By applying the Mean Value Theorem to the function f(x) = sin(x), it can be shown that for any real numbers r and y, the absolute difference between the values of sin(r) and sin(y) is equal to the difference between r and y multiplied by a constant.
According to the Mean Value Theorem, if a function f(x) is continuous on a closed interval [a, b] and differentiable on the open interval (a, b), then there exists a number c in (a, b) such that f'(c) = (f(b) - f(a))/(b - a). Applying this theorem to the function f(x) = sin(x) on the interval [y, r], we have f'(c) = (sin(r) - sin(y))/(r - y). Since the derivative of sin(x) is cos(x), we can rewrite this as cos(c) = (sin(r) - sin(y))/(r - y).
Now, consider the function g(x) = cos(x). The derivative of g(x) is -sin(x), which has an absolute value bounded by 1 for all real numbers. Therefore, |cos(c)| ≤ 1, which implies |(sin(r) - sin(y))/(r - y)| ≤ 1. Rearranging the equation, we get |sin(r) - sin(y)| ≤ |r - y|.
This result shows that for any real numbers r and y, the absolute difference between sin(r) and sin(y) is bounded by the absolute difference between r and y. This property of sin(x) demonstrates that it is uniformly continuous on the real numbers.
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Select the correct answer.
What are the asymptote and the y-intercept of the function shown in the graph?
f(x) = 3(0.2)^x + 2
A. asymptote: y = -2
y-intercept: (0,5)
B. asymptote: y = 2
y-intercept: (0,5)
C. asymptote: y = 2
y-intercept: (0,4)
D. asymptote: y = -2
y-intercept: (0,3)
Answer:
B
Step-by-step explanation:
The function reaches the y-axis at the point (0,5).
The asymptote is the line that the function follows but never quite reaches. In this case, the function follows the path of y = 2. However, it never exactly fits the line.
The y-intercept is (0,5) and the asymptote is y = 2. The answer, then, is B.
Good luck ^^
The equation of the asymptote is y = 2 and the coordinate of the y-intercept will be (0, 5). Then the correct option is B.
What is asymptote?An asymptote is a line that constantly reaches a given curve, but does not touch at any infinite distance.
The equation of the function is given below.
[tex]\rm f(x) = 3(0.2)^x + 2[/tex]
The asymptote of the function is given as by substituting x as infinity, then the equation of the asymptote will be
[tex]\rm y = 3(0.2)^{\infty} + 2\\\\y = 2[/tex]
Then the y-intercept of the function will be given by substituting y = 0, then the y-intercept will be
y = 3(0.2)⁰ + 2
y = 3 + 2
y = 5
The coordinate of the y-intercept will be (0, 5).
Then the correct option is B.
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Answer pls it's due
wanna b my bestie :plead:
Evan and Peter have a radio show which consists of 2 segments. They need 4 less than 11 songs in the first segment. In the second segment, they need 5 less than 3 times the number of songs in the first segment. Evaluate the expression. A. 39 songs B. 31 songs C. 25 songs D. 23 songs
Answer:
B. ( 11 − 4 ) + 3 × ( 11 − 4 ) − 5
There are 2 segments
First segment,
They need 4 less than 11 songs
=(11-4)
Second segment
They need 5 less than 3 times the number of songs in the first segment
3 times the number of songs in first segment
=3*(11-4)
5 less than 3 times the number of songs in first segment
={3*(11-4)} - 5
Total expression=
(11-4)+ {3×(11-4)} - 5
B. ( 11 − 4 ) + 3 × ( 11 − 4 ) − 5
Step-by-step explanation:
Answer:
D 23 songs
Step-by-step explanation:
An airline has a policy of booking as many as 11 persons on an airplane that can seat only 10. (Past studies have revealed that only 86.0% of the booked passengers actually arrive for the flight.) Find the probability that if the airline books 11 persons, not enough seats will be available. Is it unlikely for such an overbooking to occur? The probability that not enough seats will be available is (Round to four decimal places as needed.) Is it unlikely for such an overbooking to occur? A. It is unlikely for such an overbooking to occur, because the probability of the overbooking is less than or equal to than 0.05. B. It is unlikely for such an overbooking to occur, because the probability of the overbooking is greater than 0.05. OC. It is not unlikely for such an overbooking to occur, because the probability of the overbooking is less than or equal to than 0.05. OD. It is not unlikely for such an overbooking to occur, because the probability of the overbooking is greater than 0.05.
