I have no idea how to do this pls help
picture attached

The eigen values of the first matrix is λ=4, λ=0 and λ=-3. The eigenvalues of the second matrix is 0 and 6.

If there is a scalar such that Ax = x, then a non-zero vector x is an eigenvector of A given a square matrix A. The scalar eigenvalue of the eigenvector x is known as the scalar.

To put it another way, when an eigenvector x is added to a matrix A, the outcome is a scalar multiple of x, where the scalar is the eigenvalue.

Many applications of linear algebra depend on eigenvectors and eigenvalues, such as the solution of differential equation systems, identifying the major variables in a dataset, and assessing the stability of dynamic systems.

The eigenvalues of the matrix can be found using the equation:

det(A - λI) = 0

Substituting the values we have:

[tex]\left[\begin{array}{ccc}4&2&0\\0&0&0\\1&0&-3\end{array}\right] - \lambda \left[\begin{array}{ccc}1&0&0\\0&1&0\\0&0&1\end{array}\right][/tex]

[tex]\left[\begin{array}{ccc} 4 - \lambda &0&0\\0&- \lambda & 0\\1 &0 & -3 - \lambda\end{array}\right][/tex]

Now determine the det of the matrix:

(4 - λ) (-3λ + λ² ) - 0 + 0 = (4 - λ)(λ)(-3 + λ)

Thus the eigen values are:

λ= 4, λ = 0, and λ = 3.

For the second matrix we have:

Given that B has identical rows throughout, B has a rank of 1, and B's null space has a dimension of 2. With two eigenvalues equal to zero and one eigenvalue equal to the trace of B, which is 6, B has two eigenvalues equal to zero.

Hence, the eigenvalues of B are 0 and 6.

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The BEST answer from the choices provided is Option (A) -2.

The cumulative relative frequency for flossing 3 times per week is 58.57%.

a. Let's complete the table.

We can calculate the missing relative frequency for 0 times flossing per week by dividing the frequency (4) by the total number of people (70).

Relative Frequency for 0 times flossing = 4/70 = 0.0571 (rounded to 4 decimal places)

For 6 times flossing per week, the frequency is missing.

We can calculate it by summing up the frequencies for all other days and subtracting that from the total number of people.

Missing frequency for 6 times flossing = 70 - (4 + 11 + 15 + 11 + 6 + 7 + 6) = 70 - 60 = 10

Now, let's calculate the cumulative frequency for 5 times flossing per week.

Cumulative Frequency for 5 times flossing = Cumulative Frequency for 4 times flossing + Frequency for 5 times flossing = 47 + 7 = 54

The completed table looks like this:

of times floss per week | Frequency | Relative Frequency | Cumulative Frequency

0 | 4 | 0.0571 | 4

1 | 11 | 0.1571 | 15

2 | 15 | 0.2143 | 30

3 | 11 | 0.1571 | 41

4 | 6 | 0.0857 | 47

5 | 7 | 0.1 | 54

6 | 10 | 0.1429 | 64

7 | 6 | 0.0857 | 70

b. The cumulative relative frequency for flossing 3 times per week is the cumulative frequency for 3 times flossing divided by the total number of people (70).

Cumulative Relative Frequency for 3 times flossing = Cumulative Frequency for 3 times flossing / Total number of people = 41 / 70 = 0.5857 (rounded to 4 decimal places)

The cumulative relative frequency for flossing 3 times per week is 58.57%.

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Question 1:

(a) To find the probability that a taxi driver earns less than $1500 in a day, we need to standardize the value using the given mean and standard deviation, and then find the corresponding probability from the standard normal distribution table:

z = (1500 - 1062.5) / 350 = 1.20

Using the standard normal distribution table, the probability of a standard normal random variable being less than 1.20 is approximately 0.8849. Therefore, the probability that a taxi driver earns less than $1500 in a day is approximately:

P(X < 1500) = P(Z < 1.20) = 0.8849

(b) We need to find the value of k such that 93.7% of the drivers earn more than $k a day. This means that the probability of a driver earning less than or equal to $k a day is 1 - 0.937 = 0.063. We can standardize k using the given mean and standard deviation, and then find the corresponding z-score from the standard normal distribution table:

z = (k - 1062.5) / 350

Using the standard normal distribution table, we find that the z-score corresponding to a probability of 0.063 is approximately -1.51. Therefore:

-1.51 = (k - 1062.5) / 350

k = -1.51 * 350 + 1062.5 = $499.25 (rounded to the nearest cent)

(c) The mean of the total daily earning is:

μT = μ1 + μ2 = 1062.5 + 235.5 = 1298

The variance of the total daily earning is the sum of the variances of the two earnings, since they are assumed to be independent:

σT² = σ1² + σ2² = 350² + 84.5² ≈ 128681

Therefore, the standard deviation of the total daily earning is:

σT ≈ √128681 ≈ 358.5

(rounded to the nearest integer)

(d) To find L1 and L2, we need to find the z-scores corresponding to the lower and upper 2.2% tails of the standard normal distribution:

z1 = -1.81

z2 = 1.81

Then we can use the formula for standardizing a normal random variable to find the corresponding values of T:

z1 = (L1 - μT) / σT

z2 = (L2 - μT) / σT

Solving for L1 and L2, we get:

L1 = μT + z1σT ≈ 1298 + (-1.81) * 358.5 ≈ $645

L2 = μT + z2σT ≈ 1298 + 1.81 * 358.5 ≈ $1951

(rounded to the nearest integer)

Question 2:

(a) We can model the transaction time of a single customer as a normal random variable with mean 20 and standard deviation 5. Then the total transaction time for 6 customers can be modeled as a normal random variable with mean 6 * 20 = 120 and standard deviation √(6 * 5²) = 15. To find the probability that 5 customers can finish the transaction within 20 seconds, we need to standardize the value using this mean and standard deviation, and then find the corresponding probability from the standard normal distribution table:

z = (5 * 20 - 120) / 15 = -0.53

this is answer 44rrrrrrrrrrrrrrrrrrrrfrrrrrrrrrrr

Therefore, the overall difference in loss or gain between selling at the current day's high price or low price would be $3460.

An expression is a mathematical or logical statement that represents a value or a result. It can consist of numbers, variables, operators, and/or functions that are combined in a specific way to form a valid statement. Expressions can be simple, such as a single number or variable, or complex, involving multiple operations and functions. In mathematics, expressions can be used to represent mathematical operations such as addition, subtraction, multiplication, division, exponentiation, and more.

Here,

To calculate the difference in overall loss or gain between selling at the current day's high price or low price for the stocks purchased, we need to know the current day's high and low prices for stock A and stock B. Once we have that information, we can use the following formula:

Difference = (Current day's high price - Purchase price) * Number of shares

Let's assume the current day's high price for stock A is $100 per share and the low price is $80 per share, while the high price for stock B is $150 per share and the low price is $130 per share.

For stock A:

Purchase price = $90 per share

Number of shares = 120 shares

Difference in overall loss or gain for stock A when selling at the high price:

Difference = ($100 - $90) * 120

= $1200

Difference in overall loss or gain for stock A when selling at the low price:

Difference = ($80 - $90) * 120

= -$1080

For stock B:

Purchase price = $145 per share

Number of shares = 35 shares

Difference in overall loss or gain for stock B when selling at the high price:

Difference = ($150 - $145) * 35

= $175

Difference in overall loss or gain for stock B when selling at the low price:

Difference = ($130 - $145) * 35

= -$525

So, the overall difference in loss or gain between selling at the current day's high price or low price would be the sum of the differences for stock A and stock B:

