Determine if the following series converges or diverges. Give reasons for your answer. 00 n+ 1 Σ + 1 n2 + 5n on n=1 Choose the correct answer below. n+ 1 1 O A. Since .->nfor all n >1 and the series Er? diverges, the given series diverges by the comparison test. na +5n on n=1 1 1 O B. Since n+1 1 n2 + 5n 6n for all n> 1 and the series converges, the given series converges by the comparison test. 6n 6n2 n=1 00 1 1 O C. Since n+ 1 1 na + 5n 6n for all n >1 and the series diverges, the given series diverges by the comparison test. 2 On n=1 623

Answer: b.) 14

Step-by-step explanation:

Answer:

14

Step-by-step explanation:

The absolute value is always positive and 18-4 =14

Answer:

 1728000

Step-by-step explanation:

You always work from the parenthesis first because of order of operation. You have 12( because 2 times 6) then mulitply 12 times 10. You get 120 then you multiply it but itself 3 times. 120 x 120 x 120= 1728000

Answer:

Step-by-step explanation

(2×6)×10^3

(12)10^3

(12)1000

=12,000

When Helen plans to give Jose $0.25 in the first week and triples the amount each subsequent week then after 7 weeks, Jose will have a total of $1,093.75.

Helen plans to give Jose $0.25 in the first week and triples the amount each subsequent week.

We need to determine how much Jose will have after 7 weeks.

In the first week, Jose receives $0.25.

In the second week, Helen triples the amount, so Jose receives $0.25 * 3 = $0.75.

Similarly, in the third week, Jose receives $0.75 * 3 = $2.25.

This pattern continues, with Jose receiving triple the amount from the previous week.

To calculate how much Jose will have in 7 weeks, we can set up a geometric progression.

The first term (a) is $0.25, and the common ratio (r) is 3.

We want to find the sum of the first 7 terms of this geometric progression.

The formula for the sum of a geometric progression is:

S = a * (1 - \(r^n\)) / (1 - r),

where S is the sum, a is the first term, r is the common ratio, and n is the number of terms.

Plugging in the values, we have:

S = 0.25 * (1 - \(3^7\)) / (1 - 3),

Simplifying further, we get:

S = 0.25 * (-2,187) / (-2),

S = 1,093.75.

Therefore, after 7 weeks, Jose will have a total of $1,093.75.

Learn more about Ratio here:

https://brainly.com/question/14023900

#SPJ11

Answer:

0.3

Step-by-step explanation:

Jim needs a score of 97 on his third test to keep an average of 85 or greater.

Average refers to the sum of a set of numbers divided by the count of numbers in the set. It gives a typical or central value that represents the set of numbers.

Given,

The average of his first two tests is (69 + 82) / 2 = 75.5.

To get an average of 85,

he needs the sum of his three tests to be 3 * 85 = 255.

So, the sum of his first two tests is 255 - x, where x is the score he needs on the third test.

Therefore, x = 255 - (69 + 82) = 255 - 151 = 104.

So, he needs a score of 104 on his third test.

Jim needs a score of 97 on his third test to keep an average of 85 or greater.

Learn more about average :

https://brainly.com/question/24057012

#SPJ4

Answer: -6x

Step-by-step explanation: 24=-4x

24/-4 = -6x

Answer: -6

Step-by-step explanation:

|2x-12|=-4x

         |2x-12|=2x-12

         2x-12=-4x

         6x=12

          x=2 to exclude since x ≥6

        |2x-12|=-(2x-12)

        -2x+12 =-4x

         2x =-12

           x=-6

Answer x=-6

Answer: 5.22

Step-by-step explanation:

The apothem = 87 cm = 0.87 m.

Using the formula \(A=\frac{1}{2}ap\) to find the area of the base, where a is the apothem and p is the perimeter, we get \(A=\frac{1}{2}(0.87)(6)=2.61\)

So, using the formula \(V=Bh\), we get the volume to be \(2.61(2)=5.22 \text{ m}^{3}\)

The expected product(s) resulting from addition of br2 to (e)-3-hexene is 1,2-dibromohexane.

What is hexene?

Hexene is a linear chain alkene with six carbon atoms and one double bond. Hexene is also known as hexylene. It is an unsaturated hydrocarbon, which means it contains a carbon-carbon double bond.What is Br2?Bromine (Br2) is a diatomic molecule consisting of two bromine atoms that are covalently bonded to form a reddish-brown liquid at room temperature and pressure.

Bromine is an oxidizing and a halogen element that is a member of Group 17 of the periodic table.

What is the product of Br2 addition to hexene?

The expected product(s) resulting from addition of br2 to (e)-3-hexene would be 1,2-dibromohexane. The addition of Br2 to an alkene is an electrophilic addition reaction in which Br2 adds across the double bond to produce vicinal dibromides.

In the case of (e)-3-hexene, the Br2 will add across the double bond in an anti-addition manner (i.e. adding on the opposite sides) to give 1,2-dibromohexane, as shown below:

Therefore, the answer is 1,2-dibromohexane.

To know more about sides, visit

https://brainly.com/question/29082532

#SPJ11

The sample space for the experiment, S= {Q, R, S, T}.

A sample space is a set of potential results from a random experiment. The letter "S" is used to denote the sample space. Events are the subset of possible experiment results. Depending on the experiment, a sample area could contain a variety of results.

Given:

From the Spinner we can see four portions as

Q(Orange)

R(Green)

S(Blue)

T(Purple)

So, if the spinner spined then it will point Q, R, S or T which is the Sample space for the Spinner.

Hence, the Sample space is {Q, R, S, T}.

Learn more about Sample space here:

https://brainly.com/question/28043513

#SPJ1

Answer: B: S = {Q, R, S, T}

Step-by-step explanation:

This is the only answer listed with the letters on the spinner.

Answer:

5 + 5 = 10

Step-by-step explanation: ok

Answer:

90,217.77

Step-by-step explanation:

We can use the equation S+RS=M to figure this out where S is the initial salary before the raise, R being the rate at which the salary is increased, and M being the Salary after the raise.

By plugging it in for the first year we get

77,000+2%*77,000=M

Solving it, we get 78,540 and since there is a new salary increase 78,540 is the new starting salary

78,540+78,540*2%=80,110.8

80,110.8+80,110.8*2%=81,713.016

83,347.27632

85,014.2218464

86,714.506283328

88,448.796408995

90,217.772337175

Or rounded up

90,217.77

Answer:

Positive

Step-by-step explanation:

Answer:

<x = 55 degrees

<y = 55 degrees

<z = 70 degrees

Step-by-step explanation:

The 125 degree angle and x are supplementary since they form a straight line, which means that their degrees add up to 180. To find x, the interior angle, we must subtract 125 from 180.

180 - 125 = 55

Angle x is 55 degrees. Since the sides opposite x and y are marked with lines, they are congruent, and since the sides are congruent, the angles must be, too. So, y is also 55 degrees.

Finally, the angles in any triangle add up to 180 degrees. To find z, we must subtract the values of x and y from 180.

180 - 55 - 55 = 70, so z is 70 degrees.

Brainliest, please :)

❄Hi there,

the external angle & the interior angle form a linear pair, which means, if you add these angles together, you'll arrive at 180°.

Using this knowledge let's set up an equation and find x:

\(\triangleright \ \sf{125+x=180}\). We let x be the desired angle.

\(\triangleright \ \sf{x=180-125=55}\)

So the interior angle is \(\angle\sf{55}\textdegree\).

❄

The standard deviation of the sample proportions (i.e., the standard error of the proportion) is 10.5.

The sample proportion is a random variable that can't be predicted with certainty because it fluctuates from sample to sample.

n = 525

Population Proportion(p) = 0.3

q = 1 - 0.3

q = 0.7

σ = √npq

σ = √(525 × 0.3 × 0.7)

σ = √110.25

σ = 10.5

So The standard deviation of the sample proportions = σ/n

The standard deviation of the sample proportions = 10.5/525

The standard deviation of the sample proportions = 0.02

The standard deviation of the sample proportions = 2%

To learn more about sample proportion link is here

brainly.com/question/29912751

#SPJ4

The complete question is:

Random samples of size 525 are taken from an infinite population whose population proportion is 0.3. The standard deviation of the sample proportions (i.e., the standard error of the proportion) is

a.0.0004

b.0.2100

c.0.3000

d.0.0200

Answer:

Rs. 320

Step-by-step explanation:

Contribution of Non Fiction books towards the sale = (degree of non fiction books / total degrees in a circle ) x 100

degree of non fiction books = 80

total degrees in a circle = 360

(80 / 360) x 1440 = Rs. 320

After performing the linear regression evaluation, the equation of the regression line is:

(i) y = 1.40x + 1.45

To locate the linear regression line for the given records, we will use a statistical software program or a calculator. By analyzing the data points, we can decide the equation of the road that satisfactorily represents the connection between the hours of the stand being open (x) and the profit (y).

After performing the linear regression evaluation, the equation of the regression line is:

y = 1.40x + 1.45

This equation shows that for each extra hour the stand is open, the profit increases by using $1.40. The y-intercept, represented with the aid of the regular term 1.45, shows that although the stand isn't always open, there may be nevertheless a base income of $1.45.

The linear regression line for the given statistics indicates a positive relationship between the hours of the stand being open and the earnings earned. As the hour's increase, the earnings have a tendency to increase as nicely.

To know more about linear regression,

https://brainly.com/question/30401933

#SPJ4

The correct question is:

The linear regression line for the given data is y = 1.28x + 2.93. This equation represents the relationship between the hours the stand is open (x) and the corresponding profit (y).

To find the linear regression line for the given data, we can use statistical software or a calculator. The linear regression line represents the best fit line through the data points.

First, we list the given x and y values:

x: 1, 2, 3, 4, 5, 6, 7

y: 3.58, 5.18, 6.24, 7.97, 7.09, 8.31, 11.33

Using the software, we calculate the linear regression line. The result is y = 1.28x + 2.93, rounded to two decimal places.

Learn more About linear from the given link

https://brainly.com/question/2030026

#SPJ11

QUESTION

gabriel and raj were running a lemonade stand at the local park. they decided to pay their sister to operate the stand. the following values represent the profit y after x hours of the stand being open. using a calculator or statistical software, find the linear regression line for the data. enter your answer in the form y =mx+b, with m and b both rounded to two decimal places.

X    Y

1   3.58

2   5.18

3   6.24

4    7.97

5   7.09

6    8.31

7    11.33

Answer:

9.5

Step-by-step explanation:

Is that what you mean by value?

I need a better explanation

Answer:

Step-by-step explanation:

It is nine and a half. What do you exactly mean by value?

Answer:

A

Step-by-step explanation:

The Reflexive property of congruence can be used to prove

ΔPQR≅ΔPSR .

Given:

∠QPR≅∠SPR

∠PQR≅∠PSR

What is Reflexive property of congruence ?

In geometry, the reflexive property of congruence states that an angle, line segment, or shape is always congruent to itself.

We learned that the reflexive property of equality means that anything is equal to itself. The formula for this property is a = a. This property tells us that any number is equal to itself. For example, 3 is equal to 3.

PR≅PR (Reflexive property of congruence)

If two angles and a non-included side of one triangle are equal to two angles and a non-included side of another triangle, then the triangles are congruent.(AAS theorem)

Hence, ΔPQR≅ΔPSR.

Learn more about Reflexive property of congruence at:

https://brainly.com/question/8741371

#SPJ1

The directional derivative of the function h(x, y) = x² - 2x'y + 2xy + y at the point P(1, -1) in the direction of u = (-3, 4) is 8.

To find the directional derivative, we need to compute the dot product between the gradient of the function and the unit vector representing the given direction.

First, let's calculate the gradient of h(x, y):

∇h = (∂h/∂x, ∂h/∂y) = (2x - 2y, -2x + 2 + 2y + 1) = (2x - 2y, -2x + 2y + 3)

Next, we normalize the direction vector u:

||u|| = sqrt((-3)² + 4²) = 5

u' = u/||u|| = (-3/5, 4/5)

Now, we find the dot product:

D_uh = ∇h · u' = (2(1) - 2(-1))(-3/5) + (-2(1) + 2(-1) + 3)(4/5) = 8

Therefore, the directional derivative of h(x, y) at P(1, -1) in the direction of u = (-3, 4) is 8.

LEARN MORE ABOUT directional derivative here: brainly.com/question/29451547

#SPJ11

Answer:

d

Step-by-step explanation:

The function is nonlinear. Linear is a straigt line and this function has a curve. You can find that by thinking of the story or placing it on a graph.

Answer:

d

Step-by-step explanation:

the answer is non-linear because a linear function  would only have the first part not 9x+4  

Answer:

A) \({2s + 5t = 49.50\\\\s = 2t\)

B) Keegan paid $5.50 for each t-shirt and $11 for each short.

Step-by-step explanation:

A)

⭐ What is a system of equations?

We are asked to create a system of equations for Keegan's situation.

Let s = the price for every short

Let t = the price for every t-shirt

So, if Keegan buys 2 shorts and 5 t-shirts, his cost will be $49.50.

As an equation, this situation would be:

\(2s + 5t = 49.50\)

It's given that the cost of 1 short is twice the cost of 1 t-shirt.

As an equation, this situation would be:

\(s = 2t\)

B)

⭐How can we solve a system of equations?

For this problem, the best way to solve this system of equations is through substitution. I will demonstrate how to use substitution for this problem.

Using the equations \(2s + 5t = 49.50\) and \(s = 2t\), we will literally substitute a variable from one equation into another equation to solve for the other variable.

Given that \(s = 2t\):

\(2s + 5t = 49.50\)

\(2(2t) + 5t = 49.50\)

\(4t + 5t = 49.50\)

\(9t = 49.50\)

\(t = 5.50\)

∴ It costs Keegan $5.50 for one t-shirt.

Now, we can substitute the value of t into the same equation to solve for the value of s.

Given that \(t = 5.50\):

\(2s + 5(5.50) = 49.50\)

\(2s + 27.5 = 49.50\)

\(2s = 22\)

\(s = 11\)

∴ It costs Keegan $11 for one short.

The equation to solve is

We need to isolate x.

That means dividing 13 by 4.

So,

This is the value of x, 3 and 1/4th.

In the number line, it is just past "3".

Answer is

Answer:

D

Step-by-step explanation:

We know that Y represents Sofia's age

Diego is 8 years older than 3 times Sofia's age

means to get Diego's age we have to multiply Sofia's age by 3 and add 8

The mean number of accidents that would be expected to be more than 7 accidents is 0.6554.

By dividing the sum of the given numbers by the entire number of numbers, the mean—the average of the given numbers—is determined.

A statistical measurement known as the Z-score indicates how closely a value relates to the mean of a collection of values. The Z-score is calculated using standard deviations from the mean. When a data point's Z-score is 0, it means that it has the same score as the mean. One standard deviation from the mean would be indicated by a Z-score of 1.0.

Given that mean is 6.4 and the standard deviation is 1.5.

The z score is used to determine the accidents:

z = 7 - 6.4 / 1.5

z = 0.4

Using the table of normal distribution we have, P(x > 7 ) = P(z > 0.4) = 0.6554

Learn more about mean here:

https://brainly.com/question/28670966

#SPJ4

The dimensions of the rectangle are a width of 13 inches and a length of 32 inches.

To find the dimensions of the rectangle with a perimeter of 90 inches, follow these steps:

Let the width of the rectangle be represented as w.
Since the length is six more than double the width, we can represent the length as 2w + 6.
The formula for the perimeter of a rectangle is P = 2L + 2W, where P is the perimeter, L is the length, and W is the width.
Substitute the given perimeter (90 inches) and the expressions for length and width into the formula: 90 = 2(2w + 6) + 2w.
Simplify the equation: 90 = 4w + 12 + 2w.
Combine the terms with w: 90 = 6w + 12.
Subtract 12 from both sides of the equation: 78 = 6w.
Divide both sides by 6 to solve for w: w = 13.
Substitute the value of w back into the expression for the length: L = 2(13) + 6 = 26 + 6 = 32.

The rectangle is a size of 13 inches in width and 32 inches in length.

Learn more about "Rectangle perimeter": https://brainly.com/question/19819849

#SPJ11

Step-by-step explanation:

5,200,000 = 5.2 × 10⁶

so, we have

(5.2 × 10⁶) × (8.3 × 10²) - (3.1 × 10⁸)

(5.2 × 8.3 × 10⁸) - (3.1 × 10⁸)

(43.16 × 10⁸) - (3.1 × 10⁸) = 40.06 × 10⁸ = 4.006 × 10⁹

29/200. 145 / 5 = 29, and 1000 / 5 = 200. 29 is a prime, so that's the lowest you can go: 29/200.