The direction of t+ u+ v is 155°.
What is a vector?A vector is a quantity that possesses magnitude, direction, and adheres to the law of vector addition.
Given:
The magnitude and direction of vectors t, u, and v are shown in the table.
Vector Magnitude Direction
t 5 250°
u 6 60°
v 12 330°
The coordinates of the resultant vectors:
t + u + v,
= (5 cos250° + 6cos60° + 12cos330°, 5 Sin250° + 6Sin60° + 12Sin330°)
= (11.7, -5.5)
Now, the direction of t+ u+ v = arc tan(-5.5/11.7)
= 155°
Therefore, 155° is the direction.
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Answer:
335°
Step-by-step explanation:
I took the test and got it right :)
Find m angle ABC
m angle ABC = 41 deg
m angle ABC = 71 deg
m angle ABC = 83 deg
m angle ABC = 73 deg
Suppose that there was a cancer diagnostic test that was 95% accurate both on those that do and those that do not have the disease. If 40 percent of the population has cancer, compute the probability that a tested person has cancer, given that their test result indicates so.
The conditional probability that a tested person has cancer, given that their test result indicates so, is given as follows:
0.9268 = 92.68%.
What is Conditional Probability?Conditional probability is the probability of one event happening, considering the result of a previous event. The formula is:
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]
In which:
P(B|A) is the probability of the event B happening, given that the event A happened.[tex]P(A \cap B)[/tex] is the probability of both the events A and B happening.P(A) is the probability of the event A happening.The events for this problem are given as folows:
Event A: positive test result.Event B: person has cancer.The probability of a positive test result are given as follows:
95% of 40% -> has cancer.5% of 60% -> does not have cancer.Hence:
P(A) = 0.95 x 0.4 + 0.05 x 0.6 = 0.41.
Hence the conditional probability is given as follows:
P(B|A) = 0.95 x 0.4/0.41 = 0.9268 = 92.68%.
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What is the decimal equivalent of the binary number 111010?
Answer:
23
Step-by-step explanation:
You have 6 numbers
So starting at 2^0, we write out 6 of those to get a benchmark. Well also solve them for now. To the left, we put your numbers, which are 111010
1: 2^0 = 1
1: 2^1 = 2
1: 2^2 = 4
0: 2^3 = 8
1: 2^4 = 16
0: 2^5 = 32
^ Everywhere there's a one, we use the number, everywhere there's a 0, we throw that out. Theres a 1 next to the first, second, third, and fifth numbers. Taking those numbers, we add them
1 + 2 + 4 + 16
Which equals 23, your decimal equivalent
Please help me 10 points
Answer: Its 4(x+1)
Step-by-step explanation:
You combine all the x's, creating 4x+4.
In the last answer, it has 4(x+1) which by distributing you should get 4x+4!
find the values of x and y.
The values of x and y in the parallel lines are 10 and -5 respectively.
How to find the angles in parallel lines?When parallel lines are cut by a transversal line, angle relationships are formed such as corresponding angles, linear angles, alternate interior angles, alternate exterior angles, same side interior angles, vertically opposite angles etc.
Therefore, using same side interior angles,
6x + 2y + 130 = 180
2x - 4y + 140 = 180
Recall same side interior angles are supplementary
Hence,
6x + 2y = 50
2x - 4y = 40
multiply equation(ii) by 3
6x + 2y = 50
6x - 12y = 120
subtract the equations
14y = - 70
y = -70 / 14
y = -5
Let's find x
6x + 2y = 50
6x = 50 - 2(-5)
6x = 50 + 10
6x = 60
x = 60 / 6
x = 10
Therefore,
x = 10 and y = -5
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a significant positive correlation is found between variables x and y. which of the following may be safely inferred?
It can be inferred that as one variable increases, so does the other. Additionally, a change in one variable is likely to be accompanied by a corresponding change in the other.
