Suppose v is an eigenvector of a matrix A with eigenvalue 5 and further an eigenvector of a matrix B with eigenvalue 3 . Find the eigenvalue λ corresponding to v as an eigenvector of 2A^2+B^2

The machine lifts the block 2 m high if 15 N of force was applied.

When an object is moved over a distance by an external force, at least a portion of that force must be applied in the direction of the displacement. The SI unit of work is the joule. A joule is the amount of effort that a force of one newton does to move an object one meter. Sometimes, newton meters are used to measure work (N-m). Work is not a vector quantity but a scalar one.

Given:

The0 by the block and the tackle machine = 30 Joules

The force applied by the block and tackle machine = 15 N

We know that W=FD

Here W=30 J

F= 15 N

So, the distance will be

D = W/F

=30/15

=2 m

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\(\\ \tt\hookrightarrow 2x-8+30-3x+2x+5=25\)

\(\\ \tt\hookrightarrow x+27=25\)

\(\\ \tt\hookrightarrow x=25-27\)

\(\\ \tt\hookrightarrow x=-2\)

The answer to this equation is

18

First of all, we expand the individual brackets

Solving the first internal bracket would be:

(41-36)= 5

Solving the second internal bracket would be:

(8+14) =  22

Then based on BODMAS, we would multiply 5 by 5= 25

Next 25-22= 3

Finally 6 x 3= 18

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The radius and center of the translated circle are,

Radius = 7 units

Center = (10, - 2)

The circle is a closed two dimensional figure , in which the set of all points is equidistance from the center.

Given that;

The equation of circle is,

x² + y² - 18x + 8y + 48 = 0

Now, We can simplify the equation as;

x² + y² - 18x + 8y + 48 = 0

x² - 18x + 81 - 81 + y² + 8y + 16 - 16 + 48 = 0

(x - 9)² + (y + 4)² = 49

(x - 9)² + (y + 4)² = 7²

Hence, The radius of circle = 7

And, Center = (9, - 4)

Let the center of circle after translated one unit right and two units down is, (h', k')

Hence, We get;

h' = 9 + 1 = 10

k' = - 4 + 2 = - 2

Thus, The equation of the translated circle is,

(x - 10)² + (y - (- 2))² = 7

Hence, the radius and center of the translated circle are,

Radius = 7 units

Center = (10, - 2)

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Given the word problem above, the maximum number of oranges she could have started with is x < 1,142. See the solution below.

In math, sometimes, mathematical problems are stated using words rather than equations. When this occurs, we call it a word problem. The best way to solve this kind of problem is by putting it in form of an equation so that it is easy to solve.

Let the total number of Oranges that the vendor has be x.

⇒ She sells to the first customer (Half of all and half of one)

that is, (x/2) + 1/2

= (x+1)/2

stock balance = x - ((x+1)/2))

= (x-1)/2

⇒ She sells to the second customer (Half of the balance and half of one)

that is, 1/2 ( (x-1)/2) + 1/2

= (x-1)/4 + 1/2

= (x-1+2)/4

= (x+1)/4

Stock balance = ((x-1)/2) - ((x-1)/4)

= (2x−2−x−1)/4

= (x-3)/4

⇒  She sells to the third customer (Half of the balance and half of one)
That is 1/2 ((x-3)/4) + 1/2
= ((x-3)/8)  + 1/2
= (x−3+4)/8
= (x+1)/8


Thus if x < 1000 the original number of oranges she could have started with is:

[ ((x+1)/2)  + ((x+1)/4) + ((x+1)/8)] < 1,000


From here, we solve by first finding the common denominator

[(4(x+1)/8) + 2(x+1)/8) + ((x+1)/8) < 1000

Next - combine fractions with common denominators
[(4x+1) + 2(x+1) + x +1]/8 < 1000


Next, Simplify
[(4x + 7 + 2x + x)/8] <1000

⇒ [(7x + 7)/8] < 1000

⇒ 7x < 7993

⇒ 7x/x < 7993/7

Thus,

x < 7993/7

x < 1,141.8571428

x < 1,142

Thus the maximum number of oranges she could have started with is 1,142 oranges.

