Review the proof of de Moivre’s theorem (not in order).

Proof of de Moivre's Theorem
[cos(θ) + isin(θ)]k + 1
A = [cos(θ) + isin(θ)]k ∙ [cos(θ) + isin(θ)]1
B = cos(kθ + θ) + isin(kθ + θ)
C = cos(kθ)cos(θ) − sin(kθ)sin(θ) + i[sin(kθ)cos(θ) + cos(kθ)sin(θ)]
D = [cos(kθ) + isin(kθ)] ∙ [cos(θ) + isin(θ)]
E = cos[(k + 1)θ] + isin[(k + 1)θ]
Which steps must be switched to put the proof in order?

steps B and C
steps B and D
steps C and D
steps C and E

Answer:

Yes

Step-by-step explanation:

Integers are whole numbers that are positive and negative. Since -5 is an integer then is also a rational number because all integers are rational numbers

Answer:

Angle 1 and Angle 7

Step-by-step explanation:

Angle 1 and angle 7 are supplementary angles. Angle 3 and angle 7 are corresponding angles and angle 1 + angle 3 = 180

Answer:

Step-by-step explanation:

supplementary angles adds up to 180

angle 1 and angle 7 is an example of supplementary angles.

other options do not apply.

Answer:

a

[tex]\= x  =  82 [/tex]

b

[tex]s =  9.64 [/tex]

Step-by-step explanation:

From the question we are told that

    The data is  87  91  86  82  72  91   60  77  80  79  83  96

Generally the point estimate for the mean is mathematically represented as

    [tex]\= x  =  \frac{\sum  x_i }{n}[/tex]

=>  [tex]\= x  =  \frac{87 +91 + 86 + \cdots  + 96}{12}[/tex]

=>    [tex]\= x  =  82 [/tex]

Generally the point estimate for the standard deviation  is mathematically represented as

      [tex]s =  \sqrt{\frac{ \sum ( x_i  - \= x )^2 }{ n -1 } }[/tex]

=>     [tex]s =  \sqrt{\frac{ ( 87 - 82  )^2 +( 91 - 82  )^2 + \cdots + ( 96 - 82  )^2  }{ 12 -1 } }[/tex]

=>     [tex]s =  9.64 [/tex]

Part(a): The required mean is 82

Part(b): The required standard deviation is 9.639

Mean:

The mean is one of the measures of central tendency.

Part(a):

The formula for finding the mean is,

[tex]\bar{x}=\frac{\sum x_i}{n}[/tex]

Now, calculating the mean for the [tex]n=12[/tex] observation

[tex]\bar{x}=\frac{87+91+86+82+72+91+60+77+80+79+83+96}{12}\\ \bar{x}=82[/tex]

Part(b):

The formula for the standard deviation is,

[tex]S=\sqrt{\frac{\sum (x_i-\bar{x})^2}{n-1} }[/tex]

Substituting the given values into the above formula we get,

[tex]S=\sqrt{\frac{((87-82)^2+(91-82)^2)+(86-82)^2+(82-82)^2+(72-82)^2+(91-82)^2+(60-82)^2+(77-82)^2+...+(96-82)^2}{12-1} } \\S=9.639[/tex]

Learn more about the topic Mean:

https://brainly.com/question/11853639

Answer: there is 90 players in total

Step-by-step explanation:

6x 2= 12

78 + 12 = 90

Answer:

x=15

Step-by-step explanation:

6(x−2)=78 (or 6x−12=78), x=15

Answer:

the answer is B because it make a 90* angle

Answer:

1.x=3

2. x= -7    

3. x=7

Step-by-step explanation:

Answer:

no

Step-by-step explanation:

Right triangles follow the Pythagorean theorem:

[tex]a^2+b^2=c^2\\c=\sqrt{a^2+b^2}\\18=\sqrt{10^2+15^2} \\18=\sqrt{325} \\18 != 18.0277\\[/tex]

Because this statement isn't true, the side lengths are not for a right triangle.

Answer:

0.8186

Step-by-step explanation:

The formula to use to solve this question is given as:

z = (x-μ)/σ/√n, where

x is the raw score

μ is the population mean

σ is the population standard deviation.

n is the random number of samples

P(z < (x-μ)/σ/√n)

(x-μ) = 1.6 watts

σ = 10 watts

n = 32 amplifiers

Hence,

P(z < 1.6/10/√32)

P(z < 1.6/1.767766953)

P(z < 0.9050966799)

Approximately to 2 decimal places)

P(z < 0.91)

= 0.81859

Rounded to four decimal places, the probability that the mean of the sample would differ from the population mean by less than 1.6 watts is 0.8186.

