If
α
,
β
are the roots of the equation
[
1

25
]
[
0
1
2
−
1
1
2
]
5
[
1
−
1
2
0
]
10
[
0
1
2
−
1
1
2
]
5
[
x
2
−
5
x
+
20
x
+
2
]
=
[
40
]
, then
(
1
−
α
)
(
1
−
β
)
−
50
is equal to ___

Based on the policy limit of $50,000, the total amount that the insurance company must pay out for these three people involved in Craig's personal injury protection policy is $73,500.

The total amount that the insurance company will indemnify the three persons involved in the accident is determined by the policy or liability limit of $50,000 for each person.

Policy limit in Craig's personal injury protection policy for each = $50,000

The medical expense for the first person = $23,000 (below limit)

The medical expense for the second person = $500 (below limit)

The medical expense for the third person (Craig) = $70,000 (above limit)

Total indemnity = $73,500 ($23,000 + $500 + $50,000)

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[tex]y = (1/5) x^5 + Ce^ {(-x^5)}[/tex] is the general solution of the given differential equation.

The given differential equation is:

y' + 5x⁴ y = x⁴

To solve this equation, we can use an integrating factor. First, we need to multiply both sides of the equation by the integrating factor, which is [tex]e^{(int 5x^4 dx)}[/tex]:

[tex]e^{(int 5x^4 dx) }y' + 5x^{4} e^{(int 5x^4 dx)} y = x^4 e^{(int 5x^4 dx)}[/tex]

The integral of 5x⁴ is (5/5)x⁵ = x, so the integrating factor is [tex]e^{(x^5)}[/tex]:

[tex]e^{(x^5)} y' + 5x^{4} e^{(x^5)} y = x e^(x^5)[/tex]

Now we can recognize the left-hand side as the product of the derivative of the product of [tex]e^{(x^5)[/tex]and y:

[tex](d/dx)[e^{(x^5)} y] = x^4 e^{(x^5)}[/tex]

Integrating both sides with respect to x, we get:

[tex]e^{(x^5)} y = (1/5) x^5 e^{(x^5)} + C[/tex]

where C is the constant of integration. Dividing both sides by [tex]e^{(x^5)}[/tex], we get the general solution:

[tex]y = (1/5) x^5 + Ce^(-x^5)[/tex]

where C is an arbitrary constant.

[tex]y = (1/5) x^5 + Ce^{(-x^5)}[/tex] is the general solution of the given differential equation.

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When x = 10, b takes the value 1. The values of a and b when x = 10 are a = 25 and b = 1.

To find the values of a and b when x = 10, we can substitute x = 10 into the given expressions for a and b and simplify the equations.

a = 5x/2

Replacing x with 10:

a = 5(10)/2

a = 50/2

a = 25

So, when x = 10, a takes the value 25.

b = 2x*(x - 5)/10x

Replacing x with 10:

b = 2(10)(10 - 5)/(1010)

b = 2(10)(5)/(100)

b = 205/100

b = 100/100

b = 1.

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The required equation is VW/UW = YW/XW for the given similar triangles.

The figure is given as shown.

As per the question, given that triangles ΔUVW and ΔXYW are similar.

As we know that similar triangles are defined as two triangles with the same shape, equal pair of corresponding angles, and the same ratio of the corresponding sides.

Therefore, we can be written as follows:

VW/UW = YW/XW

This signifies that the corresponding angles and sides of the two triangles are equal and proportionate.

Therefore, the required equation is VW/UW = YW/XW.

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It's also worth noting that there may be other factors that impact sales that are not included in the regression equation. For example, changes in consumer preferences, economic conditions, or competition from other businesses could all have an impact on sales that is not captured by the variables included in the equation.

