(20points) Let A be a 4 x 4 matrix and let A be a eigenvalue of multiplicity 3. If A - AI has rank 1, is A defective? Explain.
Answer: No
Step-by-step explanation: If A − λI has rank 1, then the geometric multiplicity of λ is 4 − 1 = 3, equal to the algebraic multiplicity of λ.
The Matrix A is not defective.
What is the rank nullity theorem?A theorem in linear algebra known as the rank-nullity theorem states that the domain dimension of a linear map is equal to the sum of the rank (or the dimension of its image) and the nullity of the map (the dimension of its kernel).
Given:
We have A be a 4 x 4 matrix
let λ be an eigenvalue of multiplicity 3 and rank 1, then by rank nullity theorem we have
Rank(A-λI) + Nullity((A-λI) =4
dimN(N-λI) = Nullity(A-λI)
dimN(N-λI) = 4 - Rank(A-λI)
dimN(N-λI) = 4-1
dimN(N-λI) = 3
As a result, eigenvalue is made up of 3 linearly independent eigenvectors.
This guarantees that there is another eigenvalue other than since is an eigenvalue of multiplicity 3. This provides us 4 linearly independent eigenvectors in the matrix A, in addition to the 3 linearly independent eigenvectors in the eigenspace of. Now we If and only if A has n linearly independent eigenvectors, then A is diagonalizable. A thus has no defects.
Hence, matrix A is not defective.
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4. Suppose y varies directly with x. If y = 6 when x = -2, find x when y = 15.
Answer:
x is -7.5 or -14/2 or -7½
Step-by-step explanation:
- Supposing y varies directly with x
[tex] { \tt{y \: \alpha \: x}} \\ \: \: \: \: { \tt{y = kx}} [/tex]
[k is a constant of proportionality (k ≠ 0)]
- When y is 6, x is -2
[tex] \: \: \: \: \: \: \: \: \: { \tt{6 = (k \times ^{ - }2) }} \\ { \tt{6 = - 2k}} \\ { \tt{k = - 3 \: \: }}[/tex]
- Therefore, the equation is;
[tex]{ \boxed{ \tt{y = - 2x}}}[/tex]
- What is x when y is 15
[tex]{ \tt{15 = - 2x}} \\ { \tt{x = - 7.5}}[/tex]
The value of x is -5
The equation for a direct variation is y = kx, where k is the constant of variation. Since we know that y = 6 when x = -2, we can solve for k:
k = y/x
k = 6/-2
k = -3
Therefore, the equation for this direct variation is y = -3x. To find x when y = 15, Substitute k = -3 and y = 15 into the equation
15 = -3x
Then solve x,
x = [tex]\frac{-15}{3}[/tex]
x = -5
Therefore, when y = 15, x = -5.
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An airplane covers 50 miles in 1 hour. How many miles can the airplane cover in 1/2 an hour
If f(x) = 3x + 1
Find f(-4)
The line of best fit is given as y = -2 - 2x. Find the value of y when x = 2.
A. Find m
B. Using the answer above, Find m
Answer:
∠ b = 108° , ∠ d = 72°
Step-by-step explanation:
(a)
the sum of the 3 angles in a triangle = 180° , that is
∠ a + ∠ b + ∠ c = 180°
25° + ∠ b + 47° = 180°
∠ b + 72° = 180° ( subtract 72° from both sides )
∠ b = 108°
(b)
the exterior angle of a triangle is equal to the sum of the 2 opposite interior angles , then
∠ d = ∠ a + ∠ c = 25° + 47° = 72°
Which inequality matches the graph? X, Y graph. X range is negative 10 to 10, and y range is negative 10 to 10. Dotted line on graph has positive slope and runs through negative 3, negative 8 and 1, negative 2 and 9, 10. Above line is shaded. a −2x + 3y > 7 b 2x + 3y < 7 c −3x + 2y > 7 d 3x − 2y < 7
The inequality equation of the given description of the inequality graph is; 3x - 2y < 7
What is the inequality of the graph?Given :
X range is negative 10 to 10, and Y range is negative 10 to 10.
Dotted line on graph has positive slope and runs through points: (-3,-8), (1,-2), and (9,10).
Now, since we know the coordinates through which the graph runs, we can pick two coordinates and use it to find the slope through the formula;
m = (y₂ - y₁)/(x₂ - x₁)
If we pick (-3,-8), (1,-2), we have;
m = (-2 - (-8))/(1 - (-3)
m = 6/4
m = 3/2
We will use formula for equation of a line in point slope form to get;
y - y₁ = m(x - x₁)
y - 10 = (3/2)(x - 9)
2y - 20 = 3x - 27
3x - 2y = 7
Because, above the line is shaded, therefore, the correct inequality matching the graph is 3x - 2y < 7
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Drag and drop a statement or reason to each box to complete the proof. Given: parallelogram MNPQ Prove: ∠N≅∠Q Parallelogram M N P Q with diagonal M P drawn. Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse. Statement Reason parallelogram MNPQ Given MN¯¯¯¯¯¯¯≅QP¯¯¯¯¯MQ¯¯¯¯¯¯≅NP¯¯¯¯¯¯ Response area Response area Response area △MQP≅△PNM Response area Response area CPCTC
After solving the problems the answers obtained are MN ≅ QP and MQ ≅ NP, MP ≅ MP, Δ MQP ≅ Δ PNM, ∠ N ≅ ∠ Q.
What is Parallelogram?The phrase "parallelogram" is a translation of the Greek phrase "parallelogrammon," which means "bound by the contract by parallel lines." As a consequence, a quadrilateral that is bordered by parallel lines is called a parallelogram. It has parallel and equal opposite sides on all sides.
1. According to the parallelogram's feature that its opposed sides are congruent, the opposite sides of the given parallelogram MNPQ,
So, MN ≅ QP and MQ ≅ NP.
2. According to the reflexive feature of congruence, a line or other geometric figure is both a reflection of and consistent with itself. Therefore, in the example of the parallelogram MNPQ,
So,
MP ≅ MP
3. The SSS congruence postulate, which stands for Side-Side-Side congruence postulate, argues that when three adjacent sides of two triangles are congruent, the two triangles are congruent. As the sides MNQ, MQ, NP, and MP are in the given parallelogram MNPQ
Hence,
Δ MQP ≅ Δ PNM
4. Part 4 demonstrated that MQP and PNM are congruent, hence in accordance with a CPCTC property,
∠ N ≅ ∠ Q
5. The acronym CPCTC stands for congruent portions of congruent triangles.
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In one day, 500 people played a fairground game.
The relative frequency of winning the game was
0.38
How many times was the game won that day?
Answer:
190
Step-by-step explanation:
500x0.38=190
I just see it that way
PLEASEEEEEEEEEEE HURRY WILL GIVE BRAINLYEST
The proportion to calculate triangle side LM in the given triangle is 3/2
How to calculate the side LMThe side LM is calculated using the idea of similar triangle, in this case the triangles are equal in proportion to each other
To find the proportion we take the ratio of the sides this is done as follows
LM / HJ = MN / JK = LN / HK
substituting the values
MN / JK = 9 / 6 = 3 / 2
the proportion is = 3/2
to find LM
4.5 * 3/2
= 6.75 cm
Using proportion of 3/2 the length of side LM is solved to be 6.75 cm
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#7
Write an equation in
slope-intercept form of
the line shown.
Please help
Answer:
y = -x - 4
Step-by-step explanation:
m = y2-y1 / x2-x1
(-4, 0) and (1, -5)
m = -5+0 / 1+4
m = -5 / 5
m = -1
y = -x + b
0 = -(-4) + b
0 = 4 + b
b = -4
y = -x - 4
Analyze the data with a nonparametric test and comment on the results and write a conclusion.
Rank in Weight Rank in Dominance Hierarchy
1 3
2 4
3 1
4 8
5 7
6 2
7 5
8 6
9 9
OR
7C
Here are some data based on a study by St. Leger, et al. (1978 and described in Howell, 1995). The data come from 10 countries. One variable is the number of physicians per 10,000 population. The other variable is an infant mortality rate that is adjusted so that the wealth of the country is not being measured. Analyze the data with a nonparametric test and comment on the results and write a conclusion.
Physicians Rank Mortality Rank
1 2
2 1
3 4
4 3
5 6
6 5
7 9
8 8
9 10
10 7
On solving the provided question, we can say that - correlation coefficient , r= .95
What is correlation coefficient ?The Pearson's correlation coefficient, also known as the Pearson's r, Pearson's product-moment correlation coefficient, bivariate correlation, or simply correlation coefficient, is a statistical indicator of the linear relationship between two sets of data.
[tex]S_{xx}[/tex] = ∑[tex]x^2[/tex] + [tex]nx^2[/tex] = 60
[tex]S_{yy} = 60[/tex]
r = .95
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Jim has to choose between two gym membership plans. Plan A: $50 monthly membership fee and $10 per visit. Plan B: $25 one time membership fee and $15 per visit. How many visits must Jim make to make Plan A the cheaper option?
How many visits for them to cost the same?
