T is the linear transformation described by T(w,z) in L(C2). This indicates that the linear transformation T changes two-dimensional vectors of the type (w,z) to (-z,w).
To get T's eigenvalues, solve the equation T(v) = v, where is the eigenvalue and v is the eigenvector. By solving this equation, we discover that T's eigenvalues are λ1 = -1 and λ2 = 1.
For each eigenvalue, the associated eigenspaces are the subspaces of C2 that are spanned by the eigenvectors of T. The eigenspace is the subspace covered by the eigenvector λ1= -1 is (1,0). The eigenspace is the subspace spanned by the eigenvector λ2= 1 is (0,1).
As a result, the subspaces covered by (1,0) and (1,1) are the generalized eigenspaces corresponding to the different eigenvalues of T. (0,1).
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find the rate of change of the area of a square when the side of the square is 2 meters and the side is growing at a rate of 3 meters per second.
The rate of change of the area of a square is 12m^2/sec.
What do you mean by rate of change?
The term "rate of change" refers to the rate at which one quantity changes in respect to another. Consequently, if y value is the dependent variable and x value is the independent variable.
Rate of Change is equal to [tex]\frac{Change in y}{Change in x}[/tex].
Change rates may be positive or negative. This reflects a change in the y-value between the two data points, either up or down. Zero rate of change is the state where a quantity does not change over time.
Solution Explained:
Given,
S = 2m and ds/dt = 3m/s
So, we use
Area = s^2
dA/dt = 2s ds/dt
= 2 X 2 X 3
Therefore, the rate of change of the area is 12m^2/s.
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Jakob wants to invite 20 friends to his birthday, which will cost his parents $250. If he decides to invite 15 friends instead, how much money will it cost his parents?.
It will cost his parents $187.5 to invite 15 friends to his party because it cost $12.5 to invite just one.
What is unitary method?The unitary approach involves calculating the value of a single unit, from which we may calculate the values of the necessary number of units. A single or distinct unit is referred to by the word unitary. Therefore, the goal of this strategy is to establish values in reference to a single unit. The unitary technique, for instance, may be used to calculate how many kilometers a car would go on one litre of gas if it travels 44 km on two litres of fuel.
Here,
For inviting 20 friends, The cost of party was $250.
So for 1 friend,
=250/20
=$12.5
Now he wish to invite 15 friends,
=12.5*15
=$187.5
The cost of inviting 15 friends to his party will cost $187.5 to his parents as cost of inviting 1 friend was $12.5.
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7/9 divided by 4/3 please help i need help
Answer: 7/12
Step-by-step explanation: First, flip the 4/3 to its reciprocal and change it to multiplication. Then, you can simplify the 9 and 3 to 3 and 1. After that, multiply straight across. Hope this helps! :)
Answer:
1. 7/9 ÷ 4/3 As a fraction) 21/36
2. 7/9 ÷ 4/3=21/36 as a simplified fraction) 7/12
3. 7/9 ÷ 4/3 As a decimal) 0.583
4. 7/9 ÷ 4/3 As a percentage) 58.3%
Let's see how it's done!
7/9 ÷ 4/3:
7/9 ÷ 4/3 (Invert or flip the second fraction and multiply across)
7/9 x 3/4 = 21/36
How to simplify 21/36
21/36 ÷ 3 (Divide the numerator "the top part of the fraction" and the denominator "the bottom part of the fraction" by 3. This will equal 7/12
How to turn 21/36 into a decimal
21 divided by 36 = 0.5833333333333333...
Round to the nearest thousandth: 0.583
How to turn 0.583 into a percent
Move the decimal point 2 places to the left, drop the zero(s)
and add the percent sign! 58.3%
These are all the same answer but in different forms and how to do them!
Hope it helps!
Let be the vector space of polynomials in with degree less than 3 and be the subspace.
the polynomial will be 2x² + 11x+6, with degree less than 3 and be the subspace.
What is vector space?
