Consider the series ∑n=1∞an where
an=(n+9)n(2n+8)n
In this problem you must attempt to use the Root Test to decide whether the series converges.

Compute
L=limn→∞|an|−−−√n
Enter the numerical value of the limit L if it converges, INF if it diverges to infinity, MINF if it diverges to negative infinity, or DIV if it diverges but not to infinity or negative infinity.
L=


Which of the following statements is true?
A. The Root Test says that the series converges absolutely.
B. The Root Test says that the series diverges.
C. The Root Test says that the series converges conditionally.
D. The Root Test is inconclusive, but the series converges absolutely by another test or tests.
E. The Root Test is inconclusive, but the series diverges by another test or tests.
F. The Root Test is inconclusive, but the series converges conditionally by another test or tests.

Answer:

A. 2(2e + 4f + 10g)

Step-by-step explanation:

Answer:

2 3/10

Step-by-step explanation:

3/5x2=6/10

6/10-3/10=3/10

Answer:

It has 1 term and a degree of 4.

Step-by-step explanation:

3j⁴k-2jk³+jk³-2j⁴k+jk³

= 3j⁴k-2j⁴k-2jk³+jk³+jk³

= j⁴k

So, in this expression, there is 1 term, and it has a degree of 4.

Answer:

n=4

Step-by-step explanation:

f(x+n)=3(x+n)^2-7=3x^2+24x+41

3x^2+3n^2+6xn-7=3x^2+24x+41

Comparing and we will get, n=4

Answer:

s snsnnssjsjjsnsnsjs

es 17 es

Answers:

===========================================

Explanation:

Side MO is twice as long as the midsegment XY. Note how XY and MO are parallel.

This makes

MO = 2*XY = 2*10 = 20

Side MO breaks into two equal halves MZ and ZO

Each of MZ and ZO are 20/2 = 10 units long.

Put another way: XY, MZ and ZO are all the same length (all 10 units long).

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

The diagram shows that segment NO is 18 units long, which cuts in half to 18/2 = 9. This is the length of NY, YO and XZ

Also, MN = 14 which cuts in half to 7. This means MX, XN and YZ are all 7 units each.

Answer:

See attached

Step-by-step explanation:

Answer:

n = 112/13 = 8.615

Step-by-step explanation:

(3/8) n + 5n - 30 = (17/8)n - 2

(3/8)n +5n - (17/8)n = 30-2

(13/4)n = 28

n = 28 * 4/13

n = 112/13

n = 8.615

Answer:

Step-by-step explanation:

3\4 bc on a nuberline it would be 3 3\4

                                                        I--I----(etc)

so yeah hope i helped

Step-by-step explanation:

[tex] \longrightarrow \sf{ \dfrac{ \cfrac{ - 2}{x} + \cfrac{ 5}{y}}{\cfrac{ 3}{y} -\cfrac{ 2}{x} }} \\ \\ \longrightarrow \sf{ \dfrac{ \cfrac{ - 2y + 5x}{xy}}{\cfrac{ 3x - 2y}{xy} }} \\ \\ \longrightarrow \sf{ \cfrac{ - 2y + 5x}{xy}} \times{\cfrac{ xy}{3x - 2y} } \\ \\ \longrightarrow \boxed{ \sf{ \cfrac{ - 2y + 5x}{3x - 2y}}}[/tex]

Option A is correct!

The expression into an equivalent form would be; A [-2y + 5x ] / [3 x- 2y]

Those expressions that might look different but their simplified forms are the same expressions are called equivalent expressions.

To derive equivalent expressions of some expressions, we can either make it look more complex or simple. Usually, we simplify it.

[-2/x + 5/y] / [3/y - 2/x]

This expression could also be given by;

[-2y + 5x /xy] / [3 x- 2y /xy]

Now, we know that x would cancel out;

[-2y + 5x ] / [3 x- 2y]

Hence, the expression into an equivalent form would be; A [-2y + 5x ] / [3 x- 2y]

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Answer:

theres no question....

Step-by-step explanation:

???

9514 1404 393

Answer:

Step-by-step explanation:

The sum of torques about the pivot point is zero when the system is in equilibrium. That means the total of clockwise torques is equal to the total of counterclockwise torques. For this purpose, torque can be modeled by the product of mass and its distance from the pivot. The uniform beam can be modeled as a point mass at its center.

__

a) Let E represent the location of the center of mass of the beam. So, AE = 1.5 m. Then the distance from C to E is AC-AE = AC -1.5 and the CCW torque due to the beam's mass is (16 kg)(AC -1.5 m).

The distance from B to C is 3 m - AC, so the CW torque due to the particle at B is (7 kg)(3 -AC m)

These are equal, so we have ...

  16(AC -1.5) = 7(3 -AC)

  16AC -24 = 21 -7AC . . . . . eliminate parentheses

  23AC = 45 . . . . . . . . . . . add 7AC+24

  AC = 45/23 ≈ 1.957 . . divide by the coefficient of AC

  AC ≈ 2.0 meters . . . . rounded to 1 dp

__

b) The torques in this scenario are ...

  M(0.7) = 16(0.8) +7(2.3) . . . . . . AD = 0.7 m, DE = 0.8 m, DB = 2.3 m

  M = 28.9/0.7 ≈ 41.286 . . . . simplify, divide by the coefficient of M

  M = 41.3 kg . . . . rounded to 1 dp

_____

Additional comment

Torque is actually the product of force and distance from the pivot. Here, the forces are all downward, and due to the acceleration of gravity. The gravitational constant multiplies each mass, so there is no harm in dividing the equation by that constant, leaving the sum of products of mass and distance.

Firstly , before solving the equation , we should know about the chain rule and its formula.

Formula For the Chain rule-

$\rightarrow$ $\sf\dfrac\pink{dy}\pink{dx}$=$\sf\dfrac\pink{dy}\pink{du}$ $\times$ $\sf\dfrac\pink{du}\pink{dx}$ $\leftarrow$

_____________________________

$\sf\huge\underline{\underline{Question:}}$

$\sf\small{Differentiate\: x\: the \:function: (3x² - 9x + 5²)}$

$\sf\huge\underline{\underline{Solution:}}$

$\sf{Let\:y = (3x^2 - 9x + 5)^9}$

$\space$

☆ Differentiating both the sides w.r.t.x using chain rule-

$\mapsto$ [tex]\sf\dfrac{dy}{dx}=[/tex][tex]\sf\dfrac{d}{dx}[/tex][tex]\sf{(3x^2 - 9x + 5)^9}[/tex]

$\space$

$\space$

$\mapsto$ [tex]\sf\dfrac{dy}{dx}[/tex]=[tex]\sf{9(3x^2-9x+5)^8}[/tex] [tex]\times[/tex] [tex]\sf\dfrac{d}{dx}[/tex]$\sf\small{(3x^2-9+5)}$

$\space$

$\space$

$\mapsto$ [tex]\sf\dfrac{dy}{dx}[/tex]=[tex]\sf{9(3x^2-9x+5)^8}[/tex] [tex]\times[/tex][tex]\sf(6x-9)[/tex]

$\space$

$\space$

$\mapsto$ [tex]\sf\dfrac{dy}{dx}[/tex]=[tex]\sf{9(3x^2-9x+5)^8}[/tex] $\times$ [tex]\sf{3(2x-3)}[/tex]

$\space$

$\space$

$\mapsto$ [tex]\sf\dfrac{dy}{dx}[/tex]=[tex]\sf{27(3x^2-9x+5)^8(2x-3)}[/tex]

$\space$

$\space$

$\sf\underline\bold\green{❍ dy:dx=27(3x^2-9x+5)^8(2x-3)}$

______________________________

Answer:

$7,256.07

Step-by-step explanation:

A = p(1+r/n)^nt

A = 4000(1+.06/4)^(10*4)

Answer:

The 90% confidence interval for the difference of proportions is (0.01775,0.18225).

