Consider the following.
f(x) =
ex if x < 1
x4 if x ≥ 1
, a = 1
(a)
lim x→1− f(x)=

The general solution to the differential equation s" + b s' + 9s = 0 can be written as:

[tex]s(t) = c1*e^(-bt/2)*cos(({4b-36)/2)t} 4b-36)/2)t) + c2e^(-bt/2)*sin\sqrt{(4b-36)/2)*t)} (4b-36)/2)*t)[/tex]

where c1 and c2 are constants determined by the initial conditions.

The behavior of the solutions to this equation depends on the value of the parameter b. Specifically, there are three cases to consider:

Overdamped: If b > 6, then the roots of the characteristic equation[tex]s^2 + bs + 9 = 0[/tex] are real and distinct, i.e., [tex]b^2 - 4ac[/tex] > 0. In this case, the general solution is a linear combination of two decaying exponentials, and the system is said to be overdamped. To find the interval for b for which the equation is overdamped, we solve the inequality b > 6, which gives the interval (6, infinity).

Critically damped: If b = 6, then the roots of the characteristic equation are real and equal, i.e., [tex]b^2 - 4ac[/tex]= 0. In this case, the general solution is a linear combination of two decaying exponentials, where one of the exponentials has an additional factor of t. The system is said to be critically damped. To find the interval for b for which the equation is critically damped, we solve the equation b = 6, which gives the singleton set {6}.

Underdamped: If b < 6, then the roots of the characteristic equation are complex conjugates, i.e., [tex]b^2 - 4ac[/tex]  < 0. In this case, the general solution is a linear combination of two decaying exponentials, where the exponentials have a sinusoidal factor. The system is said to be underdamped. To find the interval for b for which the equation is underdamped, we solve the inequality b < 6, which gives the interval (-infinity, 6).

Therefore, the interval for b that makes the general solution overdamped is (6, infinity), the singleton set {6} makes the general solution critically damped, and the interval for b that makes the general solution underdamped is (-infinity, 6).

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Answer:

____________________________________________________________

   Why?

Trapezoids have only one pair of parallel sides; parallelograms have two pairs of parallel sides. A trapezoid can never be a parallelogram. The correct answer is that all trapezoids are quadrilaterals.

____________________________________________________________    

   What's a  parallelogram?                                                                                      

 Its a four-sided plane rectilinear figure with opposite sides parallel.

____________________________________________________________

Please don't be afraid to point out errors :)  

____________________________________________________________

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The correct shape which is not a parallelogram is shown in Option D.

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

There are four shapes are shown.

Now, We know that;

In a parallelogram, there are two pair of parallel lines.

But In option D;

There are only one pair of parallel lines.

Hence, The correct shape which is not a parallelogram is shown in Option D.

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Answer:

5x+4y-40=0

Step-by-step explanation:

Answer:

3:2

Step-by-step explanation:

a square has the same side lengths so just √36 = 6 to find the sides of the squares then compare the two sides in ratio form 6:4 then reduce

Answer:

1) 1.2 minutes

2) 8.3 laps

3) 25.2 minutes

A = $4,312.00

I = A - P = $2,112.00

hey!

Equation:

A = P(1 + rt)

Calculation:

First, converting R percent to r a decimal

r = R/100 = 8%/100 = 0.08 per year.

Solving our equation:

A = 2200(1 + (0.08 × 12)) = 4312

A = $4,312.00

The total amount accrued, principal plus interest, from simple interest on a principal of $2,200.00 at a rate of 8% per year for 12 years is $4,312.00.

-------------------------------------------------

have a good day! hope i helped in some way

Let λ be an eigen value of an invertible matrix. Then, [tex]\lambda^{-1}[/tex] is surely an eigenvalue of [tex]A^{-1}[/tex].

What is an invertible matrix?

For a matrix to be invertible, it must have a unique matrix that, when multiplied with the original matrix, gives the identity matrix.

[tex]A * B = B * A = I[/tex]

Suppose A is an invertible matrix and λ is an eigenvalue of A with a corresponding nonzero eigenvector x, i.e., Ax = λx.

To show that [tex]\lambda^{-1}[/tex] is an eigenvalue of [tex]A^{-1}[/tex], we need to find a nonzero vector y such that [tex]A^{-1}y[/tex] = [tex]\lambda^{-1}y[/tex].

Let's start by multiplying both sides of the equation Ax = λx by [tex]A^{-1}[/tex]:

[tex]A^{-1}(Ax) = A^{-1}(\lambda x)[/tex]

(x is nonzero, so we can divide by x)

[tex]A^{-1}(Ax/x) = A^{-1}(\lambda x/x)\\A^{-1}(A(x/x)) = A^{-1}(\lambda)[/tex]    

Since [tex]A^{(-1)}A = I[/tex] (identity matrix), and x/x = 1, we have:

[tex]A^{(-1}(I) = A^{(-1)}[/tex] λ

[tex]A^{(-1)}[/tex] = λ[tex]A^{(-1)}[/tex]

Now, let y = A^(-1)x. We can rewrite the equation above as:

[tex]A^{(-1)}x[/tex] = λ[tex]A^{(-1)}y[/tex]

([tex]A^{(-1)}x[/tex]/λ) = [tex]A^{(-1)}y[/tex]/λ

(x is nonzero, so we can divide by x)

([tex]A^{(-1)}x/x[/tex])/λ = [tex](A^{(-1)}y/y[/tex])/λ

([tex]A^{(-1)}(x/x)[/tex])/λ = ([tex]A^{(-1)}y/y[/tex])/λ

([tex]A^{(-1)}(1)[/tex])/λ = ([tex]A^{(-1)}y/y[/tex])/λ

([tex]A^{(-1)}[/tex])/λ = ([tex]A^{(-1)}y[/tex])/λ

Since [tex]A^{(-1)}[/tex] is a matrix and λ is a scalar, we can rearrange the equation as follows:

([tex]A^{(-1)}[/tex])/λ = [tex]A^{(-1)}[/tex]y/λ

(1/λ)[tex]A^{(-1)}[/tex] =[tex]A^{(-1)}[/tex]y/λ

This shows that 1/λ is an eigenvalue of [tex]A^{(-1)}[/tex] with the corresponding eigenvector y. Therefore, we have shown that if λ is an eigenvalue of A, then [tex]\lambda^{(-1)}[/tex] is an eigenvalue of [tex]A^{(-1)}[/tex]

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Answer:

x ≈ 121.2 ft

Step-by-step explanation:

Using the tangent ratio in the right triangle

tan60° = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{x}{70}[/tex] ( multiply both sides by 70 )

70 × tan60° = x , then

x ≈ 121.2 ft ( to 1 dec. place )

Answer: a. 50 African Americans

b. Pool B will have a smaller​ p-value because that pool's number of AA people is further from the hypothesized number of AA people.

Step-by-step explanation:

Answer:

x=6 and x=-2

Step-by-step explanation:

so

x(x-4)=12

first distribute

then move the terms

and the u get

x=6 and x=-2

hope this helped

Answer:

x=6, x=-2

Step-by-step explanation:

x(x-4)=12

distributive property, x^2-4x=12

x^2-4x-12=0

(x-6)(x+2)

therefore, x=6, x=-2

(a) Binomial probability distribution does X have. The option 1 is correct answer.  

(b) 0.5265 is the sample proportion [tex]\hat{P}[/tex] of sampled adults who say the President is doing a good job.

(c) n * p is the R formula for the expected value of X in terms of n and p. The option 4 is correct answer.

(d) 1.645 is the z critical value that we would use to construct a classical 90% confidence interval for p.

(e) A 90% classical confidence interval for p is 0.5104, 0.5428.

(f) 0.0324 is the 90% classical confidence interval for p.