A collection of vectors collected collectively and multiplied ("scaled") by scalars forms a vector space, also known as a linear space. Real numbers are typically thought of as scalars. Nevertheless, there aren't many instances of scalar multiplication with vector spaces using rational, complex, etc. numbers. Axioms and other preconditions must be met by the vector addition and scalar multiplication techniques. A space made up of vectors is referred to as a vector space when the addition of vectors is governed by the associative and commutative law and when vectors are multiplied by scalars is governed by the associative and distributive process.
W = span (9x-4-2x²,5+x+2x²)
Now, a(9x42x²)+b(5+x+2x²) = 0
⇒(9a+b)x+(2b-2a)x² + (5b-4a) = 0
⇒9a+b= 0; 2b2a = 0; 5b-4a=0
a = b =0
p(x)=(9x-4-2x²) + 2(5+x+2x²) = 9x-4-2x² + 10 + 2x + 4x² = 2x² + 11x+6
Hence the polynomial will be 2x² + 11x+6.
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plsss I need help
define a variable right and inequality and solve each problem. the sum of a number and -4 is at least 8
The inequality x - 4 ≥ 8 represents the sentence " the sum of a number and -4 is at least 8" and the solution of the inequality is the value of variable x is x ≥ 12.
What is inequality?Inequality is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are not equal.
Let's assume that the number would be x
The sum of a number and -4 is at least 8
According to the given question, translate the phrase into an algebraic form :
x - 4 ≥ 8
Add 4 both sides of the above inequality,
x - 4 + 4 ≥ 8 + 4
x ≥ 12
Therefore, the inequality x - 4 ≥ 8 represents the sentence " the sum of a number and -4 is at least 8" and the solution of the inequality is the value of variable x is x ≥ 12.
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if you good at geometry help pls lol
the solar system is 25 000 light years from the center of our milky way galaxy. one light year is the distance light travels in one year at a speed of 3.0 x108 m/s. astronomers have determined that the solar system is orbiting the center of the galaxy at a speed of 230 km/s what is the period of the solar system’s orbit. give your answers in years?
The period of the solar system's orbit is 2.05 x 108 years.
What is the time period?
A period is a number that in algebraic geometry can be expressed as the integral of an algebraic function over an algebraic domain. Periods form a ring because their sums and products always remain in the same period.
Don Zagier and Maxim Kontsevich presented some theories and gave a survey of the eras. Periods also appear when computing the integrals that result from Feynman diagrams, and extensive work has been done to understand the relationships.
Solution Explained:
Given,
Radius of the solar system, r=25000 light year
Speed v=230 km/s
Calculate time period by
T = 2πr / v
T = 2πr X (25000 X 3 X 10^8 X 365 X 24 X 60 X 6) / (230 X 10^3)
= 6.46 X 10^15 X (1 year / 365 X 24 X 60 X 60)
= 2.05 X 10^8 years
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how many sequences of 0s and 1s of length 19 are there that begin with a 0, end with a 0, contain no two consecutive 0s, and contain no three consecutive 1s? (2019 amc 10 b)
There are 65, 19-bit sequences of 0s and 1s that start with a 0 and end with a 0 that exist.
Explain the term sequences?A grouping of numbers in such a specific order is known as a sequence. On the other perspective, a series is described as the accumulation of a sequence's constituent parts.Any subsequent 0 in the sequence must come exactly two or three spots down from the previous one.
We begin at point 1 and finish at position 19 in this instance.
That is, we advance along the line a whole of 18 positions.
In order to achieve 18, we must add all series consecutive 2s and 3s.
There are numerous methods for doing this:
Case 1: There is just one possible arrangement for nine 2s.
Case 2: Two 3s with six 2s - thus ⁸C₂ ways = 28 ways
Case 3: Four 3s with three 2s - thus ⁷C₄ ways = 35 ways
Case 4: Six 3s - Only 1 way to arrange.
Thus, the number of arrangements = 1 + 28 + 35 + 1 = 65 .