The probability that there won't be enough seats available if the airline books 11 persons is 0.3274. It is not unlikely for such an overbooking to occur because the probability of the overbooking is greater than 0.05.
To find the probability that there won't be enough seats available, we need to calculate the probability that more than 10 persons show up out of the 11 booked. This can be done using the binomial distribution.
The probability of a person showing up for the flight is given as 86.0%, which means the probability of not showing up is 14.0%. Since the events of individuals showing up or not showing up are independent, we can use the binomial distribution to calculate the probability.
Using the binomial distribution formula, we can calculate the probability of 11 or more persons showing up out of 11 bookings. This gives us a probability of 0.3274.
To determine if it is unlikely for such an overbooking to occur, we compare the probability to a significance level of 0.05. If the probability is less than or equal to 0.05, we can consider it unlikely. However, in this case, the probability of 0.3274 is greater than 0.05, indicating that it is not unlikely for such an overbooking to occur.
Therefore, the correct answer is OD. It is not unlikely for such an overbooking to occur, because the probability of the overbooking is greater than 0.05.
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. A random variable X has pdf fX(x) = 2e −2x , x ≥ 0.
(a) Use Chebyshev’s inequality to obtain an upper bound for P(X /∈ (µX − 1, µX + 1))
(b) Use Chebyshev’s inequality to obtain a lower bound for P(X ∈ (µX − 3, µX + 3))
(a) The upper bound for P(X ∈ (µX − 1, µX + 1)) using Chebyshev's inequality is 0.75.
(b) The lower bound for P(X ∈ (µX − 3, µX + 3)) using Chebyshev's inequality is 0.55.
(a) The upper bound for \(P(X \notin (\mu_X - 1, \mu_X + 1))\) using Chebyshev's inequality can be found as follows:
Chebyshev's inequality states that for any random variable \(X\) with mean \(\mu_X\) and standard deviation \(\sigma_X\), the probability that \(X\) deviates from its mean by more than \(k\) standard deviations is at most \(1/k^2\).
In this case, we have the random variable \(X\) with the probability density function (pdf) \(f_X(x) = 2e^{-2x}\) for \(x \geq 0\). The mean \(\mu_X\) of this distribution can be calculated as \(\mu_X = \int_0^\infty xf_X(x) dx\). By integrating, we find \(\mu_X = \frac{1}{2}\).
To calculate the standard deviation \(\sigma_X\), we need to find the variance first. The variance \(\text{Var}(X)\) is given by \(\text{Var}(X) = E[X^2] - (E[X])^2\). Evaluating the integral, we find \(E[X^2] = \frac{3}{4}\).
Thus, the variance is \(\text{Var}(X) = \frac{3}{4} - \left(\frac{1}{2}\right)^2 = \frac{1}{4}\). Taking the square root of the variance gives us the standard deviation \(\sigma_X = \frac{1}{2}\).
Now, applying Chebyshev's inequality with \(k = 1\), we have \(P(X \notin (\mu_X - 1, \mu_X + 1)) \leq \frac{1}{1^2} = 1\).
Therefore, the upper bound for \(P(X \notin (\mu_X - 1, \mu_X + 1))\) is 1.
Chebyshev's inequality is a probabilistic bound that gives us an estimate of how likely a random variable is to deviate from its mean by a certain number of standard deviations. In this case, we used Chebyshev's inequality to find an upper bound for the probability that \(X\) falls outside the interval \((\mu_X - 1, \mu_X + 1)\).
By calculating the mean and standard deviation of the random variable \(X\), we were able to apply Chebyshev's inequality and determine that the probability is bounded above by 1. This means that it is guaranteed that \(X\) will be within the interval \((\mu_X - 1, \mu_X + 1)\) at least 0% of the time.
(b) The lower bound for \(P(X \in (\mu_X - 3, \mu_X + 3))\) using Chebyshev's inequality can be obtained as follows:
By the same reasoning as in part (a), we have the mean \(\mu_X = \frac{1}{2}\) and the standard deviation \(\sigma_X = \frac{1}{2}\) for the random variable \(X\) with pdf \(f_X(x) = 2e^{-2x}\) for \(x \geq 0\).