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Answer:

the answer is e and d

Step-by-step explanation:

x squared=36/121

x  squared square root =6/11

The irrational numbers among these given are:

\(\sqrt{83}, 24\pi, 90.790170..., \sqrt{109}\)

The remaining numbers are all rational.

The irrational numbers in this problem are:

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Answer:

The answer is given below

Step-by-step explanation:

1) The persons are given by the matrix:

The number of different pie flavours is given by the matrix:

\(n=\left[\begin{array}{cccc}3&4&1&1\\6&6&4&6\\2&2&5&4\end{array}\right]\)

The cost of ingredients for each pie is given by the matrix:

\(I=\left[\begin{array}{ccc}3\\5\\2\\6\end{array}\right]\)

2)

\(\left[\begin{array}{ccc}Pauline\\Patricia\\Polly\end{array}\right] =\left[\begin{array}{cccc}3&4&1&1\\6&6&4&6\\2&2&5&4\end{array}\right] \left[\begin{array}{ccc}3\\5\\2\\6\end{array}\right] \\\left[\begin{array}{ccc}Pauline\\Patricia\\Polly\end{array}\right] =\left[\begin{array}{ccc}37\\92\\50\end{array}\right]\)

3) The cost of pie for Patricia = $92

The total cost of pie for all bakers = 37 + 92 + 50 = $179

The ratio of cost of Patricia pie to that of all three bakers = $92/$179 = 0.514

Patricia pie cost of ingredients is more than half of that of all three bakers

4)

The price of pie at Samuels sweet is represented by the matrix:

\(SA=\left[\begin{array}{ccc}8\\10\\7\\12\end{array}\right]\)

The income of each baker made by selling at samuels sweets is:

\(\left[\begin{array}{ccc}Pauline\\Patricia\\Polly\end{array}\right] =\left[\begin{array}{cccc}3&4&1&1\\6&6&4&6\\2&2&5&4\end{array}\right] \left[\begin{array}{ccc}8\\10\\7\\12\end{array}\right] \\\left[\begin{array}{ccc}Pauline\\Patricia\\Polly\end{array}\right] =\left[\begin{array}{ccc}83\\208\\119\end{array}\right]\)

The price of pie at Sugary Sarah is represented by the matrix:

\(SS=\left[\begin{array}{ccc}8\\9\\8\\13\end{array}\right]\)

The income of each baker made by selling at Sugary Sarah is:

\(\left[\begin{array}{ccc}Pauline\\Patricia\\Polly\end{array}\right] =\left[\begin{array}{cccc}3&4&1&1\\6&6&4&6\\2&2&5&4\end{array}\right] \left[\begin{array}{ccc}8\\9\\8\\13\end{array}\right] \\\left[\begin{array}{ccc}Pauline\\Patricia\\Polly\end{array}\right] =\left[\begin{array}{ccc}81\\212\\126\end{array}\right]\)

5) Patricia yielded the greatest income. She made $208 + $212 = $420

6) Polly made $126 from selling at Sugary Sarah

When data are positively skewed, the mean will be greater than the median.

This is because the mean will be pulled in the direction of the higher values in the data set, while the median will ignore the higher values and be more affected by the lower values in the data set.

Positively skewed data is characterized by a long tail on the right side of the distribution graph. This means that the data set contains more values that are higher than the mean and median. As a result, the mean will be a higher value than the median, as the mean will be pulled in the direction of the higher values. The median, however, will remain unaffected by the higher values and will be more affected by the values at the lower end of the distribution.

the complete question is :

When data are positively skewed, the mean will usually be:

a. greater than the median

b. smaller than the median

c. equal to the median

d. positive or negative depending on the data set

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The Square has equall sides thus if we suppose that square has a side which is x inches then the Perimeter is :

\(perimeter = 4 \times x\)

Thus

\(80 = 4 \times x\)

Divide both sides by 4

\( \frac{80}{4} = \frac{4x}{4} \\ \)

\(20 = x\)

\(x = 20\)

Thus each side has a value of 20 inches .

