Juan and his little brother Miquel ran around a circular track together. Juan ran on the inner track, which has a radius of 30 feet. Miquel ran on the outer track which has a radius of 40 feet. How much further did Miquel run than Juan after two loops around the track? A. 31.4 ft. B. 62.8 ft. C. 125.6 ft. D. 219.8 ft.

Eigenvalues λ ₁ = -6 and λ ₂ = 9 Eigenvectors X ₁ = ( 1, 4) and X ₂ = ( 1,-11)

To write the given system of discriminational equations in matrix form, we define the vector function X( t) = ( x( t), y( t)). The system can also be written as dX/ dt = A × X,

where A is the measure matrix and X is the vector X( t). The measure matrix A is attained by taking the portions of x and y in the original equations

A = ((- 2,-1),

( 28, 9)).

To find the eigenvalues and eigenvectors, we need to break the characteristic equation

 det( A- λI) = 0,

where λ is the eigenvalue and I is the identity matrix. Substituting the values of A into the equation, we have

det((- 2- λ,-1),

( 28, 9- λ)) = 0.

Expanding the determinant, we get

- 2- λ)( 9- λ)-(- 1)( 28) = 0,

λ ²- 7λ- 54 = 0.

working this quadratic equation,

we find the eigenvalues λ ₁ = -6 and λ ₂ = 9.

To find the eigenvectors, we substitute each eigenvalue back into the equation( A- λI) X = 0 and break for X. For λ ₁ = -6, we have

( 4,-1),

( 28, 15)) × X ₁ = 0.

working this system, we gain X ₁ = ( 1, 4).

For λ ₂ = 9, we have

(- 11,-1),

( 28, 0)) × X ₂ = 0.

working this system, we gain X ₂ = ( 1,-11).

The general result to the system of discriminational equations can be expressed as

X( t) = c ₁ × e(- 6t) ×( 1, 4) c ₂ × e( 9t) ×( 1,-11),

where c ₁ and c ₂ are constants determined by original conditions. The eigenvalues and eigenvectors give information about the stability and geste of the system.

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The equation of the line is y = 13/6x - 5

From the question, we have the following parameters that can be used in our computation:

Points: (0, -5) and (6, 8)

A linear equation is represented as

y = mx + c

Where

c = y when x = 0

This means that

c = -5

So, we have

y = mx - 5

Also, we have

(x, y) = (6, 8)

This means that

8 = m x 6 - 5

So, we have

6m = 13

This gives

m = 13/6

So, we have

y = 13/6x - 5

Hence, the equation is y = 13/6x - 5

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Answer:

  $57,700

Step-by-step explanation:

The deductions are ...

  for pension and employment insurance, (5+2.4)% of $70,000

     = 0.074 × $70,000 = $5,180

  for income tax, ...

     8% of the 14,000 between $11,000 and $25,000 = $1,120

     12% of the 25,000 between $25,000 and $50,000 = $3,000

     15% of the 20,000 between $50,000 and $70,000 = $3,000

Then the total of deductions is ...

  $5,180 +1,120 +3,000 +3,000 = $12,300

Net salary after these deductions is ...

  $70,000 -12,300 = $57,700

Answer:

probability for 3 on a dice (P3) in one dice =

\( \frac{1}{6} \)

probability for even no. of a dice (Pe) =

\( \frac{3}{6} = \frac{1}{2} \)

Therefore, the probability of finding 3 on one dice and even on another (P) = P3 + Pe

\( = \frac{1}{6} + \frac{1}{2} = \frac{1 + 3}{6} = \frac{4}{6} = \frac{2}{3} \)

The clearinghouse and research middle on servant management is now called c. The Greenleaf Center for Servant Leadership.

The middle turned into named after Robert K. Greenleaf, who first brought the idea of servant leadership in his essay "The Servant as Leader" published in 1970. The Greenleaf Center for Servant Leadership serves as a worldwide useful resource for promoting the knowledge and exercise of servant leadership.

It conducts studies, provides educational applications, and gives a platform for individuals and businesses to study and interact with servant management ideas. The middle's recognition is on nurturing moral and compassionate management that prioritizes the nicely-being and growth of individuals and the groups they serve. Through its initiatives, the Greenleaf Center pursuits to inspire and empower leaders to create a superb and impactful exchange by embracing the servant management philosophy.