Step-by-step explanation:

Before building the confidence interval, we need to understand the central limit theorem and subtraction of normal variables.

Central Limit Theorem

The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]

Subtraction between normal variables:

When two normal variables are subtracted, the mean is the difference of the means, while the standard deviation is the square root of the sum of the variances.

p1 -> 1993

20 out of 100, so:

[tex]p_1 = \frac{20}{100} = 0.2[/tex]

[tex]s_1 = \sqrt{\frac{0.2*0.8}{100}} = 0.04[/tex]

p2 -> 1997

10 out of 100, so:

[tex]p_2 = \frac{10}{100} = 0.1[/tex]

[tex]s_2 = \sqrt{\frac{0.1*0.9}{100}} = 0.03[/tex]

Distribution of p1 – p2:

[tex]p = p_1 - p_2 = 0.2 - 0.1 = 0.1[/tex]

[tex]s = \sqrt{s_1^2+s_2^2} = \sqrt{0.04^2 + 0.03^2} = 0.05[/tex]

Confidence interval:

[tex]p \pm zs[/tex]

In which

z is the z-score that has a p-value of [tex]1 - \frac{\alpha}{2}[/tex].

90% confidence level

So [tex]\alpha = 0.1[/tex], z is the value of Z that has a p-value of [tex]1 - \frac{0.1}{2} = 0.95[/tex], so [tex]Z = 1.645[/tex].  

The lower bound of the interval is:

[tex]p - zs = 0.1 - 1.645*0.05 = 0.01775 [/tex]

The upper bound of the interval is:

[tex]p + zs = 0.1 + 1.645*0.05 = 0.18225 [/tex]

The 90% confidence interval for the difference of proportions is (0.01775,0.18225).

Step-by-step explanation:

let's convert the statement into equation..

let the charge of 1st mechanic be x and second be y..

by the question..

10x+5y=750...(i)

x+y=105..(ii)

from eqn(ii)..

x+y=105

or, x=105-y...(iii)

substituting the value of x in eqn (i)..

10x+5y=750

or, 10(105-y)+5y=750

or, 1050-10y+5y=750

or, 1050-750=5y

or, y=300/5

•°• y=60

substituting the value of y in eqn(iii).

x=105-y

or, x=105-60

•°• x= 45..

the rate charged by two mechanics per hour was 60$ and 45$

Answer:

Step-by-step explanation:

They travel 500 - 300 = 200 miles in 2 hours so their combined speed is

100 mph.

If their respective speed are x and y mph then we have the system

x + y = 100

x - y = 20

Adding the 2 equations

2x = 120

x = 60

and y = 40.

The other solution is that y = 60 mph and x = 40 mph.

Answer:

36 am I wright

because in this case we should always multiply

Answer:

1. Using the cost-plus pricing method, the selling price = $5.25

2. The change in selling price from 2018 to 2019 is $3.69 or 33.5% reduction.

3. To break-even, unit sales = 4,000 units

To realize a target return of $200,000, the unit sales = 5,600 units

4. Units to break-even = 12,500 meals

Sales revenue at break-even point = $125,000

Step-by-step explanation:

a) Data and Calculations:

Fixed costs = $3,000

Variable costs per unit = $5

Units manufactured = 100 units

Total variable costs = $500 ($5 * 100)

Total costs = $3,500 ($500 + $3,000)

Cost per unit = $3.50

Markup percentage = 50%

Using the cost-plus pricing method, the selling price = $5.25 ($3.50 * 1.5)

b) Fixed costs per year = $150,000

Variable costs per unit = $3

Production units = 30,000

Total variable costs = $90,000 ($3 * 30,000)

Cost-based pricing with a profit margin = $3 per unit

Total costs = $240,000 ($90,000 + $150,000)

Cost per unit = $8 ($240,000/30,000)

Selling price per unit = $11 ($8 + $3)

Variable cost = $2 per unit

Production units = 65,000 units

Total costs = ($2 * 65,000 + $150,000)

= $280,000 ($130,000 + $150,000)

Unit cost = $4.31 ($280,000/65,000)

Selling price = $7.31 ($4.31 + $3)

Change in selling = $3.69 ($11 = $7.31) = 33.5%

c) Fixed costs = $500,000

Per unit costs = $75

Proposed price = $200

Contribution margin per unit = $125 ($200 - $75)

To break-even, unit sales = $500,000/$125 = 4,000 units

To realize a target return of $200,000, the unit sales = $700,000/$125 = 5,600 units

d) Kitchen and related equipment costs = $100,000

Other fixed costs per year = $50,000

Variable costs = $6 per platter

Price per meal = $10

Contribution margin per meal = $4 ($10 - $6)

Units to break-even = $50,000/$4 = 12,500 meals

Sales revenue at break-even point = $50,000/40% = $125,000

Answer:

200 kilometers and 150 kilometers

no the square root of 113 is rounded to 56x2

Answer:

95% provides more information

Step-by-step explanation:

The confidence interval is obtained by using the relation :

Xbar ± Zcritical * σ/√n

(Xbar - (Zcritical * σ/√n)) = 5.22 - - - (1)

(Xbar + (Zcritical * σ/√n)) = 5.98 - - (2)

Adding (1) and (2)

2xbar = 5.22 + 5.98

2xbar = 11.2

xbar = 11.2 / 2 = 5.6

Margin of Error :

Xbar - lower C.I = Zcritical * σ/√n

Zcritical at 90% = 1.645

5.6 - 5.22 = 1.645 * (σ/√n)

0.38 = 1.645 * (σ/√n)

(σ/√n) = 0.38 / 1.645 = 0.231

Therefore, using the se parameters to construct at 95%

Zcritical at 95% = 1.96

Margin of Error = Zcritical * σ/√n

Margin of Error = 1.96 * 0.231 = 0.45276

C.I = xbar ± margin of error

C. I = 5.6 ± 0.45276

C.I = (5.6 - 0.45276) ; (5.6 + 0.45276)

C. I = (5.147 ; 6.053)

Hence, 95% confidence interval provides more information as it is wider.

The guidance director is conducting a sample poll in this experimental design.

Sample is a part of population. It does not comprises whole population. It is representatitive of whole population.

We are required to fill the blank with appropriate term among the options.

The correct option is sample poll because the guidance director collects data in his school only.

Census collects the whole population of the country.

Sample poll means collecting data from small population.

Random sample means collecting data from a part of popultion without identifying any variable.

Hence we found that he was doing sample poll.

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Whole numbers are natural numbers, and natural numbers do not include negatives, decimals, fractions, or roots, so all whole numbers can indeed satisfy the inequality.

$560-$500

=$500

therefore, other roommate will be paying $500 per month

Answer:

24 km/h

Step-by-step explanation:

Given:

Constant speed of submarine = 24 km/h

Depth under sea = 5 km

Distance of submarine from lighthouse = 13 km

Find:

Speed of the submarine

Computation:

At steady speed, the distance between both the submarine and the lighthouse base decreases at a rate of 24 km/hr.

So, when it is 13 kilometres from its starting point, the speed remains constant at 24 kilometres per hour.

Answer:

1.6 ft

Step-by-step explanation:

If you use the Pythagorean Theorem to solve for x, you get:

[tex]x=\sqrt{2.1^2-1.4^2}[/tex]

[tex]x=\sqrt{2.45} = 1.56524758425[/tex]

Rounded to the nearest tenth, the answer is 1.6