Answer: 84π √(17) (rounded to 3 significant figures)
a) To find the arc length of the given curve we need to first evaluate the derivative of y w.r.t. x:dy/dx = 4. The arclength of the curve is given by L = ∫√(1+(dy/dx)^2) dx The value of dy/dx is already given and hence we can substitute the value and integrate .L = ∫√(1+(4)^2) dx = ∫√(17) dx Between the limits z = 1 and 2, x varies from 9 to 13. We need to substitute these values in the integral. L = ∫√(17) dx = √(17) * [x]9^13= √(17) * [13 - 9]= 4 √(17)Answer: 4√17 (rounded to 3 significant figures)
b) The area of the surface of revolution, A, that is obtained when the curve is rotated by 2 radians about the a-axis is given by:A = ∫2π * y √(1+(dy/dx)^2) dx We know that dy/dx = 4 and the value of y is given by 4x+5.A = ∫2π * (4x+5) √(1+(4)^2) dx= ∫2π * (4x+5) √(17) dx Between the limits z = 1 and 2, x varies from 9 to 13. We need to substitute these values in the integral. A = ∫2π * (4x+5) √(17) dx = 2π * √(17) * ∫(4x+5) dx= 2π * √(17) * [2x^2/2 + 5x]9^13= 2π * √(17) * [(26 + 60) - (18 + 20)]= 84π √(17)
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Use elimination to solve for x and y:
9x - 2y = 46
x + 2y = 14
Answer:
(6, 4 )
Step-by-step explanation:
Given the 2 equations
9x - 2y = 46 → (1)
x + 2y = 14 → (2)
Adding the 2 equations term by term will eliminate the y- term
10x + 0 = 60
10x = 60 ( divide both sides by 10 )
x = 6
Substitute x = 6 into either of the 2 equations and solve for y
Substituting into (2)
6 + 2y = 14 ( subtract 6 from both sides )
2y = 8 ( divide both sides by 2 )
y = 4
solution is (6, 4 )
Simplify (8y6)
what’s the answer?
Can pls someone help with my homework pls I need help
Answer:
[tex] \sin(m < q) = \frac{7}{9} \\ \sin(m < q) =(0.77777777778) \\ m < q = { \sin 0.77777777778}^{ - 1} \\ m < q = (51.05755873102)[/tex]
at a meeting ,everyone shakes hands exactly once with every other person . if there are 55 handshakes . then what Is the number of people attending
Bon Air Elementary School has 300 students. The principal of the school thinks that the average IQ of students at Bon Air is at least 110. To prove her point, she administers an IQ test to 20 randomly selected students.
Among the sampled students, the average IQ is 108 with a standard deviation of 10. Based on these results, should the principal accept or reject her original hypothesis? Assume a significance level of 0.01.
The principal should reject her original hypothesis, as the lower bound of the interval is less than 110.
What is a t-distribution confidence interval?The t-distribution is used when the standard deviation for the population is not known, and the bounds of the confidence interval are given according to the equation presented as follows:
[tex]\overline{x} \pm t\frac{s}{\sqrt{n}}[/tex]
The variables of the equation are listed as follows:
[tex]\overline{x}[/tex] is the sample mean.t is the critical value.n is the sample size.s is the standard deviation for the sample.The critical value, using a t-distribution calculator, for a two-tailed 90% confidence interval, with 20 - 1 = 19 df, is t = 2.8609.
The parameters for this problem are given as follows:
[tex]\overline{x} = 108, s = 10, n = 20[/tex]
Then the lower bound of the interval is given as follows:
[tex]108 - 2.8609 \times \frac{10}{\sqrt{20}} = 101.6[/tex]
The upper bound of the interval is given as follows:
[tex]108 + 2.8609 \times \frac{10}{\sqrt{20}} = 114.4[/tex]
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Test the claim that the proportion of people who own cats is significantly different than 70% at the 0.02 significance level. The null and alternative hypothesis would be: 0.7 Hop 0.7 Hop - 0.7 H:P < 0.7 HP >0.7 HP 0.7 HOP The test is: right tailed left-tailed two-tailed Based on a sample of 500 people, 62% wned cats The p-value is:
Test the claim that the proportion of people who own cats is significantly different than 70% at the 0.02 significance level. The p-value is 0.024.
The null and alternative hypotheses for the claim that the proportion of people who own cats is significantly different than 70% at the 0.02 significance level are:
H0: p = 0.7 (null hypothesis
)H1: p ≠ 0.7 (alternative hypothesis)
The test is a two-tailed test because the alternative hypothesis includes not equal to (<>) which means either p is less than 0.7 or greater than 0.7
Based on a sample of 500 people, 62% owned cats.
This means that the sample proportion, p = 0.62.
To calculate the p-value, we will use the z-test statistic.
The formula for calculating the z-test statistic is given as:
z = (p - P) / √(PQ/n) where P is the hypothesized proportion (P = 0.7), Q is the complement of P (Q = 1 - P), and n is the sample size.
Using the given values in the formula, we have; z = (0.62 - 0.7) / √(0.7 × 0.3 / 500) = -2.52
The p-value for a two-tailed test at 0.02 level of significance is obtained from the standard normal table.
The area in both tails beyond the z-score of 2.52 is 0.012.
Therefore, the p-value is:
p-value = 2 × 0.012 = 0.024
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[tex]12 \frac{3}{6} + 14\frac{4}{6} [/tex]
i don't know what's the answer i been trying it this but i can't
Answer:
27 1/6
Step-by-step explanation:
14 + 12=26
4+3=7
26 7/6= 27 1/6
Prove the following using a proof by contradiction:
The average of four real numbers is greater than or equal to at least one of the numbers.
Our assumption that the average of four real numbers is less than all of the numbers is false. By contradiction, we conclude that the average of four real numbers is greater than or equal to at least one of the numbers.
To prove the statement using a proof by contradiction, we assume the opposite, namely, that the average of four real numbers is less than all of the numbers. Let's denote the four numbers as a, b, c, and d. We assume that the average of these numbers, which we'll denote as avg, is less than a, b, c, and d.
Now, let's consider the sum of these four numbers: a + b + c + d. The average of these numbers, avg, is calculated by dividing the sum by 4. Therefore, we have avg = (a + b + c + d)/4.
If avg is less than a, b, c, and d, then (a + b + c + d)/4 < a, (a + b + c + d)/4 < b, (a + b + c + d)/4 < c, and (a + b + c + d)/4 < d.
Now, let's consider the sum of these inequalities: (a + b + c + d)/4 + (a + b + c + d)/4 + (a + b + c + d)/4 + (a + b + c + d)/4 < a + b + c + d.
Simplifying the left-hand side, we have (a + b + c + d) + (a + b + c + d) + (a + b + c + d) + (a + b + c + d) < 4(a + b + c + d).
This simplifies to 4(a + b + c + d) < 4(a + b + c + d), which is a contradiction. The left-hand side is greater than the right-hand side, which contradicts our initial assumption.
Therefore, our assumption that the average of four real numbers is less than all of the numbers is false. By contradiction, we conclude that the average of four real numbers is greater than or equal to at least one of the numbers.
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4 people can dig a trench in 3 hours.
How long would it take 9 people?
Give your answer in minutes.
Answer:
80 minutes.
Step-by-step explanation:
do I need to explain? I hate explaining :(
You guy's will get 40 points if you help me!
Answer:
mean = 5+9+9+6+6+11+8+4/7 = 8.29
median = 6
mode = 6
range = 11 - 4 = 7
Answer:
Step-by-step explanation:
5 , 9 , 6 , 6 , 11 , 8 , 4
Mean = sum of all data ÷ number of data
[tex]= \frac{5+9+6+6+11+8+4}{7}\\\\= \frac{49}{7}\\\\= 7[/tex]
Median: To find median, arrange in ascending order and medianis the middle term
4 , 5 , 6 , 6 , 8 , 9 , 11
Middle term = 4th term
Median = 6
Mode: a number that appears most often is mode
6 appears 2 times
Mode = 6
Range:
Range = maximum value - minimum value
= 11 - 4
= 7
Plz help no links I will give brainiest to whoever helps
Answer:
110.92
Step-by-step explanation:
Assuming that the parameters (P), (h), and (B) all represent dimensions of the given prism, then based on the given information, the following can be concluded:
P = 6.6
h = 4.5
B = 2.2
The surface area is the two-dimensional area around a three-dimensional surface. In other words, if one was going to wrap the figure, the surface area is the amount of paper one would need. One can find the surface area by finding the area of each individual side and then adding all the results together. To find the area of a 2-dimensional figure by multiplying the length by the width.
