if k is a positive integer, find the radius of convergence, R, of the series [infinity]Σ (n!)^k+3 / ((k + 3)n)! x^n n = 0 . R =

Answers

Answer 1

For any positive integer k, the radius of convergence R is: If k ≥ -2, R = 0 (the series diverges for all x). If k < -2, R = ∞ (the series converges for all x).

To find the radius of convergence,

R, of the series Σ[tex][n!^{k+3} / ((k + 3)n)!][/tex][tex]x^n[/tex]  (n = 0 to infinity),

we can use the ratio test.

Step 1: Apply the ratio test

Consider the ratio of consecutive terms:

L = [tex]\lim_{n \to \infty}[/tex] |[tex](n+1)!^{k+3}[/tex] / ((k + 3)(n + 1))!| / [tex]n!^{k+3}[/tex]/ ((k + 3)n)!|

= [tex]\lim_{n \to \infty}[/tex] |[tex](n+1)!^{k+3}[/tex] / [tex]n!^{k+3}[/tex] × ((k + 3)n)! / ((k + 3)(n + 1))!|

= [tex]\lim_{n \to \infty}[/tex] |[tex]n+1^{k+3}[/tex]/ ((k + 3)(n + 1))|

Step 2: Simplify the ratio

L =[tex]\lim_{n \to \infty}[/tex][tex]|(n + 1)^k / (k + 3)|[/tex]

= ∞ if k ≥ -2 (the limit diverges)

= 0 if k < -2 (the limit converges to 0)

Step 3: Determine the radius of convergence

According to the ratio test, the series converges if L < 1,

and diverges if L > 1.

Since the limit L depends on the value of k,

the radius of convergence R varies accordingly:

If k ≥ -2, the series diverges for all values of x.

If k < -2, the series converges for all values of x.

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Related Questions

Use the following probability distribution to answer questions
x -15 -10 -5 0 5 10 15
P(X=x) 0.05 0.34 0.13 0.24 0.08 0.11 0.05
1. Find P(X=0) a. 0
b. 0.24 c. 0.48 d. 0.52 e. 0.08

Answers

The probability P(X=0) is equal to 0.24.

In the given probability distribution, we are provided with the probabilities associated with each value of the random variable X. To find P(X=0), we need to identify the probability assigned to the value 0.

Looking at the table, we see that the probability P(X=0) is given as 0.24. Therefore, the correct answer is option b. 0.24.

The probability distribution assigns probabilities to specific values of the random variable X. In this case, the value 0 has a probability of 0.24. This indicates that there is a 0.24 chance of observing the value 0 when the random variable X is sampled from this distribution.

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Which quadrilateral's diagonals are congruent and perpendicular bisectors of each other?

Answers

Diagonals congruent: rectangle, square, isosceles trapezoid

Perpendicular bisectors: Rhombus, Square

Cheryl moves houses. Her old house is 3 kilometers from her new house. How many meters is it from the old house to the new house?

Answers

Answer:

3000 here hope this helps you out

Find the Range of the following set of data. (Round to the
nearest whole number.)
1, 1, 3,0, 7, 2, 0, 3, 1, 6, 8, 1
PLEASE HELP IM DESPERATE

Answers

Step-by-step explanation:

put them in least to greatest, so that would be: 0,0,1,1,1,1,2,3,3,6,8,7,8, then do the greatest minus the lowest: 8-0=8

A running track consists of two parallel lines that are connected at each end but the curved boundary of a semicircle. The parallel lines are 30 meters long and 7 meters apart. Fine the area inside the running track.

Answers

Answer:

The area inside the running track is 248.5 m².

Step-by-step explanation:

The area inside the running track is given by the sum of the area of a rectangle and the area of a semicircle:

[tex] A_{t} = A_{r} + 2A_{c} [/tex]                

[tex] A_{t} = x*(2r) + 2*(\frac{\pi r^{2}}{2}) [/tex]      

Where:

x: is one side of the rectangle = 30 m            

r: is the radius = half of the other side of the rectangle = 7/2 m = 3.5 m

Hence, the total area is:

[tex] A_{t} = 30*7 + \pi (3.5)^{2} = 248.5 m^{2} [/tex]                            

Therefore, the area inside the running track is 248.5 m².

I hope it helps you!                                                    

What is the equation of the line shown in the graph?

Answers

Answer:

-6

Step-by-step explanation:

it is going through the y axis

Four times a first number decreased by a second number is 19. The first number increased by four times the second number is −8. Find the numbers.

Answers

Answer:

a = 4

b = -3

Step-by-step explanation:

Let a and b be the two numbers.

According to question,

4a - b = 19........(i)

And,

a + 4b = -8........(ii)

From (i),

4a - b = 19

or, b = 4a - 19

Replacing b in (ii),

a + 4(4a - 19) = -8

a + 16a - 76 = -8

17a = -8 + 76

17a = 68

a = 68/17

a = 4

And,

b = 4a - 19

= 4 x 4 - 19

= 16 - 19

= -3

Which function is equivalent to (x)=-7(x+4)2-1?

a : f(x)=-7x2 + 8x+15

b : F(x)=-7x2-56x-113

C : f(x)=-7x2-56x-105

d : f(x)=-7x2 + 111

Answers

Answer:

answer : b

Step-by-step explanation:

hello :

calculate : f (x)=-7(x+4)²-1

f(x) = -7(x²+16+8x) -1  use  identity : (a+b)² = a²+b²+2ab

f(x) = -7x²-112 -56x -1

f(x) = -7x²-56x -113  

5 in=? feet fraction form​

Answers

Five inches is 5/12 of a foot. To solve this, you need to know that there are 12 inches in a foot.

The Zombie Apocalypse has come to Panama City Beach. It starts when 3 Spring Breakers become zombie after an encounter with a deadly fish. Waking up the next day, each Spring Breaker can infect 4 more people per day before needing a rest. Each of these zombies can, in turn, infect an additional 4 people per day. Write an Exponential Function to represent this situation. Then find out how many crazy Spring Break Zombies will be roaming the beach at the end of the week (Day 7)?

Answers

Answer:

By the end of the week there will be 49,152 zombies in Panama City Beach.

Step-by-step explanation:

Since the Zombie Apocalypse has come to Panama City Beach, starting when 3 Spring Breakers become zombie after an encounter with a deadly fish, and since waking up the next day, each Spring Breaker can infect 4 more people per day before needing a rest , and each of these zombies can, in turn, infect an additional 4 people per day, to determine how many crazy Spring Break Zombies will be roaming the beach at the end of the week the following exponential function has to be solved:

3 x 4 ^ 7 = X

3 x 16,384 = X

49.152 = X

Therefore, by the end of the week there will be 49,152 zombies in Panama City Beach.

The number of crazy Spring Break Zombies will be roaming the beach at the end of the week 7 are 49,152 and the equation for the situation is,

[tex]x=3\times(4)^7\\[/tex]

What is an exponential function?

Exponential function is the function in which the function growth or decay with the power of the independent variable. The curve of the exponential function depends on the value of its variable.

The exponential function with dependent variable y and independent variable x can be written as,

[tex]y=ba^x+c[/tex]

Here, a, b and c are the real numbers.

The Zombie Apocalypse has come to Panama City Beach. It starts when 3 Spring Breakers become zombie after an encounter with a deadly fish.

In the next morning, each Spring Breaker can infect 4 more people per day before needing a rest. Each of these zombies can, in turn, infect an additional 4 people per day.

As total number of weeks are 7. Thus, for this situation, the exponential function for the variable x can be given as,

[tex]x=3\times(4)^7\\[/tex]

Now to find the number of crazy Spring Break Zombies will be roaming the beach at the end of the week 7, simplify the above equation as,

[tex]x=3\times(4)^7\\\\x=3\times16384\\x=49152[/tex]

Hence, the number of crazy Spring Break Zombies will be roaming the beach at the end of the week 7 are 49,152 and the equation for the situation is,

[tex]x=3\times(4)^7\\[/tex]

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Find the Laplace Transform of number 1 using the definition via integration. F(t) = 5 sin 3t Solve for the Laplace transform using the formula for numbers 2 and 3. G(t) = t^5 — 1/4 e^-9t + 5(t − 1)² F(t) = e^-2t-5

Answers

The Laplace Transform of the function F(t) = 5sin(3t) can be found by using the definition of the Laplace Transform, which involves integrating the function with respect to time. The Laplace Transform of F(t) is not a number, but rather a function in the complex domain.

To find the Laplace Transform of F(t) = 5sin(3t) using the definition, we need to integrate the function with respect to time from 0 to infinity. The Laplace Transform is defined as L{F(t)} = ∫[0,∞] F(t)e^(-st) dt, where s is a complex number.