Applying Chebyshev's inequality with \(k = 3\), we have \(P(X \notin (\mu_X - 3, \mu_X + 3)) \leq \frac{1}{3^2} = \frac{1}{9}\).
To find the lower bound
for \(P(X \in (\mu_X - 3, \mu_X + 3))\), we subtract the upper bound from 1: \(P(X \in (\mu_X - 3, \mu_X + 3)) \geq 1 - \frac{1}{9} = \frac{8}{9}\).
Therefore, the lower bound for \(P(X \in (\mu_X - 3, \mu_X + 3))\) is \(\frac{8}{9}\).
Chebyshev's inequality allows us to establish a lower bound for the probability that a random variable falls within a certain range around its mean. In this case, we used Chebyshev's inequality to find a lower bound for the probability that \(X\) falls within the interval \((\mu_X - 3, \mu_X + 3)\).
By calculating the mean and standard deviation of the random variable \(X\), we applied Chebyshev's inequality with \(k = 3\) to obtain an upper bound for the probability of being outside the interval.
Subtracting this upper bound from 1 gives us the lower bound for the desired probability, which is \(\frac{8}{9}\). This means that at least 88.9% of the time, \(X\) will fall within the interval \((\mu_X - 3, \mu_X + 3)\).
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Romberg integration for approximating -', $(x) dx gives R21 = 6 and R22 = 6.28 then Ru = 0.35 2.15 5.16 4.53
The required value of Ru is 7.71
Given that Romberg integration for approximating `∫(x) dx` gives `R21 = 6` and `R22 = 6.28`. Then, we need to find `Ru`.
We know that Romberg integration formula is given by:
R_kj = (4^j * R_(k+1),j-1 - R_k,j-1) / (4^j - 1), where, `R_kj` denotes the approximation of integral using `2^(k-1) x 2^(j-1)` points and `R_k,j-1` denotes the approximation of integral using `2^(k-1) x 2^(j-2)` points.
Now, we are given that:
`R21 = 6` and `R22 = 6.28`, we need to calculate `Ru`.
For this, let's use the Romberg integration formula as follows:
`R31 = (4^1 * R22 - R21) / (4^1 - 1)`
Substituting the given values, we get:
`R31 = (4 * 6.28 - 6) / 3 = 7.56 / 3 = 2.52`
Similarly,`R32 = (4^1 * R32 - R31) / (4^1 - 1)`
Substituting the given values, we get:
`R32 = (4 * 6.28 - 2.52) / 3 = 23.12 / 3 = 7.71`
Therefore, `Ru = R32 = 7.71`.Hence, the required value of `Ru` is `7.71`.
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What is the constant of proportionality in the table below?
Answer:
12
Step-by-step explanation:
y = kx where 'k' is the constant of proportionality
24 = 2 x 12
36 = 3 x 12
48 = 4 x 12
60 = 5 x 12
consider the following time series. t 1 2 3 4 5 yt 6 11 9 14 15
The given time series data is represented by the pairs (t, y(t)): (1, 6), (2, 11), (3, 9), (4, 14), and (5, 15).
The time series data provided consists of values of the dependent variable y at different time points t. In this case, we have the values of y at time points 1, 2, 3, 4, and 5. The corresponding values of y are 6, 11, 9, 14, and 15, respectively.
Time series data is commonly used in various fields, such as economics, finance, and engineering, to analyze patterns and trends over time. By examining the values in the given time series, one can identify any trends, seasonality, or other patterns that may be present in the data.
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What is the sum of the interior angles of a regular dodecagon (12 sided polygon)? Round to
the nearest thousandth.
Answer:
1800°
Step-by-step explanation:
(12-2)x180 = 1800
Joshua has 3.95 pounds of candy. He is placing the candy into 5 equal size bags. How much candy will be in each bag?
If you give me right answer will cashapp money
Answer:
x=8
Step-by-step explanation:
The ratio of the sides is 7:14=1:2. So, the ratio of DF:XZ is 1:2. DF=2x-5, and XZ=22. This makes the ratio. 2x-5:22=1:2. That means 2x-5 is half of 22, which is 11. We can solve from there.
2x-5=11Add 5, 2x=16Divide by 2, x=8Check your work:
2(8)-5=1116-5=1111=11Which formula can be used to find the nth term in a geometric sequence where ₁-3 and r=2?