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The clearinghouse and research center on servant leadership is called The Greenleaf Center for Servant Leadership.

The clearinghouse and research center on servant leadership is called The Greenleaf Center for Servant Leadership. It is a nonprofit organization that was founded in 1964 by Robert K. Greenleaf. The center is dedicated to promoting the principles of servant leadership, which emphasizes serving others and putting their needs first.

The Greenleaf Center conducts research, provides resources and training, and serves as a hub for individuals and organizations interested in servant leadership.

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Answer:

x = -1

Step-by-step explanation:

The axis of symmetry is a line that divides the two sides of a parabola through the vertex.

It is assumed that angle C is unknown. The answers for ZB, ZC, and C are calculated, rounded to 3 decimal places. If no answer exists, it will be represented as DNE (Does Not Exist).

The Law of Sines states that for any triangle, the ratio of the length of a side to the sine of its opposite angle is constant. Mathematically, it can be expressed as

a/sin(A) = b/sin(B) = c/sin(C), where a, b, and c are the lengths of the sides, and A, B, and C are the opposite angles.

In the given triangle, we have ZA = 112°, a = 33, and b = 13. Let's assume angle C is unknown.

Using the Law of Sines, we can set up the following ratios:

a/sin(A) = b/sin(B) = c/sin(C)

Substituting the given values, we have:

33/sin(112°) = 13/sin(B) = c/sin(C)

To find angle B, we can solve the equation:

sin(B) = (13 * sin(112°)) / 33

B = arcsin((13 * sin(112°)) / 33)

To find angle C, we can solve the equation:

sin(C) = (c * sin(112°)) / 33

C = arcsin((c * sin(112°)) / 33)

To find side c, we can use the Law of Sines again:

c/sin(C) = 33/sin(112°)

c = (33 * sin(C)) / sin(112°)

By calculating the above equations, we can determine the values of ZB, ZC, and side c rounded to 3 decimal places. If there are no valid solutions, it will be represented as DNE (Does Not Exist).

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Newton's Forward Difference formula is a finite difference equation that can be used to determine the values of a function at a new point. For this purpose, it uses a set of known data points to produce an approximation that is more accurate than the original values.

To begin, we'll set up the forward difference table for the given data set. This is accomplished by finding the first difference between each pair of successive data points and recording those values in the first row.

Similarly, we'll find the second, third, and fourth differences and record them in the next rows of the table.

To find f(0.5), we'll use the following forward difference formula:

\(f(x+0.5)=f(x)+[(delta f)(x)/1!] (0.5)+[(delta²f)(x)/2!] (0.5)²+[(delta³f)(x)/3!] (0.5)³+[(delta⁴f)(x)/4!] (0.5)⁴\)

where delta f represents the first difference, delta²f represents the second difference, delta³f represents the third difference, and delta⁴f represents the fourth difference.

The data points are given as follows: y = foxo is known at the following 1234 хо XO12 81723 55 109

Finding the forward difference table below: x  y  delta y delta²y delta³y delta⁴y12  1  3   4   1   8   10   8 817  2  9   9   9  18  18  73 23  3  0  -9   9   0 -55 12755  4 -54 -9 -54  72 182

Total number of entries: 6. We can see from the table that the first difference of the first row is [1, 6, 7, -48, -63], which means that the first data point has a difference of 1 with the next data point, which has a difference of 6 with the next data point, and so on.

Since we need to find f(0.5), which is between x=1 and x=2,

we'll use the data from the first two rows of the table: x  y  delta y delta²y delta³y delta⁴y12  1  3   4   1   8   10   8 817  2  9   9   9  18  18  73

To calculate f(0.5), we'll use the formula given above:

f(0.5)=3+[(delta y)/1!]

(0.5)+[(delta²y)/2!]

(0.5)²+[(delta³y)/3!]

(0.5)³+[(delta⁴y)/4!]

(0.5)⁴=3+[(6)/1!]

(0.5)+[(1)/2!]

(0.5)²+[(8)/3!]

(0.5)³+[(10)/4!] (0.5)⁴=3+3(0.5)+0.25+8(0.125)+10(0.0625)=3+1.5+0.25+1+0.625=6.375

Therefore, f(0.5)=6.375.

