An n x n matrix a with an eigenvalue of multiplicity n is diagonalizable if and only if a = i, where i is the identity matrix.
Suppose a is diagonalizable. Then there exists an invertible matrix P such that a = PDP^(-1), where D is a diagonal matrix. Since a has an eigenvalue of multiplicity n, the diagonal entries of D are all equal to that eigenvalue. Therefore, a = PDP^(-1) = P(lambda I)P^(-1) for some scalar lambda. But since the eigenvalue has multiplicity n, lambda must equal the eigenvalue, which implies that D = lambda I. Therefore, a = [tex]P(lambda I)P^(-1) = PDP^(-1)[/tex] = P(lambda I)P^(-1) = lambda PPP^(-1) = lambda I. Thus, a = lambda I, and since the eigenvalue has multiplicity n, we have lambda = 1. Therefore, a = i.
Conversely, suppose a = i. Then a is trivially diagonalizable, since any matrix is diagonalizable if and only if it is already diagonal. Therefore, a is diagonalizable, and the proof is complete.
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Write an equation of the line that passes through (2, 0) and is perpendicular to the line
y = -x-3.
An equation of the perpendicular line is y =
Answer:
y =x - 2
Step-by-step explanation:
If the slope of the line is 'm', then the slope of the perpendicular to the given line = [tex]\sf \dfrac{-1}{m}[/tex] (opposite reciprocal)
y = -x - 3
Compare with equation of line in slope y-intercept form: y = mx +b
m = -1
[tex]\sf \text{Slope of the perpendicular line = $-(\dfrac{1}{-1})= 1$}[/tex]
This line passes through (2, 0);
Equation of the line in slope - point form:
[tex]\sf y - y_1 = m(x - x_1)[/tex]
y - 0 = 1 (x - 2)
y = x - 2
When preparing a representative sample from a list of 200 customers who complained about errors in their statements, a _____ might select every tenth customer for review. a. stratified sample b. comprehensive sample c. random sample
When preparing a representative sample from a list of 200 customers who complained about errors in their statements, a systematic sample might select every tenth customer for review.
What is systematic random sampling?Systematic random sampling is known to be a form of a random sampling method that needs one to select samples using a system of intervals where one has ranges of numbered population.
Note that When preparing a representative sample from a list of 200 customers who complained about errors in their statements, a systematic sample might select every tenth customer for review.
See options below
a. stratified sample
b. comprehensive sample
c. random sample
d. Systematic sample
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Use the scale of 1cm=45 km
The actual distance between two cities is 333 km. What is the distance between them on the map
Answer:
d = 7.4 cm is the distance between the two cities on the map.
Step-by-step explanation:
Let d = the distance measured on the map in centimeters (cm) between any two locations and let D be the actual distance in kilometers (km) between these same two locations.
Since the scale on the map is 1 cm = 45 km, then the ratio of the distance on the map to the actual distance is equal to 1cm/45 km; therefore the quotient of any measured distance d on the map divided by the corresponding much longer actual distance D would have to maintain (equal) this same ratio; In other words, we can set up the following proportion to solve for d given the actual distance D = 333 km as follows:
1 cm/45 km = d/D
Substituting, we get:
1 cm/45 km = d/333 km
d/333 km = 1 cm/45 km
(d/333 km)(333 km) = (1 cm/45 km)(333 km)
d = (333 km/45 km)(1 cm)
d = 7.4 cm is the distance between the two cities on the map.
Check:
1 cm/45 cm = d/333 km
1 cm/45 cm = 7.4 cm/333 km
1 cm/45 cm = 1 cm/45 km (Therefore, the distance ratio of the map has been maintained
how many 3cm cubes can be put in a box 3cm long 6cm wide 12cm high?
Answer:
8
Step-by-step explanation:
A cube is equal on all sides. Therefore the cubes must be 3cm x 3cm x 3cm. Therefore, each cube has an area of 27cm^3. The box that the cube has an area in is 3cm x 6cm x 12 cm which = 216cm^3. If you do [tex]216cm^3/27cm^3 = 8 cubes[/tex]
22. If 1 m,m/19 - 118°, and m/16 - 48°, calculate m/12.
0 0
103"
98
109⁰
110"
18
17
19 20
14
16
13
15
11
10
12
9
63
5
m
Answer: Option 4
Step-by-step explanation:
[tex]m\angle 20=62^{\circ}[/tex] (linear pair)
[tex]m\angle 11=70^{\circ}[/tex] (angle sum in a triangle)
[tex]m\angle 12=110^{\circ}[/tex] (linear pair)
Does the expected value of a random variable have to equal one of the possible values of the random variable? explain
No, just like the average (mean) it is a mathematical quantity that is determined by its mathematical definition and the everyday meaning of “expected” is only a descriptive hint toward what it represents.