(4.5) * (6.8) = 30.6
(4.5) * (6.8) = 30.6
(2.2) * (6.8) = 14.96
(2.2) * (6.8) = 14.96
(4.5) * (2.2) = 9.9
(4.5) * (2.2) = 9.9
Now add up all of the values,
30.6 + 30.6 + 14.96 + 14.96 + 9.9 + 9.9
= 110.92
Hey guy pls help me with dis due today pls help no links pls
I did number one
pls explain answer
mode is 4 and the median is also 4
mode is the number that appears the most which is 4 and median is the number that is in the middle when you line up all the numbers in order (0,2,2,3,3,4,4,4,4,5,5,5,6,6,10)
What is the description of angle 4 as it relates to the situation below?
angle 4 is the angle of elevation from the person to the radar tower.
angle 4 is the angle of depression from the radar tower to the person.
angle 4 is the angle of depression from the person to the radar tower.
angle 4 is the angle of elevation from the radar tower to the person.
In the given situation, "angle 4 is the angle of elevation from the radar tower to the person" is the description of angle 4.In trigonometry, an angle of elevation or inclination is the angle between the horizontal and the line of sight of an observer looking upwards. An angle of depression is the angle between the horizontal and the line of sight of an observer looking downwards.
In the given situation, angle 4 refers to the angle formed between the horizontal and the line of sight from the radar tower to the person. As the angle is formed while looking upwards from the radar tower to the person, it is called the angle of elevation. Hence, the correct description of angle 4 in this situation is "angle 4 is the angle of elevation from the radar tower to the person."
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CAN SOMEONE HELP ME!!!!
Thion Drones is a newly established manufacturer of drones for recreational use. The firm produced 180 drones last month and sold these for an average price of $230. Thion Drones had average variable costs of $190 per drone. Its fixed costs per month are $4,500.
a. Calculate the average fixed cost (AFC) for Thion Drones.
b. Calculate the monthly profit or loss made by Thion Drones.
The average fixed cost of each case will be $25
What is the average fixed cost ?Fixed cost is the cost that does not change with the number of lawyers hired or the number of cases. Fixed cost remains fixed regardless of the number of lawyers or the number of cases. Examples of fixed cost include rent, electricity.Average fixed cost is the total fixed cost per case. Average fixed cost can be determined by dividing the fixed cost by the number of cases.Average fixed cost = fixed cost / number of cases.
$4500/ 180= $25
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Let a < b. If ƒ is continuous on [a, b], and ƒ(a) = f(b), then there there exists c € (a,b) such that f'(c) = 0. d) If f is differentiable on (0, 1), then f is uniformly continuous on (0,1).
Yes, if ƒ is differentiable on (0, 1), then ƒ is uniformly continuous on (0, 1).
In mathematics, the concept of differentiability plays a crucial role in understanding the behavior of functions. If a function ƒ is differentiable on the interval (0, 1), it means that the derivative ƒ'(x) exists for every point x in that interval.
The answer states that if a function is differentiable on (0, 1), then it is uniformly continuous on the same interval.
To understand this result, we need to consider the properties of differentiability and uniform continuity.
Differentiability implies that the function has a well-defined tangent line at every point within the interval. This implies that the function cannot exhibit abrupt changes or discontinuities, as it must be smooth and continuous.
Uniform continuity, on the other hand, deals with the behavior of a function as the input values get arbitrarily close to each other. It ensures that the function does not exhibit extreme fluctuations or rapid oscillations.
If a function is differentiable on (0, 1), then it satisfies the conditions required for uniform continuity. This is because the derivative of the function acts as a measure of its rate of change.
If the derivative is bounded (i.e., it does not become infinitely large or small), then the function can be guaranteed to be uniformly continuous.
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We wish to estimate what percent of adult residents in a certain county are parents. Out of 200 adult residents sampled, 166 had kids. Based on this, construct a 90% confidence interval for the proportion, p. of adult residents who are parents in this county. Give your answers as decimals, to three places.
_________________ < p < _________________
Based on this, a 90% confidence interval for the proportion, p. of adult residents who are parents in this county is 0.787 < p < 0.873.
The point estimate for the proportion is calculated by dividing the number of adults with kids by the total sample size. In this case, the point estimate is 166/200 = 0.83.
