Answers
T satisfies the homogeneity property.
To prove that T is a linear transformation, we need to show that it satisfies two properties: additivity and homogeneity.
Additivity:
Let's consider two arbitrary vectors z₁ = [x₁, y₁] and z₂ = [x₂, y₂] in R².
T(z₁ + z₂) = T([x₁ + x₂, y₁ + y₂])
= [-2(x₁ + x₂) - 1, -2(x₁ + x₂) + 2(y₁ + y₂)]
= [-2x₁ - 2x₂ - 1, -2x₁ - 2x₂ + 2y₁ + 2y₂]
= (-2x₁ - 1, -2x₁ + 2y₁) + (-2x₂ - 1, -2x₂ + 2y₂)
= T(z₁) + T(z₂)
Therefore, T satisfies the additivity property.
Homogeneity:
Let's consider an arbitrary vector z = [x, y] in R² and a scalar k.
T(kz) = T([kx, ky])
= [-2(kx) - 1, -2(kx) + 2(ky)]
= (-2kx - 1, -2kx + 2ky)
= k(-2x - 1, -2x + 2y)
= kT(z)
Since T satisfies both additivity and homogeneity, we can conclude that T is a linear transformation.
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Related Questions
Fill in the blank to find the y-intercept.
(0,_____)
Answers
Answer:
-2
Step-by-step explanation:
Answer:
-2
Step-by-step explanation:
the y intercept is the point on the graph where the line crosses the x axis
What is 3 divided by 68
Answers
Answer:
0.04411764705
Step-by-step explanation:
Answer:
0.04411764705 is the correct answer ┌(・。・)┘♪
what is the scale factor form polygon ABCD to the polygon PQRS
Answers
The scale factor in this polygon comparison can easily be found as 1.5 because when we divide the length of for example side PS (3 units) by the size of side AD (its pre-image which measures 2 units) we get:
3/2 = 1.5
We could try also the same with any other of the sides in image and pre-image, like PQ comared to AB. PQ has a length of 1.5 units, while AB has a length of 1 unit. Then:
PQ/AB = 1.5/1 = 1.5
HELP WILL GIVE BRAINLIEST
The graphs of the functions f(x)-40¹, 6x-4(1-0).
400-4 (1+1)
are shown below.
Answers
If the graph of \(f(x) = 4e^{0.1x}\) is blue, then the graph of \(f(x) = 4(1+\frac{0.1}{0.5} )^{0.5x}\) is: C. red.
What is an exponential function?In Mathematics and Geometry, an exponential function can be modeled by using this mathematical equation:
\(f(x) = a(b)^x\)
Where:
a represents the initial value or y-intercept.x represents x-variable.b represents the rate of change, common ratio, decay rate, or growth rate.For the rate of change of the blue exponential function \(f(x) = 4e^{0.1x}\), we have the following:
b = \(e^{0.1}\)
b = 1.11
For the rate of change of this exponential function \(f(x) = 4(1+\frac{0.1}{0.5} )^{0.5x}\), we have the following:
b = 1 + 0.1/0.5
b = 1.2
Therefore, this exponential function \(f(x) = 4(1+\frac{0.1}{0.5} )^{0.5x}\) is represented by the red line on the graph.
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For each proof, you must include (i.e., write) the premises in that proof. I do not want to see any proofs without premises. YOU CANNOT USE CONDITIONAL PROOF (CP), INDIRECT PROOF (IP), OR ASSUMED PREMISES (AP). Additionally, use only the 18 rules of inference found in the text and in the notes. If you use an inference rule such as Resolution or Contradiction, you will lose points. 1. 1. C ---> (~D ---> ~X)2. C3. X /D (Note: /D means you have to prove that D validly follows from the premises.)_________________________________________________________________2. 1. A ---> ~B2. B3. ~A ---> (C v ~ B) /C____________________________________________________________________3. 1. A ---> ~D2. ~D ---> (~B v ~~A)3. A4. B /~~A___________________________________________________________________Note:you don't need to use DN and when you have iterated negation signs, do not use parentheses.~~A does not need parentheses.
Answers
B is true, so we can conclude ~~A by disjunctive syllogism.
This proof is based on the inference rules you provided.
D Proof: Premises:
C ---> (~D ---> ~X)
The Modus Ponens Rule was used.