The number of visits Jim must make to make Plan A the cheaper option is 6 and 5 visits will cost the same.
How to form an equation?Determine the known quantities and designate the unknown quantity as a variable while trying to set up or construct a linear equation to fit a real-world application.
Suppose n number of visits will make plan A cheaper than B.
The total cost of A < total cost of B
50 + 10n < 25 + 15n
15n - 10n > 50 - 25
5n > 25
n > 5
n = 6
At n = 5
Total cost of A = 50 + 10 x 5 = $100
Total cost of B = 25 + 15 x 5 = $100
Hence "Jim needs to visit 6 times, and 5 visits will cost the same, for Plan A to be more affordable".
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Bela"s globe has great 12 parallels and 12 great meridians, breaking the surface into many parts. Bela and Jenn each pick one of these parts uniformly at random. What is the probability they pick the same part
The probability that Bela and Jenn pick the same part is; 0.006944
What is the probability of selection?In maps, it is pertinent to note that parallels are the lines that run from east to west and never intersect with each other while meridians run from north to south and intersect at the north and south poles.
Now, since bella's globe has 12 parallels and 12 great meridians, then it means that the total number of parts in this globe will be 12 * 12 = 144 parts.
Thus, probability that they both pick the same part is;
P(same part picked) = (12/144) * (12/144)
= 0.006944
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A survey was given to people who own a certain type of car. What percent of the people surveyed were completely satisfied with the car?
Write the tangent equation to solve for angle f
Answer:
Tan(f) = 24/7
Step-by-step explanation:
Tan is opposite over adjacent.
The opposite of angle F is 24 and the adjacent is 7.
A pipeline has to be laid along the boundry of the garden.What do we need to know to find the total length of the pipe needed
Answer:
length and breadth
Step-by-step explanation:
Since the pipeline has to be laid along the boundary of the garden, we need to know the perimeter of the garden. Here, the two variables necessary are length (l) and breadth (b). Hence we need to know the length and breadth in order to find the total length of the garden
Answer:
Step-by-step explanation:
To find the total length of the pipe needed to lay a pipeline along the boundary of a garden, you would need to know the following information:
The shape of the garden: The total length of the pipe needed will depend on the shape of the garden. For example, a rectangular garden will require less pipe than a circular garden of the same size.
The dimensions of the garden: Knowing the dimensions of the garden (such as its length, width, and perimeter) will allow you to calculate the total length of the pipe needed.
The diameter of the pipe: The length of the pipe needed will depend on the diameter of the pipe being used. A larger diameter pipe will require more length than a smaller diameter pipe.
The spacing between the pipes: If the pipes are being laid side by side, the total length of the pipe needed will depend on the spacing between the pipes. If the pipes are being laid end to end, the spacing between the pipes will not affect the total length of the pipe needed.
Any curves or corners in the garden: If the garden has curves or corners, the total length of the pipe needed will be greater than if the garden were a straight line. You will need to account for the additional length needed to bend the pipes around the curves or corners.
m/JHI =(2x+7)° and m/GHI = (8x - 2)° and m/JHG= 65°. Find m/JHI and m/GHI
The value of m/JHI and m/GHI is angle 19 and 46.
What is angle ?
An angle is a figure in Euclidean geometry made up of two rays that share a common terminal and are referred to as the angle's sides and vertices, respectively. Angles created by two rays are on the plane where the rays are located. The meeting of two planes also creates angles. Dihedral angles are these.
[tex]\begin{aligned}2 x+7+8 x-2 & =65 \\10 x+5 & =65 \\10 x & =60 \\x & =6\end{aligned}[/tex]
m/JHI =(2x+7) = (2* 6+7)=12+7=19.
m/GHI = (8x - 2)° = (8*6-2)=48-2=46
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Consider the problem of computing (xy)for given integers x and y: we want the whole answer.We know two algorithms for doing this: the iterative algorithm which performs (y - 1) multiplications by x; and the recursive algorithm based on the binary expansion of y.Compare the time requirements of these two algorithms, assuming that the time to multiply an n-bit number by an m-bit number is O(mn).
The recursion tree is log2m and has log2m nodes .
A recursive algorithm calls itself with smaller input values and returns the result for the current input by carrying out basic operations on the returned value for the smaller input.
A iterative method is a mathematical procedure that uses an initial value to generate a sequence of improving approximate solutions for a class of problems, in which the n-th approximation is derived from the previous ones.
In the analysis of algorithms, the master theorem for divide-and-conquer recurrences provides an asymptotic analysis for recurrence relations of types that occur in the analysis of many divide and conquer algorithms.
Two integers x and y are given. x and y require n bit and m bit respectively. Two algorithms to compute x y need to be analyzed.
Iterative: The pseudocode for this algorithm is as follows.
product = x;
for i = 2 to y do
product = product * x
The result after the multiplication of two integers, one p bits long and another one q bits long requires p q bits to to store. Therefore, for a given i , we are multiplying one ( i − 1)n bits long integer with an n bit long integer. This multiplication cost is ( i − 1)n2 .
The resulting number after the multiplication is i.n bits long. Thus
adding up all the multiplication cost we get
n2 + 2n2 + 3n2 + . . . + (y − 1)n2. Thus the complexity of the iterative algorithm is O(n2y2) which exponential in
the input length of y which is m = log2 y.
Recursive: The pseudocode for this algorithm is as follows:
function recursive (x ,y)
if y is even then return (x(by2c))2
if y is odd then return x ∗ (x(by2)c)2.
Computing (x(by2c))2
requires a multiplication involving two y2
n bits integers. The cost of this operation is y24.n2 which is O(y2n2). The recurrence relation for this
recursive routine is
T(y) = O(n) when y is 1-bit long.
T(y) = T(y2) + O(y2n2) otherwise.
Applying the Master Theorem we can conclude that T(y) ∈ O(y2n2). The height
of the recursion tree is log2m and has log2m nodes.
Thus both the algorithms have the same worst case complexity.
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Two integers x and y are given. x and y require n bit and m bit respectively. Two algorithms to compute x y need to be analyzed.
product = x;
for i = 2 to y do
product = product * x
The result after the multiplication of two integers, one p bits long and another one q bits long requires p q bits to to store. Therefore, for a given i , we are multiplying one ( i − 1)n bits long integer with an n bit long integer. This multiplication cost is ( i − 1)n2 .
n2 + 2n2 + 3n2 + . . . + (y − 1)n2. Thus the complexity of the iterative algorithm is O(n2y2) which exponential in
the input length of y which is m = log2 y.
function recursive (x ,y)
if y is even then return (x(by2c))2
if y is odd then return x ∗ (x(by2)c)2.
Computing (x(by2c))2
requires a multiplication involving two y2
n bits integers. The cost of this operation is y24.n2 which is O(y2n2). The recurrence relation for this
recursive routine is
T(y) = O(n) when y is 1-bit long.
T(y) = T(y2) + O(y2n2) otherwise.
Thus both the algorithms have the same worst case complexity.
Diego says that x=5 is a solution to -3 x>9 because when you divide both sides by -3, you get x>-3.
Is this correct?
Yes No I'm not sure
Giving BRAINLIEST to the correct answer! ASAP please <3
The solution is
a) Option A.
The equation to determine the messages sent by Bria is t/4 = 20
b) Option C.
The student is 1.25 feet above sea level , and the absolute value is 1.25 ft
c) Option C.
The values are opposites of each other , and they are both 5/2 units from zero
What is an Equation?
Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the equation be represented as A
Now , the value of A is
a)
Let the number of texts sent by Bria be = t
The number of texts sent by April = 20
April sent one fourth of the texts sent by Bria
So ,
The number of texts sent by Bria t = 4 x number of texts sent by April
Substituting the values in the equation , we get
The number of texts sent by Bria t = 4 x 20
Divide by 4 on both sides of the equation , we get
t/4 = 20 be equation (1)
And , t = 80 texts
Therefore , the number of texts sent by Bria is given by the equation
t/4 = 20
b)
Let the sea level be represented as = 0
The number 1.25 is above the sea level of 0
The absolute value of 1.25 is = 1.25
Therefore , the expression will be the student is 1.25 ft above the sea level and the absolute value is 1.25 ft
c)
Let the first number be = -5/2
Let the second number be = 5/2
Now , the difference of the numbers from the point zero = 5/2 units
Because the distances are always positive
The numbers -5/2 and 5/2 are opposite numbers
Hence , the expression will be the numbers are opposites of each other and they are 5/2 units from 0
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Choose Yes or No to tell whether the fraction and percent are equivalent.
40/1000 and 40%
6/5 and 120%
50/33 and 117%
1/8 and 12.5%
How do fractions 1/4 and 1/8 compare
Answer the questions below about the quadratic function
f(x)=-x^2-10x-27
a) Does the function have a minimum or maximum value?
b) What does the functions minimum or maximum value?
c) Where does the minimum or maximum value occur?
Answer:
a) The function has a minimum value.
b) The minimum value of the function is -27.
c) The minimum value occurs at x=3.
Step-by-step explanation:
What is the missing number, what property did you use? 0=–––×3×4
Answer:
0, zero product property
Step-by-step explanation:
Consider the polynomial g(x) = 4x³ - x2 - 24x+6
a. List all possible rational zeros of the polynomial. (Assume all numbers shown are both + and -).
O1, 2, 4, 1/2, 1/3, 2/3, 4/3, 1/6
1, 2, 3, 4, 6, 1/2, 3/2, 1/3, 2/3, 4/3, 1/4, 3/4, 1/6
O 1, 2, 3, 4, 6, 1/2, 3/2, 1/4, 3/4
O1, 2, 3, 6, 1/2, 3/2, 1/4, 3/4
b. List all actual zeros of the polynomial (rational, irrational, real, and complex).
Give exact answers, separated by commas as necessary.
Zeros:
Answer:
a. x = 1/4
b. x = [tex]+\sqrt{6}[/tex], [tex]-\sqrt{6}[/tex], 1/4
Step-by-step explanation:
a. I factorised the polynomial.
[tex]g(x) = 4x^3 - x^2 -24x +6 = 0[/tex]
[tex]-x^2 (-4x + 1) +6 (-4x +1)[/tex]
[tex](-4x+1)(-x^2+6)[/tex]
Solved for the roots.
[tex]-4x + 1 = 0[/tex]
[tex]-4x = -1[/tex]
[tex]x = \frac{1}{4}[/tex]
[tex]-x^2+6 = 0[/tex]
[tex]-x^2 = -6[/tex]
[tex]x^2 = 6[/tex]
[tex]x = +\sqrt{6}[/tex]
[tex]x=-\sqrt{6}[/tex]
A rational number is a real number that's digits terminate and/or repeat. Therefore, 1/4 is the only rational zero.
b. All of the zeros we found in part A. are [tex]+\sqrt{6}, -\sqrt{6}, and \frac{1}{4}[/tex]
PLEASE HELP ILL DO ANYTHING
20. A triathlon is about 51 kilometers. One participant completed
two of the three legs of the race and traveled 42 kilometers.
Solve the equation 42+ d = 51 for the distance, d, of the
third leg of the race.
21. Analyze and Persevere w
Answer:
d=9
Step-by-step explanation:
42 km is 2 of the 3 legs
51 is the total triathlon
51 - 42 = 9
Need help with this question for my practice
Answer:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex] and [tex]m=\frac{-5-3}{12+4}[/tex]
Step-by-step explanation:
The correct formula for finding the slope is:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
This formula represents the change in y over a corresponding change in x. This is a mathematical representation of "rise" (y-axis movement) over "run" (x-axis movement).
For the second question, let
[tex](x_1,y_1)=(-4,3)\\(x_2,y_2)=(12,-5)[/tex]
So,
[tex]m=\frac{(-5)-(3)}{(12)-(-4)}\\m=\frac{-5-3}{12+4}[/tex]
A bag contains 1 gold marbles, 6 silver marbles, and
28 black marbles. Someone offers to play this game:
You randomly select one marble from the bag. If it
is gold, you win $3. If it is silver, you win $2. If it is
black, you lose $1.
What is your expected value if you play this game?
Step-by-step explanation:
the expected value is the sum of all values multiplied by their corresponding probabilities.
and a probability is always
desired cases / totally possible cases.
in the bag are
28 + 6 + 1 = 35 marbles
the probability to pull the gold is
1/35
the probability to pull a silver is
6/35
the probability to pull a black is
28/35 = 4/5
the expected value = $3×1/35 + $2×6/35 - $1×28/35 =
= 3/35 + 12/35 - 28/35 =
= -13/35 = -0.371428571... ≈
≈ -$0.37
that means (like with all games of that kind like all casino games) the bank will win in the long run.
your only chance to win is to play very few times and get a winner by pure chance. the longer you play you might actually hit a winner somewhere in between, but the surer you still lose in total.
Use distributive property to solve 4/7x4 5/8
Applying distributive property of multiplication the solution of the multiplication problem is 5 11/56
What is distributive property of multiplication?The distributive property states that multiplying the total of two or more addends by a number produces the same outcome as multiplying each addend separately by the number and adding the products together.
This applied mathematically in the problem
4/7 x 4 5/8
dividing by 4 for the multiplicand and multiplier
4/7 ÷ 4 = 1/7
4 5/8 ÷ 4 = 37/32
4/7 x 4 5/8
= 4 * (1/7 + 37/32) - distributive property applied
= 4 * (291/224)
= 291 / 56
= 5 11/56 as mixed number
using distributive property the solution of the multiplication is 5 11/56
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