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The general solution for the given differential equation is the sum of the complementary function and the particular solution:

\(y = y_h + y_p\\\\= C_1e^{6x} + C_2e^{-6x} + (-1/70)e^{3x} + (-1/70)e^{-3x}\)

where C₁ and C₂ are arbitrary constants determined by the initial or boundary conditions of the problem.

We are given the differential equation: d²y/dx - 36y = cosh(3x).

In this case, the homogeneous equation is d²y/dx - 36y = 0.

The characteristic equation associated with the homogeneous equation is obtained by replacing the derivatives with their corresponding algebraic expressions. In our case, we have r² - 36 = 0. Solving this quadratic equation, we find the roots to be r = ±6.

Since the roots are distinct and real, the general solution for the homogeneous equation is given by:

\(y_h = C_1e^{6x} + C_2e^{-6x}\)

where C₁ and C₂ are arbitrary constants determined by the initial or boundary conditions of the problem.

The term cosh(3x) can be written as a linear combination of exponential functions using the identities:

\(cosh(ax) = (e^{ax} + e^{-ax})/2, \\\\sinh(ax) = (e^{ax} - e^{-ax})/2.\)

Therefore, \(cosh(3x) = (e^{3x} + e^{-3x})/2.\)

Now, we assume the particular solution has the form:

\(y_p = A_1e^{3x} + A_2e^{-3x}\)

where A₁ and A₂ are undetermined coefficients.

Substituting these derivatives into the original differential equation, we get:

\((9A_1e^{3x} + 9A_2e^{-3x}) - 36(A_1e^{3x} + A_2e^{-3x}) = (e^{3x} + e^{-3x})/2.\)

To satisfy this equation, the coefficients of the exponential terms on both sides must be equal. Therefore, we have the following system of equations:

9A₁ - 36A₁ = 1/2,

9A₂ - 36A₂ = 1/2.

Solving these equations, we find A₁ = -1/70 and A₂ = -1/70.

Thus, the particular solution is:

\(y_p = (-1/70)e^{3x} + (-1/70)e^{-3x}\)

Finally, the general solution for the given differential equation is the sum of the complementary function and the particular solution:

\(y = y_h + y_p\\\\= C_1e^{6x} + C_2e^{-6x} + (-1/70)e^{3x} + (-1/70)e^{-3x}\)

where C₁ and C₂ are arbitrary constants determined by the initial or boundary conditions of the problem.

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(a) False: Just because a matrix is diagonalizable does not guarantee that it has an LU-decomposition. Diagonalizability relates to eigenvectors and eigenvalues, while LU-decomposition involves triangular matrices.

(b) True: If a real and symmetric matrix has distinct eigenvalues, then it is guaranteed to have an orthonormal basis of eigenvectors. This is a property of real symmetric matrices known as the Spectral Theorem.

(c) True: If a matrix is invertible, then it is also diagonalizable. In fact, any invertible matrix is diagonalizable.

(d) True: If a matrix is diagonalizable and the eigenvectors come from different eigenspaces, then they are mutually orthogonal. Eigenvectors corresponding to distinct eigenvalues are always orthogonal.

(e) False: The existence of an LU-decomposition does not imply diagonalizability. An LU-decomposition involves triangular matrices, while diagonalizability is related to eigenvectors and eigenvalues.

(f) True: If a matrix has distinct eigenvalues, then it is always diagonalizable. This is a property of matrices with distinct eigenvalues.

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Answer:

32.7%

explanation:

Mrs. Go gle

Answer:

Infinite solutions

Step-by-step explanation:

you add 2x to both sides of the bottom equation and then BAM they are coinciding

The missing part of the equation is \(-7.0\times10^4 s^2kg⋅m^2 / 1000000.\)

To fill in the missing part of the equation, let's analyze the given information and the desired conversion. The equation is:

\((-7.0\times 10^4 s^2g⋅m^2)\cdot \pi = ? s^2kg\cdot m^2\)

In this equation, we have a quantity expressed in\(s^2g\cdot m^2\) units on the left-hand side. To convert it to \(s^2kg\cdot m^2\) units, we need to multiply it by a conversion factor.