A significant positive correlation between two variables means that as one variable increases, the other also increases. This implies that when one variable changes, the other is likely to follow suit. For example, if Variable X increases, Variable Y is likely to increase as well. This can be interpreted as a direct relationship between the two variables. Additionally, a significant positive correlation indicates that the two variables have a strong relationship, meaning that as one variable increases or decreases, the other is likely to follow suit. This can be used to help make predictions and draw conclusions about the relationship between the two variables.
The complete question: A significant positive correlation is found between variables x and y. Which one of the following may be safely inferred? a. As x increases, y increases. b. As x increases, y decreases. c. y causes x. d. x causes y.
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the empirical rule provides precise statements regarding the percentage of observations that fall within a specified number of standard deviations from the mean. which of the following is a correct statement? select all that apply!
The correct answer is option A. The empirical rule provides precise statements regarding 1, 2, or 3 standard deviations.
The Empirical Rule, also known as the 68-95-99.7 rule, states that for a normal distribution (or approximately normal distribution), about 68% of the data falls within one standard deviation of the mean, 95% within two standard deviations, and 99.7% within three standard deviations. This rule assumes that the mean, median, and mode are equal and the data is symmetrical.
It is a quick and easy way to get a rough estimate of the spread of data in a normal distribution and the proportion of values that fall within certain intervals. However, it should be noted that this is an approximation and not always accurate, especially for distributions that are not close to being normal.
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Complete Question:
When applicable, the empirical rule provides the approximate percentage of observations that fall within how many standard deviations from the mean?
A. 1, 2, or 3 standard deviations
B. 4, 6, or 9 standard deviations
C. 2, 2, or 7 standard deviations
Dough has 5 hours to make an on time delivery 273 mile# away. Dough drives at a constant speed of 55 miles per hour. Will Doug make the delivery by the deadline. Explain
Answer:
Yes, He'll make it
Step-by-step explanation:
If Doug travels at 55 MPH for 5 hours, he will have driven 275 miles. Since the deadline and his current speed allow him to drive farther than his set location at 273 miles, then Doug should be able to make it within the time given.
simplify by adding or subtracting the matrices. Write "undefined" for ions that are undefined. -4 0 -1 -9 0 5 -6 0 3 -5 -7 10 2 -3 0
The matrix is undefined.
What is a Matrix?A matrix, which is used to represent a mathematical object or an attribute of one, is a rectangular array or table containing numbers, symbols, or expressions that are organized in rows and columns.
Matrix addition or subtraction can only be performed if the matrices have the same dimensions, i.e. the same number of rows and columns. In this case, two matrices are given, but their dimensions are not specified, so it is impossible to determine if they are the same or not. Therefore, the result is undefined.
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Estimate the sum of 9/10 and 5/6
The estimate the sum of 9/10 and 5/6 is 1 1/15
How to estimate the sum of 9/10 and 5/6From the question, we have the following parameters that can be used in our computation:
The sum of 9/10 and 5/6
Mathematically, this can be represented as
9/10 + 5/6
Take the LCM of teh numbers
So, we have
(54 + 50)/60
Evaluate the like terms
104/60
Simplify the fraction
1 1/15
Hence, the estimate is 1 1/15
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Halla el FCM de 126, 119 y 196 usando el método de factorización prima
The HCF of the numbers 126, 119 and 196 is 7.
What is HCF?The Highest Common Factor (HCF) of two numbers is the highest possible number that divides both the numbers completely.
The Highest Common Factor (HCF) is also called the Greatest Common Divisor (GCD).
Given are the numbers -
126, 119, 196
We can write the Prime factorization of the numbers given as -
126 = 2 × 3 × 3 × 7
119 = 7 × 17
196 = 2 × 2 × 7 × 7
7 is common in the prime factorization of all the numbers.
Therefore, the HCF of the numbers 126, 119 and 196 is 7.
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{
Complete question in english -
Find the FCF of 126, 119, and 196 using the prime factorization method
}
13 Answer:
Find the x-intercept of the graph of the equation: x + 6y = 7
14 Answer:
Find the x-intercept of the graph of the equation: 4x + y = 3
15 Answer:
Find the y-intercept of the graph of the equation: y - 3x = 4
16 Answer:
Find the y-intercept of the graph of the equation: 2y + x = 8
17 Answer:
Find the slope of the line passing through the points: (2,4) and (1,3)
18 Answer:
Find the slope of the line passing through the points: (2,7) and (5,6)
The slope, x intercept and y intercepts of the graph of the equations given are found as below.
What is Slope?Slope of a line is the ratio of the change in y coordinates to the change in the x coordinates of two points given.
13. x intercept is the point on a line where the line touches the X axis.
y coordinate will be zero at that point.
x + 6y = 7
y = 0, then x = 7
x intercept = 7
14. 4x + y = 3
y = 0, then 4x = 3 or x = 3/4
x intercept = 3/4
15. y intercept is the point where the line touches the Y axis.
x coordinate will be 0 there.
y - 3x = 4
x = 0, then y = 4
y intercept = 4
16. 2y + x = 8
x = 0, then 2y = 8 or y = 4
y intercept = 4
17. Points given are (2,4) and (1,3).
Slope = (3 - 4) / (1 - 2) = -1 / -1 = 1
18. Points given are (2,7) and (5,6)
Slope = (6 - 7) / (5 - 2) = -1/3
Hence the required values are found.
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A psychology professor wants to know whether verbal ability is related to memory quality in current first-year students at his small college. Participants in the study (first-year students at his college) complete an online memory task. The students are first shown a list of 60 words. Next they are shown a list that includes 10 words that were on the original list. Then they are asked to identify the words on the second list that appeared on the original list. He uses the percentage of words that were correctly recognized on the original list as his measure of memory quality. He also asks the students to report several characteristics such as their age, gender, and verbal SAT score. Each of the 500 first-year students (268 males and 232 females) at his school volunteered to participate. The professor chose 50 students at random to complete the memory task and answer the questions. The average percentage of words that were correctly recognized on the original list was 68%. The professor infers that if all 500 first-year students had completed the study, the results would show that an average of 68% (plus or minus sampling error) of the words were correctly recognized as being on the original list. Which of the following are variables in the study? Check all that apply. The 500 students The students' percentage of words that were correctly recognized on the original list The students' verbal SAT scores The 50 students What is the population in the study? The 500 first-year students at the college The 68% of words correctly recognized as being on the original list The 50 students who participated in the study What is the sample in the study? The 50 students who participated in the study The 500 student volunteers The 68% of words correctly recognized as being on the original list What is an example of a statistic in the study? 68%, the average percentage of the original list expected to be correctly recognized by the 500 students 232 females and 268 males 68%, the average percentage of words that were correctly recognized as being from the original list by the 50 students What is an example of a parameter in the study? 68% of words that were correctly recognized on the original list by the 50 first-year students The actual average percentage of words that would be correctly recognized as being from the original list by the 500 first-year students 50 students What is an example of the professor using descriptive statistics? He characterizes the first-year students at the college as consisting of 268 males and 232 females. He randomly chooses the 50 students to represent the 500 volunteers. He infers that if all 500 students had done the experiment, the results would show that an average of 68% (plus or minus sampling error) of the words were correctly recognized as being on the original list. What is an example of the professor using inferential statistics? He infers that if all 500 students had done the experiment, the results would show that an average of 68% (plus or minus sampling error) of the words were correctly recognized as being on the original list. He characterizes the first-year students at the college as consisting of 268 males and 232 females. He reports that the average percentage of words that were correctly recognized on the original list was 68%.