Therefore ,the total possible number of the sequence that cane be made is 65 .
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Train A has 75 cars. if train B has 15 cars, how many times more cars does train A have than train B?
Answer:
3
Step-by-step explanation:
75/15=
__3_________
15 / 75
- 75
---------------------------------
0
Have a great day
10. Find the slope of the line.
Answer: y = 1.75x - 1
Step-by-step explanation: The slope of the line is 1.75
select the curve generated by the parametric equations. indicate with an arrow the direction in which the curve is traced as t increases. x
The curve with parametric equations x = [tex]e^{- t}[/tex] + t, y = [tex]e^t[/tex] − t, − 2 ≤ t ≤ 2 can be plotted on a graph. The arrow shows the direction where t increases in the interval (-2,2).
The length of a curve of the provided parametric equations is indicated by the arrow pointing in the direction wherein the curve is traced given data.
Think about the equations for the parameterized curve in the x-y plane.
x = x( t )
y = y( t )
where the argument is t. The graph of the curve is created by charting the series of points as the variable t changes (x,y).
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The question is -
Select the curve generated by the parametric equations. Indicate with an arrow the direction in which the curve is traced as t increases. x = [tex]e^{- t}[/tex] + t , y = [tex]e^t[/tex] − t , − 2 ≤ t ≤ 2
the bookstore marked some notepads down from $2.00 but still kept the price over $1.00. it sold all of them. the total amount of money from the sale of the pads was $29.45. how many notepads were sold? what was the price of each notepad?
There were 13 notepads, each of which cost $1.05 when the bookstore reduced the price of various notepads from $2.00 to $1.00.
Given that,
The bookstore reduced the price of various notepads from $2.00 to $1.00 while maintaining the price. The whole lot was sold. The selling of the pads generated a total profit of $29.45.
We have to find what number of notepads were sold and how much did each notepad cost.
We know that,
One approach to solving this issue is to divide $29.45 by each of the values from $1.01 to $1.99. That is the price for each notepad if one of them fits evenly with no leftovers. The number of pads is the quotient (result of division). The number has to be placed evenly because we cannot use half of the pad (leave no remainder).
Although we can check each of them, I realized that $29.45 ends in a 5 and is therefore divisible by 5, so I chose to check 1.05 as a potential price and it entered evenly. 13 is the quotient.
Therefore, There were 13 notepads, each of which cost $1.05 when the bookstore reduced the price of various notepads from $2.00 to $1.00.
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do not guess please ty
Answer:
Step-by-step explanation: find a point and find another point
y=1x+1/2
the circumference of the base of a 5 -foot-high cylinder is 46 inches. what is the volume of the cylinder? (use the formula v
The volume of the cylinder is 10,099.09 inches³.
Here we have to find the volume of the cylinder.
Given data:
Circumference = 46 inches
height(h) = 5 foot = 12 × 5 = 60 inches
Circumference = 2πr
46 = 2 ×π × r
r = 23/π
The formula for the volume of the cylinder = πr²h
Volume = π( 23/π)² 60
= 529× 60 / π
= 10,099.09 inches³
Therefore the volume is 10,099.09 inches³.
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Round 565.948063818 to 1 decimal place
Answer:
565.9
Step-by-step explanation:
joe has dime and nickels in his piggy bank totaling $1.45 the number of nickels he has is 5 more than twice the number of dimes , d . which equation could be used to find the number of dimes he has ?
The expression 0.3d = 0.95 could be used to find the number of dimes he has.
What is a expression? What is a mathematical equation? What is Equation Modelling?A mathematical expression is made up of terms (constants and variables) separated by mathematical operators. A mathematical equation is used to equate two expressions. Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem.
We have joe who has dime and nickels in his piggy bank totaling $1.45 the number of nickels. He has is 5 more than twice the number of dimes [d].
We can write the the number of nickels as -
[n] = 2d + 5
0.1d + 0.1(2d + 5) = 1.45
0.1d + 0.2d + 0.5 = 1.45
0.3d = 0.95
Therefore, the expression 0.3d = 0.95 could be used to find the number of dimes he has.