So while a regression equation can be a useful tool for predicting sales, it's important to keep in mind that it's not a perfect predictor and should be used in conjunction with other information and analysis. To estimate a regression equation for sales as a function of population, advertising in the current year, and advertising in the previous year, you would need to gather data on sales, population, and advertising expenditures for both the current and previous years. Once you have this data, you can use regression analysis to determine how much of the variation in sales can be explained by population and advertising. As for whether or not predictions of sales in future years would be very accurate based on this regression equation, it really depends on how well the equation fits the data.

If the equation has a high R-squared value (meaning that a large percentage of the variation in sales can be explained by the independent variables), then predictions based on the equation are likely to be more accurate. However, if the equation has a low R-squared value, then predictions based on the equation may not be very accurate.

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The solution to the system of differential equations is x(t) = -29[tex]e^{-0.2t}[/tex] + 18[tex]e^{0.1t}[/tex] and y(t) = -9[tex]e^{-0.2t}[/tex] + 5[tex]e^{0.1t}[/tex] with initial conditions x(0)=-7 and y(0)=-2. The eigenvalues and eigenvectors are also given.

We can solve the system of differential equations using the eigenvalues and eigenvectors as follows

Let V be the matrix whose columns are the eigenvectors of the system

V = [ -7 4 ]

[ -2 1 ]

Then the diagonal matrix D whose diagonal entries are the eigenvalues of the system is

D = [ -0.2 0 ]

[ 0 0.1 ]

We can express the solution of the system as

[ x(t) ] [ -7 4 ] [ [tex]e^{-0.2t}[/tex] 0 ] [ x(0) ]

[ y(t) ] = [ -2 1 ] * [ 0 [tex]e^{0.1t}[/tex]] * [ y(0) ]

Substituting the given initial conditions, we get:

[ x(t) ] [ -7 4 ] [ [tex]e^{-0.2t}[/tex] 0 ] [ -7 ]

[ y(t) ] = [ -2 1 ] * [ 0[tex]e^{0.1t}[/tex] ] * [ -2 ]

Simplifying, we get

x(t) = (-7[tex]e^{-0.2t}[/tex] + 4[tex]e^{0.1t}[/tex](-7) + (-2[tex]e^{-0.2t}[/tex] + [tex]e^{0.1t}[/tex](-2)

= -29[tex]e^{-0.2t}[/tex] + 18[tex]e^{0.1t}[/tex]

y(t) = (-7[tex]e^{-0.2t}[/tex] + 4[tex]e^{0.1t}[/tex](-2) + (-2[tex]e^{-0.2t}[/tex] + [tex]e^{0.1t}[/tex](1)

= -9[tex]e^{-0.2t}[/tex] + 5[tex]e^{0.1t}[/tex]

Therefore, the solution to the system of differential equations with the given initial conditions is

x(t) = -29[tex]e^{-0.2t}[/tex] + 18[tex]e^{0.1t}[/tex]

y(t) = -9[tex]e^{-0.2t}[/tex] + 5[tex]e^{0.1t}[/tex]

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--The given question is incomplete, the complete question is given below " Solve the system of differential equations { x'=2.2x−8.4y, y' =0.6x−2.3y}

 with the initial condition x(0)=−7,y(0)=−2 The eigenvalues and their eigenvectors are found as follows. The lesser of the two eigenvalues is −0.2 and its corresponding eigevector is [ −7  −2]. The greater of the two eigenvalues is 0.1 and its corresponding eigevector is [ 4  1]. "--

Step-by-step explanation:0

The slope is 1/2, and the y-intercept is (0,-1).

The area shaded is what x could be

The estimated mean of the time for completion of race is 220 minutes where as the MAD to the mean ratio is 22.272%.

We have,

In statistics, the mean is one of the measures of central tendency. Another two are median and mode. Mean is  the average of the given set of data.

You interviewed a random sample of 25 marathon runners and compiled the following statistics.

Mean time to complete the race = 220 minutes and MAD = 50 minutes.

So from given data it can be concluded that

mean = 220             MAD= 50

Now we find ,

(MAD/Mean ) × 100%

= (50/220)× 100%

= (5×100)/22 %

≈ 22.272%

Hence , the estimated mean of the time for completion of race is 220 minutes where as the MAD to the mean ratio is 22.272%.