(g) 0.0357 is the longest possible length of this interval.

a)  The random variable X, representing the number of sampled adults who say the President is doing a good job, follows a binomial probability distribution. Therefore, the correct answer is option 1.

b) The sample proportion, [tex]\hat{P}[/tex], of sampled adults who say the President is doing a good job can be calculated by dividing the number of adults who said the President was doing a good job (x = 2222) by the total sample size (n = 4220):

[tex]\hat{P}[/tex] = x / n

   = 2222 / 4220

   = 0.5265

c) The expected value of X is given by

n*p,

where n is the sample size and

p is the true proportion of adults who feel the President is doing a good job.

Therefore, the correct answer is option 4.

d) To construct a classical 90% confidence interval for p, we need to find the z critical value. This value can be found using a z-table or calculator and is approximately 1.645.

e) Using the sample proportion, [tex]\hat{P}[/tex], the z critical value, and the sample size, a 90% classical confidence interval for p can be calculated. This is done using the formula:

[tex]\hat{P} \pm z \times \sqrt{\frac{\hat{P} \times (1 - \hat{P})}{n}}[/tex]

The interval is (0.5104, 0.5428).

f) The length of the 90% classical confidence interval for p can be found by subtracting the lower limit from the upper limit: 0.5428 - 0.5104 = 0.0324.

g) The longest possible length of the 90% classical confidence interval for p can be found by using the formula:

[tex]2z \sqrt{\frac{\hat{P} ( 1 - \hat{P})}{n}[/tex]

Plugging in the values from the sample, we get

21.645 √(0.5266(1-0.5266)/4220)

= 0.0357.

This means that the interval can be at most 0.0357 in length.

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It is 12 goats and 50 chickens to make those animals and that exact number of legs

Answer:

[tex]1\frac{1}{3}[/tex]

Step-by-step explanation:

Answer:

c is the only one that would result in an integer

Step-by-step explanation:

i hope this helps :)

Option c ∛ 27 would result in an integer.

An integer is the number zero, a positive natural number or a negative integer with a minus sign. The negative numbers are the additive inverses of the corresponding positive numbers.

Given here, ∛27= 3 while the other options ∛60 is not an integer because 60 is not  cubic number similarly for 9 , 18 are not cubic numbers and thus their subsequent cubic roots will not yield an integer.

Hence, Option c ∛ 27 would result in an integer.

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The 98% confidence interval for the distribution of differences is given as follows:

(-2.58%, 5.78%).

The difference of the sample means is given as follows:

6.6 - 5 = 1.6%.

The standard error for each sample is given as follows:

The standard error for the distribution of differences is then given as follows:

[tex]s = \sqrt{0.53^2 + 1.64^2}[/tex]

s = 1.72.

The critical value, using a t-distribution calculator, for a two-tailed 98% confidence interval, with 19 + 22 - 2 = 39 df, is t = 2.4286.

The lower bound of the interval is given as follows:

1.6 - 2.4286 x 1.72 = -2.58%.

The upper bound of the interval is given as follows:

1.6 + 2.4286 x 1.72 = 5.78%.

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A lamina occupies the region of a disk in the first quadrant where 2 ≤ r ≤ 16, and the density at each point is given by the function ρ(r, θ) = 3[tex](r^2).[/tex] Further analysis is required to determine the mass and other properties of the lamina.

The given information describes a lamina occupying a region in the first quadrant of a disk. The radial distance from the origin is limited to the range 2 ≤ r ≤ 16. The density of the lamina at any point within this region is determined by the function ρ(r, θ) = 3[tex](r^2)[/tex], where r represents the radial distance and θ represents the angle in the polar coordinate system.

To fully analyze the lamina, additional calculations are necessary. One important calculation is determining the mass of the lamina, which involves integrating the density function over the given region. By integrating the function ρ(r, θ) = 3[tex](r^2)[/tex] over the appropriate range of r and θ, we can find the total mass of the lamina. Additionally, other properties such as the center of mass or moment of inertia of the lamina could be determined by using appropriate formulas and integration techniques.