To construct the confidence interval, we can use the formula:
[tex]p \pm z \times \sqrt{\frac{p \times (1 - p )}{n}}[/tex]
Where:
p is the point estimate
z is the z-score corresponding to the desired confidence level (90% confidence corresponds to a z-score of approximately 1.645)
n is the sample size
Substituting the values into the formula, we get:
[tex]= 0.83 \pm 1.645 \times \sqrt{\frac{0.83 \times (1-0.83)}{200}}[/tex]
Calculating the values, we can obtain the 90% confidence interval for the proportion of adult residents who are parents.
To construct a 90% confidence interval for the proportion of adult residents who are parents in the county, we can use the sample proportion and the standard error formula. Out of the 200 adult residents sampled, 166 had kids.
we calculate the sample proportion, p-hat:
p-hat = 166 / 200
= 0.83
Next, we calculate the standard error using the formula:
SE = √((p-hat × (1 - p-hat)) / n)
SE = √((0.83 × (1 - 0.83)) / 200) ≈ 0.025
To construct the confidence interval, we use the formula:
p-hat ± (z × SE)
where, z is the z-score corresponding to the desired confidence level.
For a 90% confidence interval, the z-score is approximately 1.645.
Substituting the values into the formula, we get:
= 0.83 ± (1.645 × 0.025)
Calculating the upper and lower bounds:
Lower bound = 0.83 - (1.645 × 0.025) ≈ 0.787
Upper bound = 0.83 + (1.645 × 0.025) ≈ 0.873
Therefore, the 90% confidence interval for the proportion of adult residents who are parents in the county is approximately 0.787 < p < 0.873.
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Which line is the best model for the data in the scatter plot?
PLEASE GIVE THE CORRECT ANSWER AND FAST
Answer:
Upper right corner.
Step-by-step explanation:
I took the test and that one was right. Hope this helps!
Please help me with the question please ASAP
Answer:
The ratio of perimeter of ABCD to perimeter of WXYZ = [tex]\frac{2}{3}[/tex]
Step-by-step explanation:
First, we have to determine the multiplicative factor of the dimensions for both figures.
Considering sides AB and WX,
multiplicative factor = [tex]\frac{12}{8}[/tex]
= 1.5
So that:
XY = 6 x 1.5 = 9
YZ = 7 x 1.5 = 10.5
ZW = 7 x 1.5 = 10.5
Perimeter of ABCD = 6 + 7 + 7 + 8
= 28
Perimeter of WXYZ = 9 + 10.5 + 10.5 + 12
= 42
The ratio of the perimeters of the two quadrilaterals can be determined as;
ratio = [tex]\frac{perimeter of ABCD}{Perirmeter of WXYZ}[/tex]
= [tex]\frac{28}{42}[/tex]
= [tex]\frac{2}{3}[/tex]
The ratio of the perimeter of ABCD to perimeter of WXYZ is [tex]\frac{2}{3}[/tex].
The answer 3h - 5 < 13?
Answer: h < 6
Step-by-step explanation:
3h - 5 < 13
3h < 18
h < 6
Answer:
h<6
Step-by-step explanation:
A system of equations consists of two lines. One line passes through (8,4) and (6.3) and the second line passes through (0, -2) and (4.0).
Answer:
system is:
y = 1/2x
y = 1/2x - 2
No Solution to this system
Step-by-step explanation:
2.
It cost Enica $9 75 for the ingredients to make 30 cupcakes. She sold them for $1.00 each. What was
Erica's total profit?
Answer:
$8.75
Step-by-step explanation:
Cost price= $9.75
Selling price= $1.00
profit= C.P-.SP
= 9.75-1.00
= $8.75
Does anyone know this
Answer:
I belive the answer is A
Step-by-step explanation:
So any answer with 22t would make sense, so you have A and C. In C though, it is subtracting 22, but since 6195 is the total it would have to include the 22 so it is A.
A wardrobe has 3 pants , 5 shirts , and 7 ties .
The number of total possible outfits is 15 .
True
False
A wardrobe with 3 pants, 5 shirts, and 7 ties, has a possible outcome of 105 outfits and not 15. So the answer is False
False. The number of total possible outfits is not 15. To calculate the number of possible outfits, we need to multiply the number of choices for each item together. In this case, we have 3 choices for pants, 5 choices for shirts, and 7 choices for ties. Therefore, the total number of possible outfits would be 3 x 5 x 7 = 105.
The statement incorrectly states that there are only 15 possible outfits. It's important to consider that when selecting multiple items, the total number of combinations is found by multiplying the number of choices for each item together. In this scenario, with 3 pants, 5 shirts, and 7 ties, there are 105 possible outfits, not 15.
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Choose the equation that best describes the situation below.
Lee is 32 years younger than his mother and his mother is 67 years old. How old is Lee?
a = Lee's age
Answer:
67-32=a
if his mom is 67 and he is 32 years younger 67 minus 32 would equal a which is his age
Sophie has a box filled with trail mix the box has a length
Please help me, i'm so confused
9514 1404 393
Answer:
(d) 512√3
Step-by-step explanation:
The area (A) of a regular hexagon can be computed from its side length (s) using the formula ...
A = (3√3)/2·s²
Here, the side length is given as ...
s = 32√3/3 = 32/√3
Then the area is ...
[tex]A=\dfrac{3\sqrt{3}}{2}\cdot\left(\dfrac{32}{\sqrt{3}}\right)^2=\dfrac{3\sqrt{3}\cdot1024}{2\cdot3}=\boxed{512\sqrt{3}}[/tex]
The area of the hexagon is 512√3 square units.
Elena prepared 8 kilograms of dough after working 2 hours. How much dough did Elena prepare if she worked for 9 hours? Assume the relationship is directly proportional.
Answer:
36 kilograms
Step-by-step explanation:
Since she made 8 kilograms of dough over the span of 2 hours, you divide 8 by 2 and get 4 then you have to multiply 9 hours by 4 kilograms of dough to get 36 kilograms of dough.
Evaluate the expression for the given value of x.
3/4 x − 12 for x = 16
Answer:
if x is 16 then 3/4(16) - 12
when you simplify 4 by 16
3(4)-12
12-12=0
Is it possible for a matrix to have the vector (3, 1, 2) in its row space and (2, 1, 1)T in its null space? Ex- plain.
Let a; be a nonzero column vector of an m x n matrix A. Is it possible for a j, to be in N(AT)? Explain.
It is not possible for a matrix to have the vector (3, 1, 2) in its row space and (2, 1, 1)T in its null space. Let's explain why.
Let A be an m × n matrix, and let x be a nonzero vector in the null space of A, so Ax = 0. We can also say that x is in the null space of A transpose. So x is an element of N(AT).Let’s prove the contradiction that arises from the initial claim by assuming that 3,1,2 is a row vector in the row space of A and 2,1,1 is a column vector in N(AT).We have that A[3 1 2]T = 0 and 2,1,1 is in the null space of A transpose. We also know that if a vector v is in the row space of A, then there exists a vector y such that v = A*y, where y is a column vector. So in this case, we can say that 3,1,2 is in the row space of A if there is a column vector y such that A * y = [3 1 2]T. But if that's the case, then we have the following equation: A* y = [3 1 2]. This can be written as: TA* = [3 1 2]If we then take the transpose of both sides, we have: A* y = [3 1 2]T and TA = [3 1 2]. However, this implies that TA* = TA, which can only be true if A is a symmetric matrix. But A is an m × n matrix, where m and n are not equal, so A cannot be a symmetric matrix. Therefore, it is not possible for a matrix to have the vector (3, 1, 2) in its row space and (2, 1, 1)T in its null space.
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∑ = {C,A,G,T}, L = { w : w = CAjGnTmC, m = j + n }. For example, CAGTTC ∈ L; CTAGTC ∉ L because the symbols are not in the order specified by the characteristic function; CAGTT ∉ L because it does not end with C; and CAGGTTC ∉ L because the number of T's do not equal the number of A's plus the number of G's. Prove that L ∉ RLs using the RL pumping theorem.
If We consider the string w = [tex]CA^pG^pT^pC[/tex], then L ∉ RLs by pumping lemma.
To prove that L ∉ RLs using the RL pumping theorem, we assume L is a regular language and apply the pumping lemma for RLs. Let p be the pumping length of L.
We consider the string w = [tex]CA^pG^pT^pC[/tex], where |w| ≥ p. According to the pumping lemma, we can decompose w into uvxyz such that |vxy| ≤ p, |vy| > 0, and for all k ≥ 0, the string [tex]u(v^k)x(y^k)z[/tex] is also in L.
However, by examining the structure of L, we see that the number of A's and G's is dependent on each other and must match the number of T's.
Since pumping up or down would alter this balance, there is no way to satisfy the condition for all k, leading to a contradiction. Therefore, L cannot be a regular language, and we conclude that L ∉ RLs.
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