Finally, X /D
Explanation: Using Modus Ponens, we can conclude that D ---> X from premises 1 and 2.
Because premise 2 is true, we can conclude X via modus tollens.
We can conclude that D must be false because X is true.
Evidence for C:
Conditions: A ---> B B
Modus Tollens is the rule that was used.
Finally, C / A
Explanation: Using Modus Tollens, we can conclude from premises 1 and 2 that A.
Because A is false in premise 1, we can conclude that B is true.
Because premise 2 is true, we can conclude C using disjunctive syllogism.
Proof for ~~A:
Premises:
A ---> ~D
~D ---> (~B v ~~A)
A
B
Rule used: Modus Ponens
Conclusion:
~~A /B
Explanation:
From premise 1 and 3, using Modus Ponens, we can conclude that ~D.
From premise 2 and ~D, using Modus Ponens, we can conclude that ~B v ~~A.
From premise 4, B is true, so we can conclude ~~A by disjunctive syllogism.
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The table below represents a frequency distribution for the age (in years) of employees at a particular company.
Age (in years) Frequency
23-29
25
30-36
41
37-43
37
Use the table to answer the following questions.
Your answers should be exact numerical values
The class width used for the frequency distribution is
The class midpoint for the class 23-29 is
The class midpoint for the class 30-36 is
The class midpoint for the class 37-43 is
Check
Answers
The class width used for the frequency distribution is 6.
The class midpoint for the class 23-29 is 26.
The class midpoint for the class 30-36 is 33.
The class midpoint for the class 37-43 is 40.
To find the class width of the frequency distribution, we need to determine the range of each age class. The range is the difference between the upper and lower boundaries of each class. Looking at the table, we can see that the class boundaries are as follows:
23-29
30-36
37-43
For the class 23-29, the lower boundary is 23 and the upper boundary is 29. To find the class width, we subtract the lower boundary from the upper boundary:
Class width = 29 - 23 = 6
So, the class width for the frequency distribution is 6.
To find the class midpoint for each class, we take the average of the lower and upper boundaries of each class.
For the class 23-29:
Class midpoint = (23 + 29) / 2 = 52 / 2 = 26
For the class 30-36:
Class midpoint = (30 + 36) / 2 = 66 / 2 = 33
For the class 37-43:
Class midpoint = (37 + 43) / 2 = 80 / 2 = 40
So, the class midpoint for the class 23-29 is 26, for the class 30-36 is 33, and for the class 37-43 is 40.
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Hey! Just do the first one! :) I also need this fast- so help! :((
Answers
Answer:
the second one
Step-by-step explanation:
that's the answer
4. Approximate the solution to this system of equations.
y = -2x+6
y = 4x - 1
Answers
The solution of the system of linear equations, is (1.167, 3.667).
Given that the system of linear equations, y = -2x+6 and y = 4x - 1, we need to find the solution for the same,
y = -2x+6............(i)
y = 4x - 1.......(ii)
Equating the equations since the LHS is same,
-2x+6 = 4x-1
6x = 7
x = 1.167
Put x = 1.16 to find the value of y,
y = 4(1.16)-1
y = 4.66-1
y = 3.667
Therefore, the solution of the system of linear equations, is (1.167, 3.667).
You can also find the solution using the graphical method,
Plot the equations in the graph, the point of the intersection of both the lines will be the solution of the system of linear equations, [attached]
Hence, the solution of the system of linear equations, is (1.167, 3.667).
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Given m∥ n, find the value of x.
Answers
Answer:
Step-by-step explanation:
3x + 5 + x - 25 = 180
4x - 20 = 180
4x = 200
x = 50
X to the third power = 125
Answers
Answer:
1,953,125
Step-by-step explanation:
Answer: 5
Step-by-step explanation:
what’s the y-intercept? i found the slope already.
Answers
Answer:
3.5
Step-by-step explanation:
3.5 is the y-intercept because the point is (0,3.5). This is where it intercepts with the y-axis.
Hope it helps!
On Marlene's trip to Starved Rock, her average rate of speed for the entire five-hour trip was 62 miles per hour. For the first two hours of her trip, she kept her average speed at 50 miles per hour. Then she realized she was going to be late to meet her friend for dinner, so she started driving faster. What was her average speed for the last three hours of the trip?
Answers
Answer:
70 miles per hour
Step-by-step explanation:
Distance = speed * time
speed = distance / time
------------------------------
Total Distance
speed = 62
time = 5
62 * 5 = 310 miles
Distance travelled in first 2 hours
speed = 50
time = 2
50 * 2 = 100 miles
Remaining distance
310 - 100 = 210 miles
Speed to cover 210 miles in 3 hours
distance = 210
time = 3
210/3 = 70 miles per hour
Please help I’ll mark brainliest
Answers
Answer:
B
Step-by-step explanation:
Suppose AB has one endpoint at A(0,0). If (3, 4) is the midpoint of AB, what are the coordinates of your B?
Answers
Answer:
Step-by-step explanation:
(x + 0)/2 = 3
x + 0 =6
x = 6
(y + 0)/2 = 4
y + 0 = 8
y = 8
(6, 8)
=
Homework: HW 4.2
Question 27, 4.4.71
ler
....
If 4 coins can be exchanged for 5.9352 dubloons, how many dubloons can be obtained for 9 coins?
t.c
..
How many dubloons can be obtained for 9 coins?
om
e
(Round to the nearest hundredth.)
...
age...
Answers
Answer:
5.33
Step-by-step explanation:
Find the surface area
of the figure below:
19 cm
30 cm.
Answers
The surface area of the figure is approximately 997.5π cm².
We have,
The figure has two shapes:
Cone and a semicircle
Now,
The surface area of a cone:
= πr (r + l)
where r is the radius of the base and l is the slant height.
Given that
r = 15 cm and l = 19 cm, we can substitute these values into the formula:
= π(15)(15 + 19) = 885π cm² (rounded to the nearest whole number)
The surface area of a semicircle:
= (πr²) / 2
Given that r = 15 cm, we can substitute this value into the formula:
= (π(15)²) / 2
= 112.5π cm² (rounded to one decimal place)
The surface area of the figure:
To find the total surface area of the figure, we add the surface area of the cone and the surface area of the semicircle:
Now,
Total surface area
= 885π + 112.5π
= 997.5π cm² (rounded to one decimal place)
Therefore,
The surface area of the figure is approximately 997.5π cm².
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f(x)=2x^2 + x - 6/ x-1
Answers
Answer:
See below
Step-by-step explanation:
Zeroes:
\(f(x)=\frac{2x^2+x-6}{x-1}\)
\(0=\frac{2x^2+x-6}{x-1}\)
\(0=2x^2+x-6\)
\(0=(2x-3)(x+2)\)
\(x=\frac{3}{2},-2\)
Vertical and Horizontal Asymptotes:
\(x\neq 1\) is excluded from the domain, therefore, there's a vertical asymptote at \(x=1\)
No horizontal asymptotes as the degree of the numerator is greater than the degree of the denominator by 1.
Oblique (Slant) Asymptote:
\(f(x)=\frac{2x^2+x-6}{x-1}=2x+3,R(-3)\), so the oblique/slant asymptote is \(y=2x+3\)
Last year Kristen had $ 20 , 000 to invest. She invested some of it in the first account that paid 7 % simple interest per year, and she invested the rest of it in a second account that paid 8 % simple interest per year. After one year, she received a total of $ 1 , 540 in interest. How much did she invest in each account?
Answers
The amount invested in the account that earns 7% interest is $6,000 and the amount invested in the account that earns 8% interest is $14,000.
How much is invested in each account?The system of equations that represent the information in the question is:
a + b = 20,000 equation 1
0.07a + 0.08b = 1540 equation 2
Where:
a = amount invested in the account that earns 7% interest
b = amount invested in the account that earns 8% interest
The elimination method would be used to solve the equations.
Multiply equation 1 by 0.07
0.07a + 0.07b = 1,400 equation 3
Subtract equation 3 from equation 2
0.01b = 140
Divide both sides of the equation by 0.01
b = 140/ 0.01
b = 14,000
Substitute for b in equation 1:
a + 14,000 = 20,000
a = 20,000 - 14,000
a = 6,000
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In a survey of 2266 adults, 736 say they believe in UFOs. Construct a 90% confidence interval for the population proportion of adults who believe in UFOs. A 90% confidence interval for the population proportion is ( ?, ?).
(Round to three decimal places as needed.)
Part 2
Interpret your results. Choose the correct answer below.
A.
With 90% probability, the population proportion of adults who do not believe in UFOs is between the endpoints of the given confidence interval.
B.
The endpoints of the given confidence interval shows that 90% of adults believe in UFOs.
C.
With 90% confidence, it can be said that the population proportion of adults who believe in UFOs is between the endpoints of the given confidence interval.
D.
With 90% confidence, it can be said that the sample proportion of adults who believe in UFOs is between the endpoints of the given confidence interval.
Answers
The 90% confidence interval for the population proportion of adults who believe in UFOs is (0.309, 0.339).
C. With 90% confidence, it can be said that the population proportion of adults who believe in UFOs is between the endpoints of the given confidence interval.
To construct a 90% confidence interval for the population proportion of adults who believe in UFOs, we can use the formula:
Confidence Interval = Sample Proportion ± Margin of Error
First, we calculate the sample proportion:
Sample Proportion \(\hat{p}\) = Number of adults who believe in UFOs / Total number of adults surveyed = 736 / 2266 ≈ 0.324
Next, we need to calculate the margin of error.
Since we are dealing with a large sample size, we can use the formula for a 90% confidence interval:
Margin of Error\(= Z \times \sqrt{(\hat{p} \times (1 - \hat{p}) / n)}\)
Here, Z represents the z-value for a 90% confidence level, which corresponds to a z-value of 1.645. n represents the sample size.
Margin of Error\(= 1.645 \times \sqrt{(0.324 \times (1 - 0.324) / 2266)}\) ≈ 0.015
Finally, we can construct the confidence interval:
Confidence Interval = 0.324 ± 0.015 = (0.309, 0.339)
Therefore, the 90% confidence interval for the population proportion of adults who believe in UFOs is (0.309, 0.339).
Now, let's interpret the results.
The correct answer is:
C. With 90% confidence, it can be said that the population proportion of adults who believe in UFOs is between the endpoints of the given confidence interval.
This means that we are 90% confident that the true proportion of adults who believe in UFOs falls within the range of 0.309 to 0.339.
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what are the 6 steps to designing a statistical study
Answers
Answer:
Step 1: Write your hypotheses and plan your research design
Step 2: Collect data from a sample
Step 3: Summarize your data with descriptive statistics
Step 4: Test hypotheses or make estimates with inferential statistics
Step 5: Interpret your results
Step-by-step explanation:
Analyze the diagram below and complete the instructions that follow.
Find m
A. 15°
B. 30°
C. 75°
D. 150°
Please select the best answer from the choices provided
A
B
C
D
Answers
Answer:
I believe the answer to be c 75°
Step-by-step explanation:
a 4 sided shape is 360 total degrees
Function A is represented by the equation y= 6x-1.
Function B is a linear function that goes through the points shown in the
table.
x 13 4 6
y 0 10 15 25
Which statement correctly compares the rates of change of the two
functions?
A. The rate of change of function A is 6.
The rate of change of function B is 5.
B. The rate of change of function A is 6.
The rate of change of function B is 10.
C. The rate of change of function A is
-1.
The rate of change of function B is 5.
D. The rate of change of function A is
-1.
The rate of change of function B is 10.
Answers
The rates of change of the two functions that compare correctly is A. The rate of change of function A is 6, and the rate of change of function B is -10/9.
To compare the rates of change of the two functions, we can calculate the slope of each function. The slope represents the rate of change of a linear function.
For Function A, the equation is y = 6x - 1. The coefficient of x, which is 6, represents the slope. The rate of change of Function A is 6.
For Function B, we are given three points: (13, 0), (4, 10), and (6, 15). We can calculate the slope using the formula: slope = (change in y) / (change in x). Taking the first two points, we have: slope = (10 - 0) / (4 - 13) = 10 / (-9) = -10/9.
Comparing the rates of change, we have:
A. The rate of change of function A is 6.
The rate of change of function B is -10/9.
The correct option is A. The rate of change of function A is 6, and the rate of change of function B is -10/9.
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In an exponential function f(x)=a(b)^x it is known that f(5)=15 and f(7)=170. Which of the following is the closest to the value of ;?
Answers
Complete question is;
In an exponential function, f(x) = a(b)^x, it is known that f(5) = 15 and f(7) = 170. which of the following is closest to the value of b?