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According to the information, we can infer that no, they cannot raise their cumulative average to 2.3 after completing 15 fall semester credits. On the other hand, they would need an average GPA of 3.25 for their two junior year semesters combined (30 credits) to achieve their goal of a 2.3 cumulative GPA and 90 credits.

In order to calculate the new cumulative GPA, we need to consider both the current cumulative GPA and the GPA earned in the fall semester. Since the student's current cumulative GPA is 2.0 and they have already accumulated 60 credits, their total grade points earned so far would be 2.0 multiplied by 60, which equals 120 grade points.

To raise the cumulative GPA to 2.3, the student would need a total of 2.3 multiplied by (60 + 15) = 2.3 multiplied by 75 = 172.5 grade points by the end of the fall semester.

Since the student has already accumulated 120 grade points, they would need to earn an additional 52.5 grade points in the fall semester. To calculate the required semester GPA, we divide 52.5 by 15 credits, which gives us a required semester GPA of 3.5.

So, the student would need a semester GPA of 3.5 in order to raise their cumulative average to 2.3 after completing 15 fall semester credits.

They would need an average GPA of 3.25 for their two junior year semesters combined (30 credits) to achieve their goal of a 2.3 cumulative GPA and 90 credits.

Explanation: To calculate the average GPA for the two junior year semesters, we need to consider the total grade points earned and the total number of credits taken.

Currently, the student has accumulated 60 credits and 120 grade points. In order to achieve a cumulative GPA of 2.3 after completing 90 credits, they would need a total of 2.3 multiplied by 90 = 207 grade points.

To calculate the required grade points for the two junior year semesters, we subtract the current grade points (120) from the desired total grade points (207), which gives us 207 - 120 = 87 grade points needed for the junior year.

Since the student plans to take 30 credits during their junior year, they would need to earn 87 grade points in those 30 credits. Dividing 87 by 30 gives us an average GPA of approximately 2.9 for the two junior year semesters.

According to the above, the student would need an average GPA of 3.25 (rounded up) for their two junior year semesters combined to achieve their goal of a 2.3 cumulative GPA and 90 credits.

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The solution to the system of differential equations is x₁(t) = e⁻⁵ˣ + 3e³ˣ and x₂(t) = 2e⁻⁵ˣ + 5e³ˣ

Let's solve the given system of differential equations: x₁' = -5x₁ + 0x₂ ...(1) x₂' = -16x₁ + 3x₂ ...(2)

To solve this system, we can rewrite it in matrix form. Let's define the vector X = [x₁, x₂] and the matrix A as:

A = [[-5, 0], [-16, 3]]

The system can then be written as X' = AX, where X' is the derivative of X with respect to time.

Now, let's find the eigenvalues and eigenvectors of matrix A. The eigenvalues are obtained by solving the characteristic equation det(A - λI) = 0, where I is the identity matrix.

A - λI = [[-5 - λ, 0], [-16, 3 - λ]]

det(A - λI) = (-5 - λ)(3 - λ) - 0(-16) = λ² + 2λ - 15 = (λ + 5)(λ - 3)

Setting the characteristic equation equal to zero, we find the eigenvalues: λ₁ = -5 λ₂ = 3

To find the corresponding eigenvectors, we substitute each eigenvalue back into the matrix A - λI and solve the system of equations (A - λI)v = 0, where v is the eigenvector.

For λ₁ = -5: A - (-5)I = [[0, 0], [-16, 8]]

Using Gaussian elimination, we can solve the system of equations to find the eigenvector corresponding to λ₁: -16v₁ + 8v₂ = 0 => -2v₁ + v₂ = 0 => v₁ = (1/2)v₂

Let v₂ = 2, then v₁ = 1. Therefore, the eigenvector corresponding to λ₁ is v₁ = [1, 2].

For λ₂ = 3: A - 3I = [[-8, 0], [-16, 0]]

Solving the system of equations, we find: -8v₁ = 0 => v₁ = 0

Thus, the eigenvector corresponding to λ₂ is v₂ = [0, 1].

Now, let's express the solution of the system in terms of the eigenvalues and eigenvectors.

X(t) = c₁e(λ₁t)v₁ + c₂e(λ₂t)v₂

Substituting the eigenvalues and eigenvectors we found earlier, we have: X(t) = c₁e⁻⁵ˣ[1, 2] + c₂e³ˣ[0, 1]

Using the initial conditions, x₁(0) = 1 and x₂(0) = 5, we can find the values of c₁ and c₂.

At t = 0: [1, 5] = c₁[1, 2] + c₂[0, 1] 1 = c₁ 5 = 2c₁ + c₂

Solving these equations, we find: c₁ = 1 c₂ = 3

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Complete Question:

Solve the system of differential equations

x₁' = – 5x₁ + 0x₂

x₂' = – 16x₁ + 3x₂

x₁(0) = 1, x₂(0) = 5

Answer:

80 tsp.

Step-by-step explanation:

400 divided by 5 is 80, so 80 tsp's.

Answer:

80 tsp.

Step-by-step explanation:

400 mL = 80 tsp

Answer:

Step-by-step explanation:

By triangle sum theorem,

Sum of all angles of a triangle is 180°.

m∠1 + m∠2 + m∠3 = 180°

(m∠1 + m∠3) + m∠2 = 180°

2(m∠1) + 70° = 180° {Given → m∠1 = m∠3]

2(m∠1) = 110°

m∠1 = 55°

Therefore, m∠1 = m∠3 = 55°

Answer:

If you just solve normally, you will get x=2 and x=-3. But if you plug these in to check your work, you will find that they are wrong. Your answer is no solution

Step-by-step explanation:

ln(2x+3)+ln(x-2)=ln(x^2-2x)

Rule: log(a) + log(b) = log(a*b)

ln( (2x+3)(x-2) ) = ln(x^2-2x)

Rule: If log(a) = log(b) then a = b

(2x+3)(x-2) = x^2 - 2x

2x^2-x-6=x^2-2x

x^2+x-6=0

Using Quadratic Formula:

x = 2 and x = -3

But, plugging these numbers back into the original equation is false!

Answer:

46 degrees

Step-by-step explanation:

x equals 23 so just multiply by 2

Answer:

[tex]46^{o}[/tex]

Step-by-step explanation:

Bottom-right angle is 65 as 180 - 90 - 25 = 65

Top-left angle is also 65 as angles opposite a point are equal (when divided by straight lines)

Angles around a point = 360 so 360 - 65 - 65 - 90 - 25 = 115

5x = 115

x = 23

23 x 2 = 46

Answer: Gina and Rhonda work for different real estate agencies. Gina earns a monthly salary of $5,000 plus a 6% commission on her sales. Rhonda earns a monthly salary of $6,500 plus a 4% commission on her sales. How much must each sell to earn the same amount in a month?

Step-by-step explanation:

$5,000 + 6% + $6,500 + 4% = 11500.1 or 11500

Answer

6 and 2/3 percent of an hour OR 6.666.... hour

I don’t know if you have to round or not but if it does just round

Step-by-step explanation:

Well 4 minutes of an hour is basically 4/60

4/60=1/15

1/15=x/100

solve the proportion by cross multiplying

100=15x

x=6.66666666

That is yoru percent

The velocity of the Pacific plate, expressed in centimeters per year (cm/yr), can be determined from the slope of the best-fit line in a geologic study.

In a geologic study, if data points representing the position of the Pacific plate are collected over a period of time, a best-fit line can be calculated to represent the trend of plate movement.

- The slope of this line represents the rate of change of position over time, which corresponds to the velocity of the plate. By examining the slope of the best-fit line and converting it to centimeters per year, we can determine the velocity at which the Pacific plate is moving.

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Answer: i would say A and D but i'm not sure of the others