lim sup an = sup P and lim inf an = inf P.
What is the equivalent expression?
Equivalent expressions are expressions that perform the same function despite their appearance. If two algebraic expressions are equivalent, they have the same value when we use the same variable value.
First, we will prove that [tex]$\limsup a_n = \sup P$[/tex].
Let[tex]M = \limsup a_n$[/tex]. By definition, M is the smallest real number that satisfies the following two conditions:
For every [tex]$\epsilon > 0$[/tex], there exists a positive integer N such that [tex]a_n < M + \epsilon$[/tex] for all [tex]n \geq N$[/tex].
For every [tex]$\epsilon > 0$[/tex], there exists an infinite number of terms in the sequence that are greater than [tex]M - \epsilon$[/tex].
Since [tex]${a_n}$[/tex] is a bounded sequence, we know that P is non-empty and bounded above. Therefore, [tex]\sup P$[/tex] exists.
We will now show that [tex]$\limsup a_n \leq \sup P$[/tex]. Suppose for the sake of contradiction that [tex]$\limsup a_n > \sup P$[/tex]. Then, there exists some [tex]$\epsilon > 0$[/tex] such that [tex]$\limsup a_n > \sup P + \epsilon$[/tex].
By the definition of [tex]$\limsup$[/tex], this means that there are only finitely many terms in the sequence that are greater than [tex]$\sup P + \epsilon$[/tex].
However, since [tex]$\sup P[/tex] is an upper bound for P, there must be infinitely many terms in the sequence that are greater than sup P, which contradicts the definition of sup P.
Therefore, [tex]$\limsup a_n \leq \sup P$[/tex].
Next, we will show that[tex]$\limsup a_n \geq \sup P$[/tex].
Suppose for the sake of contradiction that [tex]$\limsup a_n < \sup P$[/tex].
Then, there exists some [tex]$\epsilon > 0$[/tex] such that[tex]$\limsup a_n < \sup P - \epsilon$[/tex] .
By the definition of [tex]$\sup P$[/tex], there exists a limit point p of [tex]${a_n}$[/tex] such that [tex]$p > \sup P - \epsilon$[/tex].
Since p is a limit point of [tex]${a_n}$[/tex], there must be infinitely many terms in the sequence that are within [tex]$\epsilon$[/tex] of p.
But this contradicts the fact that [tex]$\limsup a_n < \sup P - \epsilon$[/tex] since any terms in the sequence that are within [tex]$\epsilon$[/tex] of p are greater than [tex]$\sup P - \epsilon$[/tex] Therefore, [tex]$\limsup a_n \geq \sup P$[/tex]
Putting the above two inequalities together, we have [tex]$\limsup a_n = \sup P$[/tex].
Next, we will prove that [tex]$\liminf a_n = \inf P$[/tex].
Let [tex]$m = \liminf a_n$[/tex]. By definition, m is the largest real number that satisfies the following two conditions:
For every [tex]$\epsilon > 0$[/tex], there exists a positive integer N such that [tex]a_n > m - \epsilon$[/tex] for all [tex]$n \geq N$[/tex].
For every [tex]$\epsilon > 0$[/tex], there exists an infinite number of terms in the sequence that are less than [tex]$m + \epsilon$[/tex].
We will show that [tex]$m = \inf P$[/tex].
First, we will show that [tex]$m \leq \inf P$[/tex].
Suppose for the sake of contradiction that [tex]$m > \inf P$[/tex].
Then, there exists some [tex]$\epsilon > 0$[/tex] such that [tex]$m > \inf P + \epsilon$[/tex].
By the definition of [tex]$\liminf$[/tex], this means that there are only finitely many terms in the sequence that are less than [tex]$\inf P + \epsilon$[/tex].
But this contradicts the fact that [tex]$\inf P$[/tex] is a lower bound for P, since there must be infinitely many terms in the sequence that are less than or equal to [tex]$\inf P$[/tex]
Therefore, lim sup an = sup P and lim inf an = inf P.
To learn more about the equivalent expression visit:
https://brainly.com/question/2972832
#SPJ4
Run a regression where customer satisfaction rating is the dependent (outcome) variable and all other numerical variables predict it. Although there is a relationship between sales rep age and customer satisfaction rating, it is likely only due to chance. [Save the analyses you run to answer this question somewhere on the page.] a This is true because the p value is less than 0.05 b This is false because the p value is greater than 0.05 c This is true because the p value is greater than 0.05 d This is false because the p value is less than 0.05
The correct answer is either (a) if the p-value is less than 0.05, or (b) if the p-value is greater than 0.05.
What is the equivalent expression?
Equivalent expressions are expressions that perform the same function despite their appearance. If two algebraic expressions are equivalent, they have the same value when we use the same variable value.
Without knowing the specific p-value for the relationship between sales rep age and customer satisfaction rating, it is not possible to determine the correct answer to this question.
In general, a p-value less than 0.05 indicates that there is a statistically significant relationship between the predictor variable and the outcome variable.
