2) 5 2 (6) Consider the matrix E = 3 4 (a) Compute the eigenvalues of E. (b) Compute an eigenvector for each eigenvalue of E. (c) Prove that these eigenvectors are linearly independent.

Answer:

Step-by-step explanation:

It expresses how much money he had to pay in total for the sheet music and drumsticks altogether.

Have an amazing day!

Please mark brainliest!

Answer:

angle C because they are the same line

Step-by-step explanation:

a. The mean is 569.5 minutes and the standard deviation is approximately 8.7366 minutes. b. The probability that a flight arrives late (later than 9:25 am) is approximately 0.68.

What is probability?

Probability is a measure or quantification of the likelihood or chance of an event occurring. It is a way to express the uncertainty associated with a particular outcome or set of outcomes in a given situation.

a. To calculate the mean and standard deviation of the continuous uniform distribution, we first need to convert the time data to a minute scale.

Early arrival time: 9:17 am = 9 * 60 + 17 = 557 minutes

Late arrival time: 9:42 am = 9 * 60 + 42 = 582 minutes

The continuous uniform distribution is defined by the following formula:

Mean (μ) = (early arrival time + late arrival time) / 2

Standard Deviation (σ) = (late arrival time - early arrival time) / √12

Plugging in the values:

Mean (μ) = (557 + 582) / 2 = 569.5 minutes

Standard Deviation (σ) = (582 - 557) / √12 ≈ 8.7366 minutes (rounded to 4 decimal places)

Therefore, the mean is 569.5 minutes and the standard deviation is approximately 8.7366 minutes.

b. To calculate the probability that a flight arrives late (later than 9:25 am), we need to find the area under the probability density function (PDF) curve beyond 9:25 am.

Since the distribution is continuous uniform, the PDF is a rectangle with a base of (late arrival time - early arrival time) = 582 - 557 = 25 minutes and a height of 1/(late arrival time - early arrival time).

The probability of a late arrival can be calculated as:

Probability of late arrival = (late arrival time - 9:25 am) / (late arrival time - early arrival time)

Converting 9:25 am to minutes: 9 * 60 + 25 = 565 minutes

Probability of late arrival = (582 - 565) / (582 - 557)

= 17 / 25 ≈ 0.68 (rounded to 2 decimal places)

Therefore, the probability that a flight arrives late (later than 9:25 am) is approximately 0.68.

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One strategy that may help Emilio write more fluently is practicing speed writing or shorthand techniques.

Practicing speed writing or shorthand techniques can help Emilio increase his writing speed without sacrificing legibility. Speed writing involves using abbreviations, symbols, and shortcuts to represent words or phrases, allowing for faster transcription of thoughts onto paper.

Shorthand systems, such as Gregg shorthand or Pitman shorthand, provide structured methods for condensing words and phrases into simplified symbols.

By learning and practicing speed writing or shorthand techniques, Emilio can improve his writing efficiency and reduce the time it takes to write a few sentences. This strategy allows him to maintain neatness while increasing his writing speed, enabling him to express his thoughts more fluently.

With regular practice and familiarity, Emilio will become more comfortable with the shorthand system and experience a significant improvement in his writing speed and fluency.

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To complete the square for the expression x2 − 11x + ____, we need to add a constant term that will make the expression a perfect square trinomial.

We can do this by taking half of the coefficient of the x-term (-11/2) and squaring it (121/4). Thus, x2 − 11x + 121/4 can be written as (x - 11/2)2.

We can check this by expanding (x - 11/2)2:

(x - 11/2)2 = x2 - 11/2 x - 11/2 x + (121/4)

= x2 - 11x + 121/4

Therefore, the complete expression is (x - 11/2)2, which is equivalent to x2 − 11x + 121/4.
In summary, to complete the square for x2 − 11x + ____, we add the constant term 121/4. This turns the expression into a perfect square trinomial, which can be written as (x - 11/2)2.

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Answer:

22.5

Step-by-step explanation:

we can use the ratios to turn x+y+z=180 to x+4x+3x= 180

then solve for 180

x = 22.5

Answer: D.) 22.5°

Have a nice day!

Answer:

hi it -2 3

Step-by-step explanation:

Answer:

1/18 there you go

Step-by-step explanation:

Based on the recipe, 3 cups of flour are required to make 7 cookies.

The number of cups of flour can be calculated using ratio and proportion. Now equating the two ratio based on original recipe and preparation of cookies.

Forming the proportion -

12 : 5 = 7 : x

Rewriting the equation as per the x

x = (7 × 5) ÷ 12

Performing multiplication in numerator on Right Hand Side of the equation to find the value of x

x = 35 ÷ 12

Performing division on Right Hand Side of the equation to find the value of x

x = 2.92

Rounding off the number to find the number of cups of flour.

Number of cups of flour = 3

Thus, 3 cups of flour are needed for 7 cookies.

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Answer:

this two graph is not same because they have different slopes for this they are not same

If regular octagon is inscribed in a circle of radius 1 a side of the octagon is \(\sqrt{ 2-\sqrt{2} }\)

A polygon with 8 sides and 8 angles is called an octagon. That indicates that an octagon has 8 edges and vertices, respectively. The octagon is a two-dimensional, 8-sided polygon, often known as an 8-gon, in plain English. All of the sides of a regular octagon will be the same length.

Given that the radius= 1

The angle between adjacent sides of regular octagon can be expressed as  

\(\frac{(8 -2)180}{8}\)

=135

We can represent the side length of regular octagon  as (a) the sing the sine rule ,

\(\frac{a}{sin45} =\frac{1}{sin(62.5)}\)

\(a= \frac{sin45}{sin(62.5)}\)

= \(\sqrt{ 2-\sqrt{2} }\)

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Answer:

the y intercept is 5

Step-by-step explanation:

Answer:

-1/2

Step-by-step explanation:

P(x < 1

a) P(x ≤ 6), n = 9, p = 0.8

Using the binomial cumulative distribution function, we can compute P(x ≤ 6) as follows:

P(x ≤ 6) = Σ P(x = i) for i = 0 to 6

= Σ (9 choose i) * (0.8)^i * (0.2)^(9-i) for i = 0 to 6

= 0.000015 + 0.000459 + 0.005902 + 0.042467 + 0.181904 + 0.393668 + 0.328126

= 1.352541 * 10^-5 + 0.000458818 + 0.005902008 + 0.042467328 + 0.181904316 + 0.393668288 + 0.328126005

= 0.952446763

Therefore, P(x ≤ 6) = 0.952.

(b) P(x > 8), n = 9, p = 0.3

Using the binomial cumulative distribution function, we can compute P(x > 8) as follows:

P(x > 8) = 1 - P(x ≤ 8)

= 1 - Σ P(x = i) for i = 0 to 8

= 1 - (0.43046721 + 0.25412184 + 0.07886593 + 0.016515105 + 0.002316831 + 0.000218700 + 1.0776 * 10^-5 + 2.43 * 10^-7 + 2.43 * 10^-9)

= 0.000011

Therefore, P(x > 8) = 1.1 * 10^-5.

(c) P(x < 1), n = 9, p = 0.1

Using the binomial cumulative distribution function, we can compute P(x < 1) as follows:

P(x < 1) = Σ P(x = i) for i = 0 to 0

= (9 choose 0) * (0.1)^0 * (0.9)^9

= 0.387420489 * 10^-9

= 3.874 * 10^-10

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i < 3u

Step-by-step explanation:

6i < 5i + 3u

6i - 5i < 3u

i < 3u

The correct interpretation of a bleach and water solution with a 2:3 ratio would be option B: 2 cups of bleach and 3 cups of water.

A bleach and water solution with a 2:3 ratio means that for every 2 parts of bleach, there should be 3 parts of water. This ratio is typically expressed in terms of volume or quantity.

To understand this ratio, let's break it down using different units:

A. 1/3 part bleach and 2/3 part water:

If we consider 1/3 part bleach, it means that for every 1 unit of bleach, there should be 2 units of water. However, this does not match the given 2:3 ratio.

B. 2 cups of bleach and 3 cups of water:

If we consider cups as the unit of measurement, this means that for every 2 cups of bleach, there should be 3 cups of water. This matches the given 2:3 ratio, making it a valid interpretation.

C. 3 cups of bleach and 2 cups of water:

If we consider cups as the unit of measurement, this means that for every 3 cups of bleach, there should be 2 cups of water. However, this interpretation does not match the given 2:3 ratio.

Based on the given options, the correct interpretation of a bleach and water solution with a 2:3 ratio would be option B: 2 cups of bleach and 3 cups of water.

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Answer:

The greates amount of pieces he would be able to use would be 9 because 8 divided by 5/6= 9 and 3/5.the 3/5 piece is too short.

Step-by-step explanation:

Answer:

i think its function notation is

Step-by-step explanation:

f(x) = x - 3

Answer:

x=3

Step-by-step explanation:

hope this helps:)

Answer:

135°

Step-by-step explanation:

The sum of interior angles of a regular polygon is (n-2) x 180

N is the number of sides, this shape has 8

(8-2) 180

= 1080 total degrees in the shape. Reach angle is equal so then divide by 8.

1080/8 = 135°

Since segment AD bisects angle BAC, the value of x is equal to 14.6.

In Mathematics, an angle bisector can be defined as a type of line, ray, or segment, that bisects or divides a line segment exactly into two (2) equal angles.

By applying the angle bisector theorem to this triangle (ΔABC), we have:

AB/BD = AC/DC

19/x = 17/(20 - x)

17x = 19(20 - x)

17x = 380 - 19x

19x + 17x = 380

26x = 380

x = 380/26

x = 14.6.

In conclusion, we can reasonably infer and logically deduce that the value of x in triangle ABC is 14.6.

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Answer:

-385y

Step-by-step explanation:

This expression cannot be factored with rational numbers, so -385y is your answer.

Let's solve the following equation to see where Maya made a mistake:

2 (3x + 6) = 3 (x - 10)

Step 1: Solving parenthesis

6x + 12 = 3x - 30

Step 2: Like terms

6x - 3x = -30 - 12

Step 3: Complete the subtractions at both sides

3x = -42

Step 4: Dividing by 3 at both sides

3x/3 = -42/3

x = -14

Maya didn't multiply correctly 3 * - 10

Yes, Javionery, option B is the correct one.

Answer:

1/ Heidi earned $61.20 in commission

2/ The jewelry store makes $618.80 from hers sales

Step-by-step explanation:

9% = 0.09

First, take 680 times 0.09 = $61.20

Heidi earned $61.20 in commission

For the second question

Take 680 - 61.20 = $618.8

The jewelry store makes $618.80 from its sales

Answer:

7x-y = 2

Step-by-step explanation:

i think it is right I"m not very sure

True, a pie chart should be considered when you have just one data series to plot. A pie chart is a circular chart that is divided into slices to represent numerical proportions.

Each slice of the pie chart represents a category or percentage of a whole. Pie charts are useful when you want to display relative proportions or percentages of a single data series. They are easy to understand and provide a quick visual representation of data. However, pie charts are not recommended for complex data sets or when comparing multiple data series. In such cases, a bar chart or a line graph may be a better option. It is important to choose the right type of chart based on the nature of the data and the purpose of the visualization.

True, a pie chart should be considered when you have just one data series to plot. A pie chart is a circular graphical representation of data that displays the size of items in one data series as a proportion of the total sum of the items. The individual data points are shown as slices or segments of the pie, with each segment's size representing the proportion of the whole.

Pie charts are particularly useful for visualizing percentages and proportions of a whole, and they work best when there are a limited number of categories in the data series. They are simple and easy to understand, making them a popular choice for presenting information to a broad audience.

However, pie charts may not be the best choice for every situation. If there are too many categories, the segments may become too small to easily distinguish between them. Additionally, if you need to compare multiple data series or trends over time, other chart types, such as bar or line charts, might be more appropriate.

In summary, pie charts are an effective choice for visualizing a single data series with a limited number of categories, especially when the goal is to show proportions or percentages. If these conditions are met, a pie chart can be a useful and easily understood way to display your data.

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Answer:

=Rs.10

Step-by-step explanation:

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A piece of cloth costs Rs. 200. If the piece was 5m longer and each meter of cloth costs Rs. 2 less the cost of the piece would have remained unchanged. How long is the piece and what is the original rate per meter?

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Solution

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Let the length of the piece be x metres. Then, rate per metre =Rs.

x

200

New length =(x+5) metres

Since the cost remains same

New rate per metre =Rs.

x+5

200

It is given that

x

200

−

x+5

200

=2

⇒

x(x+5)

200(x+5)−200x

=2⇒

x(x+5)

1000

=2

⇒x

2

+5x=500⇒x

2

+5x−500=0$

⇒x

2

+25x−20x−500=0

⇒(x+25)(x−20)=0⇒x+25=0

orx−20=0⇒x=20orx=−25

But x cannot be negative. So, x=20

Rate per metre Rs.

x

200

=Rs

20

200

=Rs.10

The expression -8 less than a number is no more than 12 will be given as x - 8 ≤ 12

Let the unknown values be "x"

a) The sum of a number and 12 is expressed as x + 12

If the result is at most -8, the required inequality will be x + 12 ≤ 8

c) If a number is increased by -8, the result will be x - 8. the expression -8 is greater than 12 will be given as x - 8 > 12 greater than 12.