To perform the conversion, we can use the fact that 1 kg is equal to 1000 g. Therefore, the conversion factor we need is:

1 kg / 1000 g

To ensure that the units cancel out correctly, we need to square this conversion factor because we have \(s^2g\cdot m^2\) on the left-hand side. So the missing part of the equation is:

\((-7.0\times 10^4 s^2g\cdot m^2)\cdot \pi = (-7.0\times 10^4 s^2g\cdot m^2)\cdot (1 kg / 1000 g)^2\)

Simplifying this expression, we get:

\((-7.0\times10^4 s^2g\cdot m^2)\cdot \pi = -7.0 \times10^4 s^2kg\cdot m^2 / 1000000\)

Therefore, the missing part of the equation is \(-7.0 \times 10^4 s^2kg\cdot m^2 / 1000000.\)

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Answer:

68.4 miles

Step-by-step explanation:

7.6 * 9 = 68.4

The probability that at least 4 will be winners is 0.0155

p = 10/40 = 0.25

n = 5

According to the binomial distributions,

\(p(x) = ^{n} C_{x}p^{x}(1-p)^{n-x}\)

Now,

P ( at least 4 )  = \(P(X\geq 4)\)

P (at least 4 ) =

\(=P(4) +P(5)\\\\= ^{5} C_{4}0.25^{4}(0.75)^{5-4} + ^{5} C_{5}0.25^{5}(0.75)^{0}\\\\= 0.0146 +0.009 = 0.0155\)

Thus, the probability that at least 4 will be winners is 0.0155

The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1, where, broadly speaking, 0 denotes the event's impossibility and 1 denotes certainty.

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Answer:

3/4 of a hour

Step-by-step explanation:

2 miles  = 0.5 hours

Divide by 2

1 mile = 0.25 hours

Multiply by 3

3 mile = 0.75 hours

Answer:

45 minutes or .75 of an hour or 3/4 of an hour

Step-by-step explanation:

if you walk 2 miles in a half-hour (30 minutes) , how long will it take to walk 3 miles. Well the answer is simple, we need to use proportions to solve it though. For example:

\(\frac{miles}{hours}\)   =    \(\frac{2}{.5}\)

therefore, half of .5 is .25

so for someone to complete 1 mile, it takes .25 of an hour. .25 of an hour is 15 minutes. Therefore, the correct simplified proportion is : \(\frac{1}{.25}\)

Now we need to find out what the denominator (bottom number/time) would be when the numerator (top number of the fraction) is =3.

Since we have the simplified version as a 1, we can just multiply .25 by 3 which is .75, and .75 of an hour is 45 minutes. Therefore the answer is 45 minutes.

Answer:

\(\frac{1}{3} x^3 - x^2 + 4x\)

Step-by-step explanation:

All this takes is the use of the power rule, which, for integrals, says that

∫\(x^n\) = \(\frac{1}{n+1}x^{n+1}\).

With this in mind, we can integrate:

∫\(x^2 - 2x + 4\)

= \(\frac{1}{3} x^3 - x^2 + 4x\).

We can also check our answer by differentiating our answer:

\(\frac{d}{dx} (\frac{1}{3}x^3 - x^2 + 4x)\\\\ = x^2 - 2x + 4\)

so we are correct!

hope this helped!

a. John Underpar's possible monetary outcomes are either winning, which is worth -$5 (the cost of the ticket).

b. the driver (worth $300) or having a worthless ticket (worth $0).

c) Probability of getting nothing = 79/80 = 0.9875
Probability of winning the driver = 1/80 = 0.0125
d. the expected value of buying a ticket is -$1.19, which means on average, a person can expect to lose $1.19 by buying a ticket.
e.the expected return to the club is $100 if all 80 tickets are sold.

a. John Underpar's possible monetary outcomes are either winning the Taylormade R9 10.5 regular flex driver, which is worth $300, or having a worthless ticket, which is worth -$5 (the cost of the ticket).

b. Actually, winning the driver is worth $300, not $295. So, Mr. Underpar's possible monetary outcomes are either winning the driver (worth $300) or having a worthless ticket (worth $0).

c. Mr. Underpar's "experiment" can be summarized as a probability distribution with the following probabilities:

Probability of getting nothing = 79/80 = 0.9875
Probability of winning the driver = 1/80 = 0.0125

d. The mean or expected value of the probability distribution can be calculated as:

Expected value = (Probability of winning the driver x Value of winning) + (Probability of getting nothing x Value of nothing)
Expected value = (0.0125 x $300) + (0.9875 x -$5)
Expected value = $3.75 - $4.94
Expected value = -$1.19

Therefore, the expected value of buying a ticket is -$1.19, which means on average, a person can expect to lose $1.19 by buying a ticket.

e. If all 80 tickets are sold, the expected return to the club can be calculated as:

Expected return = (Number of tickets sold x Price of a ticket) - Value of the prize
Expected return = (80 x $5) - $300
Expected return = $400 - $300
Expected return = $100

Therefore, the expected return to the club is $100 if all 80 tickets are sold.