Answer:

1. 6x^2-6

2. 18

Step-by-step explanation:

1. f(g(x))= 3(2x^2)-6= 6x^2-6

2. f(g(-2))= 3 (2(-2)^2)-6= 3(2(4))-6= 3(8)-6=24-6=18

Answer:

Step-by-step explanation:

The air plane is rising so the change in elevation is +1000 feet. The temp dropped and is -20 degrees ferhenhite.

Answer:

Step-by-step explanation:

in decimal it is 20.00, in fraction it is 1/5.

Answer:

5+3 =8

Step-by-step explanation:

absolute value

Answer:

x = 5

Step-by-step explanation:

Answer:

c

Step-by-step explanation:

Answer:

C. y = 2x − 5

Step-by-step explanation:

Given equation of line

2x − y = 3

rewriting the equation in slope intercept form as answer are given slope intercept form

y = 2x - 3

slope intercept form of equation is

y = mx + c

where m is the slope

c is y intercept

thus

slope for y = 2x - 3 when comparing with y = mx + c is 2

now we know slope of two parallel line is same

thus,

the slope of  line that is parallel to the line 2x − y = 3

is 2

Let the equation of required line be y = mx + c

where m = 2

thus

y = 2x + c is the new required equation

it passes through the point (2, −1)

using y = -1 and x = 2 in y = 2x + c

-1 = 2*2 + c

c = -1 - 4

c = -5

thus,

equation of required line is option c

y = 2x - 5 ----answer

Answer:

C. strong negative correlation

Step-by-step explanation:

I would say the answer is C. a strong negative correlation.

Firstly, the graph is 'going downwards', meaning that the relationship is negative. This is because one variable decreases when the other is increased. I think it is a strong relationship because the trend is quite clear through the points and the slope is moderately steep.

Hope this helped!

Answer:

The data given is  

    235,000 271,900 183,300 203,000 182,900 225,500 189,000 214,200 237,900 233,500 217,000 230,400 202,950, 216,500 209,900, 245,500

  The sample size is  n =  16

   The population is  [tex]\mu  =  \$201,800[/tex]

  The sample mean is mathematically represented as

             [tex]\= x =\frac{\sum x_i}{n}[/tex]

=>  [tex]\= x  =\frac{235,000 + 271,900 + \cdots + 245,500 }{16}[/tex]

=>    [tex]\= x  = 218653.125[/tex]

Generally the sample standard deviation is mathematically represented as

     [tex]s =  \sqrt{\frac{\sum (x_i - \= x)^2}{n} }[/tex]

=>   [tex]s =  \sqrt{\frac{ (235,000 -  218653.125)^2+ (271,900 -  218653.125)^2 + \cdots +  (245,500 -  218653.125)^2}{16} }[/tex]

=>   [tex]s =  23946.896 [/tex]

The null hypothesis is  [tex]H_o : \mu =  \$201,800[/tex]

The alternatively hypothesis is  [tex]H_o : \mu >  \$201,800 [/tex]

Generally the test statistics is mathematically represented as

     [tex]t =  \frac{\= x  - \mu }{ \frac{s}{\sqrt{n} } }[/tex]

=>  [tex]t =  \frac{218653.125  - 201800 }{ \frac{23946.896 }{\sqrt{16} } }[/tex]

=>  [tex]t =  2.82[/tex]

Generally the degree of freedom is mathematically represented as

     [tex]df =  n - 1[/tex]

=>   [tex]df =  16 - 1[/tex]

=>   [tex]df =  15[/tex]

Generally the probability of  [tex]t =  2.82[/tex] at a degree of freedom of  [tex]df =  15[/tex] from the t - distribution table  is  

     [tex]p-value  = P( t >2.82 ) =0.00646356[/tex]

The

From the values obtained we see that [tex]p-value  < \alpha[/tex]

The decision rule is  

   Reject the null hypothesis

The conclusion is

 There is sufficient evidence to conclude that the real estate company's  projection is true

Given that the population variance is unknown then the best statistical distribution to be applied is the t -distribution

Type I  Error

 The type 1 error occur when the null hypothesis is wrongfully rejected

  The consequence in this case is the company will assume that the average selling price has increase and this will lead the company to start expanding the business while in the real sense the average selling price is still  $201,800

   Type II  Error

 The  type 11 error occur when the null hypothesis is wrongfully  accepted(i.e wrongfully failed to reject the null hypothesis)

    The consequence in this case is that the company will assume that the average selling price  is still $201,800 and will not make plans to increase the business while in the real sense the average selling price has increased

   Given that resource is scare the management of the company will want a  smaller  significance level in order not to commit type I error which will lead to wrongly expanding the business and wastes of resources

generally the critical value  of  [tex]\frac{\alpha }{2}[/tex] from the normal distribution table is    

     [tex]Z_{\frac{\alpha }{2} } = 1.96[/tex]

Generally the margin of error is mathematically represented as

   [tex]E  =Z_{\frac{\alpha }{2} } *  \frac{s}{\sqrt{n} }[/tex]

=>[tex]E  =1.96*  \frac{23946.896}{\sqrt{16} }[/tex]

=>[tex]E  = 11733.96[/tex]

Generally the 95% confidence interval is  mathematically represented as

     [tex]218653.125 - 11733.96  < \mu  <  218653.125 + 11733.96[/tex]

=>  [tex]206919.165  < \mu  <  230387.085[/tex]  

Generally there is 95% confidence that the actual average selling price is within this interval  

Step-by-step explanation:

9514 1404 393

Answer:

  G

Step-by-step explanation:

The one point with a y-value of 0 is the one on the x-axis: G.

Answer:

rvefncoqjefadsNofvewnvfeeljjnfvqe

Step-by-step explanation:

fdcopjsfddcaxjefwpojdsjandipewhhqdaspcixpjewfs;odkcnewoasjjncikkjasn;kcjnnsixjfiasxhcjnsdaxo[okckiefihihehabficphbkjckd khksdk a help me

Answer:

lol im confused aswell

Step-by-step explanation:

Answer:

Form what?

Step-by-step explanation:

Step-by-step explanation:

what are you taking about ?

Answer:

5 pounds

Step-by-step explanation:

50 pounds of dog food divided by 10 days = 5 pounds per day for 10 days.

Answer:

As our computed test statistic falls in critical region, so we reject our null hypothesis. Also p-value=0.0009 is less than significance level, so we reject our null hypothesis and conclude that the average number of simulated drives differs by brand of golf ball at 5% significance level.

Step-by-step explanation:

Excel output print out

Anova: Single Factor      

SUMMARY      

Groups Count Sum Average Variance  

Alpha 5 1268 253.6 609.3  

Best 5 1532 306.4 740.3  

Century 5 1209 241.8 469.7  

Divot 5 1583 316.6 1235.3  

ANOVA      

Source of Variation SS df MS F P-value F crit

Between Groups 20960.4 3 6986.8 9.149217573 0.000925804 3.238871517

Within Groups 12218.4 16 763.65    

Total 33178.8 19    

The six steps of hypothesis are

1. Null hypothesis: The average number of simulated drives are same by brand of golf ball

Alternative hypothesis: The average number of simulated drives differs by brand of golf ball

2. Significance level: α=0.05

3. Test statistic: F-ratio for one way anova

4. Computations

F=9.149

5. Critical region: F>3.239

6. Conclusion:

As our computed test statistic falls in critical region, so we reject our null hypothesis. Also p-value=0.0009 is less than significance level, so we reject our null hypothesis and conclude that the average number of simulated drives differs by brand of golf ball at 5% significance level.

Answer:

30 is saved

Step-by-step explanation:

20 x 3 = 60 - 50 = 10, you get 10 three times because of 9 / 3 = 3 you get 10 x 3 = 30

Answer:

1.0.00015*0.33333...

2.(3^4*2^6)

HOPE THIS HELPS

Answer:

use slope intercept formula

y=Mx +b

Step-by-step explanation:

3X-4Y=8

3X-8 = 4Y

y = 3/4x-2

our new equation just needs to have the same slope  M= 3/4

y-y1=M(x-x1)

y-4=3/4(x-(-16))

y=3/4x+12+4

y=3/4x+16  answer a

for a perpendicular line.. just take the inverse of the slope... and change the sign.  so now our slope is - 4/3

plug in our new point (9,-7)

y-(-7) = -4/3(x-9)

y+7=-4/3x+12

y= -4/3x +5 answer b

Answer:

1.92

Step-by-step explanation:

Answer:

$1.92

Step-by-step explanation:

8% of 24

= 1.92

Answer:

x=(y+2b)/3m

Step-by-step explanation:

y+2b=3mx

(y+2b)/3m=x