b) If a number is increased by -8, the result will be x - 8. The expression -8 less than a number is no more than 12 will be given as x - 8 ≤ 12

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Given: Radius of the wheel = 30 inches, Revolutions per minute = 401 rpmThe linear speed of the car in miles per hour can be calculated as follows:

Step 1: Convert the radius from inches to miles by multiplying it by 1/63360 (1 mile = 63360 inches).30 inches × 1/63360 miles/inch = 0.0004734848 milesStep 2: Calculate the distance traveled in one minute by the wheel using the circumference formula.Circumference = 2πr = 2 × π × 30 inches = 188.496 inchesDistance traveled in one minute = 188.496 inches/rev × 401 rev/min = 75507.696 inches/minStep 3: Convert the distance traveled in one minute from inches to miles by multiplying by 1/63360.75507.696 inches/min × 1/63360 miles/inch = 1.18786732 miles/minStep

4: Convert the distance traveled in one minute to miles per hour by multiplying by 60 (there are 60 minutes in one hour).1.18786732 miles/min × 60 min/hour = 71.2720392 miles/hour Therefore, the linear speed of the car is 71.3 miles per hour (rounded to the nearest tenth).Answer: 71.3

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The radius of the wheel on a car is 30 inches. If the wheel is revolving at 401 revolutions per minute, The linear speed of the car is approximately 19.2 miles per hour.

To find the linear speed of the car in miles per hour, we need to calculate the distance traveled in one minute and then convert it to miles per hour. Here's how we can do it step by step:

Calculate the circumference of the wheel:

The circumference of a circle is given by the formula

C = 2πr

where r is the radius of the wheel.

In this case, the radius is 30 inches, so the circumference is

C = 2π(30)

   = 60π inches.

Calculate the distance traveled in one revolution:

Since the circumference represents the distance traveled in one revolution, the distance traveled in inches per revolution is 60π inches.

Calculate the distance traveled in one minute:

Multiply the distance traveled in one revolution by the number of revolutions per minute.

In this case, it is 60π inches/rev * 401 rev/min = 24060π inches/min.

Convert the distance to miles per hour:

There are 12 inches in a foot, 5280 feet in a mile, and 60 minutes in an hour.

Divide the distance traveled in inches per minute by (12 * 5280) to convert it to miles per hour.

The final calculation is (24060π inches/min) / (12 * 5280) = (401π/66) miles/hour.

Approximating π to 3.14, the linear speed of the car is approximately (401 * 3.14 / 66) miles per hour, which is approximately 19.2 miles per hour.

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Answer:

32 songs

Step-by-step explanation:

60 - 12 = 48

48 ÷ 1.5 = 32

32 songs

Answer:

yes they are the same

Step-by-step explanation:

2x + 28 =40

you subtract 28 from both sides

2x + 28 - 28 = 40 - 28

2x=12

divide 12 by 2 and get 6

2(6)=12

2(x + 14)= 40

So, 2(x) + 2(14)

2x + 28 = 40

So they're both the same, just with 2 different ways to solve the same equation...Hope this helps!!

The solution for 2x + 28 = 40 is 6.

The solution for 2(x + 14) = 40 is 6.

Yes, they have the same solution.

Solutions are the values of an equation where the values are substituted in the variables of the equation and make the equality in the equation true.

We have,

2x + 28 = 40

Solve for x.

2x = 40 - 28

2x = 12

x = 6

2(x + 14) = 40

Solve for x.

2x + 28 = 40

2x = 40 - 28

2x = 12

x = 6

Thus,

The solution for both equations is the same.

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The variance function of {Xt,t∈Z} is given by Var(Xt)=t^2, t∈Z. None of the given options is correct

Given, Xt=tεt,t∈Z where {εt,t∈Zt is white noise with unit variance.

The variance function of {Xt,t∈Z} can be calculated as follows:

The variance of a random variable is the average value of the squares of the differences between the individual values of the random variable and the mean.

Thus, the variance of {Xt,t∈Z} can be calculated as follows:V(Xt)=E[(Xt−E(Xt))^2]V(Xt)=E[Xt^2−2XtE(Xt)+E(Xt)^2]

Since E(Xt)=0 for all t∈Z, we getV(Xt)=E[Xt^2]Now,E[Xt^2]=E[t^2εt^2]=t^2E[εt^2]=t^2(1)=t^2

Hence, V(Xt)=E[Xt^2]=t^2

The variance function of {Xt,t∈Z} is given by Var(Xt)=t^2, t∈Z.

Therefore, none of the given options are correct.

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