Answer:
b = 3.37
Step-by-step explanation:
The function given is f(x) = a(b)^x,
Now, f(5) = 15, Thus;
15 = a(b)^(5)
Also, f(7) = 170
Thus; 170 = a(b)^(7)
From first equation, a = 15/(b)^(5))
Putting this in second equation;
170 = (15/(b)^(5))) × (b)^(7)
170 = 15b²
b² = 170/15
b² = 11.333
b = √11.333
b = 3.37
Photo attach please help
Answers
Answer:
Option D: 5√5 is the correct answer.
Step-by-step explanation:
Given that:
√20 + √45
These can also be written in simplified form;
√5*4 + √5*9
We will take square root of 4 and 9.
The square root of 4 and 9 is,
√4 = 2
√9 = 3
Thus,
2√5 + 3√5
Adding the roots,
5√5
Hence,
Option D: 5√5 is the correct answer.
1. Find the area. *
5 ft
5 ft
16 ft
16 ft
Answers
Answer:
25 cm square and 256 cm square
Step-by-step explanation:
Does anyone know what 1/2*1/2*1/2*1/2 equals?
answers:
4/48
5/16
1/20736
4/12
Answers
•ω• Hewo fren!
☆☆●◉✿Answer:✿◉●☆☆
1/2*1/2*1/2*1/2= \(\frac{1}{2} ^{4}\) Which is apparently none of these answers since it’ll be 1/16.
(Did you make a mistake with 5/16?)
☆☆●◉✿Step-by-step explanation:✿◉●☆☆
I know it is not 4/48 because that’ll be 1/12.
I know it would not be 1/20736 because the number is too small.
I know it would not be 4/12 beacuse that’ll be 1/3
And Iast but now Ieast I know it wouldn’t be 5/16 because that cannot be simplified.
HOPE I HELPED! ∧∧
→⇒brainliest please? ∑(OΔO )♥♥︎
Two identical gardens are to be weeded, each by a two-person team. Team A includes one gardener who could weed the garden in 2 h and another who could weed the garden in 4 h. Team B includes two gardeners, either of whom could weed the garden in 3 h. Which team will finish first? Explain.
Answers
Step-by-step explanation:
Team A time is 1 garden / ( 1 garden/ 2 hr + 1 garden/4 hr) = 1 1/3 hr
Team B = 1 / ( 1/3 + 1/3) = 1 1/2 hr
Team A wins !
How many solutions does the following equation have?
-4(2 + 5) = -40 - 20
Answers
Answer:
0
Step-by-step explanation:
I don't see any variables so simplify both sides.
-8 - 20 = -40 - 20
-28 = -60
is a false statement. No solutions.
Which statement is true about the geometric figure thatcan contain thesp points?O No line can be drawn through any pair of the points.O One line can be drawn through all three points.O One plane can be drawn so it contains all threepoints.OTwo planes can be drawn so that each one containsall three points.
Answers
In order to see which of the statements is true, we must prove the other three false.
First statement:
It is false since there can be three lines drawn that join a pair of points.
Second statement:
A line could only join a pair of the point but not the three of therm
Third statement:
It would be correct to say that one plane could contain all three points.
Fourth statement:
There cannot be another plane that contains the same three points.
The correct answer is the thord statement.
I need help with this please
Answers
The total amount of sugar that was consumed by Kylie in the past nine (9) days is equal to 3 units of sugar.
What is a line plot?In Mathematics and Statistics, a line plot refers a type of graph that is used to graphically represent a data set above a number line, while using crosses, dots, or any other mathematical symbol.
Based on the data and information provided in the line plot shown in the image attached above, we can calculate the total amount of sugar that was consumed by Kylie in the past nine (9) days as follows:
Total sugar consumed = (1/8 + 1/8 + 1/8) + 1/4 + (3/8 + 3/8 + 3/8) + (5/8 + 5/8)
Total sugar consumed = 3(1/8) + 1/4 + 3(3/8) + 2(5/8)
Total sugar consumed = 3/8 + 1/4 + 9/8 + 10/8
Total sugar consumed = 22/8 + 1/4
Total sugar consumed = (22 + 2)/8
Total sugar consumed = 24/8
Total sugar consumed = 3 units of sugar.
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