Answer:

B or 40.67mph

Step-by-step explanation:

To solve we will use formula distance over total time, so are distance is 183miles and are time is 4 hours and 30 minutes. If we put that in hours we get 4.5 hours. Now we simply divide 183/4.5 to get about 40.67 .

Answer:

11.25 kg of coffee worth $9.40/kg must be mixed with 0.75 kg of coffee worth $11/kg to give 12 kg of coffee worth $9.50/kg.

Step-by-step explanation:

Let x be the amount of coffee worth $9.40/kg that needs to be mixed with coffee worth $11/kg to get 12 kg of coffee worth $9.50/kg.

We can start by setting up a system of linear equations based on the information given:

Equation 1: x + y = 12 (the total amount of coffee is 12 kg)

Equation 2: (9.4x + 11y)/12 = 9.5 (the average price of the mixed coffee is $9.50/kg)

Simplifying equation 2, we get:

9.4x + 11y = 114

We can now use substitution to solve for x. Solving equation 1 for y, we get:

y = 12 - x

Substituting this into equation 2, we get:

9.4x + 11(12 - x) = 114

Simplifying and solving for x, we get:

9.4x + 132 - 11x = 114

-1.6*x = -18

x = 11.25

Therefore, 11.25 kg of coffee worth $9.40/kg must be mixed with 0.75 kg of coffee worth $11/kg to give 12 kg of coffee worth $9.50/kg.

Different logs measure different physical properties of the formation that are related to porosity, and the relationship between the log measurement and porosity can be expressed through equations.

The different logs used to obtain porosity and their principles of measurement, quantities measured, and relation to porosity.
There are three main types of logs used to obtain porosity: neutron logs, density logs, and sonic logs.
Neutron logs: These logs measure the hydrogen content in a formation, which is directly related to porosity. The tool emits neutrons that interact with hydrogen atoms, and the resulting gamma rays are measured. The count rate decreases with increasing porosity. The neutron log can be expressed as:
Porosity = (neutron log reading - matrix reading) / (fluid reading - matrix reading)
Density logs: Density logs measure the bulk density of a formation, which can be related to porosity. The tool emits gamma rays that interact with the formation, and the scattered gamma rays are measured. The bulk density decreases with increasing porosity. The density log can be expressed as:
Porosity = (matrix density - bulk density) / (matrix density - fluid density)
Sonic logs: Sonic logs measure the travel time of sound waves through a formation, which can be related to porosity. The tool sends an acoustic wave and measures the time it takes to travel a specific distance. The travel time increases with increasing porosity. The sonic log can be expressed using Wyllie's time-average equation:
Porosity = (sonic log reading - matrix reading) / (fluid reading - matrix reading)
In summary, neutron logs measure hydrogen content, density logs measure bulk density, and sonic logs measure travel time of sound waves. These measurements can be used to calculate porosity using the respective equations provided.

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Answer:

Step-by-step explanation:

You need to add both of the angles you already know (1 and 2). If you add angle 1 and angle 2 you get 74. This means m < J K M would be 74°.

Answer:

74 degrees

Step-by-step explanation:

You have to add angles 1 and 2

35 +39=74

Therefore, 74 is the answer

I believe the answer is BC, AB, AC

Answer:

BC, AB, AC

Step-by-step explanation:

Let's first find m∠BAC, which is 180° - ( 95° + 55° )

(interior angle theorem)

That equals 30°.

Now that we know all of the angles, we can order the sides.

Each side in a triangle is as big as its corresponding angle (opposite angle), so the bigger the opposite angle, the larger the side, and vice versa.

Since ∠BAC is the least, its corresponding side, BC will also be the smallest. Next is ∠ACB at 55°, so side AB is the medium sized side. Finally at 95°, ∠ABC is the greatest angle, putting its opposite side, AC at the greatest.