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Company g also sells fat quarters. The mean and standard deviation of the number of defects on a fat quarter that can be sold by company g are 0. 40 and 0. 66, respectively. The fat quarters sell for $5. 00 each, but are discounted by $1. 50 for each defect found. (c) what are the mean and standard deviation of the selling price for the fat quarters sold by company g?
From the given information given, the mean and standard deviation of the probability distribution is; Y will be 0.4899 and 0.699 respectively.
How to create the probability distribution?
From the given probability distribution, it should be noted that the probability distribution for y will be:
Y 0 1. 2
Probability 0.63. 0.25. 0.12
The mean of Y will be:
Mean = (0 × 0.63) + (1 × 0.25) + (2 × 0.12)
Mean = 0 + 0.25 + 0.25
Mean = 0.49
The variance will be 0.4899. Therefore, the standard deviation will be:
standard deviation = ✓0.4899
Standard Deviation = 0.699
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Solve for 3z-1 = 1
what is Z
Answer:
x=2/3
Step-by-step explanation:
3x - 1 = 1
+ 1 + 1
---------------
3x = 2
÷3 ÷3
------------------
x=2/3
-----------------------
using subtraction and division properties of equality, you can simplify the expression to solve it. you can use other properties of equality for different equations as well, but for this one you only need subtraction and division. :)
a woman decides to purchase a $23,800 car and makes a down payment of $3,500. she arranges to borrow the remainder from a bank that will charge her 4.5% interest. she will make monthly payments for 4 years. a. find her monthly payment amount.
The monthly payment amount a woman has to pay for the car is $462.91.
Here we have to find the monthly payment amount.
The cost of car = $23,800
Down payment = $3,500
Rate(r) = 4.5%
time(t) = 4 years
Periodic interest(i) = 0.045/12
Formula to calculate monthly payment:
A = P i( 1 + i[tex])^{n}[/tex] / ( 1 + i[tex])^{n}[/tex] - 1
Loan amount = 23800 - 3500
= $ 20300
A = 20300 ( 0.045 /12 ( 1 + 0.045/12[tex])^{48}[/tex])/ (1 + 0.045/12[tex])^{48}[/tex] - 1
= 20300× 0.004488 / 0.196814
= 462.91
Therefore the monthly payment is $462.91.
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What is the value of √m = ∓ 17
Answer:
What is the value of √m = ∓ 17
The value of √m = ∓ 17 is undefined.
please help, no idea what to do
Find the measure of each angle listed in the picture.
**Please Show All Work**
Angle AEB:
Angle CED:
Angle C:
Step-by-step explanation:
so, if I understand correctly :
angle A = 22°
angle B = 53°
angle D = 38°
remember : the sum of all 3 angles in every triangle is always 180°.
so,
180 = 22 + 53 + AEB
angle AEB = 180 - 22 - 53 = 105°
per the attributes of crossing lines the angles between them are the same on both sides of any of the lines (just left-right mirrored).
so, CB and AD are crossing lines, therefore
angle AEB = angle CED = 105°
and then
180 = 105 + 38 + C
angle C = 180 - 105 - 38 = 37°
What is the range of g(x)=-1/2 |x-6|+1? A. (-∞, 1] B. [1, ∞) C. [6, ∞) D. (-∞, ∞)
PLEASE HELP RIGHT NOW!
The required range of the given function g(x) = -1/2 |x-6| + 1 will be g(x) ≤ 1 or in internal notation form as (-∞, 1]. which is the correct answer would be an option (A).
The function is given in the question below as:
g(x) = -1/2 |x-6| + 1
We have to determine the range of the given function.