What does the expected value of a random variable mean?
E[X] stands for the expected value of a random variable. The expected value of a random variable is also known as its mean, in which case we use the notation X. It can be thought of as the "average" value obtained by the random variable.Is the expected value always equal to the mean?
The primary distinction between "mean" and "expected value" is that the former is typically used to describe a frequency distribution and the latter, a probability distribution. In frequency distribution, variables and their occurrence frequencies make up the sample space.Learn more about expected value of a random variable brainly.com/question/22435257
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HELP ASAP AND GET 20 POINTS!!!
Answer:
A
Step-by-step explanation:
point H is the point of intersection of the perpendicular bisectors of the triangle's sides and is the circumcentre.
Answer:
A. Circumcenter
Step-by-step explanation:
this is the point that has the same distance from all 3 vertexes.
being on the median line of DE, every point of that line has the same distance to D and E.
being also on the median line of FE means it has the same distance from F and E as every other point on that line.
and the same for DF.
H as the crossing point of all 3 median lines is the only point that has the same distance to D, E and F.
so, H is the center of a circle that goes through all 3 points.
Use vector operations to draw the resultant vector. Draw u – v + w
Based on the above, the graph of the resultant vector is shown in the image attached (x-axis).
What is the graph about?In the graph construction, We need to carry out a sum of vectors and then draw the resultant vector.
Note that the resultant vector need to be <4, 0>
Hence when we view the graph attached, we can say that the vectors areas:
w = <3, 3>
u = <-3, -4>
v = <-4, -1>
So, the sum = u - v + w
Note also that in the sum of the vectors we need to add and subtract the correspondent parts and it will be:
u - v + w
= <-3, -4> - <-4, -1> + <3, 3>
= <-3 + 4 + 3, -4 + 1 + 3>
= <4, 0>
Therefore, Based on the above, the graph of the resultant vector is shown in the image attached (x-axis).
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Triangle JKL is graphed on the coordinate plane. -5 -4 -3 y B MD N In L 2 4 5 X What are the coordinates of its image, JKL, if this triangle is dilated by a factor of 5 with respect to the origin? O J(2, 7), K (8, 7), and L'(5, 1) O J'(-5, 2), K'(5, 2), and L'(0, -5) O J'(-3, 2), K'(8, 2), and L'(0, -9) O J'(-15, 10), K'(15, 10), and L'(0, -20)
The coordinate of the image of JKL when dilated by a factor of 5 with respect to the origin is J'(-15, 10), K'(15, 10) and L'(0, 20).
What is transformation?Transformation is the movement of a point from its initial location to a new location. Types of transformations are reflection, rotation, translation and dilation.
Translation is the movement of a point either up, left, right or down in the coordinate plane.
Let us assume that triangle JKL has vertices at J(-3, 2), K(3, 2) and L(0, 4).
The coordinate of the image of JKL when dilated by a factor of 5 with respect to the origin is J'(-15, 10), K'(15, 10) and L'(0, 20).
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O 40
O 13
O 80
05
R
T
8x
12x + 20
I am thinking of a two digit number.it is smaller then 5 tens but greater then 4 tens. its ones digit is 3 more than its tens digit.what number am i thinking of?
The two digit number larger than 40 and lesser than 50, and the difference between the ones and tens digits gives the two digit number as 41
How can the two digit number be found?Let XY represent the two digit number;
From the question, we have the following inequalities and equations;
40 < XY < 50X = Y + 3Therefore;
4 ≤ X < 5Y > 0Which gives;
4 ≤ Y + 34 - 3 = 1 ≤ YY = 1
X = 4
Therefore;
XY = 41The two digit number, XY = 41
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If t = 18 and r = 12, find S. Round to the nearest tenth.
Answer:
13.4 or √180
Step-by-step explanation:
Pythagorean theorem states
a² + b² = c²
C^2 is the longest side. The corner of the right angle points to it. The other sides are your a and b squared. They are called the legs or Opposite and Adjacent sides.