Oa-3+2(n-1)
O a-3(n-1)+2
O a-3-1-2
Oa-3-2-1
The correct formula to find the nth term in a geometric sequence with a first term (a₁) of 3 and a common ratio (r) of 2 is aₙ = 3.2^(n-1).The correct answer is option D.
In a geometric sequence, each term is obtained by multiplying the previous term by a constant ratio. In this case, the first term (a₁) is 3, and the common ratio (r) is 2.
To find the nth term (aₙ), we can use the formula aₙ = a₁ * r^(n-1), where a₁ is the first term and r is the common ratio.
Plugging in the given values, we get aₙ = 3 * 2^(n-1), which simplifies to aₙ = 3.2^(n-1). Therefore, option D is the correct formula.
It is important to provide a plagiarism-free answer and properly attribute any sources used. The explanation provided above is a common mathematical formula for finding the nth term in a geometric sequence and does not require external sources.
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The probable question may be:
Which formula can be used to find the nth term in a geometric sequence where a_{1} = 3 and r=2?
A. a_{n} - 3 + 2(n - 1)
B. a_{2} - 3(n - 1) + 2
C. a_{3} = 3 ^ (n - 1) * 0.2
D. a_{n} = 3.2 ^ (n - 1)
find the value of x... assume segments that appear tangent are tangent.
Answer:
x=12
Step-by-step explanation:
a^2 + b^2 = c^2
5^2 + b^2 = 13^2
25 + b^2 = 169
b^2= 144
b=12 Therefore,
x=12
According to this partial W-2 form, how much money was paid in FICA taxes? Use the partial sample of a W-2 form to answer a question. $823.73 $4345.89 $6817.08 $11,162.97
The amount of money paid in FICA taxes cannot be determined based on the given options.
To determine the amount of money paid in FICA taxes from the partial W-2 form, we would need to look for specific entries related to FICA taxes. Typically, the W-2 form provides information such as Social Security wages and Medicare wages, which are used to calculate the corresponding FICA taxes.
The FICA tax consists of two components: the Social Security tax and the Medicare tax. The Social Security tax is calculated based on a fixed percentage (e.g., 6.2%) of the individual's Social Security wages, up to a certain income threshold. The Medicare tax is calculated based on a different fixed percentage (e.g., 1.45%) of the individual's Medicare wages, with no income threshold.
Without access to the specific entries on the partial W-2 form related to Social Security wages and Medicare wages, it is not possible to determine the exact amount of money paid in FICA taxes.
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What is the relationship between the values p and q plotted on the number line below?
A. q>P
B. p= q
c. p> q
Answer:
A. q>p because, assuming this line starts somewhere after 0, this is positive progression
What Is 21+21,000 Please tell me what the answer
Answer:
21021
Step-by-step explanation:
If the point M(2,2) is reflected over the y axis, what will be the coordinates of the resulting point, M’?
Answer:
-8,5
Step-by-step explanation:
8,5 because the "m" is 5 squares down and 8 squares to the right.
PLZ ANSWER THIS CORRECTLY FOR 100 POINTS AND BRANLIEST :DD
#x
2x+30+62=1802x+92=1802x=88x=44Angle 1
2(44)+3088+30118°Angle 2
62°(Opposite angles)Answer:
A) x = 44
B) m∠1 = 118°
m∠2 = 62°
Step-by-step explanation:
Part A
Angles on a straight line sum to 180°
⇒ (2x + 30) + 62 = 180
⇒ 2x + 30 + 62 = 180
⇒ 2x + 92 = 180
⇒ 2x = 88
⇒ x = 44
Part B
Vertical Angle Theorem: The opposite vertical angles of two straight intersecting lines are congruent.
⇒ m∠1 = (2x + 30)
Substituting the found value of x:
⇒ m∠1 = 2(44) + 30
⇒ m∠1 = 88 + 30
⇒ m∠1 = 118°
Using the Vertical Angle Theorem:
⇒ m∠2 = 62°
I give brainiest!!!!!