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Check the picture below.

Make sure your calculator is in Degree mode.

Answer:

8x + 2y

Step-by-step explanation:

12x + 3y = 8 you need to transfer the no. 8 to left since it's positive, it will be negative once you tranfer that and the result is this 8x + 3y -8 =0. Then do it again on the second given, -4x = y + 8.

Tranfer the y variable to left, y is positive then it will be a negative. No need to transfer the no. 8. Then the result would be -4x - y + 8=0

To this solve this, wrote it like this:

12x + 3y –8

-4x - y + 8

——————

8x + 2y

Answer:

5050

Step-by-step explanation:

To solve via calculator, go to the MATH menu, then the 0th option should say "summation" and insert it from there.

To solve algebraically, break the summation into 2 parts. Excuse the strange formatting, I can't find a way to do it normally.

4(\(\frac{50}{1}\)∑n) -

= 4( \(\frac{50(50+1)}{2}\)) - 50(1)

= 5100 - 50

= 5050

Answer:

8

Step-by-step explanation:

Answer:

y=7*3^x

Step-by-step explanation:

y=ab^x

(0,7) ⇒ 7=ab^0 ⇒ 7=a

(5, 1701) ⇒ 1701= 7b^5 ⇒ b^5=243 ⇒ b^5= 3^5 ⇒ b=3

y=7*3^x

On a scale drawing of a basketball court, 1 inch equals 8 feet the actual area of the basketball court if the scale drawing is 11. 75 inches by 6. 25 inches will be 4,700 square feet.

Given:

To solve the given question we will assume the court is rectangular in shape so we will solve by using formula of Area of rectangle

\(\rm Area \;of\;rectangle\;= l\times b\)

Where, l=length

            b=breadth

According to the given question,

    \(\rm Area = 94\; feet \times 50\; feet\\\\ = 4,700 \;square\; feet.\\\)

Therefore, Area of the basketball court will be 4,700 square feet.

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Answer:

YOU HAVE TO WRITE YOUR QUESTION ON COMPUTER AS ,

Step-by-step explanation:

  4/(2*x-3)

I hope it will work

Answer:

It's A,E,F,H

Step-by-step explanation:

Got it right on test

The median is 120, The lower quartile is 112 and The upper quartile is 140

and  interquartile range is 28.

The difference between the third and first quartiles is referred to as the interquartile range. Quartiles are the parceled values that partition the entire series into 4 equivalent parts. There are then three quartiles. The lower quartile is represented by Q1, the second quartile is represented by Q2, and the third quartile is represented by Q3, which is the upper quartile. As a result, the difference between the upper and lower quartiles constitutes the interquartile range.

Given data

115, 120, 118, 104, 109, 148, 135, 141, 139

arrange series in ascending order,

104, 109, 115, 118, 120, 135, 139, 141, 148

the middle term of series is 120

median = 120

for lower Quartile Q₁ = (109 + 115)/2 = 112

for upper Quartile Q₃ = (139 + 141)/2 = 140

interquartile range = Q₃ - Q₁  = 140 - 112 = 28

Hence the median = 120,  lower quartile = 112,  upper quartile = 140 and

interquartile range = 28.

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Answer:

obtuse and scalene

Step-by-step explanation:

at least one angle is larger than 90º, and so it's an obtuse angle.

scalene triangle means all sides of the triangle are different lengths.

Answer:

Obtuse and scalene

Explanation:

An obtuse triangle has one angle greater than 90° with the rest of the angles being acute.

A scalene triangle has all sides of different lengths.

Answer:

13.2

Step-by-step explanation:

We just divide 79/6 which is equal to 13.1666667 which we can round to 13.2

Answer:

13.166667 best describes the fraction 79/6