how do you prove the formula for the sum of an infinite converging series?
S∞=a1/1-r

{-2 2 22}

a) The characteristic polynomial of A is given by:
$$p_A(\lambda) = \lambda^3 - 5\lambda^2 + 18\lambda + 36$$
b) The two eigenvalues of A are:
$$\lambda_1=2, \lambda_2=-4, \lambda_3=9$$
c) A basis for the eigenspace corresponding to the smallest eigenvalue $\lambda_2=-4$ is given by the set of vectors:
$$\begin{bmatrix} 0\\1\\0 \end{bmatrix}, \begin{bmatrix} 2\\0\\1 \end{bmatrix}$$
d) A basis for the eigenspace corresponding to the largest eigenvalue $\lambda_3=9$ is given by the set of vectors:
$$\begin{bmatrix} 1\\0\\-4 \end{bmatrix}, \begin{bmatrix} -2\\2\\22 \end{bmatrix}$$

Learn more about eigen space

brainly.com/question/30968941

#SPJ11

If someone tells you about an investment that had a return that averaged 25% per year, this investment is likely to be: D. much riskier than most stocks.

In Insurance, risk tolerance can be defined as the willingness of an individual or business organization to take a risk in business transactions and investments, in order to get a potentially positive reward (returns).

Generally speaking, the high risk that is associated with investments such as stocks, high-yield bonds, etc., is often perceived by investors to be worth the higher reward these investment would bring.

In this context, we can reasonably infer that a stock with reward (returns) that has an average of 25 percent per year is most likely to be riskier than most stocks.

Read more on investments here: brainly.com/question/26164819

#SPJ1

Complete Question:

If someone tells you about an investment that had a return that averaged 25% per year, how risky is this investment likely to be?

answer choices

Not very risky at all

About as risky as the average stock

About as risky as a savings account

Much riskier than most stocks

Answer:

D) 65°

Step-by-step explanation:

Use Snell's Law

\(n_1\sin\theta_1=n_2\sin\theta_2\\\\1.00\sin\theta_1=1.47\sin38^\circ\\\\\sin\theta_1=1.47\sin38^\circ\\\\\theta_1=\sin^{-1}(1.47\sin38^\circ)\\\\\theta_1\approx64.83^\circ\)

Thus, the angle of incidence is D) 65°

Answer:  906 in^3.

Step-by-step explanation:

The volume of a triangular pyramid is the area of the base multiplied by the height divided by 3.

First, we can start by finding the area of the base.

The area of the base is equal to 19*13/2

= 123.5 in^2

Next, we plug in the formula.

So the volume = 123.5*22/3 in^3

= 905.666 repeated in ^3

Rounded to the nearest whole number is 906 in^3.

Check the picture below.

so the base of the pyramid is just a triangle with a base of 19 and an altitude of 13, and the pyramid has a height of 22.

\(\textit{volume of a pyramid}\\\\ V=\cfrac{Bh}{3}~~ \begin{cases} B=\stackrel{base}{area}\\ h=height\\[-0.5em] \hrulefill\\ B=\frac{1}{2}(19)(13)\\\\ h=22 \end{cases}\implies \begin{array}{llll} V=\cfrac{1}{3}\left[ \cfrac{1}{2}(19)(13) \right](22) \\\\\\ V=\cfrac{2717}{3}\implies V\approx 906~in^3 \end{array}\)

In general, if the sample size is large, adding an extremely large outlier to a data set will not substantially affect the mean.

A very large outlier will typically not significantly change the mean of a data set if the sample size is large. However, adding an extremely large outlier to a data set with a small sample size can have a substantial effect on the mean.

This is because the mean is heavily influenced by the values of the individual data points, and an outlier can have a disproportionately large impact on the mean if the sample size is small.

To learn more about sample size link is here

brainly.com/question/25894237

#SPJ4

The expressions will be:

and

and

The Radical Form (√x)  ,the solutions to the equation √x - 2 + 4 = x are x = 1 and x = 4.

The equation √x - 2 + 4 = x for x, we can follow these steps:

1. Begin by isolating the radical term (√x) on one side of the equation. Move the constant term (-2) and the linear term (+4) to the other side of the equation:

  √x = x - 4 + 2

2. Simplify the expression on the right side of the equation:

  √x = x - 2

3. Square both sides of the equation to eliminate the square root:

  (√x)^2 = (x - 2)^2

4. Simplify the equation further:

  x = (x - 2)^2

5. Expand the right side of the equation using the square of a binomial:

  x = (x - 2)(x - 2)

  x = x^2 - 2x - 2x + 4

  x = x^2 - 4x + 4

6. Move all terms to one side of the equation to set it equal to zero:

  x^2 - 4x + 4 - x = 0

  x^2 - 5x + 4 = 0

7. Factor the quadratic equation:

  (x - 1)(x - 4) = 0

8. Apply the zero product property and set each factor equal to zero:

  x - 1 = 0   or   x - 4 = 0

9. Solve for x in each equation:

  x = 1   or   x = 4

Therefore, the solutions to the equation √x - 2 + 4 = x are x = 1 and x = 4.