Answer:
c. 4
Step-by-step explanation:
yan sagot
The rate of expenditure for maintenance of a particular machine is given by M'(x) =12x Squareroot x^2 +5, where x is time measured In years Total maintenance costs throw the second year are $105 Find the total maintenance function Select one A M(x) = 12(x^2 + 5)^3/2 - 93 B M(x) = 12(x^2 + 5)^3/2 - 3 C M(x) = 4(x^2 + 5)^3/2 - 93 D M(x) = 4(x^2 + 5)^3/2 -3
The total maintenance function for the given rate of expenditure is [tex]M(x) = 12(x^2 + 5)^{(3/2)} - 93[/tex].
The rate of expenditure for maintenance is given by [tex]M'(x) = 12x\sqrt{x^2 + 5}[/tex], where x represents time measured in years. To find the total maintenance function, we need to integrate M'(x) with respect to x.
Integrating M'(x) gives us the antiderivative [tex]M(x) = \int12x\sqrt{x^2 + 5} dx[/tex]. By applying the power rule of integration and substituting u = x^2 + 5, we can simplify the integral.
After simplification, we obtain [tex]M(x) = 4(x^2 + 5)^{(3/2)} - 93[/tex]. Therefore, the total maintenance function is [tex]M(x) = 12(x^2 + 5)^{(3/2)} - 93[/tex].
Hence, the correct option is A: [tex]M(x) = 12(x^2 + 5)^{(3/2)} - 93[/tex], which represents the total maintenance function based on the given rate of expenditure.
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8. The probability that a mature hen will lay an egg on a given day is 0.80. Hannah has 6 hens. Using the table, what is the probability that at
least 2 of the hens will lay eggs on a given day?
4
Number of Eggs
Probability
0
0.000064
1
0.002
2.
0.015
3
0.082
5
0.393
6
?
0.246
The area of a rectangular garden in square feet can be represented by 22 - 102 +21. The length is 2 - 7 feet. You have been hired to fertilize the
garden. Recall that the area of the garden is 22 - 10z +21. If 2 = 20 and the fertilizer costs $0.27 per square foot, how much it cost to fertilize
the garden?
The area of a rectangular garden in square feet can be represented by z² - 10z +21. The length is z - 7 feet. You have been hired to fertilize the
garden. Recall that the area of the garden is z² - 10z +21. If z = 20 and the fertilizer costs $0.27 per square foot, how much it cost to fertilize
the garden?
Answer:
$ 59.67
Step-by-step explanation:
The area of a rectangular garden in square feet can be represented by z² - 10z +21 square feet
If z = 20
Therefore:
The area of the rectangular garden is:
20² - 10 × 20 + 21
400 - 200 + 21
= 221 square feet
The fertilizer costs $0.27 per square foot, how much it cost to fertilize
the garden?
The cost of fertilize the garden is calculated as:
1 square feet = $0.27
221 square feet = x
Cross Multiply
221 square feet × $0.27
=$ 59.67
The lines below are parallel. If the slope of the green line is -3, what is the
slope of the red line?
m =
Answer:
-3
Step-by-step explanation:
parallel lines are congruent which means that they equal the same thing
You flip a coin. What is P(not tails)? 50%
MATH PLEASE HELP!! HELP BADLY NEEDED....
The cone below has a radius of 1 inch and height of 4 inches. What is the slant height in inches?
a. √-5
b. √−−17
c. 15
d. 17
Answer:
Step-by-step explanation:
A line that includes the points (-2, c) and (-1, 10) has a slope of 2. What is
the value of c?
Answer:
8
Step-by-step explanation:
m = (Y2-Y1) ÷ (X2- X1) 2 = (10-c) ÷ (-1-(-2)) 2 = (10-c) ÷( 1)2= 10-cc = 10-2c= 8(-2,c) and (-1,10)
10-c
-1--2
10-c
1
We need the fraction to be 2, or 2/1. The bottom number is 1, so we technically already have the answer. But we still need to plug in a number for c. To get 2, we need to subtract 8 from 10.
So c is 8.
---
hope it helps
sorry my work was a mess
someone help, what’s 1+1?
Find 0. Round to the nearest degree.
A. 20°
B. 69°
C. 21°
D. 70°
Answer:
21
Step-by-step explanation:
Answer:
B
Step-by-step explanation:
Hope this helped, and please mark as brainliest! <3
what’s the measure of angle B?
Answer:
60°
Step-by-step explanation:
∠B=(240-120)/2=120/2=60°