Answer:

Step-by-step explanation:

First turn 10 into a faction with a denominator of 3. To do that just multiply 10 by 3 and that leaves you with 30 which is the numerator. So you turn the question into 30/3x2/3 which you can just do 30x2 which is 60. When multiplying the denominators stay the same if they're the same number so this leaves you with 60/3. If you want to simplify this divide 60 by three which is 20.

So 10x2/3 is 20

Answer:

Power, P = 80 W

Step-by-step explanation:

We have,

Weight of athlete is 960 N

It runs through a flight of stair case in 2 mins or 120 second

There are 100 stairs and each stair case has a length of 100 mm  or 0.1 m

Power is given by :

\(P=\dfrac{Fd}{t}\)

d is distance

For 100 stairs,

So,

\(P=\dfrac{960\times 100\times 0.1}{120}\\\\P=80\ W\)

So, the power of an athlete is 80 watts.

Answer:

65 miles per hour

Step-by-step explanation:

r = d/t

1 : 5 = 0.2

r = 13 : 0.2 = 65

Running this code will display the defined languages L_eq and L_neq. You can examine the output and check if they meet the stated conditions.

To explore whether L_eq and L_neq are complements, we need to define the languages L_eq and L_neq using the provided information and then compare them.

Using Jove, we can define L_eq as follows:

```python

from jove.LangDef import *

Sigma = {'0', '1'}

L_eq = {'0' + str(i) + '1' + str(i) for i in range(7)}

```

In this definition, we concatenate '0', the value of i, '1', and again the value of i to form strings in L_eq. The range of i is from 0 to 6, which ensures that the length of the strings in L_eq is less than or equal to 6.

Now let's define L_neq in the same manner:

```python

L_neq = {'0' + str(i) + '1' + str(j) for i in range(7) for j in range(7) if i != j}

```

Similar to L_eq, we concatenate '0', the value of i, '1', and the value of j to form strings in L_neq. The range of i and j is from 0 to 6, but we add the condition i != j to ensure that the strings in L_neq have i and j with different values.

To print and verify L_eq and L_neq, you can use the following code:

```python

print(L_eq)

print(L_neq)

```

Please note that the above code assumes you have the Jove library installed, which provides tools for defining and working with formal languages.

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To complete the double reflection transformation over the lines x = 1 and x = 3, we need to reflect each point twice.

For point a(-5,2), the first reflection over x = 1 will give us a'(-9,2).

The second reflection over x = 3 will give us a"(-7,2).
For point b(-1,5), the first reflection over x = 1 will give us b'(-3,5).

The second reflection over x = 3 will give us b"(-5,5).
For point c(0,3), the first reflection over x = 1 will give us c'(2,3).

The second reflection over x = 3 will give us c"(4,3).
So, the coordinates after the double reflection transformation are:
a"(-7,2), b"(-5,5), and c"(4,3).

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The inequality that is represented by the given graph is; y ≤ (3/4)x - 2

From the given inequality graph, we see that;

Slope; m = 3/4

x-intercept = -2.5

y-intercept = -2

Now, the equation of a line in slope intercept form is;

y = mx + c

where;

m is slope

c is y-intercept

Thus, our graph is ordinarily;

y = (3/4)x + (-2)

y =  (3/4)x - 2

However, it is an inequality that is shaded at the bottom with a thick line and so the inequality becomes;

y ≤ (3/4)x - 2

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Answer:

Please find attached drawing created with Microsoft word, that shows the image of of the triangle ΔABC. with coordinates of the vertices as, A(2, -4), B(0, -5), and C(6, 2), translated down 2 units to give the triangle ΔA prime B prime C prime , with coordinates of the vertices as A prime (2, -6), B prime (0, -7), and C prime (6, 0)

Step-by-step explanation:

Answer:

Here u go

Step-by-step explanation:

Because yeah

To estimate the standard deviation using the range rule of thumb, we need to find the range of the data set and divide it by 4.