As per the given question, we have
⇒ g(x) = -1/2 |x-6| + 1
The range of an absolute function of the form:-
c|ax+b|+k is :f (x) ≤ k
In this case k = 1
⇒ g(x) ≤ 1
[tex]\mathrm{Range\:of\:}-\frac{1}{2}\left|x-6\right|+1:\quad \begin{bmatrix}\mathrm{Solution:}\:&\:f\left(x\right)\le \:1\:\\ \:\mathrm{Interval\:Notation:}&\:(-\infty \:,\:1]\end{bmatrix}[/tex]
Therefore, the required range of the given function will be g(x) ≤ 1 or in internal notation form as (-∞, 1].
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⠀⠀
Walmart had 200 workers for Black Friday
but had to cut positions for after the
holidays to 152. What percent did the
amount of workers decrease?
Answer:
24%
Step-by-step explanation:
Walmart has 152/200 employees, simplify that to a number over 100, you get 76/100. 100-76=24
Answer:
Step-by-step explanation:
152/200 = .76
100-76 = 24
=24%
Therefore, the percentage the amount of workers decrease is by 24%.
Please do tell if this helps!
Many doctors rely on the use of intravenous medication administration in order to achieve an immediate response of a particular drug's effects. The concentration, C, in mg/L, of a particular medication after being injected into a patient can be given by the function C(t) = −5t2 + 10t, where the time, t, is hours after injection. Part A: What are the domain and range of the function C(t) based on the context of the problem? Show all necessary calculations. (5 points) Part B: Graph the function to determine the greatest concentration of the medication that a patient will have in their body. (5 points)
The domain and range of the function C(t) based on the context of the problem is
domain 0 ≤ t ≤ 2range 0 ≤ C ≤ 2How to find the range and domainThe range is calculated from minima and maxima, this will be achieved using derivative
C(t) = -5t² + 10t
C'(t) = 0 = -10t + 10
t = 1
substituting t = 1
C(t) = -5(1)² + 10t = 5
so at point (1, 5) it is either minima or maxima,
The second derivative test will help to confirm if point (1, 5) is minima or maxima
C'(t) = -10t + 10
C''(t) = -10
a negative value means it is a maxima
Hence the highest value of the concentration C(t) is 5 mg/L and this is at t = 1
The concentration cannot be less than zero or negative hence the lowest concentration is 0. and the range is 0 to 5
0 ≤ C ≤ 2
The time cannot be below zero so the lowest time will be zero
The domain is controlled by the input values. considering the least concentration of the drug which will be at C = 0
C(t) = -5t² + 10t
0 = -5t(t - 2)
-5t = 0
t = 0
t - 2 = 0
t = 2
The roots of the quadratic equation gives the domain to be 0 to 2
0 ≤ t ≤ 2
The graph is attached
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dr. rhodes notices an interaction in his factorial study. in describing this, which statement might he use to explain the link between independent variable a and independent variable b in predicting the dependent variable?
For the factorial study, Dr Rhodes can use the statement b) effect of variable A depends on variable B
In a factorial study, two intervention comparisons are undertaken side by side. As a result, in addition to behavioral treatment or standard medical care, individuals may be randomly randomized to receive either aspirin or a placebo. In factorial designs, three different sorts of outcomes are pertinent: main effects, interaction effects, and simple effects.
The primary effect is the impact of one independent variable on the dependent variable, averaged over the values of the other independent variable. Dr Rhodes can forecast the relationship between independent variables A and B using the assumption that the effect of variable A depends on variable B.
Complete question
Dr. Rhodes notices an interaction in his factorial study. In describing this, which statement might he use to explain the link between Independent Variable A and Independent Variable B in predicting the dependent variable? TRUE OR FALSE
Variable A cancels out Variable B.
The effect of Variable A depends on Variable B.
The effect of Variable A is confused by Variable B.
Variable A mainly affects Variable B.
The effect of Variable A is mediated by Variable B.
The effect of Variable A depends on Variable B.
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please help will brainliest!!
a triangle is bounded by a semi circle and the x axis, what length and width should the rectangle be to maximize the area
So for the maximum area, the values of the width and length of the rectangle will be 2.121.
