The sum of two numbers is 18 and their difference is 6.
What are the two numbers?
Larger number
Smaller number

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:

likes

=0.420+0.034(views) (B) on khan academy

Step-by-step explanation:

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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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:

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:

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

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

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

Answer:

5x+4y-40=0

Step-by-step explanation:

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:14 is obtuse

15 is A

Step-by-step explanation:

For 14 the only remaining angle is over 90

For 15 the first triangle has all same side and angle measures

second triangle has 2 equal side measures

and third has none

Answer:

1: Obtuse

2: A

Step-by-step explanation:

One angle is 57° and another is 12°. If we add them, we get 69. Subtract 69 from 180 to get missing angle: 180-69=111

the missing angle is 111°. We know this is not a right triangle because those have a 90° angle. Since one angle is bigger than 90 (111°), the triangle is obtuse.

For the second one, we see that the first triangle is equal on all sides, so it is equilateral. The second triangle has just two equal sides, so it is isosceles. The thrid one is different side length on all of them, so it is scalene. the answer is A.

Answer:

0.2x² - 0.2x - 42 = 0

Step-by-step explanation:

Number of counters = x

Number of blue counters =7

Probability, p = required outcome / Total possible outcomes

P(Sam picks blue ) : = 7/x

P(jill picks blue) = 6/(x - 1)

P(Sam picks blue) * P(Jill picks blue) = 0.2

7/x * 6/(x-1) = 0.2

42/x(x - 1) = 0.2

42 / x² - x= 0.2

42 = 0.2(x² - x)

42 = 0.2x² - 0.2x

0.2x² - 0.2x - 42

Option D is correct.

The relation {(-8, -6) (-5, 2) (-8, 1) (7, 3)} is not a function.

Step-by-step explanation:

Given the relation:  {(-8, -6) (-5, 2) (-8, 1) (7, 3)}

Domain is the set of all possible inputs of a relation i.e { -8, -5 , -8 , 7}

Range is the set of output values of a function i.e, {-6, 2 , 1 , 3}

The mapping as shown below in the figure:

A function is a relation in which every element of the domain is matched to not more than one element of the range.

In other words, we can say that ,no value of x gets mapped to more than 1 value of y.

Since, from the mapping you can see that the domain value -8  paired with -6 and 1;  as x is used more than once.

Therefore, this relation is not a function

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:

...

Step-by-step explanation:

the answer is 10.2 :)

(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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Answer:

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

Step-by-step explanation:

Answer:

1) 1.2 minutes

2) 8.3 laps

3) 25.2 minutes

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:

the anwser is going to be A

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:

____________________________________________________________

   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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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

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

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:

A

Step-by-step explanation: