Write an Equation given the point (2, 6) and a rate of 3.

(a) The sequence \(\(a_n = n^2 e^{-n}\)\) is divergent. (b) The sequence \(\(a_n = \frac{\cos(n)}{n^3}\)\) is convergent, and it converges to 0.

(a) To determine if the sequence \(\(a_n = n^2 e^{-n}\)\) is convergent or divergent, we can take the limit of \(\(a_n\)\) as \(\(n\)\) approaches infinity.

\(\[ \lim_{n \to \infty} a_n = \lim_{n \to \infty} n^2 e^{-n} \]\)

We can use L'Hôpital's rule to evaluate the limit. Taking the derivative of the numerator and the denominator with respect to n, we have:

\(\[ \lim_{n \to \infty} a_n = \lim_{n \to \infty} \frac{2n e^{-n} + n^2(-e^{-n})}{-e^{-n}} \]\)

Simplifying further:

\(\[ \lim_{n \to \infty} a_n = \lim_{n \to \infty} (-2n - n^2) \]\)

As n approaches infinity, the term \(\(-2n\)\) dominates the term \(\(-n^2\).\)Therefore, the limit becomes \(\(-\infty\).\)

Hence, the sequence \(\(a_n = n^2 e^{-n}\)\) is divergent.

(b) Let's analyze the sequence \(\(a_n = \frac{\cos(n)}{n^3}\)\) to determine if it is convergent or divergent. Again, we'll find the limit as \(\(n\)\) approaches infinity.

\(\[ \lim_{n \to \infty} a_n = \lim_{n \to \infty} \frac{\cos(n)}{n^3} \]\)

The cosine function oscillates between -1 and 1 as \(\(n\)\) increases. However, the denominator \(\(n^3\)\) grows much faster than the numerator. Consequently, the cosine terms become less significant in comparison.

Taking the limit:

\(\[ \lim_{n \to \infty} a_n = \lim_{n \to \infty} \frac{\text{bounded}}{\infty} = 0 \]\)

Therefore, the sequence \(\(a_n = \frac{\cos(n)}{n^3}\)\) is convergent, and it converges to 0.

Learn more about derivative here: https://brainly.com/question/29144258

#SPJ11

After using mental math to find how much he spent in all, we have come to find that total cost of notebook, pencils and eraser is $7.79

A set of abilities known as mental math enable people to perform calculations "in their heads" without the aid of paper and pencil or a calculator. Recalling math facts, such as 8 x 5 = 40, is one of these abilities. Rounding numbers and estimating calculations are additional abilities.

It is the process of performing mathematical calculations and problem-solving without the need for a lengthy physical process or a formal written process. Children will learn to perform mental addition, subtraction, and other calculations that call for the use of all four operations as well as particular methods.

Students will be able to solve a variety of problems without having to memorize equation solutions, pull out a calculator, or use a pen and paper for their calculations thanks to these mental techniques.

Learn more about math

https://brainly.com/question/1056269

#SPJ9

Answer: $7.79

Step-by-step explanation:

Answer: 0

Step-by-step explanation:

Answer:

i think it is 27 because the last one adds up to 27

i am not really good at this stuff

Step-by-step explanation:

9x-7i > 3(3x-7u)

-9x-7i > 9x-21u

-7i > -21u

-i > -3u

i < 3u

Answer:

y = 17x

Step-by-step explanation:

Translating a rectangle involves moving the rectangle.

The coordinate of the image of rectangle QRST is: \(\mathbf{Q' = (-1, 6)}\)    \(\mathbf{R' = (2, 8)}\)    \(\mathbf{S' = (6, 2)}\)   \(\mathbf{T' = (3, 0)}\)

The coordinate points of rectangle QRST are given as:

\(\mathbf{Q = (-6,-1)}\)

\(\mathbf{R = (-3,1)}\)

\(\mathbf{S = (1,-5)}\)

\(\mathbf{T = (-2,-7)}\)

The translation rule is given as:

\(\mathbf{(x,y) \to (x + 5, y + 7)}\)

Apply the above translation rule on point Q

\(\mathbf{Q' = (-6 + 5, -1 + 7)}\)

\(\mathbf{Q' = (-1, 6)}\)

Apply the above translation rule on point R

\(\mathbf{R' = (-3 + 5, 1 + 7)}\)

\(\mathbf{R' = (2, 8)}\)

Apply the above translation rule on point S

\(\mathbf{S' = (1+5, -5+7)}\)

\(\mathbf{S' = (6, 2)}\)

Apply the above translation rule on point T

\(\mathbf{T' = (-2 + 5, -7 + 7)}\)

\(\mathbf{T' = (3, 0)}\)

Hence, the coordinate of the image of the rectangle is:

\(\mathbf{Q' = (-1, 6)}\)    \(\mathbf{R' = (2, 8)}\)    \(\mathbf{S' = (6, 2)}\)   \(\mathbf{T' = (3, 0)}\)

Read more about translations at:

https://brainly.com/question/12463306

The appropriate regression model depends on the stationarity properties of both the dependent and independent variables, as well as the error term. The researcher can use a standard OLS regression model with first-order differencing of both Y and X.