Integrating [tex]5sin(3t)e^(-st)[/tex]with respect to t results in a complex function that depends on s. The integration involves applying the integration rules and evaluating the integral limits. The resulting Laplace Transform is a function of s, denoted as L{F(t)}.

However, for the functions G(t) = [tex]t^5 - (1/4)e^(-9t) + 5(t - 1)^2 and F(t) = e^(-2t - 5)[/tex], the Laplace Transform can be computed using the Laplace Transform formulas. These formulas provide specific transformations for various types of functions, making the calculation more straightforward. By applying the Laplace Transform formulas to G(t) and F(t), we can obtain their respective Laplace Transform expressions, denoted as L{G(t)} and L{F(t)}. These expressions will involve algebraic manipulations and the use of the Laplace Transform tables to identify the corresponding transformations.

Overall, the Laplace Transform is a powerful tool in the field of mathematics and engineering that allows us to transform functions from the time domain to the complex frequency domain, facilitating the analysis and solution of differential equations and systems of equations.

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what is the rate of change for y=38x+20
A. 38
B. 20
C.1
D. it has no term

Answers

Answer:

A

Step-by-step explanation:

The cone and cylinder above have the same radius, r, and height, h. The volume of the cone is 69 cubic centimeters. What is the volume of the cylinder?

A. 138 cubic centimeters
B. 207 cubic centimeters
C. 23 cubic centimeters
D. 276 cubic centimeters

Answers

Answer:

207 cubic centimeters

Step-by-step explanation:

Given

volume of cone  = 9 cubic centimeters

Since the cone and cylinder above have the same radius, r, and height, h, then r = h

volume of the cone = 1/3πr²h

69 =  1/3πr²h

πr²h = 69*3

πr²h = 207cubic cm

Since the volume of the cylinder =  πr²h

Hence volume of the cylinder is 207 cubic centimeters


Find the sum of (6x2 - 9x + 7) and (- 8x2 + 10x - 14)

Answers

Answer:

-2x² + x - 7

Step-by-step explanation:

(6x² - 9x + 7) + (-8x² + 10x - 14)

6x² - 9x + 7 - 8x² + 10x - 14

6x² - 8x² - 9x + 10x + 7 - 14

-2x² + x - 7

16. Find the perimeter of AJKL.
J
8x - 35
N
5x - 8
77-9
K
Р
M M
2y + 11
o
32
L

Answers

Answer:

Parameter OF Δ JKL = 138 unit

Step-by-step explanation:

Given:

JN = 8x - 35

NK = 7y - 9

OK = 2y + 11

OL = 32 - [2y + 11]

JM = 5x - 8

Find:

Parameter OF Δ JKL

Computation:

We know that tangent from same points are always equal

So,

ML = OL

JM = JN

5x - 8 = 8x - 35

8x - 5x = 35 - 8

3x = 27

x = 9

So,

JN = 8x - 35

JN = 8(9) - 35

JN = 37 unit

JM = 5x - 8

JM = 5(9) - 8

JM = 37 unit

NK = OK

7y - 9 = 2y + 11

5y = 20

y = 4

NK = 7y - 9

NK = 7(4) - 9

NK = 19 unit

OK = 2y + 11

OK = 2(4) + 11

Ok = 19 unit

OL = 32 - [2(y) + 11]

OL = 32 - [2(4) + 11]

OL = 13 unit

So,

LM = OL = 13 unit

Parameter OF Δ JKL = JN + NK +  OK + OL + LM + JM

Parameter OF Δ JKL = 37 + 19 + 19 + 13 + 13 + 37

Parameter OF Δ JKL = 138 unit

Answer:

Step-by-step explanation:

g


Can you say a coefficient is
significantly different from zero at 5% level if the coefficient of
a variable is twice as large as its estimated standard error?
Explain.

Answers

A coefficient is significantly different from zero at 5% level if the coefficient of a variable is twice as large as its estimated standard error. This is because, at the 5% level of significance, the critical value for the t-distribution, when a two-tailed test is used, is equal to 1.96. To be significantly different from zero, the calculated t-value has to be greater than 1.96 or less than -1.96.

Suppose the estimated standard error is SE and the coefficient of the variable is β. The standard error of β, denoted by SE(β), is equal to SE/√n, where n is the sample size. Thus, if the coefficient of the variable is twice as large as its estimated standard error, then β > 2SE.

And, the calculated t-value would be greater than (β/SE) > 2, which is greater than 1.96. Therefore, we can say that the coefficient is significantly different from zero at the 5% level.

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A combination lock with three dials, each numbered 1 through 8, is defective in that you only need to get two of the numbers right to open the lock. (For example, suppose the true combination is 4-2-7. Then 4-2-7 would open the lock, but so would 4-2-5, 4-2-2, 4-8-7 or 4-6-7. But not 2-4-7.)

Answers

Answer:

64 combination attempts

Step-by-step explanation:

Since each dial in the lock is numbered from 1-8 then there are 8 possibilities for each dial. Out of the three dials, only 2 actually need to be correct in order for the lock to open therefore, we simply raise the number of possibilities for each dial to the power of 2 which should give us the total number of tries we need in order to guarantee that it opens. Assuming that you are making the combinations in numerical order 1-1-1, 1-1-2, 1-1-3, etc.

8^2 = 64 combination attempts

Factor the expression below. A. (x + 5)(x + 5) B. (x - 5)(x + 5) C. 5(x2 - x + 5) D. (x - 5)(x - 5)

Answers

Answer:

A. x² +10x +25

B. x² - 25

C. 5x² -5x + 25

D. x²- 10x + 25

Step-by-step explanation:

A. (x+5)(x+5)

x² + 5x + 5x + 25

x² +10x + 25

B. (x-5)(x+5)

x² + 5x - 5x - 25

x² -25

C. 5(x² -x +5)

5x² -5x + 25

D. (x-5)(x-5)

x² - 5x -5x + 25

x²- 10x + 25

What is the slope, m, of the line? Enter your answer as a decimal.
Round to the nearest hundredth.

Answers

Answer:

4.56

Step-by-step explanation:

The slope (m) of the line given in the graph is -0.332.

In the given graph coordinates of the line are given, that is (2,0) and (-4, 2).

How to find the slope of the line?

Pick two points on the line and determine their coordinates. Determine the difference in y-coordinates of these two points (rise). Determine the difference in x-coordinates for these two points (run). Divide the difference in y-coordinates by the difference in x-coordinates (rise/run or slope).

Now, the slope of the line=m=0-2/2-(-4)=-2/6=-0.33333

-0.33333≈-0.332

Therefore, the slope (m) of the line given in the graph is -0.332.

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HELP ME PLEASE https://brainly.com/question/22734415
I’m gonnna fail :(

Answers

What’s your question

Simplify:
5a+6a^2+2a^0-3a^2-9a

3a^2-4a+2

-a^3+2

-a^2+2

3a^2-4a+1

Answers

Answer:

I believe that the answer is '3a^2-4a+2

Use series to approximate the definite integral to within the indicated accuracy:
the integral from from 0 to 0.4 of e^?x^3 dx with an error <10?4
Note: The answer you derive here should be the partial sum of an appropriate series (the number of terms determined by an error estimate). This number is not necessarily the correct value of the integral truncated to the correct number of decimal places.

Answers

We evaluate S_n by substituting x = 0.4 into the nth partial sum and obtain our approximation for the integral.

To approximate the definite integral ∫(0 to 0.4)

[tex] {e}^{-x^3} [/tex]

dx with an error less than

[tex] {10}^{ - 4} [/tex]

we can use a Taylor series expansion for

[tex]{e}^{-x^3} [/tex]

The Taylor series expansion of

[tex]{e}^{-x^3} [/tex]

centered at x = 0 is:

[tex] {e}^{-x^3} = 1 - x^3 + (x^3)^2/2! - (x^3)^3/3! + ...[/tex]

By integrating this series term by term, we can approximate the integral. Let's denote the nth partial sum of the series as S_n.

To estimate the number of terms needed for the desired accuracy, we can use the error estimate formula for alternating series:

|Error| ≤ |a_(n+1)|, where a_(n+1) is the absolute value of the first omitted term.

In this case, |a_(n+1)| =

[tex]|(x^3)^{n+1} /(n+1)!| ≤ {0.4}^{(3(n+1)} /(n+1)!

[/tex]

By setting

[tex]{0.4}^{(3(n+1))} /(n+1)! < 10^(-4)[/tex]

and solving for n, we can determine the number of terms required.

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Need this answer ASAP the last missing square says “take the square root of both sides”

Answers

Answer:

add 5 to both sides, divide by 2, take square root, subtract 3/4

Step-by-step explanation:

I think you maybe do the reverse order of operations, which is SADMEP (subtract/add, then divide/multiply, then take care of exponents and square roots, then do that same order for whatever's in parenthesis.)

What is the value of
[tex] \sqrt{100 \times 4} [/tex]

Answers

answer: 20

explanation: simplify the radical by breaking the radicand up into a product of known factors, assuming positive real numbers

Answer:

√{100×4)=√20²=±20 is your answer

Worth five points! it doesnt tell me if what answer is right but if i get 75% or up i will mark the first person who answered with an actual answer brainliest and i don't lie about brainliest!!
What is m∠U?
A. 17
B. 29
C. 46
D. 134

Answers

Answer:

A

Step-by-step explanation:

Remarks

The given angle is an exterior angle.It's value is 46 degrees.     An exterior angle is the sum of the two remote angles. (A remote angle is one that is not supplementary  to the given exterior angle.

Solution

46 = <u + <t<t = 2946 = <u + 29               Subtract 29 from both sides.46 - 29 = <u<u = 17 degrees

You just obtained a credit card. You immediately purchase a stereo system for $200. your credit limit is $1000. Let's assume that you make no payments and purchase nothing more and there are no other fees. The monthly interest rate is 1.42%.
What is the growth rate of your credit card balance?
A. 0.42
B. 0.0142
C. 14.2
D. 142

Answers

Answer:

its b

Step-by-step explanation:

have a great day <3

The growth rate of your credit card balance is approximately 0.0142.

Therefore, the correct option is B.

Given that you got a credit card, you purchased a stereo system for $200. your credit limit is $1000.

The monthly interest rate is 1.42%.

We need to determine the growth rate of your credit card balance,

To calculate the growth rate of your credit card balance, we need to consider the monthly interest rate and the initial purchase amount.

The monthly interest rate is 1.42%, which can be expressed as a decimal by dividing it by 100: 0.0142.

The initial purchase amount is $200.

Assuming no payments are made and no additional purchases are made, the credit card balance will increase each month due to the accrued interest.

To calculate the growth rate, we can divide the accrued interest by the initial purchase amount.

Accrued interest = Monthly interest rate x Initial purchase amount

= 0.0142 x $200

= $2.84

Growth rate = Accrued interest / Initial purchase amount

= $2.84 / $200

≈ 0.0142

Therefore, the growth rate of your credit card balance is approximately 0.0142, which corresponds to option B.

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Find the greatest common factor of 24x^2 and 42xy^3 .

Answers

Answer:

12y2

Step-by-step explanation:

Raymond has two bags of candy. • Bag A has 15 total pieces of candy, 9 are chocolate candies. Bag B has 10 total pieces of candy, 5 are chocolate candies. Which statement is true?

Answers

Answer:

The probability of selection of chocolate candy from bag A is ( 10%) bigger than from the bag B

Step-by-step explanation:

From bag A the probability (p₁ ) of selection  ( in a random sample) of one chocolate candy is

p₁ = 9/15       p₁  = 0,6

From bag B the probability ( p₂ ) of selection ( in a random sample) of one chocolate candy is:

p₂ = 5/10       p₂ = 0,5

Then the probability of selection of chocolate candy from bag A is bigger than from the bag B

p₁ > p₂      p₁ - p₂  = 0,6 - 0,5       p₁ - p₂ = 0,1    p₁ - p₂ = 10%

p

A hemisphere with diamater 17 cm

Answers

Answer:

not enough information

Step-by-stepexplanation:

Ben wants to buy a new car stereo and he has already saved some money. He used this inequality to represent the amount he still has to save to be able to buy the stereo, where a represents the amount still left to save.


a + 212 greater-than-or-equal-to 365


If Ben saves $15 a week for the next 10 weeks, will he be able to buy the stereo and why?

Answers

Answer:

Since Ben would have $362, he won't be able to buy the stereo as he needs to have an amount greater than or equal to 365.

Step-by-step explanation:

First, you need to determine the amount that Ben would have after saving $15 for the next 10 weeks:

$15*10=$150

Now, the inequality indicates that the amount left to save plus 212 should be greater than or equal to 365, so you have to add up 212 plus the amount Ben will save in the next 10 weeks to be able to determine if he would be able to buy the stereo:

150+$212=$362

Since Ben would have $362, he won't be able to buy the stereo as he needs to have an amount greater than or equal to 365.

Other Questions
Describe resources and explain the three general categories economist classify as resources. which group is more susceptible to hormonal changes? a. toddlers b. teenagers c. elderly men d. elderly women please select the best answer from the choices provided. a b c d An electrical company manufactures light bulbs for LCD projectors with life spans that are approximately normally distributed. A randomly selected sample of 29 lights bulbs has a mean life span of 550 hours with a sample standard deviation of 45 hours. Compute the margin of error at a 95% confidence level (round off to the nearest hundredths). Suppose market demand for mobile operators is expressed by Q=90-3Pwhere Q is measured by calls in hours.There are three firms that supply the market: TRCell,VFone, and Avea.Avea provide hourly calls at a unit cost of 20$, where asTRCell& VFone has a unit cost equal to 10Suppose firms are competing inprice( no capacity constraints )a)What is the market price? Why?b)Howmuch does each firm sell in Bertrand equilibrium?c)What are firms profits?d)Is there any way for all firms to get higher profits Every network attached to the internet has at least one server designated as a dns server.a. trueb.false after simplifying, how many terms does the expression 4y - 6 y 2 - 9 contain? a. 4 terms b. 2 terms c. 1 term d. 3 terms what is type of cloud is especially prevalent when the atmosphere is very stable near the base of a thunderstorm. Assume labor is the only variable input. Which of the following best explains why marginal cost (MC) is increasing when marginal product (MP) is decreasing? White light is sent through an interface of a 100% (w/v) glycerol solution (n1 = 1.474) and a 20% (w/v) sucrose solution (n2=1.364) At an angle of: A) Theta=33 degree, determine the angle of Theta2 in degrees (*) B) Theta 1 =0degree, determine the angle or Theta2 in degrees (*) A) Theta2= Number degree B) Theta2= Number degree please answer all requirementsIsland Novelties, Incorporated, of Palau makes two products-Hawaiian Fantasy and Tahitian Joy. Each product's selling price, variable expense per unit and annual sales volume are as follows: Selling p You are to make monthly deposits of $700 into a retirement account that pays an APR of 10.2 percent compounded monthly.If your first deposit will be made one month from now, how large will your retirement account be in 32 years? (Do not round intermediate calculations and round your answer to 2 decimal places)Retirement account value in 32 years = ? Write a function named avg3 that accepts three numbers and returns their average.Example: avg3(4, 2, 6) => 4 avg3(3.14159, 2.71, 2.23) => 2.69653 Assume that the amounts of weight that male college students gain their freshman year are normally distributed with a mean of u= 1.3 kg and a standard deviation of o= 4.8 kg. Complete parts (a) through (c) below.a. If 1 male college student is randomly selected, find the probability that he gains 0 kg and 3 kg during freshman year.b. If 4 male college students are randomly selected, find the probability that their mean weight gain during freshman year is between 0 kg and 3 kg.c. Why can the normal distribution be used in part (b), even though the sample size does not exceed 30? A hammer in an out-of-tune piano hits two strings and produces beats of 4 Hz. One of the strings is tuned to 129 Hz.Randomized VariablesfB = 4 Hzf1 = 129 HzPart (a) What is the highest frequency the other string could have?Part (b) What is the lowest frequency the other string could have? Three Bears Manufacturing produces an auto - quartz watch movement called OM362. Three Bears expects to sell 20,000 units of OM362 and to have an ending finished inventory of 5,000 units. Currently, it has a beginning finished inventory of 1,100 units. Each unit of OM362 requires two labor operations, two labor hour(s) of assembling and three labor hour(s) of polishing. The direct labor rate for assembling is $11 per assembling hour and the direct labor rate for polishing is $14.50 per polishing hour. The expected number of hours of direct labor for OM362 is O A. 48,300 hours of assembling; 32,200 hours of polishing OB. 32,200 hours of assembling; 48,300 hours of polishing O C. 71,700 hours of assembling; 47,800 hours of polishing OD. 47,800 hours of assembling; 71,700 hours of polishing A person with a personality disorder such that they have an extreme need to be admired and an inflated sense of self-importance most likely has _____ personality disorder. what is 5[cos(pi/4) = 1 sin (pi/4)] raised to the 3rd power? grudem suggests that someone hiding jews during wwii who was questioned by nazis ______________ . (ch12, "lying and telling the truth") what is the area of the triangle in this coordinate plane? responses 17.5 units 17.5 units 21.0 units 21.0 units 35.5 units 35.5 units 49.0 units Assume that H0: 1.38, Ha: < 1.38. What type of test is this?Group of answer choicesA.) Left-tailedB.) Two-tailedC.) Right-tailed