Answer: S ≈ 48.2°
Step-by-step explanation:
We can use trigonometry functions to solve.
Looking at angle S, t = 18 is the hypotenuse and r = 12 is the adjacent side. This means we can use the cosine function.
[tex]\displaystyle cos(S) = \frac{\text{adjacent side}}{\text{hypotenuse }}=\frac{12}{18}[/tex]
[tex]\displaystyle cos^{-1} (cos(S)) = (\frac{\text{adjacent side}}{\text{hypotenuse }}=\frac{12}{18})cos^{-1}[/tex]
[tex]S = 48.189685...\\S \;$\approx$\; 48.2^{\circ}[/tex]
HELP !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! I well give 100 point and a crown but need to be answer in less then 20 mins
If I have 419 assignments to do and i have pleated completed 79 how much work will I need to do every day to finish in one week
Answer:
Step-by-step explanation:
419-79= 340 assignments left to do
340/7days=48.57..... or about 46 assignments a day to finish them all in a week
(1 week= 7 days)
I don't know if you were serious but good luck with all the work if you are
Answer:
47 on 6 days and 48 on 1 day.
Step-by-step explanation:
Firstly you need to subtract 79 from 419. You will have 330 assignments left and the divide 330 by 7 since there are 7 days in a week and you get 47.142 and so if you double check by multiplying 47 times 7 it gives 329 so then you get 47 on 6 days and 48 on 1 day. Hope this helps!
2x - y = 4
y = 2x + 4
Solution(s):
PLEASEEE
I NEED HELP W THIS QUICK FIRST TO ANSWER CAN HAVE BRAINLIEST I GUESS
i added more pts cus idrc for em
Answer:
1. Multiply the slope by 2 and look at the numerator
2. 5/7
3. slide A
4. The run of slide a is shorter which means that its steeper because the rise is the same
5. 10
6. 5 units?
Step-by-step explanation:
#1
We would use the slopeWe know
slope=tanØ
Here in slide B
tanØ=5/9But
tanØ=Ladder/18Then
9Ladder=90Ladder=90/9=10ft#2
The slope of slide A
tanØ=15/21tanØ=5/7#3 and 4
Compare tangents
tan(5/7)>tan(5/9) as their difference is +veSlide A is steeper
#5
Found in #1
#6
Slide A is higher as 15>10
There are 4 books on a shelf. books are added to the shelf at a rate of 2 books per minute. the total number of books on the shelf, y, is a function of the number of minutes, x, that the books have been added to the shelf. write an algebraic equation for the function.
The algebraic equation to represent the given situation is as follows,
y = 4 + 2x
What is an algebraic equation?
The term "algebraic equation" refers to a formulation of the equality of two expressions using the algebraic operations of addition, subtraction, multiplication, division, raising to a power, and extraction of a root on a set of variables.
An expression that includes variables, constants, and algebraic operations is known as an algebraic expression in mathematics (addition, subtraction, etc.).
Forming the Algebraic Equation
Number of book present on the shelf initially = 4
It is given that 2 books are added per minute to the shelf.
If x is the number of minutes, then the books added will be 2x.
If y is the total number of books present on the shelf, then the algebraic equation is given as,
y = Number of books initially present on the shelf + 2x
⇒ y = 4 + 2x
Thus, y = 4 + 2x is the required algebraic equation.
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. An automobile license plate number issued by a certain state has 6 character positions. Each of the first 3 positions contains a single digit from 0 through 9. Each of the last 3 positions contains 1 of the 26 letters of the alphabet. Digits and letters of the alphabet can be repeated on a license plate. How many different such license plate numbers can be made
Answer:
17,576,000
Step-by-step explanation:
3 digits followed by 3 letters
Draw an underline character for each position with multiplication signs in between them.
_ × _ × _ × _ × _ × _
Now fill in each blank with the number of characters that can be used in that position. The first three blanks are used with digits, 0 through 9. There are 10 digits 0 through 9.
10 × 10 × 10 × _ × _ × _
For the last three blanks, each one gets a letter from A through Z. There are 26 letters to choose from fore each of the last three blanks.
10 × 10 × 10 × 26 × 26 × 26 = 17,576,000
Ummm can y’all solve these problems I’ll give extra points for this
Pls solve step by step and label which is which
What is the slope of a line that passes through the point (-3,0) and has a y-intercept of 12
The slope of a line that passes through the point (-3,0) and has a y-intercept of 12 is 4.