However, it is important to interpret the p-value in the context of the specific analysis and research question.
If the p-value for the relationship between sales rep age and customer satisfaction rating is greater than 0.05, it would suggest that the relationship is not statistically significant and may be due to chance.
However, if the p-value is less than 0.05, it would suggest that there is a statistically significant relationship between sales rep age and customer satisfaction rating, and the relationship is not likely due to chance.
Therefore, the correct answer is either (a) if the p-value is less than 0.05, or (b) if the p-value is greater than 0.05.
To learn more about the equivalent expression visit:
https://brainly.com/question/2972832
#SPJ4
compare the function with the parent function. without graphing, what are the vertex, axis of symmetry, and transformations of the given function? y
Vertex: (1/5, -5), Axis of Symmetry: x = 1/5, Transformations: vertical stretch by 10, horizontal shift 1/5 right, and vertical shift 7 down.
Let's analyze the given function, Y = |10x - 2| - 7, and compare it to the parent function, Y = |x|.
Vertex: The vertex of the given function can be found by determining the x-coordinate that will make the expression inside the absolute value equal to zero. In this case, 10x - 2 = 0. Solving for x, we get x = 1/5. The corresponding y-coordinate is found by substituting x back into the function: Y = |10(1/5) - 2| - 7, which simplifies to Y = |-2| - 7 = 2 - 7 = -5. Thus, the vertex is at the point (1/5, -5).
Axis of Symmetry: Since the given function is an absolute value function, the axis of symmetry is vertical and goes through the x-coordinate of the vertex. In this case, the axis of symmetry is x = 1/5.
Transformation: Comparing the given function to the parent function, there are a few transformations applied:
1. Vertical stretch by a factor of 10 (due to the "10x" term)
2. Horizontal shift of 1/5 units to the right (due to the "-2" term inside the absolute value)
3. Vertical shift of 7 units down (due to the "-7" term outside the absolute value)
So, to summarize:
- Vertex: (1/5, -5)
- Axis of Symmetry: x = 1/5
- Transformations: Vertical stretch by 10, horizontal shift 1/5 right, and vertical shift 7 down.
To learn more about function click here
#SPJ11
Complete Question
Compare the function with the parent function. Without graphing, what are the vertex, axis of symmetry, and transformation of the given function? Y=|10x-2|-7
Fill in the missing numbers for 6x-10y=-8 and 6x-5y=2 by using elimination.
if i was helpful Brainliests my answer ^_^
Suppose that the weight of a sack of flour has a probability distribution with moment generating function MW (t) = 1/(1 − 3t) 2 . You purchase 2 sacks of flour. Assume that the weights of different sacks of flour are independently distributed. What is the variance of the total weight of flour sacks purchased?
The variance of the total weight of flour sacks purchased is 36.
Since the moment generating function of a random variable uniquely determines its moments, we can use the moment generating function MW(t) to find the mean and variance of the weight of one sack of flour.
The first derivative of the moment generating function is:
MW'(t) = 6t/(1 - 3t)³
Setting t = 0, we get the mean:
MW'(0) = 6(0)/(1 - 3(0))³ = 0
So the mean weight of one sack of flour is zero.
The second derivative of the moment generating function is:
MW''(t) = 54t²/(1 - 3t)⁴ + 18/(1 - 3t)³
Setting t = 0, we get the second moment:
MW''(0) = 54(0)²/(1 - 3(0))⁴ + 18/(1 - 3(0))³ = 18
So the variance of the weight of one sack of flour is 18.
Now, let X and Y denote the weights of the first and second sacks of flour, respectively. Since the weights are independently distributed, the variance of the total weight of flour sacks purchased is the sum of the variances:
Var(X + Y) = Var(X) + Var(Y) = 18 + 18 = 36
Therefore, the variance of the total weight of flour sacks purchased is 36.
To know more about variance visit:
brainly.com/question/13091634
#SPJ4
total variability is the calculated by dividing the within-group variance by the between-group variance.
T/F
This statement is false. Total variability is the calculated by dividing the within-group variance by the between-group variance.
The total variability, also known as the total sum of squares (TSS), is the total variation in the response variable of a dataset. The total of the squared variances of each data point from the overall mean is used to calculate it.
The within-group variance, also known as the residual sum of squares (RSS), measures the variability of the data within each group or category. It is calculated as the sum of the squared deviations of each data point from its group mean.
The between-group variance, also known as the explained sum of squares (ESS), measures the variability of the data between the groups or categories. It is calculated as the sum of the squared deviations of each group mean from the overall mean.
To calculate the total variability or TSS, we add the between-group variance or ESS to the within-group variance or RSS. The formula for TSS is:
TSS = ESS + RSS
Therefore, the statement "Total variability is calculated by dividing the within-group variance by the between-group variance" is not accurate.
To know more about variability visit:
https://brainly.com/question/12872866
#SPJ4
Is it true that If A and B are square and invertible, then AB is invertible, and (AB)^−1=A^−1B^−1.
Yes, it is true that if A and B are square and invertible matrices, then AB is also invertible, and its inverse is given by[tex](AB)^{(-1) }= B^{(-1)}A^{(-1).[/tex]
To see why this is true, consider the product[tex](AB)(B^{(-1)}A^{(-1)}).[/tex]
Using the associative property of matrix multiplication, we can rearrange this expression as
[tex](A(BB^{(-1)})A^{(-1)}) = (AIA^{(-1)}) = AA^{(-1)} = I,[/tex]
where I is the identity matrix.
Similarly, we can show that [tex](B^{(-1)}A^{(-1)})(AB) = I,[/tex] which means that
[tex](AB)^{(-1) }= B^{(-1)}A^{(-1).[/tex]
Therefore, we conclude that if A and B are square and invertible matrices, then AB is invertible, and its inverse is given by [tex](AB)^{(-1)} = B^{(-1)}A^{(-1).[/tex]
for such more question on invertible matrices
https://brainly.com/question/31043586
#SPJ11
A reputable polling organization in a certain country surveyed 106,600 ​adults, and 18​% of those polled reported that they smoked. Complete parts a and b below.
b) Explain what this margin of error means. Select the correct choice below and fill in the answer box within your choice.
​(Round to four decimal places as​ needed.)
A.The probability that any given adult surveyed from the population smokes is ________________.
B.The probability that any given adult surveyed from the sample smokes is _____________.
C.We are 90​% confident that the observed proportion of adults that smoke is within _________of the sample proportion.
D.We are 90​% confident that the observed proportion of adults that smoke is within ________ of the population proportion
Both options C and D are correct in describing the meaning of the margin of error, but we cannot provide specific values for the margin of error without additional information.
To answer this question, first, we need to calculate the sample proportion of adults who smoke.
Calculate the sample proportion
Number of adults surveyed = 106,600
Percentage of adults who smoke = 18%
Sample proportion (p) = (Percentage of adults who smoke) / 100
p = 18% / 100 = 0.18
Now, let's address each option in part b:
A. The probability that any given adult surveyed from the population smokes is not the correct interpretation of the margin of error.
B. The probability that any given adult surveyed from the sample smokes is not the correct interpretation of the margin of error.
C. We are 90% confident that the observed proportion of adults that smoke is within the margin of error of the sample proportion.
To calculate the margin of error, we need more information, such as the standard deviation of the population and the desired confidence level.
Since we do not have this information, we cannot provide a specific value for the margin of error.
D. We are 90% confident that the observed proportion of adults that smoke is within the margin of error of the population proportion.
Similar to option C, we need more information to calculate the margin of error, so we cannot provide a specific value for the margin of error.
For similar question on sample proportion.
https://brainly.com/question/24232216
#SPJ11
Complete the proof, drag description to correct location
We have the proof statements as;
<A ≅ <C is given as the base angles
D is the midpoint of line AC; definition of midpoint
AC ⊥ BD; line of symmetry
ΔABC is an isosceles triangle; two equal sides and angles
How to prove the statementIt is important to note that properties of an isosceles triangle is given as;
An isosceles triangle has two equal sides with two equal angles.The two equal sides of an isosceles triangle are known as the legs and the angle that is found between them is called the vertex.The side opposite this vertex angle is known as the baseThe base angles are equal.The perpendicular from the apex angle divides the base and the vertexThe perpendicular drawn from the apex angle divides the isosceles triangle into two equal triangles and is line of symmetry.Learn about isosceles triangles at: https://brainly.com/question/1475130
#SPJ1
find the order of the matrix product ab and the product ba, whenever the products exist. a is 4 x 2, b is 2 x 4.A) AB is 2 x 2, BA is 4 x 4. B) AB is nonexistent, BA is 2x2. C) AB is 4 x 4, BA is nonexistent. D) AB is 4 x 4, BA is 2 x 2
The correct answer is (D) AB is 4 x 4, BA is 2 x 2.
What is order of a matrix?
The order of a matrix refers to the number of rows and columns in the matrix. If a matrix has m rows and n columns, we say that it is an m x n matrix. The order of the matrix is written as "m x n".
In general, if A is an m x n matrix and B is an n x p matrix, then the product AB is an m x p matrix and the product BA is an n x n matrix.
In this case, A is a 4 x 2 matrix and B is a 2 x 4 matrix. Therefore, the product AB is a 4 x 4 matrix, and the product BA is a 2 x 2 matrix.
So the answer is (D) AB is 4 x 4, BA is 2 x 2.
To learn more about order of a matrix, visit the link:
https://brainly.com/question/31373779
#SPJ4
If g(x)=f(x)+k g ( x ) = f ( x ) + k , what is the value of k?
The value of k for the given relation of the function represented by attached graph is equal to 3.
Two function f(x) and g(x) .
Relation between f(x) and g(x) is equal to,
g ( x ) = f ( x ) + k
From the attached graph of the function f(x) and g(x) we have,
Slope of both the function f(x) and g(x) is equal to
Slope of f(x) = ( 2 -1 )/( 0 - (-3))
= 1/3
Slope of g(x) = (5 - 4)/ ( 0 - (-3))
= 1/3
Both the lines are parallel to each other with different value of intercept.
y-intercept of f(x) is equal to 2.
y-intercept of g(x) is equal to 5.
As g(x) = f(x) + k
Substitute the value we have,
⇒ 5 = 2 + k
⇒ k = 3
Therefore, for the given attached graph the value of k is equal to 3.
Learn more about graph here
brainly.com/question/10234350
#SPJ1
The above question is incomplete, the complete question is:
If g ( x ) = f ( x ) + k , what is the value of k using the attached graph of the function?
If X1,X2,...,Xn are independent and identically distributed random variables having uniform distributions over (0,1), finda) E[max(X1,...,Xn)]b) E[min(X1,...,Xn)]
Maximum = n/n+1 and Minimum = 1/n+1
What is the uniform distribution?
Probability distributions with uniform distributions have outcomes that are all equitably likely. Results are discrete and have the same probability in a discrete uniform distribution. Results are continuous and infinite in a continuous uniform distribution. Data near the mean occur more frequently in a normal distribution.
Here, we have
Given: X1, X2,..., Xn is independent and identically distributed random variables having uniform distributions over (0,1).
a) Z = max{X₁, X₂....Xₙ}
Since Z is maximum so it is greater than X1, X2...Xn so cdf of Z will be
F(Z) = P(Z≤z) = P(X₁, X₂....Xₙ≤z) = P(X₁≤z, X₂≤z.....Xₙ≤z)
= P(X₁≤z)P(X₂≤z)....P(Xₙ≤z) = Fₓ(z)Fₓ(z).....Fₓ(z)
F(Z) = zⁿ
So pdf of Z is
F(z) = F'(z) = nzⁿ⁻¹
Expectation of Z is
F(Z) = [tex]\int\limits^0_1 {zf_Z(z)} \, dz[/tex] = [tex]n\int\limits^0_1 {} \,[/tex]zⁿdz
= n[zⁿ⁺¹/n+1]₀¹ = n/n+1
b) Let Y = min{X₁, X₂....Xₙ}
Since Y is the minimum so it is less than X1, X2...Xn so the cdf of Y will be
F(Y) = P(Y≤y) = 1 - P(Y>y) = 1- P(X₁, X₂....Xₙ≤z) = 1- P(X₁≤z, X₂≤z.....Xₙ>y)
= 1- P(X₁>y)P(X₂>y)....P(Xₙ>y) = 1- Fₓ(y)Fₓ(y).....Fₓ(y)
= 1 - [1-y]ⁿ
So pdf of Y is
F(y) = F'(y) = n[1-y]ⁿ⁻¹
The expectation of Y is
E(Y) = [tex]\int\limits^0_1 {yf_Y(y)} \, dy[/tex] = ∫₀¹ yn(1-y)ⁿ⁻¹dy = 1/n+1
Hence, Maximum = n/n+1 and Minimum = 1/n+1
To learn more about the uniform distribution from the given link
https://brainly.com/question/20815963
#SPJ4
You have a bag of 4 nickels, 10 dimes, and 2 quarters. You reach in and draw one coin randomly, then your friend does the same. What is the probability that your coin is a dime and your friend's coin is a quarter?
The probability for the event of your coin is a dime and your friend's coin is a quarter is P = 1/12.
How to find the probability?We assume that all the coins have the same probability of being randomly drawn.
Then the probability of drawing a dime is equal to the quotient between the number of dimes and the total number of coins, here we will get:
p = 10/16
Now the total number of coins is 15, because you take one, now the probability that your friend takes a quarter is:
q = 2/15
The joint probability (for the two events happening one after the other) is equal to the product of the individual ones, so we will get:
P = p*q = (10/16)*(2/15) = (5/8)*(2/15) = 1/12
Learn more about probability at:
https://brainly.com/question/25870256
#SPJ1
A football is about 2.8 x 10² millimeters long. A football field is about 1 × 105
millimeters long. How many footballs placed end to end would you need to span
the field? Use scientific notation to calculate the number of footballs.
Answer:
357 footballs-----------------------
To find out the number of footballs, we need to divide the length of the field by the length of one football:
(1 × 10⁵) ÷ (2.8 × 10²)To divide these numbers in scientific notation, we need to divide the coefficients:
1 ÷ 2.8 ≈ 0.357and subtract the exponents:
10⁵ ÷ 10² = 10⁵⁻² = 10³We get:
0.357 × 10³ = 357So, you would need approximately 357 footballs.
random numbers generated by a physical process instead of a mathematical process are pseudorandom numbers. group of answer choices true false
False. Random numbers generated by a physical process are truly random and not pseudorandom.