Overall difference in loss or gain = (Difference for stock A when selling at the high price + Difference for stock B when selling at the high price) - (Difference for stock A when selling at the low price + Difference for stock B when selling at the low price)

Overall difference in loss or gain = ($1200 + $175) - (-$1080 + -$525)

= $1855 + $1605

= $3460

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Answer:

2,000

Step-by-step explanation:

The potential rational zeros of the given polynomial are ±1, ±2, ±3, ±4, ±5, ±6, ±10, ±15, ±20, ±30, ±60, ±1/2, ±1/3, ±2/3, ±5/2, ±4/3, ±5/3, ±10/3, ±1/6, ±5/6, ±1/10, ±2/5, ±4/15, ±1/15, ±2/15.

How to calculate potential rational zeroes?

The Rational Zero Theorem states that if a polynomial with integer coefficients has any rational zeros, then they must have the form of a fraction p/q, where p is a constant term factor and q is a leading coefficient factor.

For the given polynomial q(x)=6x^3+31x^2+23x−20, the constant term is -20, and the leading coefficient is 6. Therefore, the potential rational zeros can be expressed as follows:

p/q = ± {factors of the constant term (-20)}/{factors of the leading coefficient (6)}

Possible factors of -20: ±1, ±2, ±4, ±5, ±10, ±20

Possible factors of 6: ±1, ±2, ±3, ±6

Therefore, the potential rational zeros are:

±1/1, ±2/1, ±4/1, ±5/1, ±10/1, ±20/1,

±1/2, ±2/2, ±4/2, ±5/2, ±10/2, ±20/2,

±1/3, ±2/3, ±4/3, ±5/3, ±10/3, ±20/3,

±1/6, ±2/6, ±4/6, ±5/6, ±10/6, ±20/6.

Simplifying and eliminating duplicates, we get:

±1, ±2, ±4, ±5, ±10, ±20,

±1/2, ±2/2, ±4/2, ±5/2, ±10/2, ±20/2 (which simplifies to ±1, ±2, ±3, ±5, ±10, ±20),

±1/3, ±2/3, ±4/3, ±5/3, ±10/3, ±20/3 (which simplifies to ±1/3, ±2/3, ±4/3, ±5/3, ±10/3),

±1/6, ±2/6, ±4/6, ±5/6, ±10/6, ±20/6 (which simplifies to ±1/6, ±1/3, ±2/3, ±5/6, ±5/3, ±10/3).

Therefore, the potential rational zeros of the given polynomial are ±1, ±2, ±3, ±4, ±5, ±6, ±10, ±15, ±20, ±30, ±60, ±1/2, ±1/3, ±2/3, ±5/2, ±4/3, ±5/3, ±10/3, ±1/6, ±5/6, ±1/10, ±2/5, ±4/15, ±1/15, ±2/15.

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Here, a a⁻¹ b = 1b = b shows that a⁻¹ is indeed inverse of a, and x = a⁻¹b is a valid solution to the equation ax = b.

An equation is a statement that two expressions are equal. A solution of an equation is a value (or a set of values) that makes the equation true.

In the equation ax = b, the solution x = a⁻¹b means that if we multiply a by its inverse a⁻¹, we get 1, the multiplicative identity. So, when we multiply both sides of the equation by a⁻¹, we get:

a⁻¹(ax) = a⁻¹b

Multiplying a⁻¹ and a on the left side of the equation gives:

1x = a⁻¹b

which simplifies to x = a⁻¹b. This shows that x = a⁻¹b is a solution to the equation ax = b.

The statement "a a⁻¹ b = 1b = b" means that when we multiply a by its inverse a⁻¹, we get the multiplicative identity 1, and when we multiply 1 by b, we get b. So, a a⁻¹ b = 1b = b shows that a⁻¹ is indeed the inverse of a, and x = a⁻¹b is a valid solution to the equation ax = b.

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The mean of the set is 1/2.

The mean is a statistical measure that represents the average value of a set of numbers. To calculate the mean, you add up all the values in the set and then divide by the total number of values in the set.

To find the mean of a set of numbers, you add up all the numbers in the set and then divide the result by the total number of numbers in the set.

In this case, the set has six numbers:

2/3, 1/6, 1/3, 2/3, 7/9, 1/3

Adding them up, we get:

(2/3) + (1/6) + (1/3) + (2/3) + (7/9) + (1/3) = 3

So the sum of the numbers in the set is 3.

To find the mean, we divide this sum by the total number of numbers in the set, which is 6:

3/6 = 1/2

Therefore, the mean of the set is 1/2.

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Answer:

Step-by-step explanation:

After three years, Carlo is taller than Reggie. Carlo is 179 cm tall and Reggie is 175 cm tall.

A method for measuring temperature, length, volume, weight, and distance is known as the metric system. It is founded on three fundamental units that allow us to measure almost anything in the universe.

To compare the heights of Carlo and Reggie, we need to convert their heights to the same unit. We can convert Reggie's height from millimeters to centimeters by dividing by 10:

Reggie's height = 1680 mm ÷ 10 = 168 cm

Now we can compare their heights before and after three years:

After three years:

Therefore, after three years, Carlo is taller than Reggie. Carlo is 179 cm tall and Reggie is 175 cm tall.

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Answer: Factors of a polynomial is x(x+1)

Step-by-step explanation: To find the GCF, we first seek the greatest common divisor of these two terms.

Taking common x from (x^2+x).

x(x+1)

Answer: 75%

Step-by-step explanation:

Answer:

the best answer would be 27

Step-by-step explanation:

Boom

1/6

Step-by-step explanation:

the reason is because of the tail and the spinner

England receives a total weighted score of [tex]1.9[/tex] , while Canada receives a score of [tex]1.6[/tex].

Instead of hiring an own accountant, a small business may choose to contract bookkeeping responsibilities to an accounting company in to cut expenses. Some companies find it advantageous to outsource HR department duties including payroll and medical coverage.

Outsourcing has several benefits, including better systems and service quality, access to the world's best workers, improved scheduling, avoiding personnel concerns, and many more.

a) Using the factor-rating method, we can calculate the total weighted score for each country as follows:

For England:

Total score [tex]= (2 * 0.1) + (3 * 0.6) + (1 * 0.2) + (1 * 0.1) = 1.9[/tex]

For Canada:

Total score [tex]= (3 * 0.1) + (1 * 0.6) + (3 * 0.2) + (2 * 0.1) = 1.6[/tex]

Therefore, based on the risk-avoidance criteria and weightings established by the executives, we would select Canada as the better choice.

b) If we double each of the weights used in part (a), the total weighted score for each country changes as follows:

For England:

Total score [tex]= (2 * 0.2) + (3 * 1.2) + (1 * 0.4) + (1 * 0.2) = 4.0[/tex]

For Canada:

Total score [tex]= (3 * 0.2) + (1 * 1.2) + (3 * 0.4) + (2 * 0.2) = 2.2[/tex]

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The z-score of a student who scores 97 is 2.83. In this case, since the z-score is greater than 1.96, the student is in the top 1% of performers.

It is used to indicate how many standard deviations a certain value is from the mean. It is calculated by subtracting the mean from the observed value and then dividing the result by the standard deviation.

This is calculated by subtracting the mean (80) from the student’s score (97) and dividing the result by the standard deviation (6).

97- 80/6

= 2.83

The z-score of 2.83 indicates that the student is in the top 1% of performers. This is because the z-score of 2.83 is greater than the z-score of 1.96, which is the z-score that is associated with the 1% percentile.

A z-score of 1.96 means that it is higher than 1% of the scores.

In this case, since the z-score is greater than 1.96, the student is in the top 1% of performers.

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The estimated probability that a randomly selected consumer will recognize Costco is 0.988 or approximately 98.8%.