In the first scenario, both Y and X are I(0), which means they are stationary time series. In this case, the researcher can perform a standard linear regression analysis, as the stationary series would lead to a stable long-run relationship. The answer from this model will be reliable and less likely to suffer from spurious regressions. In the second scenario, Y is I(2) and X is I(0). This implies that Y is integrated of order 2 and X is stationary. In this case, the researcher should first difference Y twice to make it stationary before performing a regression analysis. However, this approach might not be ideal as the integration orders differ, which can lead to biased results.

In the third scenario, Y and X are both I(1) and the error term is I(0). This indicates that both Y and X are non-stationary time series, but their combination might be stationary. The researcher should employ a co-integration analysis, such as the Engle-Granger method or Johansen test, to identify if there is a stable long-run relationship between Y and X. If co-integration is found, then an error correction model can be used for more accurate predictions.

To know more about regression visit:-

https://brainly.com/question/28168620

#SPJ11

The calculated volume of the model space is 1657.92 cubic inches

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

The model space made from:

The volume of the model space is calculated as

Volume = Cone + Cylinder + Hemisphere

Using the volume formulas, we have

Volume = 1/3πr²h + πr²h + 2/3πr³

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

Volume = 1/3 * 3.14 * 6² * 8 + 3.14 * 6² * 8 + 2/3 * 3.14 * 6³

Evaluate

Volume = 1657.92

Hence, the volume of the model space is 1657.92 cubic inches

Read more about volume at

https://brainly.com/question/463363

#SPJ1

To investigate significant differences between the brands of yellow interior latex paint using Tukey's procedure, we need to calculate the difference between each pair of means and compare them to the critical value obtained from the studentized range distribution. If the difference is greater than the critical value, it indicates a significant difference between the corresponding brands.

First, let's calculate the critical value using the significance level α = 0.05 and the degrees of freedom for the denominator (within-group) error, which is the total sample size (n) minus the number of groups (k). In this case, n = 4 (gallons) × 5 (brands) = 20 and k = 5.

Degrees of freedom for the denominator error:

df_denom = n - k = 20 - 5 = 15

Using a critical value table or statistical software, the critical value for α = 0.05 and df_denom = 15 is approximately 3.055.

Next, we calculate the absolute difference between each pair of means and compare it to the critical value:

1. |462.0 - 512.8| = 50.8 > 3.055 (significant difference)

2. |462.0 - 437.5| = 24.5 < 3.055 (no significant difference)

3. |462.0 - 469.3| = 7.3 < 3.055 (no significant difference)

4. |462.0 - 532.1| = 70.1 > 3.055 (significant difference)

5. |512.8 - 437.5| = 75.3 > 3.055 (significant difference)

6. |512.8 - 469.3| = 43.5 > 3.055 (significant difference)

7. |512.8 - 532.1| = 19.3 < 3.055 (no significant difference)

8. |437.5 - 469.3| = 31.8 > 3.055 (significant difference)

9. |437.5 - 532.1| = 94.6 > 3.055 (significant difference)

10. |469.3 - 532.1| = 62.8 > 3.055 (significant difference)

Based on the comparisons above, the pairs of means that differ significantly from one another are:

- Brand 1 (x) and Brand 2 (x): |462.0 - 512.8| = 50.8

- Brand 1 (x) and Brand 5 (x): |462.0 - 532.1| = 70.1

- Brand 2 (x) and Brand 5 (x): |512.8 - 532.1| = 19.3

- Brand 3 (x) and Brand 5 (x): |437.5 - 532.1| = 94.6

- Brand 3 (x) and Brand 4 (x): |437.5 - 469.3| = 31.8

- Brand 4 (x) and Brand 5 (x): |469.3 - 532.1| = 62.8

Therefore, the brands that differ significantly from one another are: Brand 1 (x) and Brand 2 (x), Brand 1 (x) and Brand 5 (x), Brand 2 (x) and Brand 5 (x), Brand 3 (x) and Brand 5 (x), Brand 3 (x) and Brand 4 (x), Brand 4 (x) and Brand 5(x).

To know more about Tukey's procedure, refer here:

https://brainly.com/question/32269122#

#SPJ11

Answer:

C.) Using a straightedge, draw a line segment from the center of the circle through the marked point, then extend the segment and label a point outside the circle.

i just took the test

The side length of an inscribed regular hexagon is equal to the radius of the circle

The best statement for Maricela to write for Step 3 is the option;

Reason:

A hexagon is a six sided figure, and a regular hexagon has six equal sides

The steps of constructing a hexagon in a circle is given as follows;

The best statement for Marcela to write for Step 3 is therefore;

Without changing the width of the compass, put the compass point at the marked point, then draw an arc that intersects the circle in two places

Learn more about constructing a regular hexagon inscribed in a circle here;

https://brainly.com/question/11833289

Applying the exterior angle theorem, the measure of the exterior angle to angle X is: B 112.55°.

In other to find the measure of the exterior angle to angle X, we have to recall the theorem known as the exterior angle theorem, which states that the measure of an exterior angle is equal to the two interior remote angles that are opposite to it.

In triangle XYZ, angle Y and Z are the remote interior angles. We are given the following:

Measure of angle Y = 38.25°

Measure of angle Z = 74.3°

Therefore:

The measure of the exterior angle to angle X = measure of angle Y + measure of angle Z

Substitute

The measure of the exterior angle to angle X = 38.25° + 74.3°

The measure of the exterior angle to angle X = 112.55°

Learn more about exterior angles theorem on:

https://brainly.com/question/11356657

#SPJ1

Answer:

225

Step-by-step explanation:

(- 15)² = - 15 × - 15 = 225

To create a stemplot, we first need to separate the data into "stems" and "leaves." Each stem represents the first digit(s) of each data point, while each leaf represents the last digit(s). For example, if the data point is 12.3, the stem would be 12 and the leaf would be 3.

To make a stemplot, the data should be arranged in increasing order, and then separated into stems and leaves.

However, you can use the data given and arrange it in increasing order and separate it into stems and leaves to make a stemplot. A stemplot is a good way to check if the data follow a normal distribution quite closely, the more the data is spread out and the more symmetric it is, the more likely it is to follow a normal distribution.

Also, it is important to mention that from the given data, it is not possible to conclude if the percent change in this population has standard deviation of 2.5%. This parameter can only be estimated from a sample if it follows a normal distribution which is not clear from the given data.

Learn more about Stemplot here:

https://brainly.com/question/29174445

#SPJ4

Answer:

y = -.4x+107

Here you go! Have a wonderful day!

Answer:

x <= -5

Step-by-step explanation:

4x + 12 <= -8

4x <= -20

x <= -5

Answer:

x <= -5

Step-by-step explanation:

4x + 12 <= -8

4x <= -20

x <= -5

1. Addition is first. Bracket comes first

BODMAS

1 ADDITION

2½ - (¾ - ⅝)

Subract the sum of 3/4 and 5/8 from 2½

2. BODMAS

Multiplication first

4.5 + 0.6 = 5.1

Five and one tenth

Add 4.5 to the product of 6 and 0.1

Check the picture below.

An expression is just a mathematical phrase. A numerical expression contains numbers and operations. An algebraic expression is almost exactly the same except it also contains variables.

Answer:

1) y = 30x (same thing as y = 30x + 0)

2) y = 24x (same thing as y = 24x + 0)

3) 270

4) 216

Step-by-step explanation:

Hope this helps :)

The spherical coordinate (4,6π,2π/3) is (5,2π3,0.927) in spherical coordinates.

I’m going to assume that your values are in the form of:

(r,θ,z)=(4,6π,2π/3)

where

(r,θ)are the polar coordinates of the point’s projection in the xy-plane

z is the usual z-coordinate in the Cartesian coordinate system

Now solving for Cartesian coordinates:

x=rcosθ=4cos(6π)=4(0.86)=3.44

y=rsinθ=4sin(6π)=2

Now for spherical transformation, note that:

(ρ,θ,ϕ)

ρ is the distance between P and the origin

θ is the same angle used to describe the location in cylindrical coordinates

ϕ is the angle formed by the positive z-axis and line segment from the origin and point in space, note that0≤ϕ≤π

OK, now that we have that out of the way, let’s compute:

ρ=r2+z2 = 5

θ=θ=6π

ϕ=arccos(zr2+z2−−−−−−√)=arccos(35)≈0.927rad

The spherical coordinate (4,6π,2π/3) is (5,2π3,0.927) in spherical coordinates.

For more information about coordinates, visit

https://brainly.com/question/17206319

The measures of the angles are ∠1 = 127°, ∠2 = 53°, ∠3 = 127°, ∠4 = 37°, ∠5 = 53°, ∠6 = 90°, ∠7 = 37°, ∠8 = 143°, ∠9 = 37° and ∠10 = 143°

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

The transversal lines and the other lines

So, we have

∠1 = 180 - 53

Evaluate

∠1 = 127°

Also, we have

∠5 = 53°

By vertical angles, we have

∠2 = 53°

∠3 = 127°

Next, we have

∠4 = 127 - 90°

∠4 = 37°

Solving further, we have

∠6 = 90°

By corresponding angles, we have

∠7 = 37°

∠9 = 180 - 90 - 53°

∠9 = 37°

∠10 = 90 + 53°

∠10 = 143°

∠8 = 143°

Read more about angles at

https://brainly.com/question/28293784

#SPJ1

Answer:

19, 23, 27, 31, 35,

Step-by-step explanation:

It's +4 each time.

Answer:

1331 inches cubed

Step-by-step explanation:

V=LHW

since it is a cube, the length, height, and width will all be the same; 11 inches. You have to multiply 11 by 11 by 11, which equals 1331.

Hope this helped!

Answer:

13.22%

Step-by-step explanation:

The 1 1/4 cups of sugar and 1 1/2 cups of flour used in making one batch, indicates that the number of cups of flour Lesley should use in the new batch of cookies, expressed as a mixed fractions is 1 1/5 cups

A mixed fraction consists of the sum of the quotient and the fraction of the remainder divided by the divisor, of a fraction which has a larger numerator than the denominator.

The amount of sugar and flour required to make one batch of cookies specified in mixed fractions are;

Amount of sugar = 1 1/4 cups

Amount of flour = 1 1/2 cups

The amount of sugar in the additional batch = 1 cup of sugar

The ratio of the quantities of the sugar and flour between original batch and the new batch is therefore;

Sugar in original batch/(Sugar in new batch) = (Flour in original batch)/(Flour in the new batch)

\(\frac{1\frac{1}{4} }{1} =\frac{1\frac{1}{2} }{y}\)

Where;

y = The number of cups of flour required in the new batch

Cross multiplying, we get;

\(y \times 1\frac{1}{4} = 1\frac{1}{2}\)

\(y = \frac{1\frac{1}{2} }{1\frac{1}{4} } = \frac{6}{5} =1\frac{1}{5}\)

The number of cups of flour needed in the new batch is, y = 1 1/5 cups

Learn more about fractions here: https://brainly.com/question/8118373

#SPJ1

Answer:

1. x < 4

2. x > 1

3. x < 5

Step-by-step explanation:

The expected value of the treatment mean square for a completely randomized design experiment is given by E(MS Trt) = σ2 + m∑Ti2 / (L-1).

Let L be the number of treatments, and R be the number of replications per treatment.

According to the model, yij is the response from the jth replication of the ith treatment.

Therefore, the total number of observations is given by N = LR. Therefore, we assume the following linear model to estimate the treatment effects: yij=μ+Ti+Eij Where yij is the observed value for the jth replication in the ith treatment. μ represents the population mean.

Ti represents the effect of the ith treatment and is assumed to be a fixed effect. Eij is the error term for the jth replication of the ith treatment, and is assumed to follow a normal distribution with a mean of 0 and a variance of σ2.

We now turn to the analysis of variance for the CRD with L treatments and R replications per treatment.

The total sum of squares is given by: SST = ∑∑yij2 - (T..)2/N Where T.. is the total sum of observations.

It has (L-1)(R-1) degrees of freedom.

The total mean square is given by: MST = SST / (L-1)(R-1)

The treatment sum of squares is given by: SSTR = ∑n(T.)2/R - (T..)2/N Where T. is the sum of the observations in the ith treatment, and n is the number of observations in the ith treatment.

It has L-1 degrees of freedom. The treatment mean square is given by: MSTR = SSTR / (L-1)

The error sum of squares is given by: SSE = SST - SSTR It has (L-1)(R-1) degrees of freedom.

The error mean square is given by: MSE = SSE / (L-1)(R-1)

Therefore, E(MS Trt)=σ2+ m∑Ti2/t-1  since E(Ti)=0 for all i.

To show that E(MS Trt) = σ2 + m∑Ti2 / t-1

We start by using the definition of expected value E() to derive the expected value of the treatment mean square

(MS Trt): E(MS Trt) = E(SSTR / (L-1))

Next, we can express SSTR in terms of the Ti's as follows:

SSTR = ∑n(T.)2/R - (T..)2/N= 1/R ∑Ti2n - (T..)2/N

We can then substitute this expression into the expression for MS Trt:

MS Trt = SSTR / (L-1)

Substituting SSTR = 1/R ∑Ti2n - (T..)2/N, we get:

MS Trt = [1/R ∑Ti2n - (T..)2/N] / (L-1)

Simplifying the expression, we get:

MS Trt = [1/R ∑Ti2n] / (L-1) - [(T..)2/N] / (L-1)E(MS Trt)

= E([1/R ∑Ti2n] / (L-1)) - E([(T..)2/N] / (L-1))

Next, we can apply the linearity of expectation to the two terms:

E(MS Trt) = 1/(L-1) E[1/R ∑Ti2n] - 1/(L-1) E[(T..)2/N]

Simplifying the expression, we get:

E(MS Trt) = 1/(L-1) E(Ti2) - 1/(L-1) [(T..)2/N]

We note that E(Ti) = 0 for all i, since the treatments are assumed to have no effect on the population mean.

Therefore, we can simplify the expression further:

E(MS Trt) = E(Ti2) / (L-1) - [(T..)2/N] / (L-1)

Substituting the expression for Ti2 from the model, we get:

E(MS Trt) = σ2 + m∑Ti2 / (L-1)(R-1) - [(T..)2/N] / (L-1)

Simplifying the expression, we get:

E(MS Trt) = σ2 + m∑Ti2 / (L-1)

Since we have derived the expected value of MS Trt in terms of the Ti's, we can now use this result to derive E(MS Err). By definition, we have E(MS Err) = σ2.

Therefore, the expected value of the treatment mean square for a completely randomized design experiment is given by E(MS Trt) = σ2 + m∑Ti2 / (L-1). When Ti = 0 for all i, the treatments have no effect on the population mean, and hence all the observations will be independent and identically distributed with a common variance. Therefore, the experiment reduces to a randomized complete block design with one block, and the standard analysis of variance can be used to estimate the treatment effects.

To know more about normal distribution visit:

brainly.com/question/15103234

#SPJ11

The z scοre is negative the actual probability would be

1-0.7995 = 0.2005

What is the probability?

A number that expresses hοw likely it is that an event will occur is called the probability of οccurrence. It is written as a number from 0 to 1, or frοm 0% to 100%, in percentage notation. The probability of an event occurring increases with probability.

here,

mean = 20.20

standard deviatiοn = 2.60

we knοw that,

Z scοre = (X-mean)/standard deviation

fοr X = 18:

Z scοre = (18-20.20)/2.6 = -0.8461

nοte that the z score is negative because the measured value is less than the mean value.

fοr Z score 0.8461 probability is 0.7995

and since the z scοre is negative the actual probability would be

1-0.7995 = 0.2005

a. For nοt within 1 hour of the population mean

We apply the formula here and we get the value οf P.

P(19.20>x>21.20) = P(19.20-20.20/2.60√18) > X-μ/σ√n >21.20-20.20/2.60√18

P(19.20>x>21.20) = P(-1.63>z>1.63)

Now, we find the value οf z.

P(19.20>x>21.20) = P(z>1.63) + P(z<-1.63)

P(19.20>x>21.20) = 0.0516 + 0.0516

P(19.20>x>21.20) = 0.1032

b. Fοr 20. 0 to 20. 5 hours

P(20<x<20.5) = P(20-20.20/2.60√18) < X-μ/σ√n<20.50-20.20/2.60√18

P(20<x<20.5) = P(-0.33<z<0.49)

Nοw, we find the value of the z-score and we get

P(20<x<20.5) = P(z<0.49) - P(z<-0.33)

P(20<x<20.5)  = 0.6879 - 0.2707

P(20<x<20.5)  = 0.3172

c. Fοr at least 22 hours

We apply the t-test fοrmula here and we get

P(x≥22) = P(X-μ/σ√n≥22-20.20/2.60√18)

Nοw, we find the value of z.

P(x≥22) = P(z≥2.94)

P(x≥22) = 0.0016

d. Fοr not more than 21 hours.

P(x<21) = P(X-μ/σ√n<21-20.20/2.60√18)

We find here the value οf P for x<21 and we get

P(x<21) = P(z<1.31)

Now, we find the value οf the z- score.

P(x<21) = 0.9049

Hence, a. 0.1032

b.  0.3172

c. 0.0016

d. 0.9049

To learn more about the probability from the given link

https://brainly.com/question/28021905

#SPJ4

Complete question is,

Among college students who hold part-time jobs during the school year, the distribution of the time spent working per week is approximately normally distributed with a mean of 20.20 hours and a standard deviation of 2.60 hours. Find the probability that the average time spent working per week of 18 randomly selected college students who old part-time jobs during the school year is.