Let's break this down:
1. Random numbers: These are numbers that have no discernible pattern or order, and each number is independent of the others. They can be generated by a physical process (such as rolling dice) or a mathematical process (like using an algorithm).Truly random numbers are important for applications that require high levels of security and unpredictability, such as in cryptography
2. Pseudorandom numbers: These are numbers generated by a deterministic mathematical process (algorithm), which may appear random but have an underlying pattern or structure. They are not truly random because their generation depends on an initial value (seed) and an algorithm.Pseudorandom numbers, on the other hand, are generated using a mathematical algorithm that attempts to mimic randomness. While pseudorandom numbers may appear random, they are actually determined by the initial seed value and the algorithm used to generate them. Physical processes that can generate random numbers include radioactive decay, thermal noise, and atmospheric noise. These sources of randomness are used in various applications such as cryptography, simulations, and games.
So, random numbers generated by a physical process are considered truly random numbers, while pseudorandom numbers are generated by a mathematical process (algorithm).
To know more about Pseudorandom and random numbers visit:
https://brainly.com/question/30441037
#SPJ11
For a normal random variable, the probability of an observation being less than the median is
For a normal random variable, the probability of an observation being less than the median is 0.5 or 50%.
This is because the median is the middle value in a set of data, and for a normal distribution, the probability of being below or above the median is equal. Therefore, half of the observations will be below the median and half will be above.
For a normal random variable, the probability of an observation being less than the median is 0.5 or 50%. This is because, in a normal distribution, the median is the value that divides the distribution into two equal halves, with 50% of the observations falling below it and 50% above it.
Visit here to learn more about probability : https://brainly.com/question/30034780
#SPJ11
The data below give the number of books checked out of the school library by 15 students
during one month. Make a frequency table of the data.
0, 3, 2, 3, 2, 1, 1, 0, 1, 2, 5, 1, 2, 3, 1. (Sorry if the photo is hard to see) I need the answer ASAP!
The frequency table for the set of data is given below:
A frequency table is a crafted arrangement and visual representation of data in a tabular shape, to show the number of times each distinct value or classification within a dataset appears.
It contains all possible values or classes of a variable in one category, along with the respective number of episodes or occurrences of each one in a second section.
Here is an example of how you could sort this data.
Interval: Frequency:
0 - 1 7
2 - 3 7
4 - 5 1
Read more about frequency table here:
https://brainly.com/question/27820465
#SPJ1
Standard form of y = - 3/4r + 2
rectangles r 1 and r 2, and squares s 1,s 2, and s 3, shown below, combine to form a rectangle that is 3322 units wide and 2020 units high. what is the side length of s 2 in units?
The side length of s 2 is approximately 1541.33 units. We can round that to the nearest unit if needed.
To find the side length of s 2 in units, we need to use the information given about the dimensions of the overall rectangle formed by combining the rectangles and squares.
We know that the overall rectangle is 3322 units wide and 2020 units high. Let's start by looking at the width. We can see that the width is made up of two squares (s 1 and s 3) and one rectangle (r 2). So we can set up an equation to represent this:
width = (side length of s 1) + (length of r 2) + (side length of s 3)
width = s + l + s
where s is the side length of each square and l is the length of r 2.
Similarly, we can look at the height of the overall rectangle. We can see that the height is made up of two rectangles (r 1 and r 2) and one square (s 2). So we can set up another equation:
height = (length of r 1) + (length of r 2) + (side length of s 2)
height = l + l + s
Now we can use these two equations to solve for the side length of s 2. We know that the width is 3322 units and the height is 2020 units, so we can substitute those values into the equations:
3322 = s + l + s
2020 = 2l + s
We can simplify the first equation by combining like terms:
3322 = 2s + l
Now we can use substitution to solve for s. We can rearrange the second equation to solve for l:
l = (2020 - s) / 2
Then we can substitute that expression for l into the first equation:
3322 = 2s + (2020 - s) / 2
Now we just need to solve for s:
6644 = 4s + 2020 - s
4624 = 3s
s = 1541.33
So the side length of s 2 is approximately 1541.33 units. We can round that to the nearest unit if needed.
to learn more about nearest unit click here:
brainly.com/question/30232398
#SPJ11
suppose the length of maize ears has narrow sense heritability (h2) ( h 2 ) of 0.70. a population produces ears that have an average length of 28 cm c m , and from this population a breeder selects a plant producing 34- cm c m ears to cross by self-fertilization.
We can expect the mean length of ears in the next generation to be 31.6 cm.
It is given that the narrow sense heritability (h2) is 0.70, which means that 70% of the total variation in maize ear length is due to genetic factors.
Let the mean length of ears in the original population be µ and the mean length of ears in the selected plant be x. Then, we can use the formula for response to selection to find the expected mean length of ears in the next generation:
x' = µ + h2 * (x - µ)
Substituting the given values, we get:
x' = 28 + 0.70 * (34 - 28) = 31.6 cm
Therefore, we can expect the mean length of ears in the next generation to be 31.6 cm.