In this case, the range is the difference between the highest and lowest heights, which is cm. Dividing by 4 gives us an estimate of the standard deviation of cm.
Comparing this estimate to the actual standard deviation of cm calculated from the data set, we can see that the estimate is off by quite a bit. This suggests that the range rule of thumb is not a very accurate method for estimating standard deviation.
In fact, the range rule of thumb is only accurate for data sets that are roughly bell-shaped and symmetrical, which may not be the case for body measurements. To get a more accurate estimate of standard deviation, we would need to use a more sophisticated statistical method.
Overall, the result suggests that we need to be cautious when using the range rule of thumb to estimate standard deviation, especially when working with data that is not well-behaved or that has outliers.

To estimate the standard deviation (s) using the range rule of thumb with body measurements, we first need the range of the heights of males provided in the dataset. Unfortunately, the low and high values in centimeters were not included in the question. However, I can explain the process step by step, and you can plug in the correct values to determine the accuracy of the estimate.
Step 1: Calculate the range
Range = High value (in cm) - Low value (in cm)
Step 2: Apply the range rule of thumb
Estimated standard deviation (s) = Range / 4
Step 3: Compare the estimated standard deviation to the given standard deviation (in cm)
Compare the estimated s value from Step 2 to the given standard deviation of cm (again, the value was not provided in the question).
Step 4: Determine the accuracy of the estimate
If the difference between the estimated s and the given standard deviation is within the specified cm (not provided in the question), then the estimate is considered accurate.
By following these steps and inputting the correct values, you can determine whether the range rule of thumb provides an accurate estimate for the standard deviation (s) of male heights in the body measurements dataset.

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The range rule of thumb provides a rough estimate of the standard deviation of data. By comparing the estimated and actual standard deviations, we can determine the accuracy of this rule for the given data set. If the estimated standard deviation is within n cm of the actual one, the estimate is considered accurate.

The range rule of thumb is a rule that provides a rough estimate of the standard deviation of a set of data. We can find it by dividing the range of the data (the difference between the largest and smallest data values) by 4. Thus, if the lowest height is cm and the highest is cm, then the estimated standard deviation ' would be ( − ) / 4.

Comparing this estimated standard deviation ' to the actual standard deviation calculated using the heights can provide a rough idea of how well the range rule of thumb works for this data set. If ' is within cm of , then the estimate can be considered accurate. If not, it suggests that the range rule of thumb may not provide a very accurate estimate for this particular data set.

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The given expression, \(\(350y \cdot C \cdot \cos(u)\)\), involves variables \(\(y\), \(C\)\), and \(\(u\)\) and their respective operations and functions.

The expression \(\(350y \cdot C \cdot \cos(u)\)\) represents a mathematical equation involving multiplication and the cosine function. Let's break down each component:

1. \(\(350y\)\) represents the product of the constant value 350 and the variable \(y\).

2. \(\(C\)\) is a separate variable that is being multiplied by \(\(350y\)\).

3. \(\(\cos(u)\)\) represents the cosine of the variable \(\(u\)\).

The overall expression represents the product of these three terms: \(\(350y \cdot C \cdot \cos(u)\)\).

To evaluate this expression or derive any specific meaning from it, the values of the variables \(\(y\), \(C\)\), and \(\(u\)\) need to be known or assigned. Without specific values or context, it is not possible to provide a numerical or simplified result for the given expression.

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Answer:

see explanation

Step-by-step explanation:

A linear function has the form

y = mx + b ( m is the slope and b the y- intercept )

B

the graph has a constant rate of change , measured by the slope m of the linear function.

Answer:

182

The number of permutations of 14 things taken 2 at a time is ...

 14P2 = 14·13 = 182

The first color can be any of the 14 on the palette. The second color must be different, so can be any of the remaining 13.

___

We assume that a "yellow/red" flag is different from a "red/yellow" flag. That is, order matters.

Answer:

Finding the dilation's center point is the first step in determining the scale factor. Next, we measure the distances between the center point and various points on the preimage and the image. We may determine the scale factor by dividing these distances by 2.

Step-by-step explanation: