Solve the following system of IVP: [3 -1 01 7 x' = Ax where A = 4 -2 0 and x(0) = 10x -4 21 Hint: The eigenvalues are λ₁ = -1,A₂ = 2, A3 = 2.
Answers
For the given system of initial value problem,
A₁ = 7,
A₂ = -1, and
y = 2exp(-t),
To solve the given system of initial value problem (IVP) with the matrix equation x' = Ax, where A is the given matrix and x(0) = [10, -4, 21], we can use the eigenvalue-eigenvector method.
The matrix A is given as:
A = | 4 -2 0 |
| 3 -1 0 |
| 1 7 2 |
Let's find the eigenvalues and eigenvectors of matrix A.
To find the eigenvalues, we solve the characteristic equation:
det(A - λI) = 0
Substituting the values, we get:
| 4-λ -2 0 |
| 3 -1-λ 0 |
| 1 7 2-λ |
Expanding the determinant, we have:
(4-λ)[(-1-λ)(2-λ)] + 2[3(2-λ) - (-1-λ)7] = 0
Simplifying and solving the equation, we find the eigenvalues:
λ₁ = -1
λ₂ = 2
λ₃ = 2
Next, let's find the corresponding eigenvectors.
For λ₁ = -1:
(A + I)v₁ = 0
| 5 -2 0 | | v₁₁ | | 0 |
| 3 -1 0 | * | v₁₂ | = | 0 |
| 1 7 1 | | v₁₃ | | 0 |
Solving the system of equations, we find the eigenvector corresponding to λ₁:
v₁ = | 2 |
| 5 |
|-1 |
For λ₂ = 2:
(A - 2I)v₂ = 0
| 2 -2 0 | | v₂₁ | | 0 |
| 3 -3 0 | * | v₂₂ | = | 0 |
| 1 7 0 | | v₂₃ | | 0 |
Solving the system of equations, we find the eigenvector corresponding to λ₂:
v₂ = | 1 |
| 1 |
|-1 |
For λ₃ = 2:
(A - 2I)v₃ = 0
| 2 -2 0 | | v₃₁ | | 0 |
| 3 -3 0 | * | v₃₂ | = | 0 |
| 1 7 0 | | v₃₃ | | 0 |
Solving the system of equations, we find the eigenvector corresponding to λ₃:
v₃ = | 2 |
| 3 |
| 1 |
Now that we have the eigenvalues and eigenvectors, we can write the general solution to the system of differential equations as:
x(t) = c₁ * exp(λ₁ * t) * v₁ + c₂ * exp(λ₂ * t) * v₂ + c₃ * exp(λ₃ * t) * v₃
Substituting the given initial condition x(0) = [10, -4, 21], we can find the specific solution by solving the following system of equations:
c₁ * v₁ + c₂ * v₂ + c₃ * v₃ = x(0)
Substituting the values of the eigenvectors and the initial condition, we get:
2c₁ + c₂ + 2c₃ = 10 (Equation 1)
5c₁ + c₂ + 3c₃ = -4 (Equation 2)
-c₁ - c₂ + c₃ = 21 (Equation 3)
Solving this system of equations will give us the values of c₁, c₂, and c₃, which will determine the specific solution.
By solving Equations 1, 2, and 3, we find:
c₁ = 1
c₂ = -5
c₃ = -3
Therefore, the specific solution to the initial value problem is:
x(t) = exp(-t) * | 2 | + exp(2t) * | 1 | + exp(2t) * |-3 |
| 5 | | 1 |
|-1 | | 1 |
Simplifying this expression, we get:
x(t) = | 2exp(-t) + 5exp(2t) - 3exp(2t) |
| 5exp(-t) + exp(2t) + exp(2t) |
|-exp(-t) + exp(2t) + exp(2t) |
Finally, we can rewrite the solution in the given form (7) - ₁ (1) ¹²+₂ (1) ¹:
x(t) = 7 * | 2exp(-t) | + (-1) * | 5exp(-t) |
| 5exp(-t) | | -exp(-t) |
Therefore, A₁ = 7, A₂ = -1, and y = 2exp(-t).
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Related Questions
(4.) Three million fifty-two thousand eight hundred fifty-six. In standard for is
(a)3,520,856
(b)3,052,856
(C)352,856
(d) 3,052,086
Answers
two fair dice are rolled. The score is the difference between the two dice.
Answers
In a dice, there is a six side
Probability of occurring a score = 1/18
= 1*2/18*2
= 2/36
= preferred outcome/ Total outcome
Only 5 is a number that has occurred twice
The score that has a probability of occurring of 1/18 is 5.
The two dice having different values 30/36 = 5/6 (because the probability of the two dice having equal values is 6/36 = 1/6.)
The probability of the second dice being less than the first dice is the same as the probability of the first dice is less than the second dice: (5/6) / 2 = 5/12.
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in most public health and related research will the resulting 95% confidence interval definitely contain the value of the population quantity of interest being estimated with the study results?
Answers
No, it is simply the likelihood that the interval would include the population of the important quantity. Even though it is unlikely, it is possible that the 95% confidence interval does not include the desired population size.
The mean of your estimate plus and minus the range of that estimate constitutes a confidence interval.
You have a 5% probability of being incorrect with a 95% confidence interval. You have a 10% probability of being incorrect with a 90% confidence interval. A 95% confidence interval is narrower than a 99% confidence interval (for example, plus or minus 4.5 percent instead of 3.5 percent).
No, it is simply the likelihood that the interval would include the population of the important quantity. Even though it is unlikely, it is possible that the 95% interval does not include the desired population size.
No, it is merely the chance that the population of the significant quantity would be present during the interval. Although uncommon, there is a chance that the target population size is not included in the 95% interval.
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a university interested in tracking its honors program believes that the proportion of graduates with a gpa of 3.00 or below is less than 0.16. in a sample of 190 graduates, 28 students have a gpa of 3.00 or below. the value of the test statistic and its associated p-value are .
Answers
For the given information, the value of the test statistic is -1.724 and its associated p-value is 0.0426.
In order to calculate the p value of students with GPA of 3.00 or below, the standard score (z -score or test statistic) must be determined first. In statistics, the standard score refers to the number of standard deviations by which the scores differs from the mean value of the observed or measured data. Scores above the mean have positive standard scores, while those below the mean have negative standard scores.
In a sample of 190 graduates, 28 students have a GPA of 3.00 or below, x = 28/190 = 0.15
The standard deviation = √(p(1 – p)/n) = √(0.2(1-0.2)/190) = 0.029 (where p is the probability of success and n is the total number of data)
The z-score = (x - µ)/σ = (0.15 – 0.2)/0.029 = - 1.724
From the table,
The P (z < -1.724) = 0.0426 or 4.26%.
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Which of the following discrete probability distributions do not have a specified maximum value of X. Select all that apply. a. Binomial b. Hypergeometric c. Negative Binomial d. Geometric e. Poisson
Answers
The negative binomial, geometric, and Poisson distributions do not have a specified maximum value of X.
In the negative binomial distribution, X represents the number of trials needed to achieve a fixed number of successes. The number of trials can vary indefinitely, so there is no maximum value for X.
Similarly, in the geometric distribution, X represents the number of trials needed to achieve the first success. Since the number of trials can continue indefinitely until the first success occurs, there is no predetermined maximum value for X.
The Poisson distribution models the number of events occurring in a fixed interval of time or space. The number of events can be arbitrarily large, and thus there is no specific maximum value for X.
On the other hand, the binomial and hypergeometric distributions have a fixed number of trials or population size, respectively, which defines the maximum value of X. In these distributions, X represents the number of successes within the specified constraints.
Therefore, the negative binomial, geometric, and Poisson distributions do not have a specified maximum value of X, making them distinct from the binomial and hypergeometric distributions.
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A family decides to have children until it has three children of the same gender. assuming p(b) = p(g) = 0. 5, what is the pmf of x = the number of children in the family?
Answers
The pmf provides the probabilities of having 1, 2, or 3 children in the family based on the condition that the family stops having children once it has three children of the same gender.
To find the probability mass function (pmf) of the number of children in the family, we need to consider the possible values of x (the number of children) and their corresponding probabilities.
Let's analyze the possibilities:
1. x = 1 (only one child): The probability of having either a boy or a girl is 0.5. Therefore, P(x=1) = P(B or G) = 0.5.
2. x = 2 (two children): The possible outcomes are BB, GG, or BG (in any order). Each of these outcomes has a probability of 0.5 * 0.5 = 0.25. Therefore, P(x=2) = P(BB or GG or BG) = 0.25 + 0.25 + 0.25 = 0.75.
3. x = 3 (three children): The only outcome that satisfies the condition is BBB or GGG (in any order). Each of these outcomes has a probability of 0.5 * 0.5 * 0.5 = 0.125. Therefore, P(x=3) = P(BBB or GGG) = 0.125 + 0.125 = 0.25.
From the above analysis, we have:
P(x=1) = 0.5
P(x=2) = 0.75
P(x=3) = 0.25
To summarize, the pmf of x (the number of children in the family) is:
P(x=1) = 0.5, P(x=2) = 0.75, P(x=3) = 0.25.
The pmf provides the probabilities of having 1, 2, or 3 children in the family based on the condition that the family stops having children once it has three children of the same gender.
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Bank of america's consumer spending survey collected data on annual credit card charges in seven different categories of expenditures: transportation, groceries, dining out, household expenses, home furnishings, apparel, and entertainment. using data from a sample of credit card accounts, assume that each account was used to identify the annual credit card charges for groceries (population 1) and the annual credit card charges for dining out (population 2). using the difference data, the sample mean difference was , and the sample standard deviation was . a. formulate the null and alternative hypotheses to test for no difference between the population mean credit card charges for groceries and the population mean credit card charges for dining out. is equal to 0 is not equal to 0 b. use level of significance. can you conclude that the population means differ? differ what is the -value? (to 6 decimals) c. which category, groceries or dining out, has a higher population mean annual credit card charge? groceries what is the point estimate of the difference between the population means? round to the nearest whole number. what is the confidence interval estimate of the difference between the population means? round to the nearest whole number. , hide feedback partially correct
Answers
The null hypothesis for the no difference test is 0 and the alternative hypothesis is 4.905 using the level of significance.
a)null hypothesis (H₀) = 0
Alternative hypothesis (H₀) ≠ 0
t = (d)/√n = 850 × √42 ÷ 1123 = 4.902
b) Now we calculate the degrees of freedom given by:
degrees of freedomf
= n-1
= 42 -1
= 41
Now we can calculate the p value, we have a left tailed test the p value is given by:
p=2× P(t₍₄₁₎>4.905) = 0.00015
We can therefore infer that we can reject the null hypothesis that the difference between the two groups is equal because the p value is less than the significance level indicated.
When there are two samples and the data in one sample can really be paired with observations in the other sample, a paired t-test is used to compare the two population means.
The system of the null and alternate hypothesis for this particular case are:
Null hypothesis: μ₁ - μ₂ = 0
Alternative hypothesis: μ₁ - μ₂ ≠ 0
Or equivalently
Null hypothesis: (H₀) = 0
Alternative hypothesis: (H₀) ≠ 0
c) now it is calculated that μ₁ - μ₂ = 0 , hence we can conclude that The standard deviation for the mean for groceries is more than the mean for dining out .
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What is the simplified form of this expression?
18 ÷ 6 + 8 × 7 – 12 + 8 × 2
A
62
B
63
C
81
D
146
help asap im being timed
Answers
Answer:
the answer is b
Step-by-step explanation:
first i did 18 divided by 6=3
then 8x7=56
3+56=59
59-12=47
8x2=16
47+16=63
Answer:
B.) 63
Step-by-step explanation:
18 divided by 6 = 3
8x7=56
3+56=59
59-12=47
8x2=16
47+16=63
Briefly discuss the difference between indefinite integral and definite integral. Give an example to provide emphasis. *
Answers
A definite integral is defined as the signed area under a function between certain limits (bounds) of integration.
An indefinite integral represents the family of antiderivatives of a function and is also known as its general integral or antiderivative.
The difference between the integralsAn indefinite integral represents the family of antiderivatives of a function and is also known as its general integral or antiderivative. An indefinite integral does not have specific limits of integration; its result includes a constant of integration (usually denoted +C), which accounts for all possible constant shifts within its antiderivative.
A definite integral is defined as the signed area under a function between certain limits (bounds) of integration. The real number that represents its net area between it and x-axis during an interval.
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For each of these relations on the set (1, 2, 3, 4). decide whether it is reflexive, symmetric, antisymmetric, and transitive. a. R1 = {(2, 2), (2.3), (2,4),(3,2), (3, 3), (3, 4); b. R2 = {(1, 1), (1, 2), (2, 1), (2, 2), (3, 3), (4,4)} c. R3 = {(2,4),(4,2)) d. R4 = {(1,2), (2, 3), (3, 4); d. R5 = {(1, 1), (2, 2), (3, 3), (4,4)}
Answers
The following are the relations on the set (1, 2, 3, 4), which are reflexive, symmetric, antisymmetric, and transitive:
a. R1 = {(2, 2), (2, 3), (2,4),(3,2), (3, 3), (3, 4)}
Reflexive: The relation R1 is not reflexive since (1,1), (2,2), (3,3), and (4,4) are missing. Symmetric: The relation R1 is not symmetric since (2,3) is an element of R1 but (3,2) is not an element of R1.
Antisymmetric: The relation R1 is not antisymmetric since (2,3) and (3,2) are elements of R1 but 2 ≠ 3.
Transitive: The relation R1 is transitive since the ordered pairs satisfy the transitive condition.
b. R2 = {(1, 1), (1, 2), (2, 1), (2, 2), (3, 3), (4,4)}
Reflexive: The relation R2 is reflexive since all the diagonal elements are present. Symmetric: The relation R2 is symmetric since if (a,b) is an element of R2, then (b, a) is also an element of R2.
Antisymmetric: The relation R2 is antisymmetric since if (a,b) and (b, a) are elements of R2, then a = b.
Transitive: The relation R2 is transitive since the ordered pairs satisfy the transitive condition.
c. R3 = {(2,4),(4,2)}
Reflexive: The relation R3 is not reflexive since (1,1), (3,3), and (4,4) are missing.
Symmetric: The relation R3 is symmetric since (2,4) and (4,2) are both elements of R3.
Antisymmetric: The relation R3 is antisymmetric since if (a,b) and (b, a) are elements of R3, then a = b.
Transitive: The relation R3 is not transitive since (2,4) and (4,2) are elements of R3, but (2,2) is not an element of R3.
d. R4 = {(1,2), (2, 3), (3, 4)}
Reflexive: The relation R4 is not reflexive since (1,1), (2,2), (3,3), and (4,4) are missing.
Symmetric: The relation R4 is not symmetric since (1,2) is an element of R4, but (2,1) is not an element of R4. Antisymmetric: The relation R4 is antisymmetric since if (a,b) and (b, a) are elements of R4, then a = b.
Transitive: The relation R4 is transitive since the ordered pairs satisfy the transitive condition.
e. R5 = {(1, 1), (2, 2), (3, 3), (4,4)}
Reflexive: The relation R5 is reflexive since all the diagonal elements are present.
Symmetric: The relation R5 is symmetric since if (a,b) is an element of R5, then (b, a) is also an element of R5.
Antisymmetric: The relation R5 is antisymmetric since if (a,b) and (b, a) are elements of R5, then a = b.
Transitive: The relation R5 is transitive since the ordered pairs satisfy the transitive condition.
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The sum of two numbers is 8. The difference between the two numbers is 2. What are the numbers? x + y = 8 x - y = 2 *Use the tables to list the possibilities
Answers
Answer:
x=5 y=3
Step-by-step explanation:
x+y=8 1
x-y=2 2
x+y=8
y=8-x
substitute into 2
x-(8-x)=2
x-8+x=2
2x=10
x=5
substitute x into 1
5+y=8
y=3
5+3=8
5-3=2
Akhira started her own landscaping business. She charges $6 an hour for mowing lawns
and $11 for pulling weeds. In September she mowed lawns for 63 hours and pulled
weeds for 9 hours. How much money did she earn in September?
Answers
Answer:
$477 in September
Step-by-step explanation:
378 + 99
So if she worked for 63 hours and earns 6 dollars a hour your answer is 378 and if she worked for 9 hours and earns 11 dollars your answer is 99
how many different-appearing ways can three identical marbles be arranged by placing them in the holes shown, if no arrangement has three marbles in three adjacent holes?
Answers
The number of different-appearing ways to arrange three identical marbles in the holes shown, with no three marbles in three adjacent holes, is: 20 - 6 = 14.
To answer your question, we need to first determine how many ways there are to place three identical marbles into the six holes shown. This can be calculated using the combination formula:
C(6,3) = 6! / (3! * (6-3)!) = 20
So there are 20 different ways to place three identical marbles into the holes.
However, we need to exclude any arrangements where three marbles are in three adjacent holes. To do this, we can count the number of arrangements where this occurs and subtract from the total.
There are three ways this can happen: the marbles can be in holes 1, 2, and 3; or in holes 2, 3, and 4; or in holes 3, 4, and 5.
In each case, we can treat the three adjacent holes as a single "super hole" and place the marbles in the remaining three holes. This can be done in 2 ways, since the marbles are identical and can be placed in any order.
So the number of arrangements with three marbles in three adjacent holes is 3 x 2 = 6.
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(36+4) divided by 10 how do I write it in a story problem
Answers
Step-by-step explanation:
you can write it as
the sum of of thirty six(36) and four(4) is divided by Ten(10)
(I honestly don’t know, I hope this works!)
According to ISM, _____ is a framework of measurable corporate policies and procedures and resulting behavior designed to benefit the workplace and, by extension, the individual, the organization, and the community.
Answers
According to ISM (Institute for Supply Management), a framework of measurable corporate policies and procedures and resulting behavior designed to benefit the workplace and, by extension, the individual, the organization, and the community is referred to as "social responsibility."
Social responsibility encompasses the idea that businesses have a responsibility to operate ethically, sustainably, and in a manner that contributes positively to society. It involves adopting policies and practices that prioritize the well-being of employees, stakeholders, and the environment. By implementing social responsibility measures, organizations aim to create a positive impact on society while also enhancing their own reputation, long-term success, and overall value. This framework encourages businesses to integrate social, environmental, and ethical considerations into their decision-making processes and day-to-day operations.
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Square ABCD has diagonals AC¯¯¯¯¯
and BD¯¯¯¯¯
. What is m∠ABD
A
180º
B
90º
C
45º
D
360º
Answers
Answer:
option (c)
Step-by-step explanation:
Given,
ABCD is a square.
AC and BD are diagonals
We know that,
Sides of the square make 90 degrees with each other.
And Diagonals bisect the opposite angles of the square.
Now,
\(\angle ABD = \dfrac{\angle ABC}{2}\)
\(\angle ABC = 90^\circ\)
\(\angle ABD = \dfrac{\angle ABC}{2}\)
\(\angle ABD = \dfrac{90^\circ}{2}\)
\(\angle ABD = 45^\circ\)
Hence, option (c) is correct.
What type of variable is required to construct a confidence interval for a population proportion?.
Answers
The type of variable required is Qualitative with two possible outcomes.
What is a confidence interval?
An estimate level of uncertainty is expressed by a range of values known as a confidence interval.
Keeping in mind, the z-score and other data's decimal places should be preserved when generating the confidence interval upper and lower bounds. The responses will be accurate and round-off errors will be prevented.
Also, the confidence interval boundaries are expressed in percentages. The maximum value of 0.8740, for instance, is 87.4% in decimal notation.
Make sure to specify the confidence level, the percentage of the population that the confidence interval actually captures, and the bounds expressed in percentages when expressing the meaning of the confidence interval.
Hence, the type of variable required to construct a confidence interval for a population proportion is Qualitative with 2 possible outcomes.
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let x(t) = cos(75t). if we sample x(t) at the nyquist frequency, what is the resulting discrete frequency
Answers
If we sample the function x(t) = cos(75t) at the Nyquist frequency, the resulting discrete frequency would be half of the Nyquist frequency, which is equal to half of the highest frequency component in the continuous signal.
In this case, the highest frequency component in x(t) is 75 Hz, as determined by the coefficient of t in the cosine function. According to the Nyquist-Shannon sampling theorem, to accurately represent a signal, the sampling frequency must be at least twice the highest frequency component. Therefore, the Nyquist frequency in this scenario would be 2 * 75 Hz = 150 Hz.
Since we are sampling at the Nyquist frequency, the resulting discrete frequency would be half of the Nyquist frequency, which is 150 Hz / 2 = 75 Hz. Hence, when sampling x(t) at the Nyquist frequency, the resulting discrete frequency would be 75 Hz.
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Increase 100 by 85%
Answers
Answer:
100, percentage increased by 85% (percent) of its value = 185 Jan 16 02:56 UTC (GMT
Answer:
=100+85%
=100.85.......
please someone useful help me it's always people who answer who say they don't know the answer
Answers
Answer:
Step-by-step explanation:
the equation is 3-8*cos(x) = 7
plugging in 45° to Cos give \(\sqrt{2}\) / 2
then the equations looks like
3-8* (\(\sqrt{2}\) / 2) = y
3-4\(\sqrt{2}\) = y
there is your answer... don't get rid of the square root.. that's an exact answer
80,000,000+1,000,000+600,000+20,000+900+40+8 how is this written in standard form
Answers
Answer:
81,620,948
Step-by-step explanation:
this what you need?
f(x) = 4x² + 7x – 18
Find f(-9)
Answers
Step-by-step explanation:
f(x) = 4x² + 7x - 18
f(-9) = 4 * (-9)² + 7 * (-9) - 18
= 324 - 63 - 18
= 243
Hope it will help :)
some one pls help quick
Answers
The solution of the function, f( ) = -8 is f(1) = -8.
How to solve function?A function relates input to output. A function assigns exactly one output to each input of a specified type.
In other words, a function is a relationship between two or more variables, such that each input has only one output.
Therefore, let's solve the function as follows:
f(x) = -7x - 1
Hence,
f(x) = -8
Let's find x as follows:
-7x - 1 = - 8
-7x = -8 + 1
-7x = -7
divide both sides by -7
x = -7 / -7
x = 1
Hence,
f(1) = -8
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A parallelogram has the vertices T(-4,2), (2,4), V(3,1), and W(-3,-1).
1. Determine the lengths of each side using the distance formula.
1. Determine if the slopes of two consecutive sides are parallel,
perpendicular or neither.
1. What type of parallelogram is created with the given points?
Explain your answer.
Brainlist so who ever gives the right answer
Answers
Answer:
T= (-4 ,2)
U= (2 ,4)
V= (3 ,1)
W= (-3, -1)
1 . LENGTH OF EACH SIDES
\(length \ of \ sides =\sqrt{(x_{2} -x_{1} )^2+(y_{2} -y_{1})^2}\)
\(length \ of \ TU = \sqrt{(2--4 )^2+(4-2)^2} = \sqrt{40}\)
\(Length \ of \ UV =\sqrt{(3-2 )^2+(1-4)^2} = \sqrt{10}\)
\(Length \ of \ VW =\sqrt{(-3-3)^2+(-1-1)^2} = \sqrt{40}\)
\(length \ of \ TW =\sqrt{(-3--4 )^2+(-1-2)^2} =\sqrt{10}\)
2. SLOPE OF CONSECUTIVE SIDES
\(Slope \ of \ the \ line \ passing \ through \ (x_{1}, y_{1} ) \ and \ (x_{2}, y_{2}) = \frac{y_{2} -y_{1} }{x_{2} -x_{1} }\)
\(Slope \ of \ TU = \frac{4-2}{2--4} = \frac{2}{6} =\frac{1}{3}\)
\(Slope \ of \ UV = \frac{1-4}{3-2} = -3\)
\(Slope \ of \ VW = \frac{-1-1}{-3-3} = \frac{-2}{-6} =\frac{1}{3}\)
\(Slope \ of \ TW = \frac{-1-2}{-3--4} = -3\)
\(Slope \ of \ lines \ parallel \ to \ each \ other = m_{1}\cdot m_{2} = 1\\Slope\ of \ lines\ perpendicular \ to \ each \ other =m_{1}\cdot m_{2} = -1\\\)
\(Slope \ of \ TU * UV = \frac{1}{3}*-3 = -1\\\\Slope \ of \ UV *VW = -3 *\frac{1}{3}= -1\\\\ Slope \ of \ VW * TW = \frac{1}{3}*-3 = -1\\\\Slope \ of \ TW * TU = -3 *\frac{1}{3}= -1\\\\\)
Therefore the consecutive sides are perpendicular to each other.
3. TYPE OF PARALLELOGRAM
The opposite sides are of same length. The consecutive sides are perpendicular to each other. So the parallelogram is a RECTANGLE.
You are the director of the customer service center in Company Alpha. You find that the mean time between calls to the center is 6 minutes with standard deviation of 4 minutes. The effective response time is 11 minutes with a standard deviation of 20 minutes. (a) Identify the following parameters: ta
tθ
∂a
∂θ
ra:
rθ:
Answers
The identified parameters are:
ta = 6 minutes
tθ = 11 minutes
∂a = 4 minutes
∂θ = 20 minutes
ra = 1/6 minutes^(-1)
rθ = 1/11 minutes^(-1)
ta: Mean time between calls to the center
tθ: Effective response time
∂a: Standard deviation of the time between calls to the center
∂θ: Standard deviation of the effective response time
ra: Rate of calls to the center (inverse of ta, i.e., ra = 1/ta)
rθ: Rate of effective response (inverse of tθ, i.e., rθ = 1/tθ)
Given information:
Mean time between calls to the center (ta) = 6 minutes
Standard deviation of time between calls (∂a) = 4 minutes
Effective response time (tθ) = 11 minutes
Standard deviation of effective response time (∂θ) = 20 minutes
Using this information, we can determine the values of the parameters:
ta = 6 minutes
tθ = 11 minutes
∂a = 4 minutes
∂θ = 20 minutes
ra = 1/ta = 1/6 minutes^(-1)
rθ = 1/tθ = 1/11 minutes^(-1)
So, the identified parameters are:
ta = 6 minutes
tθ = 11 minutes
∂a = 4 minutes
∂θ = 20 minutes
ra = 1/6 minutes^(-1)
rθ = 1/11 minutes^(-1)
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I WILL GIVE BRAINLEST
Answers
The value of the angle 4 is 96 degrees as shown in the diagram.
Application of line geometryA line is an object in geometry that is indefinitely long and has neither breadth nor depth nor curvature. Since lines can exist in two, three, or higher dimensional environments, they are one-dimensional things.
From the given diagram, the measure of angle 1 and 3 are equal as well as 2 and 4.
Given the following angles
m<3 = 84 degrees
Since the measure of <3 and <4 lies on the same straight line, hence:
m<3 + m<4 = 180
84 + m<4 = 180
m<4 = 180 - 84
m<4 = 96 degrees
Hence the measure of angle 4 from the figure is 96 degrees
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Which of these graphs represents a function?
Answers
Using the vertical line test, the graph that represents a function is: Graph C.
How to Determine if a Graph Represents a Function?A simple test we can carry out quickly to determine if a graph represents a function is the vertical line test.
Using the vertical line test, a vertical line is drawn across the curve in the given plane. If the vertical line intersect the curve more than once, it is not a function, but if it intersects the curve at just exactly one point, then the graph represents a function.
If we draw a vertical line across each of the given graphs, only the graph in option C will be intersected at exactly only one point.
Therefore, graph C represents a function.
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Write a linear function f with f(-9) = 10 and f(-1)=-2
Answers
The linear function f is y = f(x) = (-3/2)x+b, with f(-9) = 10 and f(-1)=-2.
What is slope?The value of the steepness or the direction of a line in a coordinate plane is known as the slope of a line, often known as the gradient. Given the equation of a line or the coordinates of points situated on the straight line, slope can be determined using a variety of techniques.
The formula for slope between two points (x₁, y₁) and (x₂, y₂) is,
m = (y₂ - y₁)/(x₂ - x₁)
The given values are,
f(-9) = 10 and f(-1) = -2.
The given coordinates are (-9, 10) and (-1, -2)
Let the linear function is,
y= mx+b (1)
To find the linear function,
Find the slope
m = -2 - 10 / -1 - (-9)
m = -12 / 8
m = -3 / 2.
Substitute the value of m in equation (1),
y=(-3/2)x+b
To find the value of b, substitute y = -2,
-2=(-3/2)(-1)+b
b=-7/2
The required linear function is,
y=(-3/2)x -7/2
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A-(B-C)=(A-B)U (
AnC)
Answers
A television set can be purchased with a $200 down payment plus a $39.99 monthly payment. Alternatively, the television can be purchased with no money down and monthly payments of $59.99. Solve for the number of months until the payments are of equal value.
Answers
Answer:
10 months
Step-by-step explanation:
Let x denotes number of months.
Down payment of first TV = $200
Per month payment of first TV = $39.99
Total payment of first TV \(=200+39.99x\)
Down payment of second TV = $0
Per month payment of second TV = $59.99
Total payment of second TV \(=0+59.99x=59.99x\)
To find number of months until the payments are of equal value,
solve \(200+39.99x=59.99x\)
\(200+39.99x=59.99x\\200=59.99x-39.99x\\200=20x\\x=\frac{200}{20}\\ x=10\)
So, payments become of equal value after 10 months.