To know more about mean visit:
brainly.com/question/2046711
#SPJ4
use the information from exercise 5 to determine the percent of net change from april 21 to april 22 for each of the corporations listed in that question. round answers to the nearest tenth of a percent.
The percent of net change for each corporation are:
Berkshire Hathaway = 1.75%Verizon = 0.08%McDonalds = -0.97%Nike = 0.59%Delta Airlines = -2.46%Toyota = -0.14%What is the percent of net change?The percent of net change is calculated using the formula given below as follows:
Percent of net change = (Net change / Last) x 100%a. Berkshire Hathaway:
Percent of net change = (35 / 199740) x 100%
Percent of net change = 0.0175 x 100%
Percent of net change = 1.75%
b. Verizon:
Percent of net change = (0.04 / 51.19) x 100%
Percent of net change = 0.00078 x 100%
Percent of net change = 0.08%
c. McDonalds:
Percent of net change = (-1.13 / 116.34) x 100%
Percent of net change = -0.0097 x 100%
Percent of net change = -0.97%
d. Nike:
Percent of net change = (0.37 / 62.74) x 100%
Percent of net change= 0.0059 x 100%
Percent of net change = 0.59%
e. Delta Airlines:
Percent of net change = (-1.18 / 48.02) x 100%
Percent of net change = -0.0246 x 100%
Percent of net change = -2.46%
f. Toyota:
Percent of net change = (-0.15 / 105.42) x 100%
Percent of net change = -0.0014 x 100%
Percent of net change = -0.14%
Learn more about net change at: https://brainly.com/question/30299107
#SPJ1
Complete question:
Berkshire Hathaway
Net change = +35
Last = 199740
VZ Verizon
Net change = +0.04
Last = 51.19
MCD McDonalds
Net change = -1.13
Last 116.34
NKE Nike
Net change = +0.37
Last = 62.74
DAL Delta Airlines
Net change = -1.18
Last = 48.02
TM Toyota
Net change = -0.15
Last = 105.42
use the information from exercise 5 to determine the percent of net change from april 21 to april 22 for each of the corporations listed in that question. round answers to the nearest tenth of a percent.
4x^5e^2x^6 from 0 to 1
The value of expression "4x⁵ + e²ˣ + 6" at x=0 is 7 and at x=1 is 10 + e².
In mathematics, an expression is a combination of symbols and numbers that represents a value.
To find the value of the expression "4x⁵ + e²ˣ + 6" at x=0 and x=1, we simply substitute 0 and 1 for "x" and simplify:
When x=0:
We have : 4x⁵ + e²ˣ + 6 ⇒ 4(0)⁵ + e⁰ + 6 = 1 + 6 = 7
So, the value of the expression at x=0 is 7.
When x=1:
we have : 4x⁵ + e²ˣ + 6 ⇒ 4(1)⁵ + e² + 6
⇒ 4 + e² + 6,
⇒ 10 + e²,
So, the value of the expression at x=1 is 10 + e².
Learn more about Expression here
https://brainly.com/question/15324495
#SPJ1
The given question is incomplete, the complete question is
Find the value of the expression at "4x⁵ + e²ˣ + 6" at x=0 and x=1.
In a population, µY = 100 and σ2Y = 43. Use the central limit theorem to answer the following questions. A. In a random sample of size n = 100, find Pr(Ӯ <101). B. In a random sample of size n = 64, find Pr(101< Ӯ <103). C. In a random sample of size n = 165, find Pr(Ӯ >98)
So for the population which is normally distributed using central limit theorem we get,
(A) For sample size n = 100, Pr(Ӯ <101) = 0.937.
(B) For random sample size n = 64, Pr(101< Ӯ <103) = 0.110.
(C) For sample size of n = 165, Pr(Ӯ >98) = 0.893
Given that the population mean (µY) = 100 and the population standard deviation σ2Y = 43.
For the sample size of n = 100.
Now the sample mean (Ӯ) = µY = 100 also.
The sample standard deviation (σ) = square root of (σ2Y/n) = square root of (43/100) = square root of (0.43) = 0.66 (Rounding off to two decimal places).
Now, (101 - Ӯ)/σ = (101 - 100)/0.66 = 1.53
From the normal distribution table we can find P(Z < 1.53) = 0.937 (approximately).
Hence, Pr(Ӯ < 101) = 0.937 (approximately).
For random sample size n = 64.
sample standard deviation = (σ) = square root of (σ2Y/n) = square root of (43/64) = 0.82
Now,
(101 - 100)/0.82 = 1.22
(103 - 100)/0.82 = 3.66
From standard normal table we can get,
P(Z < 3.66) = 0.999
P(Z < 1.22) = 0.889
So, P(1.22 < z < 3.66) = 0.999 - 0.889 = 0.110
Hence, Pr(101< Ӯ <103) = 0.110.
Again for sample size of n = 165.
Sample standard deviation = square root of (σ2Y/n) = square root of (43/165) = 0.51
Now,
(98 - 100)/0.51 = - 1.24
From the standard normal distribution table we get, P(Z < - 1.24) = 0.107.
Now, Pr(Ӯ >98) = 1 - Pr(Ӯ < 98) = 1 - 0.107 = 0.893.
To know more about normal distribution here
https://brainly.com/question/23418254
#SPJ4
Statistics Question | Please include an explanation if you can so I understand it better
The GCF of the number is 12 and the LCM of the number is 24.
Let's start by finding the greatest common factor (GCF) of two whole numbers less than or equal to 100. The GCF is the largest number that divides both of the given numbers without leaving any remainder. We can start by listing all the factors of each number and finding the largest one they have in common.
Let's say we have the numbers 60 and 72. We can find their factors as follows:
Factors of 60: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60
Factors of 72: 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72
From this list, we can see that the largest factor that 60 and 72 have in common is 12. Therefore, the GCF of 60 and 72 is 12.
Let's say we have the numbers 6 and 8. We can list their multiples as follows:
Multiples of 6: 6, 12, 18, 24, 30, 36, 42, 48, 54, 60, 66, 72, 78, 84, 90, 96, 102
Multiples of 8: 8, 16, 24, 32, 40, 48, 56, 64, 72, 80, 88, 96, 104
From this list, we can see that the smallest multiple that both 6 and 8 share is 24. Therefore, the LCM of 6 and 8 is 24.
To know more about GCF here
https://brainly.com/question/11444998
#SPJ4
Complete Question:
Find the greatest common factor of two whole numbers less than or equal to 100 and the least common multiple of two whole numbers less than or equal to 12.
each point of the plane is colored red or blue. show that there is a rectangle whose corners are all the same color
We can always find a monochromatic rectangle by reducing the problem to finding a monochromatic rectangle in a smaller area by moving the bottom of the rectangle up by one unit method.
What is rectangle?
A rectangle is a quadrilateral (a 2-dimensional shape with four sides) with four right angles. This means that opposite sides of a rectangle are parallel and congruent, and all four angles are equal to 90 degrees.
Let us consider a rectangle with sides parallel to the coordinate axes. Such a rectangle can be uniquely determined by two pairs of points that define its opposite corners. If all four of these points are the same color, then we have found a monochromatic rectangle. Otherwise, there are three cases to consider:
The two points at the top of the rectangle are the same color, and the two points at the bottom are the other color. In this case, we can reduce the problem to finding a monochromatic rectangle in a smaller area by moving the bottom of the rectangle up by one unit.
The two points on the left side of the rectangle are the same color, and the two points on the right side are the other color. In this case, we can reduce the problem to finding a monochromatic rectangle in a smaller area by moving the left side of the rectangle to the right by one unit.
Both pairs of points are of mixed color. In this case, we can reduce the problem to finding a monochromatic rectangle in two smaller areas by dividing the rectangle into four equal parts with a vertical or horizontal line.
By repeating this process on the smaller rectangles obtained in each case, we can eventually find a monochromatic rectangle. Since the rectangles we consider at each step have half the area of the previous ones, this process terminates after at most log_2(A) steps, where A is the area of the original rectangle.
Therefore, we can always find a monochromatic rectangle with this method.
To learn more about rectangle visit:
https://brainly.com/question/2607596
#SPJ4
Complete question:
Each point in the x-y plane colored red or blue. show that there is a rectangle whose corners are all the same color.
Which example shows how branches of government interact with each other?
A. The Supreme Court rules on a case.
B. The House of Representatives votes on a bill.
C. The president recommends legislation to Congress.
D. The president signs a treaty with a country in Europe.
The president recommends legislation to Congress shows how branches of government interact with each other. The correct answer is C.
The interaction between the executive and legislative branches of government is essential in the process of making laws in the United States. The president has the power to recommend legislation to Congress, but Congress ultimately decides whether or not to pass the bill into law.
This interaction is an example of the system of checks and balances in the US government, which ensures that no one branch becomes too powerful.
Option A is an example of the judicial branch acting alone, as the Supreme Court has the power to interpret the law and make decisions on cases. Option B is an example of the legislative branch acting alone, as the House of Representatives has the power to draft and pass bills into law.
Option D is an example of the president acting alone in foreign affairs, as the president has the power to negotiate and sign treaties with foreign countries. While these actions may have an impact on the other branches, they do not represent an example of direct interaction between branches.
The correct answer is C.
To learn more about government click on,
https://brainly.com/question/10517479
#SPJ1
Object 2: Pinecone
3D shape: Cone
Dimensions:
radius = 4 inches
height = 6.5 inches
Object 2 3D shape: Cone (Pinecone)
SA Formula:
Surface Area:
The surface area of the cone with radius 4 inches and height 6.5 inches is equal to 146.07 square inches.
Radius of the cone = 4 inches
height of the cone = 6.5 inches
Let us consider 'r' be the radius of the cone and 'h' be the height of the cone.