Since we know that the formula for the area of a rectangle is:
A = XY, where x and y are the width and length
since we are given the are, y=√(9-x²), so
A = √(9-x²)
taking the derivative on both sides and considering it to be zero, we get
A' = (x/√(9-x²)(-2x) + √(9-x²) = 0, after multiplying by √(9-x²)
A' = -x² + 9 -x² = 0
=>-2x² =-9
=>x² = 9/2
=> x = 3/√2
so x=2.121 so the for y = √(9-(2.121)^2) = √(9-4.498) = 2.121
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A rectangle is bounded by a semicircle y = radical 9 − x^2 and the x-axis. What length and width should the rectangle be to maximize the area
a simple random sample of size n is drawn from a population that is normally distributed. the sample mean, , is found to be , and the sample standard deviation, s, is found to be . (a) construct % confidence interval about if the sample size, n, is . (b) construct % confidence interval about if the sample size, n, is . (c) construct % confidence interval about if the sample size, n, is . (d) could we have computed the confidence intervals in parts (a)-(c) if the population had not been normally distributed?
A 90% confidence interval about μ if the sample size, n, is 25 is (111.6, 118.4), a 90% confidence interval about μ if the sample size, n, is 20 is (111.1, 118.9), a 80% confidence interval about μ if the sample size, n, is 25 is (112.4, 117.6) and we need population to be normal. So we can not make intervals.
In the given question,
Sample mean, x, is found to be 115.
Sample standard deviation, s, is found to be 10.
(a) We have to construct a 90% confidence interval about μ if the sample size, n, is 25.
We need to build a 90% confidence interval. So p=0.90.
t-score for confidence interval is given by the excel code is
t=1.7109
Using these values, the margin of error is
ME = 1.7109× 10/√25
ME = 3.4
So confidence interval is
CI = (115-3.4, 115+3.4)
CI = (111.6, 118.4)
(b) We have to construct a 90% confidence interval about μ if the sample size, n, is 20.
We need to build a 90% confidence interval. So p=0.90.
t-score for confidence interval is given by the excel code is
t=1.7291
Using these values, the margin of error is
ME = 1.7291× 10/√20
ME = 3.9
So confidence interval is
CI = (115-3.9, 115+3.9)
CI = (111.1, 118.9)
(c) We have to construct a 80% confidence interval about μ if the sample size, n, is 25.
We need to build a 80% confidence interval. So p=0.80.
t-score for confidence interval is given by the excel code is
t=1.3178
Using these values, the margin of error is
ME = 1.3178× 10/√25
ME = 2.6
So confidence interval is
CI = (115-2.6, 115+2.6)
CI = (112.4, 117.6)
(d) Now we have to check, could we have computed the confidence intervals in parts (a)-(c) if the population had not been normally distributed.
To use t-distribution, the population has to be normal.Otherwise we need a sample size of at least 30. Here sample size is less than 30.
So we need population to be normal. So we can not make intervals.
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The right question is:
A simple random sample of size n is drawn from a population that is normally distributed. The sample mean, x, is found to be 115, and the sample standard deviation, s, is found to be 10.
(a) Construct a 90% confidence interval about μ if the sample size, n, is 25.
(b) Construct an 90% confidence interval about μ if the sample size, n, is 20.
(c) Construct an 80% confidence interval about μ if the sample size, n, is 25.
(d) Could we have computed the confidence intervals in parts (a)-(c) if the population had not been normally distributed.
Complete the table: Rashida bought 3 tickets to a concert for $75. Using this rate, determine how much 1 ticket will cost? and how much 5 tickets will cost? Please write the answer like it is in the block.
In this case we are multiplying the numbers and dividing them.
Fist we got to work with are numbers given the equation.
Given:
[tex]1, 5[/tex]
Therefore, the equation is:
[tex]75 / 3\\5x3[/tex]
75 / 3 = 255 x 25 = 125Therefore, the correct answers are 1 = 25, 5 = 125 and 3 = 75