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complete question:

You interviewed a random sample of 25 marathon runners and compiled the following statistics.

Mean time to complete the race = 220 minutes and MAD = 50 minutes

What can you infer about the time to complete the race among the population of runners represented by your sample?

True. Role perception refers to an individual's perception of what their role or position entails and how they are expected to behave in a particular situation.

It is shaped by various factors such as the individual's personal values, beliefs, experiences, and cultural background, as well as the expectations and norms of the organization or group they belong to.

Role perception can influence an individual's behavior, performance, and job satisfaction, as it guides them on how to act and what to expect from others in their role. However, role perception may not always be accurate or aligned with the actual expectations of the role, which can lead to misunderstandings and conflicts.

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The Transformation of the original equation y=|1/2x-2|+3 one unit to the right results in the new equation y=|1/2(x-1)-2|+3

To shift the graph of the equation y=|1/2x-2|+3 one unit to the right, we can use a transformation of the form y=|1/2(x-1)-2|+3. This transformation will shift the graph one unit to the right by replacing x with (x-1) in the original equation.

To graph the transformed equation, we can start by finding the x- and y-intercepts. To find the y-intercept, we set x=0:

y=|1/2(0-1)-2|+3

y=|1/2(-1)-2|+3

y=|-1/2-2|+3

y=|-5/2|+3

y=5/2+3

y=11/2

Therefore, the y-intercept is (0, 11/2).

To find the x-intercept, we set y=0:

0=|1/2(x-1)-2|+3

-3=|1/2(x-1)-2|

-3=1/2(x-1)-2 or -3=-1/2(x-1)-2

-1=1/2(x-1) or -1=-1/2(x-1)

-2=x-1 or 0=x-1

x=-1 or x=1

Therefore, the x-intercepts are (-1, 0) and (1, 0).

Next, we can plot these points and draw the graph. The graph is symmetric about the vertical line x=1, as the absolute value function has this property.

Overall, the transformation of the original equation y=|1/2x-2|+3 one unit to the right results in the new equation y=|1/2(x-1)-2|+3.

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Answer: ABC is not a right angled triangle

Step-by-step explanation:

total = 22cm

22-8-5= 9cm

Hypotuneus = 9 cm since its the longest angle

pythagoras theorum = a2+b2=c2

so we need to see if 8² +5² =9²

64+25 need to be 81 (9² )

but its 64+25=89

therefore it is not a right angles triangle.

Answer:

-33-7x=

[tex] - 33 - 7x = 2(3 - 8x) - 3 [/tex]

[tex] - 33 - 7x = 6 - 16x - 3[/tex]

[tex] - 33 - 6 + 3 = - 16x + 7x[/tex]

[tex] \frac{ - 36}{ - 9 ?} = \frac{ - 9x}{ - 9?} [/tex]

Step-by-step explanation:

x=4

To answer your question, we need to use a combination formula, which is nCr = n! / (r! * (n-r)!).

In this case, we want to select 5 men out of 16 men, which can be done in 16C5 = 4368 ways. Then, we need to select 1 woman out of 11 women, which can be done in 11C1 = 11 ways. Therefore, the total number of committees possible if it must consist of 5 men is 4368 * 11 = 48,048.

In summary, there are 48,048 committees possible consisting of 5 men and 1 woman, out of a total of 11 women and 16 men. Finally, to find the total number of possible committees, multiply the number of ways to select the men by the number of ways to select the women: C(16, 5) * C(11, 1). This results in 4368 possible committees that consist of 5 men and 1 woman.

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Answer:

120.8

Step-by-step explanation:

The correct statement regarding the flow rate is given as follows:

The flow rate of the large tank is –10 gal/min, and the flow rate of the small tank is 10 gal/min.