Formula to calculate surface area of the cone
= πr ( r + √ h² + r² )
Substitute the value of radius and height of the cone we have,
⇒ Surface area of the cone = π × 4 ( 4 + √ ( 6.5 )² + ( 4 )² )
⇒ Surface area of the cone =4π ( 4 + √58.25 )
⇒ Surface area of the cone = 4 × 3.14 ( 4 + 7.63 )
⇒ Surface area of the cone = 12.56 × 11.63
⇒ Surface area of the cone = 146.0728 square inches
⇒ Surface area of the cone = 146.07 in²
Therefore, the surface area of the cone is equal to 146.07 square inches.
Learn more about surface area here
brainly.com/question/12347277
#SPJ1
Factor x2 − 2x + 3. (1 point) (x − 3)(x − 1) (x + 3)(x + 1) (x − 3)(x + 1) Prime
Answer:
(x-3) (x+1)
Step-by-step explanation:
Factor
x^2 − 2x + 3
What two numbers multiply to 3 and add to -2
3 and -1
(x-3) (x+1)
due to an outbreak of strep infection at a local college, all 100 students living in a particular dormitory were tested for strep infection. ten of these students actually had strep infection. in this particular sample, the test correctly identified strep infection in 90% of those who were in fact infected with strep. the test also correctly returned a negative result in 80% of those who were not infected. which table below correctly summarizes the information described above? a. actually had strep infection test positive for strep tests negative for strep total yes 10 0 10 no 0 90 90 total 10 90 100 b. actually had strep infection test positive for strep tests negative for strep total yes 9 1 10 no 10 80 90 total 19 81 100 c. actually had strep infection test positive for strep tests negative for strep total yes 9 1 10 no 72 18 90 total 81 19 100 d. actually had strep infection test positive for strep tests negative for strep total yes 9 1 10 no 18 72 90 total 27 73 100
The correct table to show the test on the outbreak of strep infection is d. actually had strep infection test positive for strep tests negative for strep total yes 9 1 10 no 18 72 90 total 27 73 100.
How to find the table ?Out of a total of one hundred students, ten have strep infection. The test is successful in correctly identifying the disease in ninety percent of those affected; meaning 0.9 x 10 equalling nine individuals tested positive and the lone tenth student tested negative.
Regarding the remaining ninety students without strep infection, the test corresponds to an accurate result with eighty percent accuracy. Thus, the calculation 0.8 x 90 performing the duty of rejection in 72 pupils and making affirmative tests with the remaining eighteen students.
Find out more on tests at https://brainly.com/question/13074925
#SPJ1
An SEO account manager is concerned website developers are using too many keywords per web page. The SEO account manager would like to carry out a hypothesis test and test the claim that a web page has, on average, more than 10 keywords. Why is this hypothesis test right-tailed?
Select the correct answer below:
This is a right-tailed test because a direction is not specified.
This is a right-tailed test because a direction is specified. The population parameter is greater than the specified value.
This is a right-tailed test because a direction is specified. The population parameter is less than the specified value.
More information is needed.
The correct answer is “This is a right-tailed test because a direction is specified. The population parameter is greater than the specified value.”
What is hypothesis testing?
In hypothesis testing, we test the null hypothesis against the alternative hypothesis. The null hypothesis (H0) is the default assumption, which states that there is no significant difference between the sample data and the population parameter. The alternative hypothesis (H1) contradicts the null hypothesis and suggests that there is a significant difference between the sample data and the population parameter.
In this scenario, the null hypothesis would be that the average number of keywords per web page is less than or equal to 10, and the alternative hypothesis would be that the average number of keywords per web page is greater than 10.
Since the alternative hypothesis specifies a direction, it is a one-tailed or one-directional test. Moreover, as the alternative hypothesis states that the average number of keywords per web page is greater than 10, the critical region is in the right tail of the distribution. Therefore, this is a right-tailed test.
So, the correct answer is: This is a right-tailed test because a direction is specified. The population parameter is greater than the specified value.
To know more about hypothesis testing visit:
brainly.com/question/14587073
#SPJ4
A constant force of 56 pounds is applied at an angle of 35º to pull a 16 foot metal door shut. How much work is done?
a
513.9 ft-lbs
b
734.0 ft-lbs
c
−383.7 ft-lbs
d
−809.7 ft-lbs
(b) 734.0 ft-lbs of work is done.
To find the work done by the force, we need to use the formula:
Work = force x distance x cos(θ)
where:
force = 56 pounds (the given constant force)
distance = 16 feet (the distance the door is being pulled)
θ = 35 degrees (the angle between the force and the displacement of the door)
We need to convert the angle to radians to use it in the formula:
theta = 35 degrees x (pi/180) = 0.6109 radians
Now we can substitute the values into the formula:
Work = 56 pounds x 16 feet x cos(0.6109 radians)
Work = 734.0 ft-lbs (rounded to one decimal place)
Therefore, the answer is (b) 734.0 ft-lbs.
To learn more about work here:
https://brainly.com/question/31277249
#SPJ1