To know more about Radical form .

https://brainly.com/question/29153583

#SPJ8

The number of green paint bottles required by Leonardo to paint 5 pictures using \(\frac{2}{3}\) of a bottle per picture is \(3 \frac{1}{3} \) bottles

Number of pictures to be painted = 5

To obtain the total Number of bottles of green paint required :

Total number of bottles = \( 5 \times \frac{2}{3} = 3 \frac{1}{3} \)

Therefore, Leonardo will need \( 3 \frac{1}{3} \) bottles of green paint.

Learn more :https://brainly.com/question/18109354

Answer:

54 words typed in one minute.

Step-by-step explanation:

1. If you divide 297 by 5.5 you will get your answer

ANSWER: 54 words/ 1 minute

Answer:

2 pie r is the measure of its circumference.

Answer:

you need to know the value of the radius in order to work out the circumfrance. do you have a picture of the math question?

Since the p - value is less than significance level . So, we will accept the null hypothesis.

​(a) State the appropriate null and alternative hypotheses to assess whether women are taller today.

Definition of null hypothesis : The null hypothesis attempts to show that no variation exists between variables or that a single variable is no different than its mean. it is denoted

Alternative Hypothesis : In statistical hypothesis testing, the alternative hypothesis is a position that states something is happening, a new theory is true instead of an old one (null hypothesis).

We are given that The mean height of women 20 years of age or older was 63.7 inches.

So, null hypothesis :  H₀ : μ = 63.7

Alternative Hypothesis :  H₁ : μ > 63.7

b)The​ P-value for this test is 0.06.

The p-value represents the probability of getting a sample mean height of 20 years old women is  64.1 inches.

c) Write a conclusion for this hypothesis test assuming an alpha equals 0.10 level of significance.

p- value = 0.06

Since the p - value is less .

So, we will accept the null hypothesis

So,  

Hence The mean height is 63.7 inches

To learn more about hypothesis testing from the given link

https://brainly.com/question/12976831

#SPJ4

Answer:Tes icahd

Step-by-step explanation:

ANSWER

0.667

EXPLANATION

We want to convert the rational number given to decimal number.

To do this, we divide the numerator by the denominator.

That is:

That is the answer, approximated to the nearest thousandth.

The probability of A given B is 0, and P(A | B) is not equal to P(A). Events A and B are mutually exclusive, meaning that they cannot both occur at the same time, and thus they are not independent. Mutually exclusive events are not necessarily independent and independent events may or may not be mutually exclusive.

P(A) = 0.30 and P(B) = 0.40, so P(A and B) = 0 because the events A and B are mutually exclusive. This means that the probability of A given B is 0, and P(A | B) = 0. P(A | B) is not equal to P(A).Events A and B are mutually exclusive, meaning that they cannot both occur at the same time, and thus they are not independent.The statement that mutually exclusive events and independent events are the same is not accurate. Mutually exclusive events are not necessarily independent and vice versa.Given the results of this problem, we can conclude that mutually exclusive events are not independent, and independent events may or may not be mutually exclusive. The two concepts are not necessarily related as mutually exclusive events do not necessarily need to be independent and independent events do not necessarily need to be mutually exclusive.

Learn more about independent here:

https://brainly.com/question/29995229

#SPJ4

The value of the expression 13 + |8 + y| if x = 2, y = -3, and z = 1 is 18

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

x = 2, y = -3, and z = 1

Also, we have

13 + |8 + y|

Substitute the known values in the above equation, so, we have the following representation

13 + |8 + y| = 13 + |8 - 3|

So, we have

13 + |8 + y| = 13 + |5|

Remove the absolute bracket

13 + |8 + y| = 13 + 5

So, we have

13 + |8 + y| = 18

Hence, the solution is 18

Read more about expression at

https://brainly.com/question/31819389

#SPJ4

Answer:

slope=3    y- intercept is -2 and the equation is y=3x-2

Step-by-step explanation:

Answer:

Answer → 63°

Step-by-step explanation:

» m<3 and m<4 are supplementary angles.

☑ Supplementary angles are angles that measure up to 180°

\({ \tt{m \angle 3 + m \angle 4 = 180 \degree}} \\ { \tt{117 \degree + m \angle 4 = 180 \degree}} \\ { \tt{m \angle 4 = 180 \degree - 117 \degree}} \\ { \tt{m \angle 4 = 63 \degree}}\)

The correct option is a) $5161.24

To evaluate the expression P(1+rt) with the given values:

P = 1575

r = 0.055

t = 168/365

First, let's calculate rt:

rt = 0.055 * (168/365)

= 0.0252836 (rounded to 7 decimal places)

Now, substitute the values into the expression P(1+rt):

P(1+rt) = 1575 * (1 + 0.0252836)

= 1575 * 1.0252836

= 1615.85846 (rounded to 5 decimal places)

The result is approximately $1615.86.

