000001 and continues.
Hence Sam will not be able to finish the large hamburger if he only bites 20% of what is left.
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1.
Find the slope of the line.
A. \(-\frac{2}{3}\)
B. \(\frac{3}{2}\)
C. \(-\frac{3}{2}\)
D. \(\frac{2}{3}\)
![1.Find the slope of the line.A. [tex]-\frac{2}{3}[/tex]B. [tex]\frac{3}{2}[/tex]C. [tex]-\frac{3}{2}[/tex]D.](https://i5t5.c14.e2-1.dev/h-images-qa/contents/attachments/yXg3TJGGewDAFhqw4jsghBvBKkZSFeHf.jpeg)
Answers
Answer:
The answer would be B (3/2)
Step-by-step explanation:
Answer:
B . 3/2
Step-by-step explanation:
lets take two random points ( it doesn't have to be a specific one but it just has to be on the line.)
(-2,-2) and (0,1)
we have to find the change in our y coordinates divided by our change in the x coordinates.
so.....
-2 - 1 / -2 - 0
that eqauls to
-3 / -2 = 3 / 2
Alvin is 14 years younger than elga. The sum of their age is 78.
Answer: 46
Answers
seven family members who are potential kidney donors. How many possible orders are there for a best match, a second-best match, and a third-best match
Answers
If there are seven family members who are potential kidney donors, the number of possible orders for a best match, a second-best match, and a third-best match can be calculated using the concept of permutations.
Since each match is selected from the remaining available donors after the previous match, the number of possibilities decreases by one for each match.
For the best match, there are 7 possible donors.
For the second-best match, there are 6 remaining donors.
For the third-best match, there are 5 remaining donors.
To calculate the total number of possible orders, we multiply these numbers together:
Total number of possible orders = 7 * 6 * 5 = 210
Therefore, there are 210 possible orders for a best match, a second-best match, and a third-best match from the seven family members who are potential kidney donors.
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6. ten students take a test and the scores are {80, 99, 83, 82, 100, 75, 83, 85, 71, 92}. (a) compute the sample mean and sample standard deviation
Answers
85 is the sample mean of the scores of ten students taken from their test
15/3 is the sample standard deviation of the scores of ten students taken from their test
What is meant by Sample Standard Deviation?Sample Standard Deviation: The sample standard deviation (s) is the square root of the sample variance and is also a measure of the spread from the expected values. In its simplest terms, it can be thought of as the average distance of the observed data from the expected values.
given ten students take a test and the scores are 80, 99, 83, 82, 100, 75, 83, 85, 71, 92
Sample mean of 80, 99, 83, 82, 100, 75, 83, 85, 71, 92 is
m= sum of observations/number of observations
sum of observations=80+99+83+82+100+75+83+85+71+92=850
number of observations=10
m=850/10=85 is the sample mean of the scores of ten students taken from their test
sample standard deviation,
s=√(assumed value-mean)²/√(number of observaionts-1)
let Assumed value be 100
s=√(100-85)²/√10-1
s= √(15)²/√9
s=15/3 is the sample standard deviation of the scores of ten students taken from their test
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The sample mean of ten students' test results, considered as a sample, is 85.
The sample standard deviation of 10 students' test scores, as determined by their scores, is 15/3.
What does "Sample Standard Deviation" mean?
Sample Standard Deviation: The sample standard deviation (s) is a measurement of the variation from the expected values and is equal to the square root of the sample variance. It can be conceptualized as the average difference between the observed data and the predicted values.
Ten pupils are given a test, and their results are as follows: 80, 99, 83, 82, 100, 75, 83, 85, 71, and 92
80, 99, 83, 82, 100, 75, 83, 85, 71, and 92 are the sample means.
m = total observations / total observations
80+99+83+82+100+75+83+85+71+92=850 is the total number of observations.
Ten observations were made.
The sample mean of ten students' test scores, calculated as m=850/10=85, is given.
sample standard deviation,
s=√(assumed value-mean)²/√(number of observaionts-1)
let Assumed value be 100
s=√(100-85)²/√10-1
s= √(15)²/√9
s=15/3 is the sample standard deviation of the scores of ten students taken from their test.
dy/dt =y+2u, y(0)=5, u= step change of unity
Answers
The solution to the provided differential equation with the initial condition y(0) = 5 and u as a step change of unity is y = -2
The provided differential equation is: \(\[\frac{{dy}}{{dt}} = y + 2u\]\) with the initial condition: y(0) = 5 where u is a step change of unity.
To solve this differential equation, we can use the method of integrating factors.
First, let's rearrange the equation in the standard form:
\(\[\frac{{dy}}{{dt}} - y = 2u\]\)
Now, we can multiply both sides of the equation by the integrating factor, which is defined as the exponential of the integral of the coefficient of y with respect to t.