The slope-intercept equation for a linear function is presented as follows:

y = mx + b

The parameters of the definition of the linear function are given as follows:

The functions are given as follows:

After 5 minutes, the two tanks have the same rate, hence the value of m is obtained as follows:

300 - 5m = 200 + 5m

10m = 100

m = 10 gal/min.

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The statements about the given parabola that are true are:

The form of a parabola is :

y = a ( x - h ) ² + k

This means that the statement that the vertex is (-2, 4) is true because the vertex is ( h, k ).

The focus is ( h,  k - p ) which would be ( -2 , 1 / 2 ). This is shown in option A.

The Directrix is:

y = 4 + 7/2

= 15 / 2

This is shown in option C.

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The margin of error for the survey is approximately 3.4% .

To calculate the margin of error for this survey at the 95% confidence level, we'll need to use the following formula:
Margin of Error = Z-score * √(p * (1-p) / n)
Where:
- Z-score represents the confidence level (1.96 for 95% confidence)
- p is the proportion of people who preferred Candidate A (0.41 or 41%)
- n is the sample size (800 voters)
Margin of Error = 1.96 * √(0.41 * (1-0.41) / 800)
After calculating, we get:
Margin of Error ≈ 0.0341 or 3.41%
So, the margin of error for this survey at the 95% confidence level is approximately 3.4% to the nearest tenth.

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When Juan fell asleep, his family had traveled approximately 59% of the total trip to the Grand Canyon.It's important to note that this calculation assumes that the distance traveled is proportional to the progress made in the trip and that no significant detours or changes in speed occurred.

To calculate the percentage of the total trip that Juan's family had traveled when he fell asleep, we need to divide the distance traveled by the total length of the trip and then multiply by 100.

The distance traveled before Juan fell asleep is given as 177 miles, and the total length of the trip is 300 miles.

Percentage = (Distance traveled / Total length of trip) * 100

Substituting the given values, we have:

Percentage = (177 miles / 300 miles) * 100Performing the calculation:

Percentage = (0.59) * 100 = 59%.

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Answer: Translate DEF 2 units to the right

Step-by-step explanation:

Each point in DEF is 2 units to the left of JKL. For example, D is at (-3, 4) and J is at (-1, 4). To map the figures on to one another, DEF must be moved 2 units to the right

This variable is a discrete variable as it can only take on three distinct values (0, 1, or more than 1) depending on how many days a student comes to campus in a week.

In other words, it is a categorical variable with three categories. This answer can be explained in a paragraph that discusses the definition of discrete variables and how they apply to the given scenario. The variable in this study, which is the number of days in a week a student comes to campus, is an example of a discrete variable. Discrete variables are variables that have a finite or countable number of possible values, often represented by integers. In this case, the number of days can only be whole numbers ranging from 0 to 7.

To summarize, the number of days a student comes to campus is a discrete variable because it can only take on a countable number of values in the form of whole numbers. This is an important distinction to make when conducting studies or analyzing data, as different statistical methods apply to discrete and continuous variables.

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The outlier in the data set of blog post comments affects the range and interquartile range in different ways. It increases the range and may also increase the interquartile range.

The range is the difference between the largest and smallest values in the data set. In this case, the range without the outlier is 16-2=14. However, if the outlier has a value greater than 16, then it increases the range. On the other hand, the interquartile range is the difference between the third quartile and the first quartile. The quartiles divide the data set into four equal parts, and the interquartile range is used to measure the spread of the middle 50% of the data. An outlier can increase the interquartile range if it falls outside the middle 50% of the data or decrease it if it falls within the middle 50%.

For example, if the outlier has a value of 20, then the range increases to 18, and the interquartile range also increases because the outlier is larger than the third quartile. If the outlier has a value of 1, then the range increases to 15, but the interquartile range decreases because the outlier is smaller than the first quartile. Therefore, outliers can have a significant impact on the range and interquartile range of a data set, and it is important to identify and handle them appropriately.

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The amount of Gatorade that Marcus would drink while walking 12 miles depends on several factors such as his personal preference, level of exertion, and the weather conditions.