Therefore, the correct option is a) $5161.24

Learn more about expression from

brainly.com/question/1859113

#SPJ11

Answer:

2.23

Step-by-step explanation:

Answer:

x=1

Step-by-step explanation:

The amount tied up in AR is $69434.12

The Gross Revenue, GR = $495,958.02

From the question:

The Annual Revenue, AR = 14% of GR

AR = (14/100) x $495,958.02

AR = 0.14 x $495,958.02

AR = $69434.12

The amount tied up in AR is $69434.12

 f(t) = L^(-1){1 / (s^2 + s)} Inverse Laplace transform tables or techniques, determine the time-domain function f(t) that satisfies the given integral equation.

The Laplace transform is a powerful mathematical tool that can be used to solve complex integral equations, like the one you've provided: f(t) + t * ∫(t - τ)f(τ)dτ = t.

To solve this equation using the Laplace transform, follow these steps:

1. Apply the Laplace transform to both sides of the equation. The Laplace transform of f(t) is F(s), and the Laplace transform of t is 1/s^2. The integral equation becomes:

  L{f(t)} + L{t * ∫(t - τ)f(τ)dτ} = L{t}

  F(s) + L{t * ∫(t - τ)f(τ)dτ} = 1/s^2

2. Next, apply the convolution theorem to the integral term. The convolution theorem states that L{f(t) * g(t)} = F(s) * G(s). In this case, f(t) = t and g(t) = (t - τ)f(τ):

  F(s) + L{t} * L{(t - τ)f(τ)} = 1/s^2

3. Now, substitute the known Laplace transforms for t and f(t):

  F(s) + (1/s^2) * F(s) = 1/s^2

4. Combine the terms containing F(s):

  F(s) * (1 + 1/s^2) = 1/s^2

5. Isolate F(s) by dividing both sides of the equation by (1 + 1/s^2):

  F(s) = (1/s^2) / (1 + 1/s^2)

6. Simplify the expression for F(s):

  F(s) = 1 / (s^2 + s)

7. Finally, apply the inverse Laplace transform to F(s) to obtain the solution for f(t):

  f(t) = L^(-1){1 / (s^2 + s)}

Using inverse Laplace transform tables or techniques, you can determine the time-domain function f(t) that satisfies the given integral equation.

To learn more about Inverse Laplace click here

brainly.com/question/30404106

#SPJ11

Answer:

The speed increases (45—>47—>49) then decreases (48—>47) over time.

Step-by-step explanation:

HOPE THIS HELPED ✨

Answer: The speed increases (45—>47—>49) then decreases (48—>47) over time.

The estimated forward LIBOR interest rate for the period between 6.00 and 6.25 years in the future is approximately 7.495%.

To estimate the forward LIBOR interest rate for the period between 6.00 and 6.25 years in the future, given the 3-month Eurodollar futures price of 95.20 and a standard deviation of the change in the short-term interest rate in 1 year of 1.1%, follow these steps:

1. Convert the Eurodollar futures price to an implied interest rate:
 Implied Interest Rate = (100 - Eurodollar Futures Price) = (100 - 95.20) = 4.80%

2. Calculate the number of standard deviations for the 6-year period:
  Number of Standard Deviations = √(6 years) = √6 ≈ 2.45

3. Multiply the number of standard deviations by the annual standard deviation of the change in the short-term interest rate:
  Change in Interest Rate = Number of Standard Deviations × Annual Standard Deviation = 2.45 × 1.1% = 2.695%

4. Add the change in the interest rate to the current implied interest rate to get the forward LIBOR interest rate for the period between 6.00 and 6.25 years in the future:
  Forward LIBOR Interest Rate = Implied Interest Rate + Change in Interest Rate = 4.80% + 2.695% = 7.495%

So, the estimated forward LIBOR interest rate for the period between 6.00 and 6.25 years in the future is approximately 7.495%.

for such more question on interest rate

https://brainly.com/question/25720319

#SPJ11

Answer:

C

Step-by-step explanation:

539/3 = 179.666

85/3 =28.3333

9285/ 3 = 3095

640/3=213.3333

Answer:

C

Hope this helps :)

Step-by-step explanation:

All the others numbers equal a decimal when divided by 3. However, C equals a whole number so it's C.

9,285 ÷ 3 = 3,095

The number of waffles can be made from 15 eggs are, 20 waffles.

the waffles can be calculates as follows

4 cups of fluor + 6 eggs +2 tbsp oil = 8 waffles

we need 6 eggs to make 8 waffles

So, the waffles can we make from 15 eggs = \(\frac{8}{6} X 15 = 20\) waffles

Hence, the number of waffles can be made from 15 eggs are 20 waffles.

Learn more about this equation at

https://brainly.com/question/14275434

#SPJ1

ansewr: the ansewr is b

explanation: did it