In this case, the coefficient of y is -1:
Integrating factor \(} = e^{\int -1 \, dt} = e^{-t}\)
Multiplying both sides of the equation by the integrating factor gives:
\(\[e^{-t}\frac{{dy}}{{dt}} - e^{-t}y = 2e^{-t}u\]\)
The left side of the equation can be rewritten using the product rule of differentiation:
\(\[\frac{{d}}{{dt}}(e^{-t}y) = 2e^{-t}u\]\)
Integrating both sides with respect to t gives:
\(\[e^{-t}y = 2\int e^{-t}u \, dt\]\)
Since u is a step change of unity, we can split the integral into two parts based on the step change:
\(\[e^{-t}y = 2\int_{{-\infty}}^{t} e^{-t} \, dt + 2\int_{t}^{{\infty}} 0 \, dt\]\)
Simplifying the integrals gives:
\(\[e^{-t}y = 2\int_{{-\infty}}^{t} e^{-t} \, dt + 0\]\)
\(\[e^{-t}y = 2\int_{{-\infty}}^{t} e^{-t} \, dt\]\)
Evaluating the integral on the right side gives:
\(\[e^{-t}y = 2[-e^{-t}]_{{-\infty}}^{t}\]\)
\(\[e^{-t}y = 2(-e^{-t} - (-e^{-\infty}))\]\)
Since \(\(e^{-\infty}\)\) approaches zero, the second term on the right side becomes zero:
\(\[e^{-t}y = 2(-e^{-t})\]\)
Dividing both sides by \(\(e^{-t}\)\) gives the solution: y = -2
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a one-way analysis of variance experiment produced the following anova table. assume normality in the underlying populations. (you may find it useful to reference the q table). summary groups count average column 1 6 0.89 column 2 6 1.31 column 3 6 2.35 source of variation ss df ms f p-value between groups 8.65 2 4.33 16.65 0.0002 within groups 3.83 15 0.26 total 12.48 17 picture click here for the excel data file a. conduct an anova test at the 1% significance level to determine if some population means differ. multiple choice reject h0; we can conclude that some population means differ. reject h0; we cannot conclude that some population means differ. do not reject h0; we can conclude that some population means differ. do not reject h0; we cannot conclude that some population means differ. b. calculate 99% confidence interval estimates of μ1 − μ2, μ1 − μ3, and μ2 − μ3 with tukey’s hsd approach. (if the exact value for nt − c is not found in the table, then round down. negative values should be indicated by a minus sign. round your answers to 2 decimal places.) c. given your response to part b, which means significantly differ?
Answers
The confidence interval for the one-way analysis of variance experiment be, (136.27 , 163.73).
On Subtracting 1 from your sample size, we get
1000 – 1 = 999.
On Subtracting confidence level from 1, and then divide by two.
(1 – .99) / 2 = 0.005
Now, df = 999 and α = 0.005
from the table at df = 999 we got 3.274.
Divide your sample standard deviation by the square root of your sample size.
150 / √(1000) = 4.74
Now, 3.274 × 4.74 = 13.73
So, the confidence interval be,
(150 - 13.73 , 150 + 13.73) = (136.27 , 163.73)
Hence, the confidence interval for the one-way analysis of variance experiment be, (136.27 , 163.73).
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Practice #2a
Determine the value of n. Show you work below or on
the diagram.
T
Do not put the units with your answer just the value
Check answer
9cm
12cm
Answers
Answer:
answer of n is 15 by pythagoras theorem
Step-by-step explanation:
n is a hypotenuse
\( \sqrt{ {12}^{2} + {9}^{2} } = 15\)
A swimming pool has a diameter of 24 feet. What is the minimum amount of fabric needed to cover the pool if the cover must hang off by 1 foot all around the pool?
Answers
Answer:
531.167 ft²
Step-by-step explanation:
Given data
Dimension of pool
Diameter =24ft
Radius =12ft
If the cover must hang by 1ft around, then the diameter is 26ft
Radius =13ft
Area of cover = πr²
Substitute
Area = 3.142*13²
Area =3.143*169
Area =531.167 ft²
Hence the minimum area is 531.167 ft²
how long would it take for a lahar to reach the town of orting? in order to get full credit, show your calculations. write your answer in hours and round to the second decimal place.
Answers
According to scientists with the USGS Cascades Volcanic Observatory, a lahar could take four hours to reach Puyallup but less than an hour to reach Orting.
The Washington Emergency Management Division has issued a survey to Pierce County residents to learn more about lahars, which are volcanic mudflows that contain a mixture of water and volcanic debris such as boulders. The survey is scheduled to close on Friday.
Hazard maps show that if Mount Rainier erupts, lahar could travel through river valleys as far as Puyallup, Tacoma, and Randle.
Some areas would have more time than others to evacuate. According to the US Geological Survey, previous Mount Rainier lahars travelled at 45-50 miles per hour.
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Please help me answer this question it’s due today HURRY!!!
Answers
How many lbs of peanuts must mike add to 9 lbs of mixed nuts containing 40% peanuts to make a mixture with 73% peanuts
Answers
The new mixture exists 56.5% peanuts.
How to estimate the total number of peanuts required for the mixture?The first batch of 9 lb of mixed nuts possesses 40% peanuts.
This means the quantity of peanuts exists:
9 \(*\) 40/100 = 3.6 lb
The second batch of 9 lb of mixed nuts possesses 73% peanuts.
This means the quantity of peanuts exists:
9 \(*\) 73/100 = 6.57 lb
The total quantity of peanuts in the mix exists
3.6 lb + 6.57 lb = 10.17 lb
There exist 9 lb + 9 lb = 18 lb of mix.
Therefore, the percent of peanuts in the mix exists:
10.17 / 18 \(*\) 100 = 56.5%
The new mixture exists 56.5% peanuts.
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12 ft 8 ft 6 ft What is the volume of the prism?