Answer:
A
Step-by-step explanation:
i) Group 1 contains 170 students, all of whom have taken at least one of the three courses listed above. Of these, 61 students have taken Calculus, 78 have taken Sociology, and 72 have taken Spanish. 15 have taken both Cal- culus and Sociology, 20 have taken both Calculus and Spanish, and 13 have taken both Sociology and Spanish. How many students have taken all three classes? (ii) You are given the following data about Group 2. 32 students have taken Calculus, 22 have taken Sociology, and 16 have taken Spanish. 10 have taken both Calculus and Sociology, 8 have taken both Calculus and Span- ish, and 11 have taken both Sociology and Spanish. 5 students have taken all three courses while 15 students have taken none of the courses. How many students are in Group 2?
The number of students that took all the three classes is 40
The number of students are in Group 2 is 51 students
How to find the number of students that tool all the three classes(i) To find the number of students who have taken all three classes, we need to subtract the number of students who have taken only two classes from the number of students who have taken at least one class.
Let's call the number of students who have taken all three classes "x".
The number of students who have taken Calculus and Sociology is 15 + x.
The number of students who have taken Calculus and Spanish is 20 + x.
The number of students who have taken Sociology and Spanish is 13 + x.
Adding these three equations, we have:
15 + 78 + 72 = 15 + x + 78 + x + 72 + x
solving for x
165 = 45 + 3x
120 = 3x
isolating x
So, x = 40.
hence, 40 students have taken all three classes.
(ii) To find the number of students in Group 2, we need to add the number of students who have taken at least one class to the number of students who have taken none of the classes.
Let's call the number of students in Group 2 "y".
The number of students who have taken at least one class is
32 + 22 + 16 - 10 - 8 - 11 + 5 = 36.
Therefore, y = 36 + 15 = 51.
So, there are 51 students in Group 2.
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accounting has its own vocabulary and basic relationships. match the accounting terms at the left with the corresponding definition or meaning at the right.
The accounting terms and their corresponding definitions and meanings are;
Posting - Copying data from the journal to the ledgerExpense - The cost of operating a business; a decrease in stockholders' equityDebit - Left side of an accountTrial Balance - Lists all accounts with their balancesEquity - Assets - LiabilitiesWhat are some accounting terms ?When a record is posted, it means that details of a transaction are copied from a journal to a ledger. Expenses are the costs incurred in operating a business.
The Debit side of transactions is the left side of an account and the Trial Balance shows the different accounts with their balances and transactions. Equity shows the assets that are not acquired by liabilities.
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The rest of the question is:
Posting - Left side of an accountExpense - Assets - Liabilities Debit - Copying data from the journal to the ledgerTrial Balance - Lists all accounts with their balancesEquity - The cost of operating a business; a decrease in stockholders' equitySolve the equation:
6x³+24x²+24x=0
x=0 and x=-2 are the solutions of the equation 6x³+24x²+24x=0
What is quadratic equation?A quadratic equation is a second-order polynomial equation in a single variable x , ax²+bx+c=0. with a ≠ 0 .
The given equation is 6x³+24x²+24x=0
Take 6x as common from the given equation.
6x(x²+4x+4)=0
6x=0 and x²+4x+4=0
x²+4x+4=0
x²+2x+2x+4=0
x(x+2)+2(x+2)=0
(x+2)(x+2)=0
(x+2)²=0
x=-2
Hence, x=0 and x=-2 are the solutions of the equation 6x³+24x²+24x=0
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What are the solutions for this inequality
X/9>9
Answer:
x > 81
In interval notation: (81, ∞)
Step-by-step explanation:
Inequality is
[tex]\dfrac{X}{9} > 9[/tex]
Multiply both sides by 9:
[tex]\dfrac{X}{9}\cdot 9 > 9 \cdot 9\\\\\implies X > 81\\[/tex]
The solution set expressed in interval notation is (81, ∞)
Find the most general antiderivative of the function. (Check your answer by differentiation. Use C for the constant of the antiderivative.) f(x) = sqrt 6 F(x) =
The most general antiderivative of the function f(x) = sqrt(6) is given by F(x) = (3/2)sqrt(6x) + C, where C is an arbitrary constant. To check the answer by differentiation, you can take the derivative of F(x) with respect to x:
F'(x) = (3/2)sqrt(6)x^(-1/2) = sqrt(6),
which is equal to f(x).
The gamma function is an extension of the factorial function to complex numbers. It is defined for all complex numbers except the non-positive integers.
The gamma function satisfies the following properties:
It is an entire function, meaning it is defined for all complex numbers.It is an increasing function, meaning that Γ(z) is greater than Γ(z-1) for all z > 0.It is a continuous function, meaning that it is continuous in the complex plane.It is a convex function, meaning that the curvature of Γ(z) is always positive.It is a logarithmically convex function, meaning that its logarithmic derivative is always positive.It has a unique positive real root, called the gamma constant, denoted by Γ(1).It satisfies the reflection formula: Γ(1-z)Γ(z) = π/sin(πz)It satisfies the duplication formula: Γ(2z) = (2^z)Γ(z)Γ(z+1/2).Learn more about functions
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fill in the blank. consider a sample with a mean of and a standard deviation of ___. use chebyshev's theorem to determine the percentage of the data within each of the following ranges (to the nearest whole number).
100% of the data lies within two standard deviations of the mean, 75% of the data lies within one standard deviation of the mean, and 50% of the data lies between 8 and 12.
Consider a sample with a mean of 10 and a standard deviation of 4. Use Chebyshev's theorem to determine the percentage of the data within each of the following ranges (to the nearest whole number):
- Between 2 and 18: 100%
- Between 6 and 14: 75%
- Between 8 and 12: 50%
Chebyshev's theorem states that at least 75% of the data will lie within two standard deviations of the mean, and at least 50% of the data will lie within one standard deviation of the mean. In this example, 100% of the data lies within two standard deviations of the mean, 75% of the data lies within one standard deviation of the mean, and 50% of the data lies between 8 and 12.
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At a plant, 30% of all the produced parts are subject to a special electronic inspection. It is known that any produced part which was inspected electronically has no defects with probability 0.90. For a part that was not inspected electronically this probability is only 0.80 Let E be the event that a part in the plant went through an electronic inspection Let D be the event that a part produced in the plant is defective. Find the following A- P(E) B- P (DE) C- P(DE) D- P(DE) A- P(E) B. P (DE) CP (DE) D- P (DE) E- P(DE) F- P(D) G- P(ED) TYPE YOUR FINAL ANSWERS. LABEL YOUR ANSWERS AS A, B
30% of parts undergo electronic inspection. If inspected, the chance of no defects is 90%. If not inspected, chance of defects is 20%. Total chance of a defect is 27%. Chance of a defective part being inspected is 33%.
A. P(E) = 0.30, the probability that a part in the plant went through an electronic inspection.
B. P(D|E) = 0.90, the probability that a produced part which was inspected electronically has no defects.
C. P(D|E') = 0.20, the probability that a part produced in the plant is defective and was not inspected electronically.
D. P(E') = 0.70, the probability that a part in the plant did not go through an electronic inspection.
E. P(D|E) + P(D|E') = 0.90 + 0.20 = 1.10, which is not a valid probability value since it is greater than 1.
F. P(D) = P(D|E)P(E) + P(D|E')P(E') = 0.90 * 0.30 + 0.20 * 0.70 = 0.27, the probability that a part produced in the plant is defective.
G. P(E|D) = P(DE) / P(D) = 0.90 * 0.30 / 0.27 = 0.33, the probability that a defective part in the plant went through an electronic inspection.
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Find cos(B) in the triangle.
A. 15/17
B. 8/17
C. 8/15
D. 15/8
Answer:
A
Step-by-step explanation:
subtract y from 5, then double the result
The expression of the given algebra word problem is; 10 - 2y
How to simplify algebraic expressions?We are told that we should subtract y from 5, then double the result.
Subtracting y from 5 gives us;
5 - y
Now, doubling the result will mean we will multiply it by 2 and this will be expressed as;
2(5 - y)
Expanding the bracket using distributive property is;
2*5 - 2*y
= 10 - 2y
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A company makes car stereos the manufacturing cost for each stereo is 45$ the company fixed cost of 4150$ per month how many stereos can they make
A company make 92 stereos in a month.
What is Division method?Division method is used to distributing a group of things into equal parts. Division is just opposite of multiplications. For example, dividing 20 by 2 means splitting 20 into 2 equal groups of 10.
We have to given that;
A company makes car stereos the manufacturing cost for each stereo is $45.
And, The company fixed cost of $4150 per month.
Now, Let number of cars manufacturing by a company in a month is,
⇒ $4150 ÷ $45
⇒ 92
Thus, Number of cars manufacturing by a company in a month is, 92.
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fill in the blank.when we have a___data set it is like the scrambled phrase. statistic is the process of using visual, numerical, and tabular display to unscramble the data and discover the message behind it
When we have a population data set it is like the scrambled phrase. statistic is the process of using visual, numerical, and tabular display to unscramble the data and discover the message behind it.
A collection of data is known as a data set (or dataset). In the case of tabular data, a data set relates to one or more database tables, where each row refers to a specific record in the corresponding data set and each column to a specific variable. The data set includes values for each of the variables, such as the object's height and weight, for each set member. Data sets can also be made up of a group of files or documents.
The analysis and manipulation of data is the essence of statistics. As we just covered in the introduction, statistics is the study of the calculation and analysis of numerical data. Let's examine other statistical definitions provided by various authors in this article.
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suppose that a die is rolled twice. what are the possible values that the following random variables can take
A) The maximum value to appear in the two rolls can take on any value from 2 to 6.
B) The minimum value to appear in the two rolls can take on any value from 1 to 5.
C) The sum of the two rolls can take on any value from 2 to 12.
D) The value of the first roll minus the value of the second roll can take on any value from -5 to 5.
If the die is assumed to be fair, the probabilities associated with the random variables in parts (a) through (d) can be calculated as follows:
A) The probability of the maximum value to appear in the two rolls is 1/6.
B) The probability of the minimum value to appear in the two rolls is 1/6.
C) The probability of the sum of the two rolls is 1/36 for each of the possible sums from 2 to 12.
D) The probability of the value of the first roll minus the value of the second roll is 1/11 for each of the possible values from -5 to 5.
Complete question:
Suppose that a die is rolled twice. What are the possible values that the following random variables can take on (a) the maximum value to appear in the two rolls: (b) the minimum value to appear in the two rolls (c) the sum of the two rolls; (d) the value of the first roll minus the value of the second roll? 4.8. If the die in Problem 4.7 is assumed fair, calculate the probabilities associated with the random variables in parts (a) through (d).
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Write equivalent fractions for the numbers 1 and 2 10.3
The fractions and the equivalent equations is solved
What is a Fraction?An element of a whole is a fraction. The number is represented mathematically as a quotient, where the numerator and denominator are split. Both are integers in a simple fraction. A fraction appears in the numerator or denominator of a complex fraction. The numerator of a proper fraction is less than the denominator.
Given data ,
Let the equation be represented as A
Now , the value of A is
Substituting the values in the equation , we get
a)
Let the value of fraction A = 3
Now , the value of 3/1 = 3
The value of 6/2 = 3
The value of 12/4 = 3
Therefore , the equivalent fractions are 3/1 , 6/2 and 12/4
b)
Let the value of fraction A = 4
Now , the value of 4/1 = 4
The value of 8/2 = 4
The value of 16/4 = 4
Therefore , the equivalent fractions are 4/1 , 8/2 and 16/4
c)
Let the value of fraction A = 1
The value of 3/3 = 1
The value of 12/12 = 1
Therefore , the equivalent fractions are 3/3 and 12/12
d)
Let the value of fraction A = 4
The value of 40/10 = 4
The value of 8/2 = 4
Therefore , the equivalent fractions are 40/10 and 8/2
e)
Let the value of fraction A = 3
The value of 12/4 = 3
The value of 18/6 = 3
Therefore , the equivalent fractions are 12/4 and 18/6
Hence , the fractions are solved
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3. suppose you are given two circularly linked lists, l and m. describe an algorithm for telling if l and m store the same sequence of elements (but perhaps with different starting points).
The logic for the algorithm is Traverse both linked lists, comparing corresponding elements.
To determine if two circular linked lists, l and m, store the same sequence of elements, we can use the following algorithm:
Start at the head of both linked lists, l and m, and traverse each list until we reach the end.At each step, compare the elements stored in the corresponding nodes of both linked lists.If the elements are not equal, the lists do not store the same sequence of elements.If we reach the end of both linked lists and all elements have been equal, the lists store the same sequence of elements, but with different starting points.In order to cover the case where the lists store the same sequence of elements but with different starting points, we can repeat the algorithm starting at each node in l and m, and continue until we have compared all possible starting points.Learn more about linked lists:
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in lecture we showed that the closed-loop transfer function from the reference r(s) to the output y (s) for the unity feedback loop takes the form
This transfer function is a ratio between the gain of the controller (K) and the plant’s open-loop transfer function (G). The denominator is the sum of the gain and the plant’s transfer function, which results in the closed-loop feedback loop.
The closed-loop transfer function from the reference r(s) to the output y(s) for a unity feedback loop is given by:
y(s) = (K*G(s))/(1+K*G(s))
Where K is the gain of the controller, and G(s) is the plant’s open-loop transfer function. This can be derived by examining the block diagram of a unity feedback loop:
The input (r) is fed into a controller (K) whose output is then multiplied by the plant’s open-loop transfer function (G). The sum of the controller output and the plant output is then fed into the summing junction, and the output (y) is the result.
Therefore, the closed-loop transfer function representing the reference r(s) to the output y(s) can be derived as follows:
[tex]y(s) = r(s)*(K*G(s))/(1+K*G(s))\\= (K*G(s))/(1+K*G(s))[/tex]
This can be rearranged to give the final expression:
[tex]y(s) = (K*G(s))/(1+K*G(s))[/tex]
This transfer function is a ratio between the gain of the controller (K) and the plant’s open-loop transfer function (G). The denominator is the sum of the gain and the plant’s transfer function, which results in the closed-loop feedback loop.
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Enter an equation in the form y=mx+b that represents the function defined by this table of values.
The linear function that represents the table values is y = 3x + 5.
What is the linear function that represents the table values?
The formula for equation of line is expressed as;
y = mx + b
Where m is slope and b is y-intercept.
Using two points from the table, (0,5) and (2,11)
First, we determine the slope m.
Slope m = change in y / change in x
Slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )
Plug in the values
Slope m = ( 11 - 5 ) / ( 2 - 0 )
Slope m = 6 / 2
Slope m = 3
Plug the slope m =3 and point (0,5) into the point-slope formula and simplify.
y - y₁ = m( x - x₁ )
y - 5 = 3( x - 0 )
y - 5 = 3x - 0
y - 5 = 3x
Add 5 to both sides
y - 5 + 5 = 3x + 5
y = 3x + 5.
Therefore, the equation of the line is y = 3x + 5.
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y=-3x+2 determine the value of y when x=2
Answer:
[tex]\huge\boxed{\sf y = -4}[/tex]
Step-by-step explanation:
Given equation:y = -3x + 2
Given that, x = 2
So,
y = -3(2) + 2
y = -6 + 2
y = -4
[tex]\rule[225]{225}{2}[/tex]
Step-by-step explanation:
replace where x is with 2
[tex]y = ( - 3 \times 2) + 2[/tex]
[tex]y = - 6 + 2[/tex]
Answer[tex]y = - 4[/tex]