However, a general rule of thumb is to drink about 8 ounces of fluid (water or sports drink) for every 20 minutes of exercise. If we assume that Marcus takes about 2 hours to walk 12 miles, he would be walking for 120 minutes, and he would need to drink about 48 ounces (8 ounces x 6 cycles of 20 minutes) of fluid during his walk. Therefore, Marcus would drink about 48 ounces of Gatorade (or any other fluid) during his 12-mile walk.

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There are 3x = 3(28) = 84 kiwis.next, we are told that the ratio of strawberries to kiwis is 5:4.

let's start by using the second piece of information to find the number of kiwis. if the ratio of kiwis to plums is 3:2, then we can represent the number of kiwis as 3x and the number of plums as 2x. we are told that there are 56 plums, so we can solve for x:

2x = 56x = 28 let's represent the number of strawberries as 5y and the number of kiwis as 4y. we already know that there are 84 kiwis, so we can solve for y:

4y = 84

y = 21

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Answer:

d

Step-by-step explanation:

took test

To find the number of bricks that a trailer will hold, we need to measure the capacity of the trailer. The most useful measure for this purpose would be volume, which is typically measured in cubic feet or cubic meters.

We would need to know the length, width, and height of the trailer in order to calculate its volume. Once we have that information, we can calculate the total number of cubic feet or cubic meters that the trailer can hold. We can then divide that number by the volume of a single brick to determine the maximum number of bricks that the trailer can hold. It's important to note that we also need to account for any empty space or gaps between the bricks in our calculation, since these will affect the total number of bricks that can be loaded into the trailer.

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Step-by-step explanation:

  One is twice as fast as the other     speeds are 2 x and x

      rate * time = distance

        (2x -x) * 50 = 750         x = 15 m/min      2x = 30 m/min

The correct inequality which is true when the value of x is -15 is,

⇒ x - 6 < - 1

⇒ - x - 6 > - 1

We have to given that;

To find inequality which is true when the value of x is -15.

Hence, Substitute x = - 15 in the inequality and find correct inequality as;

⇒ x - 6 > - 1

⇒ - 15 - 6 > - 1

⇒ - 21 > - 1

Which is not true.

⇒ - x - 6 < 1

⇒ - (- 15) - 6 < 1

⇒ 15 - 6 < 1

⇒ 9 < 1

Which is not true.

⇒ x - 6 < - 1

⇒ - 15 - 6 < - 1

⇒ - 12 < - 1

Which is true.

⇒ - x - 6 > - 1

⇒ - (- 15) - 6 > - 1

⇒ 15 - 6 > - 1

⇒ 9 > - 1

Which is true.

Thus, The correct inequality which is true when the value of x is -15 is,

⇒ x - 6 < - 1

⇒ - x - 6 > - 1

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Answer:

x=6

Step-by-step explanation:

25^3=15,625

5^6=15,625

Therefore, x=6

Answer:

x=6.........................................................

The equation that can be used to determine the reference angle, r, if θ = 7π/12 is option (b) r = π - θ.

A reference angle is the acute angle formed by the terminal side of an angle and the x-axis. To find the reference angle, we need to subtract the angle from either π/2 or π (depending on which quadrant the angle is in).
In this case, 7π/12 is in the second quadrant (between π/2 and π). Therefore, we subtract 7π/12 from π to get the reference angle:

r = π - θ
r = π - 7π/12
r = (12π/12) - (7π/12)
r = 5π/12

So the reference angle, r, for θ = 7π/12 is 5π/12.
Note that option (a) r = θ is incorrect because this would give the same angle as θ, not the reference angle. Option (c) r = θ - π is incorrect because it would give a negative angle, which is not an acute angle. Option (d) r = 2π - θ is incorrect because it would give an angle in the fourth quadrant, which is not the reference angle for an angle in the second quadrant.

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Answer:

I think that it is 18π sq in

Step-by-step explanation:

U do surface area of a cylinder

SA=2πrh+2πr^2