How to find the slope of a line?Using the point slope equation,
y = mx + b
where
m = slopeb = y-interceptTherefore, using (-3, 0)
0 = -3m + 12
-12 = -3m
divide both sides by -3
m = -12 / -3
m = 4
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If a movie starts at 13:35 and it lasts 1 hour and 27 minutes. What time does it end at?
Answer:
15:02 or 3:02 pm
Answer:
[tex]13.35 + 1.27 = 14.62 \\ \\1 hr = 60min \\ 62 min- 60min =2min \\ 14hr + 1hr = 15hr \\ \\it \: ends \: at \: 15.02[/tex]
An airplane covers 3450 km in an hour. how much distance will it cover in 7 hours?
Answer:
24,150km
Step-by-step explanation:
The plane travels 3450km in 1 hr, since we need the distance traveled in 7 hrs we need to multiply 3450 by 7.
distance in 7hrs: 3450*7 = 24,150km
Service organizations are often ideally suited for activity-based costing. In no less than 200 words, explain why the previous statement is true and discuss what some of the special considerations are in the design of cost accounting systems for service organizations
Service organizations are ideally suited for activity-based costing because virtually all of the costs for a service company are indirect and appear to be fixed.
What is activity-based costing?Activity-based costing is a method of assigning overhead and indirect costs such as salaries and utilities to products and services.
The ABC system of cost accounting is based on activities that are considered any event, unit of work, or task with a specific goal.
Here, activity-based costing has been used in manufacturing products but can also be applied to service industries, or businesses that provide a service instead of a product.
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1. sonya's salary increases at a rate of 4% per year. her starting salary is $45,000. what is her annual salary, to the nearest $100, after 8 years of service?
Her annual salary after 8 years will be $57,600.
What is the percentage?A percentage is a figure or ratio stated as a fraction of 100 in mathematics. It is frequently symbolized with the percent sign, " %". A % is a number with no dimensions; it has no unit of measurement.To find what is her annual salary, to the nearest $100, after 8 years of service:
Find 4% of 45,000
[tex]\frac{x}{45000} *100=4\\\frac{x}{450} =4\\x =1800[/tex]
So, 4% of $45,000 of $1800.
1st year = $45000
2nd year = 45000 + 1800 = $46800
3rd year = 46800 + 1800 = $48600
4th year = 48600 + 1800 = $50400
5th year = 50400 + 1800 = $52200
6th year = 52200 + 1800 = $54000
7th year = 54000 + 1800 = $55800
8th year = 55800 + 1800 = $57600
Therefore, her annual salary after 8 years will be $57,600.
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The salary of Sonya after 8 years will be $61,600 (nearest $100).
What is compound interest?The interest on the a loan or deposit that is calculated using the both initial principal as well as the accrued interest from prior periods is known as compound interest (sometimes known as compounding interest).
Some features of compounding are-
Compound interest is calculated just on initial principal of a deposit or loan, which also takes into account all of the interest accrued from prior periods.The yearly interest rate is raised to a number of compounded periods minus one, and the starting principal amount is multiplied by both of these factors.The frequency plan for compounding interest can be set to be continuous, daily, or yearly.The quantity of compounding periods has a bigl impact on compound interest calculations.Calculation for the amount after 8 years-
The principal amount is $45,000
Rate of interest is 4% per year.
Time duration is 8 years.
The formula for total amount after compounding is -
[tex]A=P\left(1+\frac{r}{n}\right)^{n t}[/tex]
A = final amount
P = initial principal balance
r = interest rate
n = number of times interest applied per time period.
t = number of time periods elapsed.
As the rate of interest is applied only one in a year ; n = 1.
Substitute the values in the formula to get the value.
[tex]A=45,000\left(1+\frac{.04}{1}\right)^{8}\\A=45,000\left(1.04}\right)^{8}\\\\A=61585.60[/tex]
Therefore, the salary of Sonya will be $61600 (nearest $100) after 8 years.
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Use the quadratic model y=-4x^2-3x+4 to predict y if x equals 5
Answer:
y = -4x^2 - 3x + 4
x = 5
y = -4(5)^2 - 3(5) + 4
y = -4(25) - 15 + 4
y = -100 - 15 + 4
y = -114
Step-by-step explanation:
rationalize the denominator !!!
please need help giving brainliest to all recent questions asked on my profile!!
Answer:
[tex]\frac{1\cdot \left(4+\sqrt{3}\right)}{\left(4-\sqrt{3}\right)\left(4+\sqrt{3}\right)}\\[/tex]
[tex]1\cdot \left(4+\sqrt{3}\right)=4+\sqrt{3}[/tex]
[tex]\left(4-\sqrt{3}\right)\left(4+\sqrt{3}\right) = 13[/tex]
[tex]= \frac{4+\sqrt{3}}{13}[/tex]
x = 4
y = 3
z = 13
Answer:
x = 4, y = 3, z = 13
Step-by-step explanation:
Multiply the equation by the opposite of the denominator
[tex]\frac{(1)(4 + \sqrt{3}) }{(4-\sqrt{3})(4+\sqrt{3} ) } \\\\\frac{4 + \sqrt{3} }{16 - 4\sqrt{3} +4\sqrt{3} -3} \\\\= \frac{4+\sqrt{3} }{13}[/tex]
h(n) = 41 - 5n
Complete the recursive formula of h(n).
h(1) =
h(n) = h(n-1)
The recursive formula of h(n) is h(1) = 36 and h(n) = h(n -1) - 5
How to determine the recursive formula?The function is given as:
h(n) = 41- 5n
Calculate h(1) and h(2)
h(1) = 41- 5(1)
h(1) = 36
h(2) = 41- 5(2)
h(2) = 31
Calculate the difference between h(1) and h(2)
d = 31 - 36
d = -5
This means that:
h(1) = 36 and h(n) = h(n -1) - 5
Hence, the recursive formula of h(n) is h(1) = 36 and h(n) = h(n -1) - 5
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2. Two rectangular lots are adjacent to each other, as shown in the diagram below. Using a function operation, determine how many times bigger the large lot is than the small lot. Clearly identify the individual component functions and simplified final equation.
The large rectangle is 8/3 times bigger than the small rectangle.
How to explain the area?Area of large rectangle will be:
= 4x(2x - 2)
= 8x² - 8x
Area of small rectangle will be:
= (3x - 3)x
= 3x² - 3x
The ratio will be:
= 8x² - 8x/3x² - 3x
= 8(x² - x)/3(x² - x)
= 8/3
The large rectangle is 8/3 times bigger than the small rectangle.
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If there are seven points on a plane and no three points are on the same line, how many lines can the points make?
The number of lines that the points can make is; 21 lines
How to find Collinear Points?We are given that;
- There are 7 points on a Plane
- No 3 points on the plane are on the same line
Thus;
No 3 points are collinear and as such the number of lines that the points can make is found from the combination formula;
C(7,2);
C(7,2) = 7!/(7 - 2)!*2!
= (7 × 6)/(2 × 1)
= 42/2
=21
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Please help due right now !! pls show work thank uuuuu
Answer:
x=9.73
Step-by-step explanation:
This is trigonometry work! :)
So cos46°=x/14
x=14×cos46°
x≈9.73
Hope this helps <3
Rule 1: Multiply by 2 then add 1 starting from 1.
Rule 2: Divide by 2 then add 4 starting from 40.
I need to make an sequence for both of them and I need help
Rule 1:
1, 3, 7, 15, 31, 63, 127, 255, 511, 1023 etc
Rule 2:
40, 24, 16, 12, 10, 9, 8.5, 8.25, 8.125, 8.0625 etc
Hope this helps!
The first sequence is 1,3,7,15,31 and second sequence is 40,24,16,12,10.
Given that first rule is that multiply by 2 then add 1 starting from 1 and second rule is that divide by 2 then add 4 starting from 40.
We have to find the sequences for each rule.
We have to start from starting point and then apply the rule to find the sequence.
Sequence of rule 1:
Second term of sequence=2*1+1=3
Third term of the sequence=2*3+1=7
Fourth term of the sequence=2*7+1=15
Fifth term of the sequence=2*15+1=31.
Sequence will be 1,3,7,15,31.
Sequence of rule 2:
Second term of sequence=40/2+4=24
Third term of sequence=24/2+4=16
Fourth term of sequence=16/2+4=12
Fifth term of sequence=12/2+4=10
Sequence will be : 40,24,16,12,10.
Hence the first sequence is 1,3,7,15,31 and second sequence is 40,24,16,12,10.
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