What is Probability ?

Probability is a branch of mathematics that deals with the study of random events or outcomes. It is a measure of the likelihood or chance of an event occurring, expressed as a number between 0 and 1, where 0 represents an impossible event and 1 represents a certain event.

In this brand recognition study, we are given that 897 consumers knew of Costco and 10 did not.

The probability of a randomly selected consumer recognizing Costco can be estimated as the number of consumers who knew of Costco divided by the total number of consumers in the study:

P(recognizing Costco) = number of consumers who knew of Costco : total number of consumers in the study

P(recognizing Costco) = 897 : (897 + 10)

P(recognizing Costco) = 897 : 907

P(recognizing Costco) = 0.988 or approximately 98.8%

Therefore, the estimated probability that a randomly selected consumer will recognize Costco is 0.988 or approximately 98.8%.

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First question:

The cost of the t-shirt for the souvenir shop is $16.88. The shop adds $3.75 to the cost and then doubles the amount to get the price that the customer pays. So, the price that the customer pays before tax is:

2 x (16.88 + 3.75) = 2 x 20.63 = 41.26

Therefore, the answer is (D) 41.26.

Second question:

The cost of the t-shirt for the souvenir shop is $12.99. The shop adds $3.75 to the cost to get the price of the t-shirt. Then, the shop adds sales tax of $1.34 to the price to get the total amount that the customer pays. So, the total amount that the customer pays is:

12.99 + 3.75 + 1.34 = 18.08

Therefore, the answer is (C) 28.40.

Answer:1152

Step-by-step explanation:monkey

Answer:

Sequence A is defined by subtracting 6 from the previous term and taking the absolute value, while Sequence B is the sum of the first n odd integers. B(9) > A(9).

To produce each new term from the previous term, subtract 6 from the previous term, then take the absolute value of the result. That is, if the previous term is x, then the next term is |x - 6|.

To find A(9) and B(9), we can apply the rules we have for each sequence:

A(0) = 19

A(1) = |19 - 6| = 13

A(2) = |13 - 6| = 7

A(3) = |7 - 6| = 1

A(4) = |1 - 6| = 5

A(5) = |5 - 6| = 1

A(6) = |1 - 6| = 5

A(7) = |5 - 6| = 1

A(8) = |1 - 6| = 5

A(9) = |5 - 6| = 1

B(0) = 0 (the sum of the first 0 odd integers)

B(1) = 1

B(2) = 1 + 3 = 4

B(3) = 1 + 3 + 5 = 9

B(4) = 1 + 3 + 5 + 7 = 16

B(5) = 1 + 3 + 5 + 7 + 9 = 25

B(6) = 1 + 3 + 5 + 7 + 9 + 11 = 36

B(7) = 1 + 3 + 5 + 7 + 9 + 11 + 13 = 49

B(8) = 1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 = 64

B(9) = 1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 = 81

Step-by-step explanation:

(1; 1,2)

Write any 4 decimal numbers that belong to this interval, for example:

1; 1,04; 1,08; 1,12; 1,16; 1,2

In summary in axis when x = 24, y = 41.1667.

Why is it?

If y varies inversely as x, then y = k/x for some constant k. To find k, we can use the initial values given:

y = k/x

38 = k/26

k = 38×26

k = 988

Now we can use k to find y when x = 24:

y = k/x

y = 988/24

y = 41.1667 (rounded to four decimal places)

Therefore, when x = 24, y = 41.1667.

In mathematics, an axis is a straight line that defines a reference direction for a coordinate system. It is used to locate or plot points, and describe geometric shapes in a plane or in space. In a two-dimensional coordinate system, there are two axes: the x-axis, which is horizontal, and the y-axis, which is vertical.

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Answer: 1,024 different ways

Step-by-step explanation:

      We will use the Fundamental Counting Principle. There are 5 questions, each with 4 possible answers. To use the principle and answer the question, we will multiply 4 by itself 5 times.

             4 * 4 * 4 * 4 * 4 = 1,024 different ways

Think of it like this:

            you have 4 objects (the 4 answer options, a, b, c, and d)

            You are going to chose a group of 5, and the order matters (your         answer to question #1 is independent of your choice on #3)

             Repetition is allowed (you can answer "c" on all of the questions if you want to)

This is a simple permutation. Use the formula:

       [tex]\bold{n^r}[/tex]

       where n is the number of objects (the number of answer choices)

       and r is the number of objects you will choose (5, one answer for each question)

To solve:

[tex]4^5[/tex]

[tex]1,024 \longleftarrow[/tex] your answer!

Hope this helps! Feel free to ask any follow up questions, and please "vote up" :)

Answer:

Yes

Step-by-step explanation:

Angle RDE =angle TVA=28°

REV=TAV=42°

DRE=VTA=110°

THEREFORE TRIANGLE DER IS SIMILAR TO TRIANGLE ATV

The prοbabiIity οf seIecting 3 peanut M&M's at randοm, and having aII 3 be a different cοIοr, is P(aII 3 are different) = 1 * 5÷6 * 2÷3 = 0.556

The study οf randοm events οr οccurrences is the fοcus οf the mathematical field οf prοbability. It is a measurement οf the likelihοοd that an event will οccur, expressed as a number between 0 and 1, where 0 denοtes an imprοbable event and 1 denοtes a specific event.

Based οn the infοrmatiοn prοvided, we are given the fοIIοwing prοbabiIities fοr the different cοIοrs οf peanut M&M's:

P (brοwn) = 0.12

P (yeIIοw) = 0.15

P (red) = 0.12

P (bIue) = 0.23

P (οrange) = 0.23

P (green) = 0.15

We can use this infοrmatiοn tο answer variοus prοbabiIity questiοns. Fοr exampIe:

What is the prοbabiIity οf selecting a bIue οr an οrange peanut M&M?

P (bIue οr οrange) = P(bIue) + P(οrange) = 0.23 + 0.23 = 0.46

Therefοre, the prοbabiIity οf selecting a bIue οr an οrange peanut M&M is 0.46 οr apprοximateIy 0.460.

What is the prοbabiIity οf nοt selecting a green peanut M&M?

P(nοt green) = 1 - P(green) = 1 - 0.15 = 0.85

Therefοre, the prοbabiIity οf nοt selecting a green peanut M&M is 0.85 οr apprοximateIy 0.850.

If yοu seIect 3 peanut M&M's at randοm, what is the prοbabiIity that aII 3 are a different cοIοr?

The prοbabiIity οf the first M&M being any cοIοr is 1, since we have nοt seIected any M&M's yet. The prοbabiIity οf the secοnd M&M being a different cοIοr than the first is:

P(secοnd is different) = 1 - P(secοnd is same)

P(secοnd is different) = 1 - (1÷6) = ÷/6

(The prοbabiIity οf the secοnd M&M being the same cοIοr as the first is 1/6, since there are 6 cοIοrs and οnIy οne οf them is the same as the first cοIοr.)

SimiIarIy, the prοbabiIity οf the third M&M being a different cοIοr than the first twο is:

P(third is different) = 1 - P(third is same as first οr secοnd)

P(third is different) = 1 - (2÷6) = 2÷3

(The prοbabiIity οf the third M&M being the same cοIοr as the first οr secοnd is 2/6, since there are twο cοIοrs that have already been seIected.)

Therefοre, the prοbabiIity οf seIecting 3 peanut M&M's at randοm, and having aII 3 be a different cοIοr, is:

P(aII 3 are different) = 1 * 5÷6 * 2÷3 = 0.556

Therefοre, the prοbabiIity οf selecting 3 peanut M&M's at randοm, and having aII 3 be a different cοIοr, is apprοximateIy 0.556.

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